to analyze the situation step by step, let's consider the components of your machine learning project : 1. * * task type * * : you are working on a regression task, which means you are trying to predict continuous values. 2. * * your approach * * : you are using a neural network with 10 layers and a linear activation function \ ( f ( x ) = 3x \ ). this means that despite having multiple layers, the output is still a linear transformation of the input, as any composition of linear functions is itself a linear function. essentially, your 10 - layer neural network is equivalent to a single linear regression model. 3. * * neighbor's approach * * : your neighbor is using linear regression with least squares, which is a standard approach for regression tasks. this method efficiently finds the best - fitting line ( or hyperplane ) for the data. 4. * * computational resources * * : you have a powerful laptop, but it is not a supercomputer. training deep networks can be computationally intensive, especially with many layers, but in this case, since your network is effectively linear, it doesn't require excessive resources. 5. * * outcome of the bet * * : since your neural network with 10 layers and a linear activation function does not provide any additional expressive power over the linear regression model your neighbor is using, both models are likely to perform similarly on the regression task. given these considerations, the outcome of the bet being a tie can be attributed to the fact that both you and your neighbor are using essentially the same scheme for regression : a linear approach. therefore, the most appropriate answer to why the outcome of the bet is a tie is : * * final answer * * : because we use exactly the same scheme.


to determine whether the statement \ ( x _ { 1 } \ perp x _ { 3 } \ mid x _ { 2 }, x _ { 5 } \ ) is correct, we need to analyze the joint distribution given and understand the implications of conditional independence in the context of the factorization provided. # # # step 1 : understanding the factorization the joint distribution is given by : \ [ p ( x _ { 1 }, x _ { 2 }, x _ { 3 }, x _ { 4 }, x _ { 5 } ) = p ( x _ { 1 } ) p ( x _ { 2 } \ mid x _ { 1 } ) p ( x _ { 3 } \ mid x _ { 2 } ) p ( x _ { 4 } \ mid x _ { 1 }, x _ { 3 } ) p ( x _ { 5 } \ mid x _ { 4 } ). \ ] from this factorization, we can observe the following dependencies : - \ ( x _ 2 \ ) depends on \ ( x _ 1 \ ). - \ ( x _ 3 \ ) depends on \ ( x _ 2 \ ). - \ ( x _ 4 \ ) depends on both \ ( x _ 1 \ ) and \ ( x _ 3 \ ). - \ ( x _ 5 \ ) depends on \ ( x _ 4 \ ). # # # step 2 : analyzing the conditional independence we want to check if \ ( x _ 1 \ ) is independent of \ ( x _ 3 \ ) given \ ( x _ 2 \ ) and \ ( x _ 5 \ ). in formal terms, we need to check if : \ [ p ( x _ 1, x _ 3 \ mid x _ 2, x _ 5 ) = p ( x _ 1 \ mid x _ 2, x _ 5 ) p ( x _ 3 \ mid x _ 2, x _ 5 ). \ ] # # # step 3 : using the d - separation criterion to analyze the independence, we can use the concept of d - separation in a directed acyclic graph ( dag ) representation of the joint distribution. the dependencies can be represented as follows : - \ ( x _ 1 \ rightarrow x _ 2 \ rightarrow x _ 3 \ ) - \ ( x _ 1 \ rightarrow x _ 4 \ ) - \ ( x _ 3 \ ) influences \ ( x _ 4 \ ) - \ ( x _ 4 \


rightarrow x _ 5 \ ) in this graph : - \ ( x _ 1 \ ) influences \ ( x _ 2 \ ), which in turn influences \ ( x _ 3 \ ). - \ ( x _ 3 \ ) is influenced by \ ( x _ 2 \ ) and also influences \ ( x _ 4 \ ), which influences \ ( x _ 5 \ ). # # # step 4 : checking the paths to check for independence, we look at the paths between \ ( x _ 1 \ ) and \ ( x _ 3 \ ) : 1. the path \ ( x _ 1 \ rightarrow x _ 2 \ rightarrow x _ 3 \ ) is active unless \ ( x _ 2 \ ) is conditioned on. 2. the other path \ ( x _ 1 \ rightarrow x _ 4 \ leftarrow x _ 3 \ ) is also active unless \ ( x _ 4 \ ) is conditioned on. since neither \ ( x _ 2 \ ) nor \ ( x _ 4 \ ) is conditioned on in the statement \ ( x _ 1 \ perp x _ 3 \ mid x _ 2, x _ 5 \ ), the presence of \ ( x _ 2 \ ) does not block the influence of \ ( x _ 1 \ ) on \ ( x _ 3 \ ) through \ ( x _ 2 \ ), and \ ( x _ 4 \ ) does not block the influence through \ ( x _ 3 \ ). # # # conclusion since there exists an active path between \ ( x _ 1 \ ) and \ ( x _ 3 \ ) that is not blocked by conditioning on \ ( x _ 2 \ ) and \ ( x _ 5 \ ), we conclude that : \ [ x _ 1 \ not \ perp x _ 3 \ mid x _ 2, x _ 5. \ ] thus, the statement \ ( x _ { 1 } \ perp x _ { 3 } \ mid x _ { 2 }, x _ { 5 } \ ) is * * incorrect * *.


the expected time complexity to find a collision in a hash function \ ( h \ colon \ { 0, 1 \ } ^ * \ rightarrow \ { 0, 1 \ } ^ n \ ) is \ ( \ theta ( 2 ^ { n / 2 } ) \ ). this result is based on the birthday paradox, which states that the probability of a collision increases significantly as more values are hashed. specifically, to find a collision with high probability, you need to hash about \ ( 2 ^ { n / 2 } \ ) random inputs. so, the concise answer is : \ ( \ theta ( 2 ^ { n / 2 } ) \ ).


to determine which properties are part of the rdf schema ( rdfs ) language, let's analyze the options step by step. # # # rdf schema overview rdf schema is a semantic extension of rdf ( resource description framework ) that provides mechanisms to describe the relationships between resources. it allows for the definition of classes and properties, enabling a more structured representation of information. # # # evaluating the options 1. * * type * * : - in rdf, the term " type " is often associated with the property ` rdf : type `, which is used to state that a resource is an instance of a class. in rdfs, ` rdfs : class ` is used to define classes, and ` rdf : type ` is a fundamental part of how rdf describes the relationships between resources and classes. thus, " type " is indeed part of rdfs. 2. * * predicate * * : - in rdf, a predicate is a property that describes a relationship between two resources ( the subject and the object ). while the term " predicate " itself is not explicitly defined in rdfs, properties in rdfs can be considered predicates. however, rdfs focuses more on defining properties and classes rather than explicitly labeling them as predicates. therefore, while related, " predicate " is not a specific property of rdfs. 3. * * description * * : - the term " description " is not a specific property or concept defined within rdfs. rdfs does not have a property called " description. " instead, it focuses on classes, properties, and their relationships. thus, this option is not correct. 4. * * domain * * : - rdfs includes the concept of " domain " through the property ` rdfs : domain `, which specifies the class of the subject of a property. this means that if a property has a domain defined, any subject using that property must be an instance of that domain class. therefore, " domain " is indeed part of rdfs. # # # conclusion based on the analysis : - * * correct options * * : 1 ) type, 4 ) domain - * * incorrect options * * : 2 ) predicate, 3 ) description # # # summary in summary, " type " and " domain " are properties of the rdf schema language. " type " relates to the classification of resources, while " domain " specifies the class of subjects for properties. " predicate " is a broader


term related to rdf but not specifically a property of rdfs, and " description " does not correspond to any defined property in rdfs.


certainly! in this analysis, we will examine the ` transfer ` method in a banking system, focusing on its implications in a multi - threaded environment with respect to two critical properties : 1. * * the balance of an account never goes below 0. * * 2. * * the total sum of money held by the bank is constant. * * # # # overview of the code hereas the code responsible for transferring money between accounts : ` ` ` scala def transfer ( from : account, to : account, amount : bigint ) : unit = { require ( amount > = 0 ) val balancefrom = from. balance if ( balancefrom > = amount ) { from. balance = balancefrom - amount val balanceto = to. balance to. balance = balanceto + amount } } ` ` ` # # # property 1 : the balance of an account never goes below 0 this property is crucial for maintaining account integrity within the banking system. the implementation ensures that no account can go negative due to the following reasons : - * * snapshot mechanism * * : each thread takes a snapshot of the balance ( ` balancefrom ` ) at the start of the transfer operation. this snapshot provides a consistent view of the balance at that moment. - * * conditional check * * : the line ` if ( balancefrom > = amount ) ` ensures that the transfer is only executed if there are sufficient funds in the ` from ` account. if the balance is insufficient, the transfer does not occur. # # # # example : assume ` account a ` has $ 100 : - * * thread 1 * * attempts to withdraw $ 100 from ` account a ` to ` account b `. - * * thread 2 * * attempts to withdraw $ 50 from ` account a ` to ` account c `. 1. * * thread 1 * * reads ` account a ` : ` balancefrom = 100 `. 2. * * thread 2 * * reads ` account a ` : ` balancefrom = 100 `. 3. * * thread 1 * * checks if ` balancefrom > = 100 ` : true. 4. * * thread 2 * * checks if ` balancefrom > = 50 ` : true. 5. * * thread 1 * * updates ` account a ` to $ 0 ( i. e., ` 100 - 100 ` ) and ` account b ` to $ 100 ( i. e., ` 0 + 100 ` ). 6. * * thread 2 * *


tries to update ` account a `, but since it reads the original balance, it would attempt to set ` account a ` to $ 50 ( i. e., ` 100 - 50 ` ). through this process, * * property 1 is upheld * * since no account can go negative. # # # property 2 : the total sum of money held by the bank is constant this property can be violated in a concurrent environment due to race conditions that lead to double spending. # # # # example : using the same account setup : 1. * * initial balances * * : - ` account a ` : $ 100 - ` account b ` : $ 0 - ` account c ` : $ 0 - * * total = $ 100 * * 2. * * concurrent transfers * * : - * * thread 1 * * transfers $ 100 from ` account a ` to ` account b `. - * * thread 2 * * transfers $ 50 from ` account a ` to ` account c `. # # # execution steps 1. * * thread 1 * * takes a snapshot of ` account a `'s balance : - ` balancefrom = 100 `. 2. * * thread 2 * * takes a snapshot of ` account a `'s balance : - ` balancefrom = 100 `. both threads check their conditions : - * * thread 1 * * checks if ` balancefrom > = 100 ` : true. - * * thread 2 * * checks if ` balancefrom > = 50 ` : true. 3. * * thread 1 * * executes its transfer : - it sets ` account a ` to $ 0 ( i. e., ` 100 - 100 ` ) and ` account b ` to $ 100 ( i. e., ` 0 + 100 ` ). 4. * * thread 2 * *, still holding its snapshot of ` balancefrom = 100 `, proceeds to execute its transfer : - it sets ` account a ` to $ 50 ( i. e., ` 100 - 50 ` ) and ` account c ` to $ 50 ( i. e., ` 0 + 50 ` ). # # # final balances after both operations, the final balances are : - ` account a ` : $ 50 ( after thread 2's operation ) - ` account b ` : $ 100 ( after thread 1's operation ) - ` account c ` : $ 50 ( after thread 2's operation ) # # # # total calculation -


* * total = account a + account b + account c = $ 50 + $ 100 + $ 50 = $ 200 * *. # # # conclusion 1. * * property 1 ( no negative balances ) * * : this property is maintained because the snapshot mechanism and conditional checks ensure that no account can go below zero. 2. * * property 2 ( constant total ) * * : this property is violated due to concurrent operations, where both threads utilize their snapshots of ` account a `'s balance. this leads to a situation where the total money in the bank increases from $ 100 to $ 200, demonstrating a double spending scenario. # # # recommendations to prevent violations of these properties in a concurrent environment : - * * use locking mechanisms * * : implement locks to ensure that only one thread can access and modify account balances at a time. - * * atomic operations * * : consider using atomic variables for account balances to ensure thread - safe updates. - * * transactional management * * : implement a transactional approach where operations are rolled back if inconsistencies occur. by applying these strategies, you can maintain the integrity of both properties in a multi - threaded banking system.


here are my assessments of the provided statements : 1. * * correct * * : " learning glove word vectors can be done using the singular value decomposition, if the \ ( f _ { dn } \ ) weights are set to 1 for all observed entries. " - explanation : glove ( global vectors for word representation ) can be formulated in a way that allows the use of singular value decomposition ( svd ) to derive word vectors, especially when simplifying the context matrix. setting \ ( f _ { dn } \ ) to 1 corresponds to treating all co - occurrences equally, which can facilitate this approach. 2. * * correct * * : " the skip - gram model for learning original word2vec embeddings does learn a binary classifier for each word. " - explanation : in the skip - gram model, the objective is to predict context words given a target word. this can be framed as a binary classification problem where for each target word, the model learns to classify whether each word in the context is part of the context or not. 3. * * incorrect * * : " fasttext as discussed in the course learns word vectors and sentence representations which are specific to a supervised classification task. " - explanation : fasttext primarily focuses on unsupervised learning of word embeddings by considering subword information ( character n - grams ) for better handling of out - of - vocabulary words. while it can be used in a supervised setting for classification tasks, its main purpose is not tied to supervised learning. 4. * * correct * * : " logistic regression used for text classification is faster at test time when using word vectors as opposed to bag - of - word representation of the input. " - explanation : word vectors ( like those from word2vec or glove ) provide a dense representation of words in a continuous space, which typically results in fewer dimensions compared to the sparse representations of the bag - of - words model. this reduced dimensionality can lead to faster computation during inference. in summary, the correct statements are : * * 1, 2, and 4 * *.


to address the statement " if a and b are rational numbers, a ^ b must be irrational, " we can examine the case where \ ( a = 1 \ ) and \ ( b = 2 \ ). here, we find that : \ [ 1 ^ 2 = 1 \ ] since 1 is a rational number, we have provided a counterexample that disproves the original statement. this means that the statement is false because we found a specific case where \ ( a \ ) and \ ( b \ ) are rational, but \ ( a ^ b \ ) is rational. now, let's analyze the options provided : 1. * * proof by contradiction * * : this method involves assuming that the statement is true and then showing that this leads to a contradiction. in our case, we are not doing this ; instead, we are simply showing a valid case that disproves the statement. 2. * * proof by counterexample * * : this method involves providing a specific example that contradicts the statement. since we provided \ ( 1 ^ 2 = 1 \ ) as a counterexample, this directly aligns with what we did. 3. * * exhaustive proof * * : this would require checking every possible case to confirm or deny the statement. that is not what we've done here ; we've only provided one specific example. 4. * * proof by cases * * : this method involves breaking the problem into different scenarios and proving each one. we did not break down into different cases ; we provided a single example. 5. * * existence proof * * : this proves that at least one example exists that satisfies certain conditions. while we did show that an example exists, it is more specific to countering the statement than simply proving existence. upon evaluating the options, the most fitting method used in our approach is " proof by counterexample, " as we provided a specific example that disproves the general statement. final answer : 2.


let's evaluate each option to determine the scenarios where they might seem plausible but ultimately fail, and then clarify why the correct option holds true in all relevant scenarios. # # # option 1 : named entities * * scenario where it might seem plausible : * * an hmm could appear to be effective in identifying named entities if one considers a simple case where the entities follow predictable patterns, such as being capitalized or positioned at the beginning of sentences. in a controlled dataset where named entities are clearly delineated, an hmm could perform adequately. * * why it ultimately fails : * * named entity recognition ( ner ) often involves ambiguous contexts and requires understanding the relationships between words and their meanings, which hmms, primarily relying on sequential probabilities, may struggle with. furthermore, hmms do not leverage rich features such as context and word embeddings, which are critical for accurately identifying entities in varied contexts. # # # option 2 : part - of - speech tags * * scenario where it might seem plausible : * * hmms are quite useful for tasks like part - of - speech tagging due to their sequential nature. in a simplified text with clear syntactic structures, an hmm could seem effective in assigning parts of speech to words based on the observed sequences. * * why it ultimately fails : * * while hmms can tag parts of speech reasonably well in some situations, they might struggle with more complex sentences or when words have multiple possible tags depending on context. advanced models like conditional random fields ( crfs ) or neural networks can incorporate more context and additional features to improve accuracy. # # # option 3 : concepts * * scenario where it might seem plausible : * * one might argue that hmms can identify concepts within a text if those concepts consistently appear in specific sequences. for instance, if " climate change " frequently appears in similar contexts, an hmm could be seen as a potential candidate for recognizing that concept. * * why it ultimately fails : * * concepts often require a deeper understanding of semantics and relationships between different words or phrases across sentences. hmms, which are based solely on the probability of sequences, do not effectively capture the nuances needed to identify and differentiate complex concepts, especially when they involve multiple words or are context - dependent. # # # option 4 : word n - grams * * correct option analysis : * * word n - grams are sequences of'n'words used primarily in statistical language modeling and text processing. hmms are not designed to work with fixed - length sequences like n


- grams but rather with transitioning states based on previous observations. while it is possible to use an hmm to model sequences of words, it does not directly align with the concept of n - grams, which focuses on the immediate context of a fixed number of words without consideration of state transitions. * * why it holds true in all relevant scenarios : * * n - grams require a model that can handle fixed - length sequences of words effectively without relying on the transition probabilities of states ( as in an hmm ). hmms are better suited for tasks where relationships evolve over time or across longer sequences, while n - grams are fundamentally about capturing local patterns of word co - occurrence without the state - based transitions that hmms use. # # # conclusion in summary, while hmms may seem plausible for some tasks, they ultimately fail in handling complex dependencies, relationships, and contextual nuances required for tasks like identifying concepts. the correct choice, " word n - grams, " is fundamentally mismatched with hmm's state - transition model and retains its validity across all relevant scenarios.


to determine the incorrect assertion among the given options concerning a multiplicative cyclic group \ ( g \ ) of order \ ( m > 1 \ ), we will analyze each option critically. 1. * * option 1 : $ \ lambda = m $, where $ \ lambda $ is the exponent of $ g $. * * the exponent of a group \ ( g \ ), denoted \ ( \ lambda \ ), is defined as the least common multiple of the orders of all elements in \ ( g \ ). in a cyclic group of order \ ( m \ ), the maximum order of any element is indeed \ ( m \ ). therefore, the least common multiple of the orders of all elements, which includes elements of order \ ( 1, 2, \ ldots, m \ ), will also be \ ( m \ ). thus, this assertion is * * correct * *. 2. * * option 2 : the order of every element \ ( x \ in g \ ) is \ ( m \ ). * * in a cyclic group of order \ ( m \ ), there exists at least one element \ ( g \ ) ( a generator ) such that the order of \ ( g \ ) is \ ( m \ ). however, not all elements must have order \ ( m \ ). for example, in \ ( \ mathbb { z } / 6 \ mathbb { z } \ ), the element \ ( 2 \ ) has order \ ( 3 \ ) and \ ( 3 \ ) has order \ ( 2 \ ). in general, the order of an element \ ( x \ ) divides the order of the group \ ( m \ ). therefore, this assertion is * * incorrect * *. 3. * * option 3 : there exists \ ( g \ in g \ ) that generates the whole group. * * by definition, a cyclic group is generated by a single element \ ( g \ ). therefore, there exists an element \ ( g \ in g \ ) such that every element of \ ( g \ ) can be expressed as \ ( g ^ k \ ) for some integer \ ( k \ ). this assertion is * * correct * *. 4. * * option 4 : for any \ ( x \ in g \ ), we have that \ ( x ^ m = e _ { g } \ ). * * in any group, it holds that if \ ( x \ ) is an element of the group


and the order of the group is \ ( m \ ), then \ ( x ^ m = e _ g \ ). this is because the order of \ ( x \ ) must divide \ ( m \ ), so raising \ ( x \ ) to the power \ ( m \ ) will yield the identity element. hence, this assertion is also * * correct * *. # # # summary of correctness of options : - * * option 1 * * : correct - * * option 2 * * : incorrect - * * option 3 * * : correct - * * option 4 * * : correct the * * incorrect assertion * * is * * option 2 * * : " the order of every element \ ( x \ in g \ ) is \ ( m \ ). "


to solve this problem, we can use the concept of the birthday problem, which deals with the probability of collisions ( i. e., picking the same number more than once ) when selecting random items from a finite set. in this case, we are picking numbers uniformly from the set \ ( \ { 1, 2, \ ldots, n \ } \ ) a total of \ ( m = \ theta \ sqrt { n } \ ) times. we want to calculate the probability of getting at least one number twice. # # # step 1 : calculate the probability of no collisions the probability of no collisions ( i. e., all selected numbers are unique ) can be calculated using the formula for the probability of unique selections in the birthday problem. the first number can be any of the \ ( n \ ) numbers. the second number can be any of the remaining \ ( n - 1 \ ) numbers, the third can be any of the remaining \ ( n - 2 \ ) numbers, and so forth. thus, the probability \ ( p ( \ text { no collisions } ) \ ) is given by : \ [ p ( \ text { no collisions } ) = \ frac { n } { n } \ cdot \ frac { n - 1 } { n } \ cdot \ frac { n - 2 } { n } \ cdots \ frac { n - m + 1 } { n } = \ frac { n ( n - 1 ) ( n - 2 ) \ cdots ( n - m + 1 ) } { n ^ m } \ ] # # # step 2 : approximate the probability for large \ ( n \ ) for large \ ( n \ ) and \ ( m = \ theta \ sqrt { n } \ ), we can approximate this product. the probability of no collisions can be rewritten using the exponential function : \ [ p ( \ text { no collisions } ) \ approx e ^ { - \ frac { m ( m - 1 ) } { 2n } } \ approx e ^ { - \ frac { ( \ theta \ sqrt { n } ) ( \ theta \ sqrt { n } - 1 ) } { 2n } } \ approx e ^ { - \ frac { \ theta ^ 2 n } { 2n } } = e ^ { - \ frac { \ theta ^ 2 } { 2 } } \ ] # # # step 3 : calculate the probability of at least one collision


now, the probability of having at least one collision is the complement of the probability of no collisions : \ [ p ( \ text { at least one collision } ) = 1 - p ( \ text { no collisions } ) \ approx 1 - e ^ { - \ frac { \ theta ^ 2 } { 2 } } \ ] # # # conclusion thus, the probability of picking at least one number twice when selecting \ ( \ theta \ sqrt { n } \ ) numbers from the set \ ( \ { 1, 2, \ ldots, n \ } \ ) is : \ [ \ boxed { 1 - e ^ { - \ frac { \ theta ^ 2 } { 2 } } } \ ]


* * to determine what the smart algorithm for query relevance feedback modifies, we first need to understand its purpose and how it operates within the vector space model of information retrieval. the smart algorithm is designed to improve search result relevance by incorporating user feedback about which retrieved documents are relevant or irrelevant. this feedback is crucial because it allows the algorithm to adjust the search parameters to better meet user needs in future queries. in the context of the vector space model, we have two key components that the smart algorithm interacts with : document weight vectors and query weight vectors. document weight vectors represent the importance of terms in the documents retrieved, while query weight vectors represent the importance of terms in the user's search query. now, let's analyze the answer choices : 1. * * the original document weight vectors * * : the smart algorithm does not modify these vectors directly ; instead, it focuses on improving the user's search query. 2. * * the original query weight vectors * * : this is a critical modification point for the smart algorithm. it adjusts these vectors based on user feedback to enhance the relevance of future search results. 3. * * the result document weight vectors * * : these vectors reflect the outcome of the retrieval process and are not modified by the smart algorithm, as it focuses on refining the query instead. 4. * * the keywords of the original user query * * : while the keywords are part of the process, the smart algorithm modifies the weights associated with these keywords in the query vector rather than altering the keywords themselves. after carefully considering each option, the correct answer is * * the original query weight vectors * *. this modification is central to how the smart algorithm utilizes user feedback to improve search results. - - - * *


# # # step - by - step breakdown of meltdown attack : 1. * * basic idea of the attack * * : - the meltdown attack exploits a vulnerability in modern processors that allows unauthorized access to protected memory. specifically, it breaks the isolation between user applications and the operating system ( os ). - it leverages speculative execution, a performance optimization where the cpu guesses which instructions will be needed and executes them ahead of time. 2. * * mechanism of the attack * * : - the attacker runs code that attempts to access memory that it should not have permissions for ( e. g., kernel memory ). - when the cpu speculatively executes this code, it processes the memory access, but the access is eventually rolled back if it ’ s determined to be unauthorized. - however, during this rollback, the cpu caches the results of the unauthorized access, which can be exploited by the attacker to infer sensitive information through timing variations. 3. * * microarchitectural mechanism targeted * * : - the primary microarchitectural mechanism targeted by meltdown is the * * speculative execution * * and the * * cache architecture * *. the attack relies on the side effects of speculative execution and how data is stored in the cpu cache. 4. * * vulnerability across processors * * : - not all processors are equally vulnerable. the meltdown attack primarily affects intel processors due to their specific implementation of speculative execution and memory protection. - some other architectures ( e. g., arm, amd ) have mitigations or do not exhibit the same vulnerabilities, making them less susceptible or not vulnerable at all. # # # conclusion : the meltdown attack exploits speculative execution to access protected memory, targeting the cpu's cache behavior. while it affects many intel processors, not all processors are vulnerable, as architectural differences can provide intrinsic protections against such attacks.


1. the pair \ ( ( e, d ) = ( 7, 223 ) \ ) does not satisfy the rsa condition \ ( e \ cdot d \ equiv 1 \ mod \ phi ( n ) \ ).


to show that \ ( \ mathbf { v } \ ) is an eigenvector of the matrix \ ( \ mathbf { a } + \ mathbf { b } \ ) with a corresponding eigenvalue, we will use the definition of eigenvectors and eigenvalues. recall that if \ ( \ mathbf { a } \ ) is a matrix and \ ( \ mathbf { v } \ ) is an eigenvector of \ ( \ mathbf { a } \ ) with eigenvalue \ ( \ lambda _ a \ ), then by definition we have : \ [ \ mathbf { a } \ mathbf { v } = \ lambda _ a \ mathbf { v } \ ] similarly, since \ ( \ mathbf { v } \ ) is also an eigenvector of \ ( \ mathbf { b } \ ) with eigenvalue \ ( \ lambda _ b \ ), we have : \ [ \ mathbf { b } \ mathbf { v } = \ lambda _ b \ mathbf { v } \ ] now, we want to show \ ( \ mathbf { v } \ ) is an eigenvector of the matrix \ ( \ mathbf { a } + \ mathbf { b } \ ). we compute the action of \ ( \ mathbf { a } + \ mathbf { b } \ ) on \ ( \ mathbf { v } \ ) : \ [ ( \ mathbf { a } + \ mathbf { b } ) \ mathbf { v } = \ mathbf { a } \ mathbf { v } + \ mathbf { b } \ mathbf { v } \ ] now substituting the expressions we have for \ ( \ mathbf { a } \ mathbf { v } \ ) and \ ( \ mathbf { b } \ mathbf { v } \ ) : \ [ ( \ mathbf { a } + \ mathbf { b } ) \ mathbf { v } = \ lambda _ a \ mathbf { v } + \ lambda _ b \ mathbf { v } \ ] factor out \ ( \ mathbf { v } \ ) : \ [ ( \ mathbf { a } + \ mathbf { b } ) \ mathbf { v } = ( \ lambda _ a + \ lambda _ b ) \ mathbf { v } \ ] this shows that \ ( \ mathbf { v


} \ ) is indeed an eigenvector of \ ( \ mathbf { a } + \ mathbf { b } \ ), and the corresponding eigenvalue is : \ [ \ lambda _ a + \ lambda _ b \ ] in conclusion, \ ( \ mathbf { v } \ ) is an eigenvector of the matrix \ ( \ mathbf { a } + \ mathbf { b } \ ) with the eigenvalue \ ( \ lambda _ a + \ lambda _ b \ ).


in a file system designed specifically for reading immutable files in a random fashion, the best block allocation strategy would typically be : * * 3. index allocation with b - tree * * # # # explanation : 1. * * linked - list allocation * * : this method involves linking blocks together in a list. while it allows for efficient space utilization and is good for sequential access, it is not optimal for random access. each block access requires following pointers, which can lead to poor performance when accessing blocks randomly. 2. * * continuous allocation * * : this method allocates blocks in contiguous locations. while this can provide excellent performance for sequential access, it is not efficient for random access, especially if the files are of varying sizes or if free space is fragmented. 3. * * index allocation with b - tree * * : this approach uses an index structure ( like a b - tree ) to keep track of the blocks of files. b - trees are well - suited for random accesses and allow for efficient searching, insertion, and deletion. since the files are immutable and accessed randomly, this strategy would provide efficient block lookups and minimize the overhead associated with accessing non - contiguous blocks. 4. * * index allocation with hash - table * * : while a hash table can provide quick access, it might not be as efficient as a b - tree for range queries or when dealing with files that may have a large number of blocks, as it typically does not maintain order and can lead to clustering issues. given these considerations, * * index allocation with b - tree * * is the best choice for efficient random access in a file system dealing with immutable files.


in model theory and related areas of mathematics, a type is an object that describes how a ( real or possible ) element or finite collection of elements in a mathematical structure might behave. more precisely, it is a set of first - order formulas in a language l with free variables x1, x2, …, xn that are true of a set of n - tuples of an l - structure m { \ displaystyle { \ mathcal { m } } }. depending on the context, types can be complete or partial and they may use a fixed set of constants, a, from the structure m { \ displaystyle { \ mathcal { m } } }. the question of which types represent actual elements of m { \ displaystyle { \ mathcal { m } } } leads to the ideas of saturated models and omitting types.


in mathematical logic and type theory, the λ - cube ( also written lambda cube ) is a framework introduced by henk barendregt to investigate the different dimensions in which the calculus of constructions is a generalization of the simply typed λ - calculus. each dimension of the cube corresponds to a new kind of dependency between terms and types. here, " dependency " refers to the capacity of a term or type to bind a term or type. the respective dimensions of the λ - cube correspond to : x - axis ( → { \ displaystyle \ rightarrow } ) : types that can bind terms, corresponding to dependent types.


in mathematics, and more specifically in graph theory, a polytree ( also called directed tree, oriented tree or singly connected network ) is a directed acyclic graph whose underlying undirected graph is a tree. in other words, if we replace its directed edges with undirected edges, we obtain an undirected graph that is both connected and acyclic. a polyforest ( or directed forest or oriented forest ) is a directed acyclic graph whose underlying undirected graph is a forest.


in some european countries, and especially in france, minitel data transmitting services were popular before the internet. minitel had many consumer - level communication services, including chatting, email, railway and broadcast timetables and travel and hotel booking. minitel used little terminals rented from telephone companies or computers with modems that accept minitel transmission protocol speed. amiga minitel communication programs were written in france, germany and italy ( amiga videotel ). amigatel ( cept2 standard, for minitel ) btx ( cept1 standard, for the german btx service ) mta ( cept2 and cept3 standards, for italian videotex which supported both ) ruby view ( cept3, for uk's prestel )


geometrically this is the problem of computing the lengths of the sides of a rectangle whose area a and side - length difference b−a are known, which was a recurring problem in old babylonian mathematics. in this case it is found that b = 1 and a = 0. 75. the solution method suggests that whoever devised the solution was using the property c2 − 2a = c2 − 2ab = ( b − a ) 2.


in statistics, multinomial logistic regression is a classification method that generalizes logistic regression to multiclass problems, i. e. with more than two possible discrete outcomes. that is, it is a model that is used to predict the probabilities of the different possible outcomes of a categorically distributed dependent variable, given a set of independent variables ( which may be real - valued, binary - valued, categorical - valued, etc. ). multinomial logistic regression is known by a variety of other names, including polytomous lr, multiclass lr, softmax regression, multinomial logit ( mlogit ), the maximum entropy ( maxent ) classifier, and the conditional maximum entropy model.


" the acoustic evidence of dialects revealed the clan to be the largest vocal, and probably matrilineal, unit. because the southern resident community is only a single clan, the nature of the larger, community level of social grouping is clearer in the multi - clan northern resident community. unlike the clan, the community is " defined by travel patterns and not on genealogy or acoustics. "


in most computers, individual instructions are stored as machine code with each instruction being given a unique number ( its operation code or opcode for short ). the command to add two numbers together would have one opcode ; the command to multiply them would have a different opcode, and so on. the simplest computers are able to perform any of a handful of different instructions ; the more complex computers have several hundred to choose from, each with a unique numerical code. since the computer's memory is able to store numbers, it can also store the instruction codes.


in object - oriented programming, a covariant return type of a method is one that can be replaced by a " narrower " type when the method is overridden in a subclass. a notable language in which this is a fairly common paradigm is c + +. c # supports return type covariance as of version 9. 0. covariant return types have been ( partially ) allowed in the java language since the release of jdk5. 0, so the following example wouldn't compile on a previous release : more specifically, covariant ( wide to narrower ) or contravariant ( narrow to wider ) return type refers to a situation where the return type of the overriding method is changed to a type related to ( but different from ) the return type of the original overridden method.


in probability theory, a distribution is said to be stable if a linear combination of two independent random variables with this distribution has the same distribution, up to location and scale parameters. a random variable is said to be stable if its distribution is stable. the stable distribution family is also sometimes referred to as the levy alpha - stable distribution, after paul levy, the first mathematician to have studied it. of the four parameters defining the family, most attention has been focused on the stability parameter, α { \ displaystyle \ alpha } ( see panel ). stable distributions have 0 < α ≤ 2 { \ displaystyle 0 < \ alpha \ leq 2 }, with the upper bound corresponding to the normal distribution, and α = 1 { \ displaystyle \ alpha = 1 } to the cauchy distribution.


in the case of the leaky bucket algorithm as a meter, the limits on the traffic can be bandwidth and a burstiness of the output. the bandwidth limit and burstiness limit for the connection may be specified in a traffic contract. a bandwidth limit may be specified as a packet or frame rate, a byte or bit rate, or as an emission interval between the packets. a limit on burstiness may be specified as a jitter or delay variation tolerance, or as a maximum burst size ( mbs ). multiple sets of contract parameters can be applied concurrently to a connection using multiple instances of the leaky bucket algorithm, each of which may take a bandwidth and a burstiness limit : see generic cell rate algorithm § dual leaky bucket controller.


in science, adversarial collaboration is a term used when two or more scientists with opposing views work together in order to jointly advance knowledge of the area under dispute. this can take the form of a scientific experiment conducted by two groups of experimenters with competing hypotheses, with the aim of constructing and implementing an experimental design in a way that satisfies both groups that there are no obvious biases or weaknesses in the experimental design. adversarial collaboration can involve a neutral moderator and lead to a co - designed experiment and joint publishing of findings in order to resolve differences. with its emphasis on transparency throughout the research process, adversarial collaboration has been described as sitting within the open science framework.


buffers are widespread in operating system ( os ) code, so it is possible to make attacks that perform privilege escalation and gain unlimited access to the computer's resources. the famed morris worm in 1988 used this as one of its attack techniques.


again, this allows data accesses to access physical memory regions beyond the 32 - bit range. the entries in the page directory have an additional flag in bit 7, named ps ( for page size ). if the system has set this bit to 1, the page directory entry does not point to a page table but to a single, large 2 mb page ( page size extension ).


in operating systems using a command line interface, the user types short commands often followed by various parameters and options.


in mathematical analysis, the hardy – littlewood inequality, named after g. h. hardy and john edensor littlewood, states that if f { \ displaystyle f } and g { \ displaystyle g } are nonnegative measurable real functions vanishing at infinity that are defined on n { \ displaystyle n } - dimensional euclidean space r n { \ displaystyle \ mathbb { r } ^ { n } }, then r n f ( x ) g ( x ) d x ≤ r n f ∗ ( x ) g ∗ ( x ) d x { \ displaystyle \ int _ { \ mathbb { r } ^ { n } } f ( x ) g ( x ) \, dx \ leq \ int _ { \ mathbb { r } ^ { n } } f ^ { * } ( x ) g ^ { * } ( x ) \, dx } where f ∗ { \ displaystyle f ^ { * } } and g ∗ { \ displaystyle g ^ { * } } are the symmetric decreasing rearrangements of f { \ displaystyle f } and g { \ displaystyle g }, respectively. the decreasing rearrangement f ∗ { \ displaystyle f ^ { * } } of f { \ displaystyle f } is defined via the property that for all r > 0 { \ displaystyle r > 0 } the two super - level sets e f ( r ) = { x ∈ x : f ( x ) > r } { \ displaystyle e _ { f } ( r ) = \ left \ { x \ in x : f ( x ) > r \ right \ } \ quad } and e f ∗ ( r ) = { x ∈ x : f ∗ ( x ) > r } { \ displaystyle \ quad e _ { f ^ { * } } ( r ) = \ left \ { x \ in x : f ^ { * } ( x ) > r \ right \ } } have the same volume ( n { \ displaystyle n } - dimensional lebesgue measure ) and e f ∗ ( r ) { \ displaystyle e _ { f ^ { * } } ( r ) } is a ball in r n { \ displaystyle \ mathbb { r } ^ { n } } centered at x = 0 { \ displaystyle x = 0 }, i. e. it has maximal symmetry.


in mathematics, a proof without words ( or visual proof ) is an illustration of an identity or mathematical statement which can be demonstrated as self - evident by a diagram without any accompanying explanatory text. such proofs can be considered more elegant than formal or mathematically rigorous proofs due to their self - evident nature. when the diagram demonstrates a particular case of a general statement, to be a proof, it must be generalisable. a proof without words is not the same as a mathematical proof, because it omits the details of the logical argument it illustrates. however, it can provide valuable intuitions to the viewer that can help them formulate or better understand a true proof.


in object oriented languages type safety is usually intrinsic in the fact that a type system is in place. this is expressed in terms of class definitions. a class essentially defines the structure of the objects derived from it and an api as a contract for handling these objects. each time a new object is created it will comply with that contract. each function that exchanges objects derived from a specific class, or implementing a specific interface, will adhere to that contract : hence in that function the operations permitted on that object will be only those defined by the methods of the class the object implements. this will guarantee that the object integrity will be preserved. exceptions to this are object oriented languages that allow dynamic modification of the object structure, or the use of reflection to modify the content of an object to overcome the constraints imposed by the class methods definitions.


in number theory, the integer complexity of an integer is the smallest number of ones that can be used to represent it using ones and any number of additions, multiplications, and parentheses. it is always within a constant factor of the logarithm of the given integer.


in mathematics, the discrete fourier transform ( dft ) converts a finite sequence of equally - spaced samples of a function into a same - length sequence of equally - spaced samples of the discrete - time fourier transform ( dtft ), which is a complex - valued function of frequency. the interval at which the dtft is sampled is the reciprocal of the duration of the input sequence. an inverse dft ( idft ) is a fourier series, using the dtft samples as coefficients of complex sinusoids at the corresponding dtft frequencies. it has the same sample - values as the original input sequence.


in mathematics, a ( left ) coherent ring is a ring in which every finitely generated left ideal is finitely presented. many theorems about finitely generated modules over noetherian rings can be extended to finitely presented modules over coherent rings. every left noetherian ring is left coherent.


in order to apply the moment distribution method to analyse a structure, the following things must be considered.


together these form the science of metrology. measurement accuracy, repeatability, reproducibility, bias, data shifts, and data drifts are only a few common issues identified in measurement, and any useful system must be evaluated from the technical point of view to assure that it addresses these criteria. it is essential that measurement error is quantified so that managers react to changes in conditions, but not changes due to measurement variation.


in the japanese kantenji braille, the standard 8 - dot braille patterns 3, 13, 34, and 134 are the patterns related to braille pattern dots - 2, since the two additional dots of kantenji patterns 02, 27, and 027 are placed above the base 6 - dot cell, instead of below, as in standard 8 - dot braille.


in the field of evaluation, and in particular educational evaluation, the joint committee on standards for educational evaluation has published three sets of standards for evaluations. the personnel evaluation standards was published in 1988, the program evaluation standards ( 2nd edition ) was published in 1994, and the student evaluation standards was published in 2003. each publication presents and elaborates a set of standards for use in a variety of educational settings. the standards provide guidelines for designing, implementing, assessing, and improving the identified form of evaluation.


in parallel to the concurrent dos 68k effort, digital research also previewed concurrent dos 286 in cooperation with intel in january 1985. this was based on mp / m - 286 and concurrent cp / m - 286, on which digital research had worked since 1982. concurrent dos 286 was a complete rewrite in the c language based on a new system architecture with dynamically loadable device drivers instead of a static bios or xios. one of its main architects was francis " frank " r. holsworth. the operating system would function strictly in 80286 native mode, allowing protected mode multi - user, multitasking operation while running 8086 emulation.


in telecommunication and computer engineering, the queuing delay or queueing delay is the time a job waits in a queue until it can be executed. it is a key component of network delay. in a switched network, queuing delay is the time between the completion of signaling by the call originator and the arrival of a ringing signal at the call receiver. queuing delay may be caused by delays at the originating switch, intermediate switches, or the call receiver servicing switch. in a data network, queuing delay is the sum of the delays between the request for service and the establishment of a circuit to the called data terminal equipment ( dte ). in a packet - switched network, queuing delay is the sum of the delays encountered by a packet between the time of insertion into the network and the time of delivery to the address.


in mathematics, the inverse function of a function f ( also called the inverse of f ) is a function that undoes the operation of f. the inverse of f exists if and only if f is bijective, and if it exists, is denoted by f − 1. { \ displaystyle f ^ { - 1 }. } for a function f : x → y { \ displaystyle f \ colon x \ to y }, its inverse f − 1 : y → x { \ displaystyle f ^ { - 1 } \ colon y \ to x } admits an explicit description : it sends each element y ∈ y { \ displaystyle y \ in y } to the unique element x ∈ x { \ displaystyle x \ in x } such that f ( x ) = y. as an example, consider the real - valued function of a real variable given by f ( x ) = 5x − 7. one can think of f as the function which multiplies its input by 5 then subtracts 7 from the result.


in one variation of monadic second - order graph logic known as mso1, the graph is described by a set of vertices and a binary adjacency relation adj (.,. ) { \ displaystyle \ operatorname { adj } (.,. ) }


in the do... while loop, the test is done after each iteration. consequently, the code is always executed at least once.


in nuclear physics these methods are used to study properties of the nucleus itself. methods for studies of the nucleus : gamma spectroscopy hypernuclear spectroscopymethods for condensed matter studies : nuclear magnetic resonance ( nmr ) mossbauer spectroscopy perturbed angular correlation ( pac, tdpac, pac spectroscopy ) muon spin spectroscopy nuclear orientation channeling nuclear reaction analysis nuclear quadrupole resonance ( nqr ) methods for trace element analysis : neutron activation analysis ( naa ) = = references = =


in mathematics, the analytic subgroup theorem is a significant result in modern transcendental number theory. it may be seen as a generalisation of baker's theorem on linear forms in logarithms. gisbert wustholz proved it in the 1980s. it marked a breakthrough in the theory of transcendental numbers. many longstanding open problems can be deduced as direct consequences.


in mathematics, a residuated lattice is an algebraic structure l = ( l, ≤, •, i ) such that ( i ) ( l, ≤ ) is a lattice. ( ii ) ( l, •, i ) is a monoid. ( iii ) for all z there exists for every x a greatest y, and for every y a greatest x, such that x • y ≤ z ( the residuation properties ). in ( iii ), the " greatest y ", being a function of z and x, is denoted x \ z and called the right residual of z by x. think of it as what remains of z on the right after " dividing " z on the left by x. dually, the " greatest x " is denoted z / y and called the left residual of z by y. an equivalent, more formal statement of ( iii ) that uses these operations to name these greatest values is ( iii )'for all x, y, z in l, y ≤ x \ z x • y ≤ z x ≤ z / y. as suggested by the notation, the residuals are a form of quotient.


for those processors that have only one pipeline per core, interleaved multithreading is the only possible way, because it can issue at most one instruction per cycle. simultaneous multithreading ( smt ) : issue multiple instructions from multiple threads in one cycle. the processor must be superscalar to do so.


in fact, these may go so far as to question the " empirical and scientific validity... of modern financial theory ". notable here are nassim taleb and benoit mandelbrot. see also mathematical finance § criticism, financial economics § challenges and criticism and financial engineering § criticisms.


in object - oriented programming theory, abstraction involves the facility to define objects that represent abstract " actors " that can perform work, report on and change their state, and " communicate " with other objects in the system. the term encapsulation refers to the hiding of state details, but extending the concept of data type from earlier programming languages to associate behavior most strongly with the data, and standardizing the way that different data types interact, is the beginning of abstraction. when abstraction proceeds into the operations defined, enabling objects of different types to be substituted, it is called polymorphism. when it proceeds in the opposite direction, inside the types or classes, structuring them to simplify a complex set of relationships, it is called delegation or inheritance.


in mathematics, the davenport constant d ( g ) is an invariant of a group studied in additive combinatorics, quantifying the size of nonunique factorizations. given a finite abelian group g, d ( g ) is defined as the smallest number such that every sequence of elements of that length contains a non - empty subsequence adding up to 0. in symbols, this is d ( g ) = min { n : ( { g n } n = 1 n ∈ g n ) ( { n k } k = 1 k : k = 1 k g n k = 0 ) }. { \ displaystyle d ( g ) = \ min \ left \ { n : \ forall \ left ( \ { g _ { n } \ } _ { n = 1 } ^ { n } \ in g ^ { n } \ right ) \ left ( \ exists \ { n _ { k } \ } _ { k = 1 } ^ { k } : \ sum _ { k = 1 } ^ { k } { g _ { n _ { k } } } = 0 \ right ) \ right \ }. }


in modern parallel computing systems, memory consistency must be maintained to avoid undesirable outcomes. strict consistency models like sequential consistency are intuitively composed but can be quite restrictive in terms of performance as they would disable instruction level parallelism which is widely applied in sequential programming. to achieve better performance, some relaxed models are explored and release consistency is an aggressive relaxing attempt.


in mathematics, and specifically in group theory, a non - abelian group, sometimes called a non - commutative group, is a group ( g, ∗ ) in which there exists at least one pair of elements a and b of g, such that a ∗ b = b ∗ a. this class of groups contrasts with the abelian groups. ( in an abelian group, all pairs of group elements commute ). non - abelian groups are pervasive in mathematics and physics. one of the simplest examples of a non - abelian group is the dihedral group of order 6.


it is licensed under the gnu lesser general public license. mapreduce - mpi library is an implementation of mapreduce for distributed - memory parallel machines, utilizing the message passing interface ( mpi ) for communication. it is developed under a modified berkeley software distribution license.


information distribution – this involves dissemination of information needed by the stakeholders and other members of the organization. performance reporting – this includes status reporting, progress measurement, and forecasting for the future of the organization. administrative closure – this involves generating, gathering, and disseminating information to formalize phase or project completion.


in mathematics, the wasserstein distance or kantorovich – rubinstein metric is a distance function defined between probability distributions on a given metric space m { \ displaystyle m }. it is named after leonid vaserstein. intuitively, if each distribution is viewed as a unit amount of earth ( soil ) piled on m { \ displaystyle m }, the metric is the minimum " cost " of turning one pile into the other, which is assumed to be the amount of earth that needs to be moved times the mean distance it has to be moved. this problem was first formalised by gaspard monge in 1781.


to satisfy the constraints σ k ( t + δ t ) { \ displaystyle \ sigma _ { k } ( t + \ delta t ) } in the next timestep, the lagrange multipliers should be determined as the following equation, σ k ( t + δ t ) : = ‖ x k α ( t + δ t ) − x k β ( t + δ t ) ‖ 2 − d k 2 = 0. { \ displaystyle \ sigma _ { k } ( t + \ delta t ) : = \ left \ | \ mathbf { x } _ { k \ alpha } ( t + \ delta t ) - \ mathbf { x } _ { k \ beta } ( t + \ delta t ) \ right \ | ^ { 2 } - d _ { k } ^ { 2 } = 0. } this implies solving a system of n { \ displaystyle n } non - linear equations σ j ( t + δ t ) : = ‖ x ^ j α ( t + δ t ) − x ^ j β ( t + δ t ) + k = 1 n λ k ( δ t ) 2 ‖ 2 − d j 2 = 0, j = 1 … n { \ displaystyle \ sigma _ { j } ( t + \ delta t ) : = \ left \ | { \ hat { \ mathbf { x } } } _ { j \ alpha } ( t + \ delta t ) - { \ hat { \ mathbf { x } } } _ { j \ beta } ( t + \ delta t ) + \ sum _ { k = 1 } ^ { n } \ lambda _ { k } \ left ( \ delta t \ right ) ^ { 2 } \ left \ right \ | ^ { 2 } - d _ { j } ^ { 2 } = 0, \ quad j = 1 \ ldots n } simultaneously for the n { \ displaystyle n } unknown lagrange multipliers λ k { \ displaystyle \ lambda _ { k } }.


therefore, the distribution is often abbreviated u ( a, b ), { \ displaystyle u ( a, b ), } where u { \ displaystyle u } stands for uniform distribution. the difference between the bounds defines the interval length ; all intervals of the same length on the distribution's support are equally probable. it is the maximum entropy probability distribution for a random variable x { \ displaystyle x } under no constraint other than that it is contained in the distribution's support.


alice sends | ψ ⟩ { \ displaystyle | \ psi \ rangle } over a public quantum channel to bob. bob receives a state ε ρ = ε | ψ ⟩ ⟨ ψ | { \ displaystyle \ varepsilon \ rho = \ varepsilon | \ psi \ rangle \ langle \ psi | }, where ε { \ displaystyle \ varepsilon } represents the effects of noise in the channel as well as eavesdropping by a third party we'll call eve. after bob receives the string of qubits, all three parties, namely alice, bob and eve, have their own states.


it is still a popular language for high - performance computing and is used for programs that benchmark and rank the world's top500 fastest supercomputers. another early programming language was devised by grace hopper in the us, named flow - matic. it was developed for the univac i at remington rand during the period from 1955 until 1959. hopper found that business data processing customers were uncomfortable with mathematical notation, and in early 1955, she and her team wrote a specification for an english language programming language and implemented a prototype.


values for parameters of the receiver method are stored in the command. the receiver object to execute these methods is also stored in the command object by aggregation. the receiver then does the work when the execute ( ) method in command is called.


in a laboratory setting, each one of these prepped systems might be used as input for one subsequent testing procedure. again, the testing procedure involves a physical apparatus and some protocols ; as a result of the testing procedure we obtain a yes or no answer. given a testing procedure e applied to each prepared system, we obtain a sequence of values meas ( e, x1 ), meas ( e, x2 ),...., meas ( e, xk ).


in number theory, vantieghems theorem is a primality criterion. it states that a natural number n≥3 is prime if and only if 1 ≤ k ≤ n − 1 ( 2 k − 1 ) ≡ n mod ( 2 n − 1 ). { \ displaystyle \ prod _ { 1 \ leq k \ leq n - 1 } \ left ( 2 ^ { k } - 1 \ right ) \ equiv n \ mod \ left ( 2 ^ { n } - 1 \ right ). } similarly, n is prime, if and only if the following congruence for polynomials in x holds : 1 ≤ k ≤ n − 1 ( x k − 1 ) ≡ n − ( x n − 1 ) / ( x − 1 ) mod ( x n − 1 ) { \ displaystyle \ prod _ { 1 \ leq k \ leq n - 1 } \ left ( x ^ { k } - 1 \ right ) \ equiv n - \ left ( x ^ { n } - 1 \ right ) / \ left ( x - 1 \ right ) \ mod \ left ( x ^ { n } - 1 \ right ) } or : 1 ≤ k ≤ n − 1 ( x k − 1 ) ≡ n mod ( x n − 1 ) / ( x − 1 ). { \ displaystyle \ prod _ { 1 \ leq k \ leq n - 1 } \ left ( x ^ { k } - 1 \ right ) \ equiv n \ mod \ left ( x ^ { n } - 1 \ right ) / \ left ( x - 1 \ right ). }


in some concurrent computing systems, communication between the concurrent components is hidden from the programmer ( e. g., by using futures ), while in others it must be handled explicitly. explicit communication can be divided into two classes : shared memory communication concurrent components communicate by altering the contents of shared memory locations ( exemplified by java and c # ). this style of concurrent programming usually needs the use of some form of locking ( e. g., mutexes, semaphores, or monitors ) to coordinate between threads. a program that properly implements any of these is said to be thread - safe. message passing communication concurrent components communicate by exchanging messages ( exemplified by mpi, go, scala, erlang and occam ).


in the 2003 version, the vysocina region was coded cz061, and the south moravian region was coded cz062.


they are closely related to reputation systems. simple forms of binary trust metrics can be found e. g. in pgp. the first commercial forms of trust metrics in computer software were in applications like ebay's feedback rating. slashdot introduced its notion of karma, earned for activities perceived to promote group effectiveness, an approach that has been very influential in later virtual communities.


in statistics, probability theory, and information theory, a statistical distance quantifies the distance between two statistical objects, which can be two random variables, or two probability distributions or samples, or the distance can be between an individual sample point and a population or a wider sample of points. a distance between populations can be interpreted as measuring the distance between two probability distributions and hence they are essentially measures of distances between probability measures. where statistical distance measures relate to the differences between random variables, these may have statistical dependence, and hence these distances are not directly related to measures of distances between probability measures.


if each item is associated to some features ( e. g. author, year, publisher, actors ) it is possible to define an embedding function, which given the item features estimates the corresponding item latent factors. the embedding function can be designed in many ways and it is trained with the data already available from warm items. alternatively, one could apply a group - specific method.


in mathematics, the prime - counting function is the function counting the number of prime numbers less than or equal to some real number x. it is denoted by π ( x ) ( unrelated to the number π ).


this approach ( often referred to as the probabilistic method ) proved highly effective in applications to extremal combinatorics and graph theory. a closely related area is the study of finite markov chains, especially on combinatorial objects. here again probabilistic tools are used to estimate the mixing time. often associated with paul erdos, who did the pioneering work on the subject, probabilistic combinatorics was traditionally viewed as a set of tools to study problems in other parts of combinatorics. the area recently grew to become an independent field of combinatorics.


mathematically, if the coordinate system undergoes a transformation described by an n × n { \ displaystyle n \ times n } invertible matrix m, so that the basis vectors transform according to = m { \ displaystyle { \ begin { bmatrix } \ mathbf { e } _ { 1 } ^ { \ prime } \ \ mathbf { e } _ { 2 } ^ { \ prime } \... \ \ mathbf { e } _ { n } ^ { \ prime } \ end { bmatrix } } = { \ begin { bmatrix } \ mathbf { e } _ { 1 } \ \ mathbf { e } _ { 2 } \... \ \ mathbf { e } _ { n } \ end { bmatrix } } m }, then the components of a vector v in the original basis ( v i { \ displaystyle v ^ { i } } ) must be similarly transformed via = m − 1 { \ displaystyle { \ begin { bmatrix } v ^ { 1 } { ^ { \ prime } } \ \ v ^ { 2 } { ^ { \ prime } } \ \... \ \ v ^ { n } { ^ { \ prime } } \ end { bmatrix } } = m ^ { - 1 } { \ begin { bmatrix } v ^ { 1 } \ \ v ^ { 2 } \ \... \ \ v ^ { n } \ end { bmatrix } } }. the components of a vector are often represented arranged in a column.


in mathematics, physics, and engineering, a euclidean vector ( sometimes called a geometric or spatial vector, or – as here – simply a vector ) is a geometric object that has both a magnitude ( or length ) and direction. a vector is what is needed to " carry " the point a to the point b ; the latin word vector means " one who carries ". the magnitude of the vector is the distance between the two points and the direction refers to the direction of displacement from a to b. many algebraic operations on real numbers such as addition, subtraction, multiplication, and negation have close analogues for vectors, operations which obey the familiar algebraic laws of commutativity, associativity, and distributivity.


in psychological literature on memory, long - term memory ( ltm ) is commonly divided into two types : semantic and episodic. semantic memories are memories that are stored in ltm without specific encoding information linked to them, and thus represent general knowledge about the world that a person has acquired across the lifespan. episodic memories are memories that are stored in long - term memory as specific " episodes " and that, therefore, have some sort of specific context information associated with them, such as where or when they were encoded. at retrieval, episodic memories are often divided into two different categories based on how much information is available about the " episode. "


right ) ideal of r is an intersection of maximal left ( resp. right ) ideals of ra commutative ring is a v - ring if and only if it is von neumann regular. = = references = =


in statistics, jackknife variance estimates for random forest are a way to estimate the variance in random forest models, in order to eliminate the bootstrap effects.


in the united states, competitors are divided into groups by age. the eight age groups are : 12 and under, 13 – 15, 16 – 17, 18 – 19, junior ( elite 15 – 18 ), senior ( elite 15 + ), collegiate, and master. in addition to these groups, younger swimmers may be divided by ability into 3 levels : novice, intermediate, and age group.


71 ). to every name or designating expression'x ', there corresponds a cluster of properties, namely the family of those properties φ such that a believes'φx '. one of the properties, or some conjointly, are believed by a to pick out some individual uniquely.


in the default mode, where extended channel interpretation is not in effect, the interface between the reader and the host is said to be in " basic channel mode ". in this mode, each octet of transmitted data is defined ( by the corresponding bar code symbology standard ) to correspond directly to a single data character code point in some default character set, normally iso / iec 8859 - 1 ( latin - 1 ). however, when eci is in effect, the data interface is said to be in " extended channel mode ". in this mode the interpretation of the transmitted data is defined by the current eci modes that are enabled, which are activated and deactivated by " eci indicators " included in the transmitted data.


in more traditional processor architectures, a processor is usually programmed by defining the executed operations and their operands. for example, an addition instruction in a risc architecture could look like the following. add r3, r1, r2 this example operation adds the values of general - purpose registers r1 and r2 and stores the result in register r3. coarsely, the execution of the instruction in the processor probably results in translating the instruction to control signals which control the interconnection network connections and function units.


in mathematics, the intersection of two or more objects is another object consisting of everything that is contained in all of the objects simultaneously. for example, in euclidean geometry, when two lines in a plane are not parallel, their intersection is the point at which they meet. more generally, in set theory, the intersection of sets is defined to be the set of elements which belong to all of them. unlike the euclidean definition, this does not presume that the objects under consideration lie in a common space.


in past decades, information governance responsibilities might have fallen under the purview of the chief information officer ( cio ). but somewhere along the line, the cio job description changed to focus solely on the information systems and associated technology that power a company — not the information itself. in today's age of big data, organizations have more information under their control than ever before.


in mathematics, nonlinear modelling is empirical or semi - empirical modelling which takes at least some nonlinearities into account. nonlinear modelling in practice therefore means modelling of phenomena in which independent variables affecting the system can show complex and synergetic nonlinear effects. contrary to traditional modelling methods, such as linear regression and basic statistical methods, nonlinear modelling can be utilized efficiently in a vast number of situations where traditional modelling is impractical or impossible. the newer nonlinear modelling approaches include non - parametric methods, such as feedforward neural networks, kernel regression, multivariate splines, etc., which do not require a priori knowledge of the nonlinearities in the relations.


for each possible value of the theoretical mean, the z - test statistic has a different probability distribution. in these circumstances ( the case of a so - called composite null hypothesis ) the p - value is defined by taking the least favourable null - hypothesis case, which is typically on the border between null and alternative. this definition ensures the complementarity of p - values and alpha - levels.


this realization consists of geometric simplices, glued together according to the rules of the simplicial set. indeed, one may view a simplicial set as a purely combinatorial construction designed to capture the essence of a " well - behaved " topological space for the purposes of homotopy theory. specifically, the category of simplicial sets carries a natural model structure, and the corresponding homotopy category is equivalent to the familiar homotopy category of topological spaces. simplicial sets are used to define quasi - categories, a basic notion of higher category theory. a construction analogous to that of simplicial sets can be carried out in any category, not just in the category of sets, yielding the notion of simplicial objects.


in survey methodology, poisson sampling ( sometimes denoted as po sampling : 61 ) is a sampling process where each element of the population is subjected to an independent bernoulli trial which determines whether the element becomes part of the sample. : 85 each element of the population may have a different probability of being included in the sample ( π i { \ displaystyle \ pi _ { i } } ). the probability of being included in a sample during the drawing of a single sample is denoted as the first - order inclusion probability of that element ( p i { \ displaystyle p _ { i } } ). if all first - order inclusion probabilities are equal, poisson sampling becomes equivalent to bernoulli sampling, which can therefore be considered to be a special case of poisson sampling.


in mathematics and computer science, the krohn – rhodes theory ( or algebraic automata theory ) is an approach to the study of finite semigroups and automata that seeks to decompose them in terms of elementary components. these components correspond to finite aperiodic semigroups and finite simple groups that are combined in a feedback - free manner ( called a " wreath product " or " cascade " ). krohn and rhodes found a general decomposition for finite automata. the authors discovered and proved an unexpected major result in finite semigroup theory, revealing a deep connection between finite automata and semigroups.


in several programming languages, index notation is a way of addressing elements of an array. this method is used since it is closest to how it is implemented in assembly language whereby the address of the first element is used as a base, and a multiple ( the index ) of the element size is used to address inside the array. for example, if an array of integers is stored in a region of the computer's memory starting at the memory cell with address 3000 ( the base address ), and each integer occupies four cells ( bytes ), then the elements of this array are at memory locations 0x3000, 0x3004, 0x3008, …, 0x3000 + 4 ( n − 1 ) ( note the zero - based numbering ). in general, the address of the ith element of an array with base address b and element size s is b + is.


however, callers typically pay a higher rate when calling mobile phones. special prefixes are used to designate mobile numbers so that callers are aware they are calling a mobile phone and therefore will be charged a higher rate. from the caller's point of view, it does not matter where the mobile subscriber is, as the technical process of connecting the call is the same. if a subscriber is roaming on a different company's network, the subscriber, instead of the caller, may pay a surcharge for the connection time. international roaming calls are often quite expensive, and as a result some companies require subscribers to grant explicit permission to receive calls while roaming to certain countries.


in physics, a characteristic length is an important dimension that defines the scale of a physical system. often, such a length is used as an input to a formula in order to predict some characteristics of the system, and it is usually required by the construction of a dimensionless quantity, in the general framework of dimensional analysis and in particular applications such as fluid mechanics. in computational mechanics, a characteristic length is defined to force localization of a stress softening constitutive equation. the length is associated with an integration point. for 2d analysis, it is calculated by taking the square root of the area. for 3d analysis, it is calculated by taking the cubic root of the volume associated to the integration point.


in mathematics, the grothendieck existence theorem, introduced by grothendieck ( 1961, section 5 ), gives conditions that enable one to lift infinitesimal deformations of a scheme to a deformation, and to lift schemes over infinitesimal neighborhoods over a subscheme of a scheme s to schemes over s. the theorem can be viewed as an instance of ( grothendieck's ) formal gaga.


repeated application of distributivity may exponentially increase the size of a formula. in the classical propositional logic, transformation to negation normal form does not impact computational properties : the satisfiability problem continues to be np - complete, and the validity problem continues to be co - np - complete. for formulas in conjunctive normal form, the validity problem is solvable in polynomial time, and for formulas in disjunctive normal form, the satisfiability problem is solvable in polynomial time.


in the emr calculation there are 4 fundamental losses that are necessary for the calculation, they are : d = expected incurred losses e = expected primary losses h = actual incurred losses claims under $ 2, 000. i = actual primary losses all claims including actual incurred lossesthe losses that are not part of this fundamental 4 are, c = expected excess losses ( d − e ) { \ displaystyle ( d - e ) } f = actual excess losses ( h − i ) { \ displaystyle ( h - i ) }


consistent language. using simple, consistent definitions for requirements described in natural language and use the business terminology that is prevalent in the enterprise. guidelines.


in the early 2020s, manufacturers began to integrate satellite connectivity into smartphone devices for use in remote areas, out of the cellular network range. the satellite - to - phone services use l band frequencies, which are compatible with most modern handsets. however, due to the antenna limitations in the conventional phones, in the early stages of implementation satellite connectivity would be limited to the satellite messaging and satellite emergency services. the apple iphone 14 can send emergency text messages via globalstar satellites.


in some languages that have verb serialization, the verbs must appear consecutively with nothing intervening. in other languages, however, it is possible for arguments, normally the object of one of the verbs, to come in between the serialized verbs. the resulting construction is a sequence of verb phrases rather than of plain verbs. the following example is from the nigerian yoruba : the object of the first verb intervenes between the verbs, resulting in two consecutive verb phrases, the first meaning " took the book ", the second " came ".


it was first used by 18th century astronomers investigating planetary revolution around the sun. the magnitude of the vector is the distance between the two points, and the direction refers to the direction of displacement from a to b. many algebraic operations on real numbers such as addition, subtraction, multiplication, and negation have close analogues for vectors, operations which obey the familiar algebraic laws of commutativity, associativity, and distributivity. these operations and associated laws qualify euclidean vectors as an example of the more generalized concept of vectors defined simply as elements of a vector space.


if n { \ textstyle n } is one less than a power of two, then this is always the case. otherwise, the search may perform log 2 ( n ) + 1 { \ textstyle \ lfloor \ log _ { 2 } ( n ) + 1 \ rfloor } iterations if the search reaches the deepest level of the tree. however, it may make log 2 ( n ) { \ textstyle \ lfloor \ log _ { 2 } ( n ) \ rfloor } iterations, which is one less than the worst case, if the search ends at the second - deepest level of the tree. on average, assuming that each element is equally likely to be searched, binary search makes log 2 ( n ) + 1 − ( 2 log 2 ( n ) + 1 − log 2 ( n ) − 2 ) / n { \ displaystyle \ lfloor \ log _ { 2 } ( n ) \ rfloor + 1 - ( 2 ^ { \ lfloor \ log _ { 2 } ( n ) \ rfloor + 1 } - \ lfloor \ log _ { 2 } ( n ) \ rfloor - 2 ) / n } iterations when the target element is in the array.


in supercomputers tracked by top500, the appearance of 64 - bit extensions for the x86 architecture enabled 64 - bit x86 processors by amd and intel to replace most risc processor architectures previously used in such systems ( including pa - risc, sparc, alpha and others ), as well as 32 - bit x86, even though intel itself initially tried unsuccessfully to replace x86 with a new incompatible 64 - bit architecture in the itanium processor. as of 2020, a fujitsu a64fx - based supercomputer called fugaku is number one. the first arm - based supercomputer appeared on the list in 2018 and, in recent years, non - cpu architecture co - processors ( gpgpu ) have also played a big role in performance. intel's xeon phi " knights corner " coprocessors, which implement a subset of x86 - 64 with some vector extensions, are also used, along with x86 - 64 processors, in the tianhe - 2 supercomputer.


y j ∈ { 0, 1 } { \ displaystyle y _ { j } \ in \ { 0, 1 \ } } ; ( if y j = 1 { \ displaystyle y _ { j } = 1 } then e j { \ displaystyle e _ { j } } is covered ) x i ∈ { 0, 1 } { \ displaystyle x _ { i } \ in \ { 0, 1 \ } } ( if x i = 1 { \ displaystyle x _ { i } = 1 } then s i { \ displaystyle s _ { i } } is selected for the cover ). a greedy algorithm will no longer produce solutions with a performance guarantee. namely, the worst case behavior of this algorithm might be very far from the optimal solution. the approximation algorithm is extended by the following way.


occupying the adjacent squares of an opposing token ( e. g. tafl ), also known as a custodian capture, custodianship or interception. occupying one immediately adjacent square to an opposing token, also known as approach. the reverse of approach : capturing an adjacent opposing token by moving away from it in a straight line ( e. g. fanorona ), also known as withdrawal.


a topic is a discrete piece of content that : focuses on one subject has an identifiable purpose does not require external context to understandtopics can be written to be independent of one another and reused wherever needed. the darwin information typing architecture is a standard designed to help authors create topic - based structured content. the standard is managed by the organization for the advancement of structured information standards dita technical committee.


if binary code compatibility is required in future releases, the constant interface must remain forever an interface ( it cannot be converted into a class ), even though it has not been used as an interface in the conventional sense. without an ide that resolves where the constant are coming from, tracking it back to its containing class or interface can be time consuming. an instance of the interface is syntactically no more useful than the interface name itself ( since it has no methods ). unless a developer checks any implemented interfaces when adding a constant to a class, or does so but makes a typo in the name of the added constant, the value of a constant can be silently changed. consider example 2 below. note that the java libraries use constant interface pattern themselves, showing that it may be a reasonable choice in some situations.


but this, on the whole, the algorithm and even the pythagorean arcs, i still reckoned almost an error compared to the indian method. therefore strictly embracing the indian method, and attentive to the study of it, from mine own sense adding some, and some more still from the subtle euclidean geometric art, applying the sum that i was able to perceive to this book, i worked to put it together in xv distinct chapters, showing certain proof for almost everything that i put in, so that further, this method perfected above the rest, this science is instructed to the eager, and to the italian people above all others, who up to now are found without a minimum. if, by chance, something less or more proper or necessary i omitted, your indulgence for me is entreated, as there is no one who is without fault, and in all things is altogether circumspect. the nine indian figures are : 9 8 7 6 5 4 3 2 1 with these nine figures, and with the sign 0 which the arabs call zephir any number whatsoever is written... in other words, in his book he advocated the use of the digits 0 – 9, and of place value.


mathematically, r 0 { \ displaystyle r _ { 0 } } is a threshold for stability of a disease - free equilibrium such that : r 0 ≤ 1 ⇒ lim t → ∞ ( c 1 ( t ), c 2 ( t ),, c n ( t ) ) = dfe { \ displaystyle r _ { 0 } \ leq 1 \ rightarrow \ lim _ { t \ to \ infty } ( c _ { 1 } ( t ), c _ { 2 } ( t ), \ cdots, c _ { n } ( t ) ) = { \ textrm { dfe } } } r 0 > 1, i ( 0 ) > 0 ⇒ lim t → ∞ ( c 1 ( t ), c 2 ( t ),, c n ( t ) ) = ee. { \ displaystyle r _ { 0 } > 1, i ( 0 ) > 0 \ rightarrow \ lim _ { t \ to \ infty } ( c _ { 1 } ( t ), c _ { 2 } ( t ), \ cdots, c _ { n } ( t ) ) = { \ textrm { ee } }. } to calculate r 0 { \ displaystyle r _ { 0 } }, the first step is to linearise around the disease - free equilibrium ( dfe ), but for the infected subsystem of non - linear odes which describe the production of new infections and changes in state among infected individuals.


an interface called " stack " might define two methods : push ( ) and pop ( ). it can be implemented in different ways, for example, faststack and genericstack — the first being fast, working with a data structure of fixed size, and the second using a data structure that can be resized, but at the cost of somewhat lower speed. though interfaces can contain many methods they may contain only one or even none at all. for example, the java language defines the interface readable that has the single read ( ) method ; various implementations are used for different purposes, including bufferedreader, filereader, inputstreamreader, pipedreader, and stringreader. marker interfaces like serializable contain no methods at all and serve to provide run - time information to generic processing using reflection.


the crawl method is an extension of aforementioned discovery method. except most search engines use sophisticated scheduling algorithms to “ decide ” when to revisit a particular page, to appeal to its relevance. these algorithms range from constant visit - interval with higher priority for more frequently changing pages to adaptive visit - interval based on several criteria such as frequency of change, popularity, and overall quality of site. the speed of the web server running the page as well as resource constraints like amount of hardware or bandwidth also figure in.


in neural network applications, the number k of possible outcomes is often large, e. g. in case of neural language models that predict the most likely outcome out of a vocabulary which might contain millions of possible words. this can make the calculations for the softmax layer ( i. e. the matrix multiplications to determine the z i { \ displaystyle z _ { i } }, followed by the application of the softmax function itself ) computationally expensive. what's more, the gradient descent backpropagation method for training such a neural network involves calculating the softmax for every training example, and the number of training examples can also become large. the computational effort for the softmax became a major limiting factor in the development of larger neural language models, motivating various remedies to reduce training times. approaches that reorganize the softmax layer for more efficient calculation include the hierarchical softmax and the differentiated softmax.


a feasible solution is a solution in which for each bin b i { \ displaystyle b _ { i } } the total weight of assigned items is at most t i { \ displaystyle t _ { i } }. the solution's profit is the sum of profits for each item - bin assignment.


in mathematics, an iterated binary operation is an extension of a binary operation on a set s to a function on finite sequences of elements of s through repeated application. common examples include the extension of the addition operation to the summation operation, and the extension of the multiplication operation to the product operation. other operations, e. g., the set - theoretic operations union and intersection, are also often iterated, but the iterations are not given separate names.


sometimes the form of this function is based on knowledge about the relationship between y i { \ displaystyle y _ { i } } and x i { \ displaystyle x _ { i } } that does not rely on the data. if no such knowledge is available, a flexible or convenient form for f { \ displaystyle f } is chosen. for example, a simple univariate regression may propose f ( x i, β ) = β 0 + β 1 x i { \ displaystyle f ( x _ { i }, \ beta ) = \ beta _ { 0 } + \ beta _ { 1 } x _ { i } }, suggesting that the researcher believes y i = β 0 + β 1 x i + e i { \ displaystyle y _ { i } = \ beta _ { 0 } + \ beta _ { 1 } x _ { i } + e _ { i } } to be a reasonable approximation for the statistical process generating the data.


in statistics, the breusch – godfrey test is used to assess the validity of some of the modelling assumptions inherent in applying regression - like models to observed data series. in particular, it tests for the presence of serial correlation that has not been included in a proposed model structure and which, if present, would mean that incorrect conclusions would be drawn from other tests or that sub - optimal estimates of model parameters would be obtained. the regression models to which the test can be applied include cases where lagged values of the dependent variables are used as independent variables in the model's representation for later observations. this type of structure is common in econometric models. the test is named after trevor s. breusch and leslie g. godfrey.


in order for indicators to be considered valid for accountability, they must meet a few minimum requirements. they need to measure marketing outcomes from the consumers ’ point of view, they need to include all marketing activities, they must be repeated over time, and they must meet statistical and technical criteria required of all measurement systems. the measurements need to be true outcome indicators. unlike sales where the outcome is easily quantifiable, marketing is more difficult to define : there is not a direct, fast - acting relationship between marketing activities and sales.


in most formalisms that use syntactic predicates, the syntax of the predicate is noncommutative, which is to say that the operation of predication is ordered. for instance, using the above example, consider the following pseudo - grammar, where x : : = y pred z is understood to mean : " y produces x if and only if y also satisfies predicate z " : s : : = a x x : : = y pred z y : : = a + bncn z : : = anbn c + bncn : : = b c anbn : : = a b given the string aaaabbbccc, in the case where y must be satisfied first ( and assuming a greedy implementation ), s will generate ax and x in turn will generate aaabbbccc, thereby generating aaaabbbccc. in the case where z must be satisfied first, anbn will fail to generate aaaabbb, and thus aaaabbbccc is not generated by the grammar. moreover, if either y or z ( or both ) specify any action to be taken upon reduction ( as would be the case in many parsers ), the order that these productions match determines the order in which those side - effects occur. formalisms that vary over time ( such as adaptive grammars ) may rely on these side effects.


in the fair cake - cutting problem, classic allocation rules such as divide and choose are not pm. several rules are known to be pm : when the pieces may be disconnected, any function that maximizes a concave welfare function ( a monotonically - increasing function of the utilities ) is pm. this holds whether the welfare function operates on the absolute utilities or on the relative utilities. in particular, the nash - optimal rule, absolute - leximin and relative - leximin rules, absolute - utilitarian and relative utilitarian rules are all pm.


in mathematical finite group theory, the dempwolff group is a finite group of order 319979520 = 215 · 32 · 5 · 7 · 31, that is the unique nonsplit extension 2 5. g l 5 ( f 2 ) { \ displaystyle 2 ^ { 5 \,. } \ mathrm { gl } _ { 5 } ( \ mathbb { f } _ { 2 } ) } of g l 5 ( f 2 ) { \ displaystyle \ mathrm { gl } _ { 5 } ( \ mathbb { f } _ { 2 } ) } by its natural module of order 2 5 { \ displaystyle 2 ^ { 5 } }. the uniqueness of such a nonsplit extension was shown by dempwolff ( 1972 ), and the existence by thompson ( 1976 ), who showed using some computer calculations of smith ( 1976 ) that the dempwolff group is contained in the compact lie group e 8 { \ displaystyle e _ { 8 } } as the subgroup fixing a certain lattice in the lie algebra of e 8 { \ displaystyle e _ { 8 } }, and is also contained in the thompson sporadic group ( the full automorphism group of this lattice ) as a maximal subgroup.


in political campaigns, an attack ad is an advertisement designed to wage a personal attack against an opposing candidate or political party in order to gain support for the attacking candidate and attract voters. attack ads often form part of negative campaigning or smear campaigns, and in large or well - financed campaigns, may be disseminated via mass media. an attack ad will generally unfairly criticize an opponent's political platform, usually by pointing out its faults.


using michell's schema, ben richards ( kyngdon & richards, 2007 ) discovered that some instances of the triple cancellation axiom are " incoherent " as they contradict the single cancellation axiom. moreover, he identified many instances of the triple cancellation which are trivially true if double cancellation is supported. the axioms of the theory of conjoint measurement are not stochastic ; and given the ordinal constraints placed on data by the cancellation axioms, order restricted inference methodology must be used ( iverson & falmagne 1985 ).


in the 1990s, digital speech recognition technology became a feature of the personal computer with ibm, philips and lernout & hauspie fighting for customers. much later the market launch of the first smartphone ibm simon in 1994 laid the foundation for smart virtual assistants as we know them today. in 1997, dragon's naturally speaking software could recognize and transcribe natural human speech without pauses between each word into a document at a rate of 100 words per minute. a version of naturally speaking is still available for download and it is still used today, for instance, by many doctors in the us and the uk to document their medical records. in 2001 colloquis publicly launched smarterchild, on platforms like aim and msn messenger. while entirely text - based smarterchild was able to play games, check the weather, look up facts, and converse with users to an extent. the first modern digital virtual assistant installed on a smartphone was siri, which was introduced as a feature of the iphone 4s on 4 october 2011.


a high return loss is desirable and results in a lower insertion loss. from a certain perspective'return loss'is a misnomer. the usual function of a transmission line is to convey power from a source to a load with minimal loss.


in mathematics, a stacky curve is an object in algebraic geometry that is roughly an algebraic curve with potentially " fractional points " called stacky points. a stacky curve is a type of stack used in studying gromov – witten theory, enumerative geometry, and rings of modular forms. stacky curves are deeply related to 1 - dimensional orbifolds and therefore sometimes called orbifold curves or orbicurves.


in pseudocode, the algorithm will be : function kahansum ( input ) var sum = 0. 0 / / prepare the accumulator. var c = 0. 0 / / a running compensation for lost low - order bits. for i = 1 to input. length do / / the array input has elements indexed input to input. var y = input - c / / c is zero the first time around.


for a vector to represent a geometric object, it must be possible to describe how it looks in any other coordinate system. that is to say, the components of the vectors will transform in a certain way in passing from one coordinate system to another. a vector, which is an example of a contravariant tensor, has components that transform inversely to the transformation of the reference axes, ( with example transformations including rotation and dilation ).


in some contexts, the value of the loss function itself is a random quantity because it depends on the outcome of a random variable x.


historically - long before anyone defined nested intervals in a textbook - people implicitly constructed such nestings for concrete calculation purposes. for example, the ancient babylonians discovered a method for computing square roots of numbers. in contrast, the famed archimedes constructed sequences of polygons, that inscribed and surcumscribed a unit circle, in order to get a lower and upper bound for the circles circumference - which is the circle number pi ( π { \ displaystyle \ pi } ). the central question to be posed is the nature of the intersection over all the natural numbers, or, put differently, the set of numbers, that are found in every interval i n { \ displaystyle i _ { n } } ( thus, for all n ∈ n { \ displaystyle n \ in \ mathbb { n } } ). in modern mathematics, nested intervals are used as a construction method for the real numbers ( in order to complete the field of rational numbers ).


in statistics, the size of a test is the probability of falsely rejecting the null hypothesis. that is, it is the probability of making a type i error. it is denoted by the greek letter α ( alpha ).


the set of all k - combinations of a set s is often denoted by ( s k ) { \ displaystyle \ textstyle { \ binom { s } { k } } }. a combination is a combination of n things taken k at a time without repetition. to refer to combinations in which repetition is allowed, the terms k - combination with repetition, k - multiset, or k - selection, are often used.


in order to reap the real benefits of a sharing economy and somehow address some issues that revolve around it, there is a great need for the government and policy - makers to create the “ right enabling framework based on a set of guiding principles ” proposed by the world economic forum. these principles are derived from the analysis of global policymaking and consultation with experts. the following are the seven principles for regulation in the sharing economy. the first principle is creating space for innovation.


at most two foster processors could be accommodated in a symmetric multiprocessing ( smp ) system built with a mainstream chipset, so a second version ( foster mp ) was introduced with a 1 mb l3 cache and the jackson hyper - threading capacity. this improved performance slightly, but not enough to lift it out of third place. it was also priced much higher than the dual - processor ( dp ) versions. the foster shared the 80528 product code with willamette.


.., x k { \ displaystyle x _ { 1 },..., x _ { k } }, and two propositional formulas are logically equivalent if and only if they express the same boolean function.


in non - overlapping methods, the subdomains intersect only on their interface. in primal methods, such as balancing domain decomposition and bddc, the continuity of the solution across subdomain interface is enforced by representing the value of the solution on all neighboring subdomains by the same unknown. in dual methods, such as feti, the continuity of the solution across the subdomain interface is enforced by lagrange multipliers.


in natural language processing, entity linking, also referred to as named - entity linking ( nel ), named - entity disambiguation ( ned ), named - entity recognition and disambiguation ( nerd ) or named - entity normalization ( nen ) is the task of assigning a unique identity to entities ( such as famous individuals, locations, or companies ) mentioned in text. for example, given the sentence " paris is the capital of france ", the idea is to determine that " paris " refers to the city of paris and not to paris hilton or any other entity that could be referred to as " paris ". entity linking is different from named - entity recognition ( ner ) in that ner identifies the occurrence of a named entity in text but it does not identify which specific entity it is ( see differences from other techniques ).


numerical software execution results or through - put on a network test, for example, provides analytical evidence that the requirement has been met. inspection of vendor documentation or spec sheets also verifies requirements. testing or demonstrating the software in a lab environment also verifies the requirements : a test type of verification will occur when test equipment not normally part of the lab ( or system under test ) is used.


in mathematics, the lower envelope or pointwise minimum of a finite set of functions is the pointwise minimum of the functions, the function whose value at every point is the minimum of the values of the functions in the given set. the concept of a lower envelope can also be extended to partial functions by taking the minimum only among functions that have values at the point. the upper envelope or pointwise maximum is defined symmetrically. for an infinite set of functions, the same notions may be defined using the infimum in place of the minimum, and the supremum in place of the maximum. for continuous functions from a given class, the lower or upper envelope is a piecewise function whose pieces are from the same class.


in mathematics, the backus – gilbert method, also known as the optimally localized average ( ola ) method is named for its discoverers, geophysicists george e. backus and james freeman gilbert. it is a regularization method for obtaining meaningful solutions to ill - posed inverse problems. where other regularization methods, such as the frequently used tikhonov regularization method, seek to impose smoothness constraints on the solution, backus – gilbert instead seeks to impose stability constraints, so that the solution would vary as little as possible if the input data were resampled multiple times. in practice, and to the extent that is justified by the data, smoothness results from this.