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@Kevin Buzzard , thank you for all the help on the previous stream - I wanted to pick your brain for second.
I just read your talk from Pittsburgh on the many examples for ... unencouraging non-retractions of peer reviewed mathematics.
Is anyone already placing beers on any given fields of maths that will fail to be formally verified?
I'm not aware of such a bet
Most maths is absolutely fine. When I give talks like that in maths departments I try and wind people up and suggest that maths is on the verge of collapse, but the truth is that humans know what they're doing and 99% of it could in theory be formally verified, except that it would take thousands of years to do it
At the end of your presentation, you mentioned confidence in a handful of results - but it seems to me one can extend a much less charitable interpretation of many results given unaligned interests of academia, peer review, and formal verification.
thousands of years is a gross overestimate. Several years and millions of people is more accurate
There will be incomplete proofs, and proofs where the missing arguments are "known to the experts" and I am concerned that one day when the experts are gone this will translate to "known to nobody". The arrogance of our community is that we believe that by the time they're gone, we will know new and better ways to prove the results for which the proofs died.
or at least a decent percentage of the people actually producing the papers
i believe that verifying a great deal of computational complexity theory will be very difficult, i haven't found any prior work in a quick search either.
i don't think that it will be difficult because stuff is wrong, but because the arguments and proofs are the way they are.
Yes, thousands of person-years is what I meant.
Kevin Buzzard said:
Most maths is absolutely fine. When I give talks like that in maths departments I try and wind people up and suggest that maths is on the verge of collapse, but the truth is that humans know what they're doing and 99% of it could in theory be formally verified, except that it would take thousands of years to do it
Well, a lot of institutions and brilliant people have believed ridiculous things, especially when they only need the approval of each other at the end of the day.
To clarify, I'm not being a catastrophist either, but I do feel some inclination to hear out more of those arguments now.
Kevin Buzzard said:
There will be incomplete proofs, and proofs where the missing arguments are "known to the experts" and I am concerned that one day when the experts are gone this will translate to "known to nobody". The arrogance of our community is that we believe that by the time they're gone, we will know new and better ways to prove the results for which the proofs died.
How easy is it for you to look at a lean proof someone else made and be able to write it own on pencil and paper, rigorously?
I guess I am also asking for the Lean community in general.
Depends on whether it's a tactic or term mode proof.
often the easiest way is ignore the Lean proof and just notice that the statement is true
Also depends on what you mean by "rigorously". Some files like data.finset
are exactly how Reid is describing. All the theorems in there can be proved by "duh, it's a trivial result about a finite set". Hence all the theorems in the other files which use those theorems -- you don't have to justify why the use is OK and no mathematician would complain. However at the top end of mathematics you have people writing down arguments which contain hugely general statements which experts understand can be justified and such people would argue until they're blue in the face that the arguments were rigorous. So your question isn't really well-defined. Rigour is in the eye of the beholder. Lean is just one example of a beholder.
Along the same lines as what Reid and Kevin are saying, there are often many Lean statements that should simply be ignored from the point of view of pencil + paper math. (Maybe we should think about adding a "hiding" feature to the mathlib docs?)
I think that things like extensionality lemmas have an important role to play in the documentation. You can understand Lean's conventions with ext
and ext_iff
if you can see them. But every one of them should be ignored from the point of view of pencil and paper maths.
Thanks for the input!
{% endraw %}Last updated: Apr 24 2020 at 19:02 UTC


A B C D F G H I J K L M N O P R S T V W Y Z
| agricolae-package | Statistical Procedures for Agricultural Research |
| agricolae | Statistical Procedures for Agricultural Research |
| AMMI | AMMI Analysis |
| AMMI.contour | AMMI contour |
| audpc | Calculating the absolute or relative value of the AUDPC |
| audps | The Area Under the Disease Progress Stairs |
| bar.err | Plotting the standard error or standard deviance of a multiple comparison of means |
| bar.group | Plotting the multiple comparison of means |
| BIB.test | Finding the Variance Analysis of the Balanced Incomplete Block Design |
| carolina | North Carolina Designs I, II and III |
| Chz2006 | Data amendment Carhuaz 2006 |
| CIC | Data for late blight of potatoes |
| clay | Data of Ralstonia population in clay soil |
| ComasOxapampa | Data AUDPC Comas - Oxapampa |
| consensus | consensus of clusters |
| corn | Data of corn |
| correl | Correlation Coefficient |
| correlation | Correlation analysis. Methods of Pearson, Spearman, Kendall and Lin |
| cotton | Data of cotton |
| cv.model | Coefficient of the experiment variation |
| cv.similarity | Coefficient of the similarity matrix variation |
| DAU.test | Finding the Variance Analysis of the Augmented block Design |
| DC | Data for the analysis of carolina genetic design |
| delete.na | Omitting the rows or columns with missing observations of a matrix (NA) |
| design.ab | Design of experiments for a factorial |
| design.alpha | Alpha design type (0,1) |
| design.bib | Randomized Balanced Incomplete Block Designs. BIB |
| design.crd | Completely Randomized Design |
| design.cyclic | Cyclic designs |
| design.dau | Augmented block design |
| design.graeco | Graeco - latin square design |
| design.lattice | Lattice designs |
| design.lsd | Latin Square Design |
| design.mat | Experimental design matrix |
| design.rcbd | Randomized Complete Block Design |
| design.split | Split Plot Design |
| design.strip | Strip Plot Design |
| design.youden | Incomplete Latin Square Design |
| diffograph | Plotting the multiple comparison of means |
| disease | Data evaluation of the disease overtime |
| duncan.test | Duncan's new multiple range test |
| durbin.test | Durbin test and multiple comparison of treatments |
| friedman | Friedman test and multiple comparison of treatments |
| frijol | Data of frijol |
| genxenv | Data of potato yield in a different environment |
| Glycoalkaloids | Data Glycoalkaloids |
| graph.freq | Histogram |
| grass | Data for Friedman test |
| greenhouse | Data in greenhouse |
| growth | Data growth of trees |
| haynes | Data of AUDPC for nonparametrical stability analysis |
| Hco2006 | Data amendment Huanuco 2006 |
| hcut | Cut tree of consensus |
| heterosis | Data of potato, Heterosis |
| hgroups | groups of hclust |
| HSD.test | Multiple comparisons: Tukey |
| huasahuasi | Data: Rainfall thresholds as support for timing fungicide applications in the control of potato late blight in Peru |
| index.AMMI | AMMI index and yield stability |
| index.bio | Biodiversity Index |
| index.smith | Uniformity soil. Smith's Index of Soil Heterogeneity |
| intervals.freq | Class intervals |
| join.freq | Join class for histogram |
| kendall | Correlation of Kendall |
| kruskal | Kruskal Wallis test and multiple comparison of treatments. |
| kurtosis | Finding the Kurtosis coefficient |
| lastC | Setting the last character of a chain |
| lateblight | LATEBLIGHT - Simulator for potato late blight Version LB2004 |
| lineXtester | Line x Tester Analysis |
| LSD.test | Multiple comparisons, "Least significant difference" and Adjust P-values |
| LxT | Data Line by tester |
| markers | Data of molecular markers |
| Median.test | Median test. Multiple comparisons |
| melon | Data of yield of melon in a Latin square experiment |
| montecarlo | Random generation by Montecarlo |
| natives | Data of native potato |
| nonadditivity | Nonadditivity model test |
| normal.freq | Normal curve on the histogram |
| ogive.freq | Plotting the ogive from a histogram |
| order.group | Ordering the treatments according to the multiple comparison |
| orderPvalue | Grouping the treatments averages in a comparison with a minimum value |
| pamCIP | Data Potato Wild |
| paracsho | Data of Paracsho biodiversity |
| path.analysis | Path Analysis |
| PBIB.test | Analysis of the Partially Balanced Incomplete Block Design |
| plot.AMMI | PLOT AMMI |
| plot.graph.freq | Histogram |
| plot.group | Plotting the multiple comparison of means |
| plots | Data for an analysis in split-plot |
| plrv | Data clones from the PLRV population |
| polygon.freq | The polygon of frequency on the histogram |
| potato | Data of cutting |
| ralstonia | Data of assessment of the population in the soil R.solanacearum |
| reg.homog | Homologation of regressions |
| REGW.test | Ryan, Einot and Gabriel and Welsch multiple range test |
| resampling.cv | Resampling to find the optimal number of markers |
| resampling.model | Resampling for linear models |
| rice | Data of Grain yield of rice variety IR8 |
| RioChillon | Data and analysis Mother and baby trials |
| scheffe.test | Multiple comparisons, scheffe |
| similarity | Matrix of similarity in binary data |
| simulation.model | Simulation of the linear model under normality |
| sinRepAmmi | Data for AMMI without repetition |
| skewness | Finding the skewness coefficient |
| SNK.test | Student-Newman-Keuls (SNK) |
| soil | Data of soil analysis for 13 localities |
| sp.plot | Splip-Plot analysis |
| ssp.plot | Split-split-Plot analysis |
| stability.nonpar | Nonparametric stability analysis |
| stability.par | Stability analysis. SHUKLA'S STABILITY VARIANCE AND KANG'S |
| stat.freq | Descriptive measures of grouped data |
| strip.plot | Strip-Plot analysis |
| sturges.freq | Class intervals for a histogram, the rule of Sturges |
| summary.graph.freq | frequency Table of a Histogram |
| sweetpotato | Data of sweetpotato yield |
| table.freq | frequency Table of a Histogram |
| tapply.stat | Statistics of data grouped by factors |
| vark | Variance K, ties, Kendall |
| waerden.test | Multiple comparisons. The van der Waerden (Normal Scores) |
| waller | Computations of Bayesian t-values for multiple comparisons |
| waller.test | Multiple comparisons, Waller-Duncan |
| weatherSeverity | Weather and Severity |
| wilt | Data of Bacterial Wilt (AUDPC) and soil |
| yacon | Data Yacon |
| zigzag | order plot in serpentine |


--- layout: page title: About header-img: "img/about-bg.png" ---
My voyage into the world of programming.


Key Capabilities of the Kaa IoT Platform:
Connectivity, Integration, and Data Processing
This page will guide you through the various aspects of Kaa so you can get a better understanding of its functionality and capabilities.
Hardware
The Kaa platform is hardware-agnostic. You can integrate pretty much any device, starting from those powered by fully-functional operating systems, all the way down to resource-constrained microcontrollers with less than 10 KB of available RAM. There are many platforms that are already pre-integrated and verified with Kaa, but even if you don’t see a particular platform listed, there is a good chance that it can be easily integrated using Kaa’s highly portable SDKs. They are now available in Java, C++, and C: just pick one that suits your case.
Data models
Kaa can handle both structured and unstructured data, but favors the former. Well-structured data provides excellent material for any manipulation and analytics.
This kind of data also helps abstract out any unimportant details of the low-level implementation and your hardware. Kaa ensures that even gadgets based on very different technologies can be managed and operated identically, as long as they share the same set of data schemas. This is why in every aspect of its functionality, Kaa makes use of a corresponding data schema that governs the semantics and generates a lot of boilerplate code automatically. Schemas are Apache Avro compatible, and thus, very powerful. Apache Avro also allows data serialization to be very efficient.
Once you start working with Kaa, you will quickly find yourself in a data schemas state of mind — and that’s a good thing.
- Works with structured and unstructured data
- Apache Avro compatible
- GUI for data schemas
SDK
Kaa endpoint SDKs are available in Java, C++, and C, and are designed to be embedded into your client application (or firmware). They handle client-server communication, authentication, data marshalling, encryption, persistence, and other functions provided by the platform.
Each generated SDK is fitted for your particular server instance. The generated SDKs contain server-specific data schemas translated into object bindings for your IoT application. The SDKs also have the knowledge of the transport layer protocol implementation in use, as well as how to establish communication with that specific server instance at which the SDK was generated.
- Auto-generated code and data bindings
- Abstracts out protocol, data consistency, and other complexities
- Easily portable to virtually any hardware and OS
#include <stdint.h> #include "kaa/kaa_error.h" #include "kaa/kaa_context.h" #include "kaa/platform/kaa_client.h" #include "kaa/kaa_profile.h" int main() { kaa_client_t *kaa_client = NULL; kaa_client_create(&kaa_client, NULL); kaa_profile_t *profile = kaa_profile_car_create(); profile->brand = ENUM_BRAND_Audi; profile->model = kaa_string_copy_create("A8"); profile->color = kaa_string_copy_create("silver"); profile->vin = kaa_string_copy_create("JTHGL1"); kaa_profile_manager_update_profile( kaa_client_get_context(kaa_client)-> profile_manager , profile); profile->destroy(profile); kaa_client_start(kaa_client, NULL, NULL, 0); kaa_client_destroy(kaa_client); return 0; }
package org.kaaproject.smartcar.test; import org.kaaproject.kaa.client.DesktopKaaPlatformContext; import org.kaaproject.kaa.client.Kaa; import org.kaaproject.kaa.client.KaaClient; import org.kaaproject.kaa.client.profile.ProfileContainer; import org.kaaproject.smartcar.Brand; import org.kaaproject.smartcar.Car; public class SmartCar { public static void main(String[] args) { DesktopKaaPlatformContext kaaContext = new DesktopKaaPlatformContext(); KaaClient kaaClient = Kaa.newClient(kaaContext, null); kaaClient.setProfileContainer( new ProfileContainer() { @Override public Car getProfile() { return new Car(Brand.Audi, "A8", "silver", "JTHGL1"); } }); kaaClient.start(); kaaClient.stop(); } }
#include ‹memory› #include "kaa/Kaa.hpp" #include "kaa/IKaaClient.hpp" #include "kaa/profile/DefaultProfileContainer.hpp" using namespace kaa; int main() { Kaa::init(); IKaaClient & kaaClient = Kaa::getKaaClient(); kaa_profile::Car profile; profile.brand = kaa_profile::Brand::Audi; profile.model = "A8"; profile.color = "silver"; profile.vin = "JTHGL1"; kaaClient.setProfileContainer( std::make_shared<DefaultProfileContainer>( profile)); Kaa::start(); Kaa::stop(); return 0; }
#import "AppDelegate.h" @import Kaa; @interface AppDelegate () <ProfileContainer> @end @implementation AppDelegate - (BOOL)application:(UIApplication *)application didFinishLaunchingWithOptions:(NSDictionary *)launchOptions { id<KaaClient> kaaClient = [KaaClientFactory clientWithContext:[[DefaultKaaPlatformContext alloc] init] stateDelegate:nil]; [kaaClient setProfileContainer:self]; [kaaClient start]; [kaaClient stop]; return YES; } - (Car *)getProfile { return [[Car alloc] initWithBrand:CarBrandAudi model:@"A8" color:@"silver" vin:@"JTHGL1"]; } @end
Connectivity
Kaa is transport-agnostic. It allows building applications that function over any type of network connection — either persistent or intermittent. You may choose one of the existing transport protocol implementations that come with Kaa, or create custom-tailored transports and plug them into your system. Kaa will automatically advertise the connection parameters to endpoints and balance the load across the servers in the cluster.
Advanced platform users may find it handy that Kaa is able to flexibly assign transport implementations to platform services. For example, notifications may be delivered to endpoints via UDP or SMS while configuration and profile data may be synced via an AES-encrypted TCP-based binary protocol.
- Transport-agnostic
- Pluggable protocols
- Multi-channel support


| 004:005 Khan | : |
And give not unto the foolish your property which Allah has made a means of support for you, but feed and clothe them therewith, and speak to them words of kindness and justice. |
| 004:005 Maulana | : |
And make not over your property, which Allah has made a (means of) support for you, to the weak of understanding, and maintain them out of it, and clothe them and give them a good education. |
| 004:005 Pickthal | : |
Give not unto the foolish (what is in) your (keeping of their) wealth, which Allah hath given you to maintain; but feed and clothe them from it, and speak kindly unto them. |
| 004:005 Rashad | : |
Do not give immature orphans the properties that GOD has entrusted with you as guardians. You shall provide for them therefrom, and clothe them, and treat them kindly. |
| 004:005 Sarwar | : |
Do not give to people weak of understanding your property for which God has made you to supervise. Feed and clothe such people and speak to them in a reasonable way. |
| 004:005 Shakir | : |
And do not give away your property which Allah has made for you a (means of) support to the weak of understanding, and maintain them out of (the profits of) it, and clothe them and speak to them words of honest advice. |
| 004:005 Sherali | : |
And give not to those weak of understanding your property which ALLAH has made for you a means of support; but feed them therewith and clothe them and speak to them words of kind advice. |
| 004:005 Yusufali | : |
To those weak of understanding Make not over your property, which Allah hath made a means of support for you, but feed and clothe them therewith, and speak to them words of kindness and justice. |
Concepts/Themes Covered: الإنسان والعلاقات الاجتماعية > اليتامى > الوصاية عليهم Man and The Social Relations>The Orphans>Guardianship on Them تنظيم العلاقات المالية > أموال السفهاء Organizing Financial Relationships>The Property of the Foolish تنظيم العلاقات المالية > الحجز Organizing Financial Relationships>Its Prevention
This tool uses eight English parallel translations for the Holy Quran imported from Mr. Clay Smith. You can also visit Qurany Concepts for browsing the Quran themes or topics. If you want to search the Holy Quran for keywords, please visit Qurany Keywords.


Treasure Island
by Robert Louis Stevenson
Part Six: Captain Silver, Chapter 32: The Treasure-Hunt—The Voice Among the Trees
Additional Information
- Year Published: 1883
- Language: English
- Country of Origin: England
- Source: Stevenson, R. L. (1883). Treasure Island. London, England: Cassell and Co.
-
Readability:
- Flesch–Kincaid Level: 7.0
- Word Count: 2,145
- Genre: Adventure
- ✎ Cite This
Downloads
Partly from the damping influence of this alarm, partly to rest Silver and the sick folk, the whole party sat down as soon as they had gained the brow of the ascent.
The plateau being somewhat tilted towards the west, this spot on which we had paused commanded a wide prospect on either hand. Before us, over the tree-tops, we beheld the Cape of the Woods fringed with surf; behind, we not only looked down upon the anchorage and Skeleton Island, but saw—clear across the spit and the eastern lowlands—a great field of open sea upon the east. Sheer above us rose the Spyglass, here dotted with single pines, there black with precipices. There was no sound but that of the distant breakers, mounting from all round, and the chirp of countless insects in the brush. Not a man, not a sail, upon the sea; the very largeness of the view increased the sense of solitude.
Silver, as he sat, took certain bearings with his compass.
“There are three ‘tall trees’” said he, “about in the right line from Skeleton Island. ‘Spy-glass shoulder,’ I take it, means that lower p’int there. It’s child’s play to find the stuff now. I’ve half a mind to dine first.”
“I don’t feel sharp,” growled Morgan. “Thinkin’ o’ Flint—I think it were—as done me.”
“Ah, well, my son, you praise your stars he’s dead,” said Silver.
“He were an ugly devil,” cried a third pirate with a shudder; “that blue in the face too!”
“That was how the rum took him,” added Merry. “Blue! Well, I reckon he was blue. That’s a true word.”
Ever since they had found the skeleton and got upon this train of thought, they had spoken lower and lower, and they had almost got to whispering by now, so that the sound of their talk hardly interrupted the silence of the wood.
I never have seen men more dreadfully affected than the pirates. The colour went from their six faces like enchantment; some leaped to their feet, some clawed hold of others; Morgan grovelled on the ground.
“It’s Flint, by——!” cried Merry.
The song had stopped as suddenly as it began—broken off, you would have said, in the middle of a note, as though someone had laid his hand upon the singer’s mouth. Coming through the clear, sunny atmosphere among the green tree-tops, I thought it had sounded airily and sweetly; and the effect on my companions was the stranger.
“Come,” said Silver, struggling with his ashen lips to get the word out; “this won’t do. Stand by to go about. This is a rum start, and I can’t name the voice, but it’s someone skylarking—someone that’s flesh and blood, and you may lay to that.”
His courage had come back as he spoke, and some of the colour to his face along with it. Already the others had begun to lend an ear to this encouragement and were coming a little to themselves, when the same voice broke out again—not this time singing, but in a faint distant hail that echoed yet fainter among the clefts of the Spy-glass.
“Darby M’Graw,” it wailed—for that is the word that best describes the sound—”Darby M’Graw!
The buccaneers remained rooted to the ground, their eyes starting from their heads. Long after the voice had died away they still stared in silence, dreadfully, before them.
“That fixes it!” gasped one. “Let’s go.”
“They was his last words,” moaned Morgan, “his last words above board.”
 He had been well brought up, had Dick, before he came to sea and fell among bad companions.
Still Silver was unconquered. I could hear his teeth rattle in his head, but he had not yet surrendered.
“Nobody in this here island ever heard of Darby,” he muttered; “not one but us that’s here.” And then, making a great effort: “Shipmates,” he cried, “I’m here to get that stuff, and I’ll not be beat by man or devil. I never was feared of Flint in his life, and, by the powers, I’ll face him dead. There’s seven hundred thousand pound not a quarter of a mile from here. When did ever a gentleman o’ fortune show his stern to that much dollars for a boozy old seaman with a blue mug—and him dead too?”
But there was no sign of reawakening courage in his followers, rather, indeed, of growing terror at the irreverence of his words.
“Belay there, John!” said Merry. “Don’t you cross a sperrit.”
And the rest were all too terrified to reply. They would have run away severally had they dared; but fear kept them together, and kept them close by John, as if his daring helped them. He, on his part, had pretty well fought his weakness down.
“Sperrit? Well, maybe,” he said. “But there’s one thing not clear to me. There was an echo. Now, no man ever seen a sperrit with a shadow; well then, what’s he doing with an echo to him, I should like to know? That ain’t in natur’, surely?”
This argument seemed weak enough to me. But you can never tell what will affect the superstitious, and to my wonder, George Merry was greatly relieved.
“Well, that’s so,” he said. “You’ve a head upon your shoulders, John, and no mistake. ‘Bout ship, mates! This here crew is on a wrong tack, I do believe. And come to think on it, it was like Flint’s voice, I grant you, but not just so clear-away like it, after all. It was liker somebody else’s voice now—it was liker—”
“By the powers, Ben Gunn!” roared Silver.
“Aye, and so it were,” cried Morgan, springing on his knees. “Ben Gunn it were!”
“It don’t make much odds, do it, now?” asked Dick. “Ben Gunn’s not here in the body any more’n Flint.”
But the older hands greeted this remark with scorn.
“Why, nobody minds Ben Gunn,” cried Merry; “dead or alive, nobody minds him.”
It was extraordinary how their spirits had returned and how the natural colour had revived in their faces. Soon they were chatting together, with intervals of listening; and not long after, hearing no further sound, they shouldered the tools and set forth again, Merry walking first with Silver’s compass to keep them on the right line with Skeleton Island. He had said the truth: dead or alive, nobody minded Ben Gunn.
Dick alone still held his Bible, and looked around him as he went, with fearful glances; but he found no sympathy, and Silver even joked him on his precautions.
 If it ain’t no good to swear by, what do you suppose a sperrit would give for it? Not that!” and he snapped his big fingers, halting a moment on his crutch.
But Dick was not to be comforted; indeed, it was soon plain to me that the lad was falling sick; hastened by heat, exhaustion, and the shock of his alarm, the fever, predicted by Dr. Livesey, was evidently growing swiftly higher.
It was fine open walking here, upon the summit; our way lay a little downhill, for, as I have said, the plateau tilted towards the west. The pines, great and small, grew wide apart; and even between the clumps of nutmeg and azalea, wide open spaces baked in the hot sunshine. Striking, as we did, pretty near north-west across the island, we drew, on the one hand, ever nearer under the shoulders of the Spy-glass, and on the other, looked ever wider over that western bay where I had once tossed and trembled in the oracle.
The first of the tall trees was reached, and by the bearings proved the wrong one. So with the second. The third rose nearly two hundred feet into the air above a clump of underwood—a giant of a vegetable, with a red column as big as a cottage, and a wide shadow around in which a company could have manoeuvred. It was conspicuous far to sea both on the east and west and might have been entered as a sailing mark upon the chart.
But it was not its size that now impressed my companions; it was the knowledge that seven hundred thousand pounds in gold lay somewhere buried below its spreading shadow. The thought of the money, as they drew nearer, swallowed up their previous terrors. Their eyes burned in their heads; their feet grew speedier and lighter; their whole soul was found up in that fortune, that whole lifetime of extravagance and pleasure, that lay waiting there for each of them.
 Certainly he took no pains to hide his thoughts, and certainly I read them like print. In the immediate nearness of the gold, all else had been forgotten: his promise and the doctor’s warning were both things of the past, and I could not doubt that he hoped to seize upon the treasure, find and board the Hispaniola under cover of night, cut every honest throat about that island, and sail away as he had at first intended, laden with crimes and riches.
Shaken as I was with these alarms, it was hard for me to keep up with the rapid pace of the treasure-hunters. Now and again I stumbled, and it was then that Silver plucked so roughly at the rope and launched at me his murderous glances. Dick, who had dropped behind us and now brought up the rear, was babbling to himself both prayers and curses as his fever kept rising. This also added to my wretchedness, and to crown all, I was haunted by the thought of the tragedy that had once been acted on that plateau, when that ungodly buccaneer with the blue face—he who died at Savannah, singing and shouting for drink—had there, with his own hand, cut down his six accomplices. This grove that was now so peaceful must then have rung with cries, I thought; and even with the thought I could believe I heard it ringing still.
We were now at the margin of the thicket.
“Huzza, mates, all together!” shouted Merry; and the foremost broke into a run.
And suddenly, not ten yards further, we beheld them stop. A low cry arose. Silver doubled his pace, digging away with the foot of his crutch like one possessed; and next moment he and I had come also to a dead halt.
Before us was a great excavation, not very recent, for the sides had fallen in and grass had sprouted on the bottom. In this were the shaft of a pick broken in two and the boards of several packing-cases strewn around. On one of these boards I saw, branded with a hot iron, the name Walrus—the name of Flint’s ship.
All was clear to probation. The cache had been found and rifled; the seven hundred thousand pounds were gone!


-1 . The E-rank Hunter-
“E-rank Hunter” Sung Jinwoo .
It was a title that followed him wherever he went .
Even as a Hunter, his abilities were barely above that of an ordinary person . If it wasn’t for his slightly more durable constitution or his slightly increased healing factor, there was but a little difference between him and a non-Hunter . As such, his Hunting career was riddled with variety of injuries . There were even times where he toed the line between life and death itself .
But he was not a Hunter because he enjoyed the job .
It was dangerous, filled with ridicule, and the pay was disappointing .
No . If it wasn’t for the fact that the Hunter Association provided support for the medical bills of his mother, he was more than ready to give it up and start an ordinary employment as an ordinary person .
But how could he, a man in his 20s with no special talents or background, afford to pay the medical bills that amounted to several million won a month[1]?
You could say he had no choice in the matter .
And so today, with a silent cry in his heart, Jinwoo took part in an Association-supervised Raid, same as any other day .
Hunters who operated in the same area knew each other well . This was due to the collective gathering of all Hunters in the area whenever a Gate opened up . And today, the Hunters who’ve gathered shared a cup of coffee while greeting each other .
“Oy, Mr . Kim, over here . ”
“Ooh, Mr . Park, what are you doing here? I thought you were done with the Hunter business . ”
“Ah that… The wife just got pregnant with number two . ”
“Hahaha, is that so? Well, nothing better than a Raid to fill the pockets of a Hunter!”
Both Mr . Kim and Mr . Park laughed .
“You know, it seems like the Association’s been calling us less and less lately . Wonder if the rate of Gate appearances decreased?”
“Eh, nonsense . It’s because the Guilds have been working harder than the Association lately .  ”
“Well then, I guess this Raid being supervised by the Association means it’ll be pretty safe, right?”
With a slight concern, Mr . Park took a look around the area . A Gate ignored by a Guild meant low pay, and a low paying Gate meant low difficulty . Of course, there was nothing in life that was 100% certain . Similar to Mr . Park, other Hunters in the area shifted their eyes with nervousness .
“Perhaps…”
As he finished the coffee, Mr . Kim suddenly waved to someone he saw approaching in the distance .
“Oh, wait, look who it is . Mr . Sung! Hey Mr . Sung!”
Other Hunters also looked at the newcomer with familiarity and relief .
“Hello . ”
It was Sung Jinwoo .
Briefly greeting Mr . Kim with a nod, Jinwoo continued his walk . After he passed, Mr . Kim lightly chuckled and loosened his worries .
“So Jinwoo came . Then this place should be safe . ”
With his eyes widened, Mr . Park asked Mr . Kim .
“What? Is Hunter Sung Jinwoo that strong?”
“Ah, Mr . Park wouldn’t know . He started the job a little after you left . There’s no Hunter here who doesn’t know Sung Jinwoo . ”
“That strong? Why is he working under the Association, then? Why not freelance or join a large Guild?”
Chuckling, Mr . Kim’s eyes narrowed .
“You know what that man’s nickname is?”. .
“How would I know? Come on, spit it out . ”
“Humanity’s Weakest Soldier”
“ . Weakest? Not Strongest?”
“Listen to yourself, that kind of title belongs only to the S-rank Hunters . That man over there is the Weakest Soldier . Probably the weakest Hunter in all of Korea . ”
“Eh?”
Mr . Park furrowed his brows . If he was that weak, why would the Hunters look so relieved at his appearance? A fellow Hunter was someone who had to be relied upon in a Raid . He could not understand the other Hunters’ reactions .
Seeing Mr . Park’s tilted head in contemplation, Mr . Park ribbed him with his elbows while laughing .
“Don’t you get it? If Sung Jinwoo appeared in today’s Raid, it means it’s gotta be an easy one . The Association wouldn’t risk putting him on anything hard . Nobody wants to see someone die pointlessly . ”
And now, Mr . Park’s face brightened .
“Is, is that so?”
Coming back to the Raiding scene after a long break, both he and his wife were ladened with uneasiness and concern . But listening to Mr . Kim’s words, his mood lightened up .
Mr . Kim continued,
“Once, that man got injured in an E-rank Gate and had to be hospitalized for a week . ”
“A Hunter got injured in an E-rank Gate?”
“Yep . Nobody expected someone to actually get hurt in an E-rank Gate . I heard they didn’t even take a Healer-class Hunter . ”
Seeing Mr . Park laugh loudly in response, Mr . Kim shifted his eyes toward Jinwoo .
“Hey, hey, not too loud . He might hear . ”
“Oops, didn’t think about that . ”
Mr . Park shifted his eyes towards Jinwoo and quieted his laughter . Fortunately, Jinwoo appeared some distance away and probably couldn’t hear their conversation .
But he did .
‘I heard everything, you geezers .  At times like this, he cursed his rather keen hearing .
‘Did I come too soon?’
It was some time before the Raid would begin . While waiting, Jinwoo approached an Association Employee for some coffee .
“Could I get a cup as well?”
“Ah, Hunter Sung Jinwoo-nim[2] . I’m so sorry, we just ran out…”
“ . ”
A cold winter breeze slapped his face . Jinwoo wiped his nose with fingers .
It was a rather sad day where even the coffee ran out just as he got to it .
“Why are you so stubborn about this whole Hunter business, Mr . Jinwoo?”
“Sorry . ”
Jinwoo bowed his head .
As she healed him, Lee Juhee’s face was filled with complaint .
“I’m not trying to get an apology from you . I’m just worried about you, you know? I swear, one of these days, you’re going to get seriously hurt . ”
Once you pass through the Gate, you would be in the Dungeon . The Dungeon this time around was probably D-rank .
Jinwoo looked over Juhee’s shoulders at his fellow Hunters . Ten-something number of Hunters were taking down monsters left and right . They did not appear to be particularly struggling . Yet here he was, injured .
It was the role of the Healer-class Hunters to heal the injured Hunters from the rear . As a man who was hurt in nearly every Raid he participated in, Jinwoo was rather famous among the Healer-class Hunters .
Juhee carefully asked him,
“Do you perhaps have a reason why you can’t quit?”
Jinwoo firmly shook his head . He didn’t like revealing personal details about himself so easily .
“I’m just doing this as a hobby . I’ll probably die of boredom if it wasn’t for this . ”
Juhee pouted in response,
“You’ll end up Raiding in the afterlife because of your ‘hobby’ ”
Not expecting such a response, Jinwoo laughed .
“Hey! Don’t laugh! You’ll open your wounds!”
Jinwoo asked while chuckling,
“Man, where did you hear such a phrase?”
“Where else? Mr . Kim ooover there . ”
“Sigh, that geezer . ”
As they laughed and conversed, the healing was completed . But it was too late, the Raid was pretty much over at that point .
Jinwoo grimaced .
‘I only killed one magic beast[3] today…’
And even then, it was only a E-rank monster .
Jinwoo fidgeted with the the E-rank magic core[4] in his hand . Such low level magic core from an E-rank magic beast was barely worth a hundred thousand won[5] . The fact that he put his life on the line to earn it made it seem all the more pathetic .
‘I heard a magic core from a C-rank magic beast is worth at least few ten millions[6]…’
But to Jinwoo, an E-rank Hunter, the thought of taking down a C-rank magic beast was an impossibility .
Suddenly, someone shouted,
“Eh? There’s another entrance here!”
The Hunters swarmed towards the voice .
“You’re right!”
“Really? Another entrance?”
As the first person noted, there indeed was another Dungeon entrance here .
“A Double Dungeon… So they really do exist . ”
A Hunter with 10 years worth of experience, Mr . Song looked at the newly found entrance with wonder . Unable to see far into the dark tunnel, Mr . Song used his specialty, fire magic . The fireball that shot out from his hand flew through the tunnel, illuminating its darkness . However, the tunnel was deeper than expected, and the fireball eventually lost its energy and fell to the ground and quickly extinguished as a spark . Darkness returned before their eyes .
“Hmm… Everyone, please gather around . ”
As the de facto leader of the Raid, Mr . Song gathered the Hunters before him . Juhee and Jinwoo, having completed Jinwoo’s healing, also joined the crowd .
Mr . Song addressed gathered Hunters,
“As you all may know, Gates do not close until the Dungeon’s boss is taken down . Since our Gate is still open, even though we’ve cleared all the mobs in the area, it appears that the real boss in down that tunnel . ”
Mr . Song gestured towards the newly found Dungeon entrance . Looking at each other, the Hunters also nodded in agreement .
“The protocol in situations like this is to exit the Dungeon, contact the Association, and let them handle things going forward… But if we do that, and some other group of Hunters take down the boss, there’s a chance that our income for this Raid will drastically decrease . ”
The gathered Hunters’ expressions hardened . Mr . Park, who came here to support his expecting wife, looked doubly troubled . ‘Postnatal care these days is really expensive…’ If he left now, the efforts he risked his life for would be wasted .
“And so I was thinking . What if we just went ahead and go kill the boss? What do you guys think?”
The Hunters fell in contemplation .
“ . ”
“ . ”
It was not a decision that could be made easily . Some knew that there was no guarantee that the Double Dungeon would be as safe as the one that they had just cleared . Others came to the conclusion that if the Outer Dungeon was this easy, perhaps the Inner Dungeon would be just as easy . Regardless, it was not a situation where everyone would be in agreement .
“Hmm…”
Mr . Song faked a cough,
“Since there’s 17 of us here, why don’t we take a vote on this? And no complaining after the vote . How about it?”
At Mr . Song’s suggestion, each Hunter nodded in agreement .
Mr . Song’s was the first to raise his hand . “I’ll go . ”
Mr . Park was the first to follow Mr . Song, “I’ll go too . ”
“Me, me too…”
“Same here . ”
“One more vote for ‘yes’ “
Mr . Kim had also joined the “go” group . But there were opposing votes as well,
“Let’s not . ”
“I think we should wait on the Association’s judgment . ”
As the “yes” crowd and the “no” crowd clashed at 8-7, all gazes fell on the two last undecided people .
“Sorry…”
Shaking her head, Juhee voted no, putting the count at 8-8 . Mr . Song turned and asked the last person for his vote .
“Mr . Sung?”
. .
Translator’s Notes:
[1]: “several million won”: ~Several thousand in USD (his mother’s medical bills)
[2]: “-nim”: Korean post-nominal honorific denoting high respect . Falls somewhere between Japanese -san and -sama . Most service employees in Korea refer to customers with “-nim” .
[3]: “magic beast” (마수; Ma-Su); “Magic” Ma + “Beast” Su
[4]: “magic core” (마정석; Ma-Jung-Suk); “Magic” Ma + “Center/Middle” Jung + “Stone” Suk . i . e . - A magic stone at the center/middle of the magic beast > “magic core” .
[5]: “hundred thousand won”: ~90 USD (value of E-rank Magic Core)
[6]: “few ten millions (won)”: ~Several ten thousand in USD (value of C-rank Magic Core) . Last time I clarify korean won to USD equivalent . As a rule of thumb, just divide the KRW number by 1,000 to get the USDE .


g[TMM]a
An open-source implementation of the Transfer Matrix Method in the field of acoustics.
Fork it
or contact me if you have comments or suggestions.
gTMMa allows to predict the sound absorption properties of porous materials
such as polymer foams or mineral wools.
gTMMa is written in ANSI C and is designed to run under multiple OS.
This code is distributed under the terms of the
new BSD License.
Copyleft Luc Jaouen.
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions
are met:
Unzip gtmma.zip.
4 sub-directories should be created:
doc contains the documentation of gTMMa,
examples contains some input files (.in),
bin contains pre-compiled versions of gTMMa (a Windows XP one and a
Linux kernel 2.4/libc6 one).
src contains the ANSI C sources of gTMMa.
At this time, only a console version of gTMMa is available: you need
to open a console to lunch gTMMa (button start/execute and type "cmd" for
Windows).
Change directory to the directory where the binary "gtmma" (lower
case) is or add this directory to your path.
Simply type "gtmma path_to_an_input_file" to compute the
response for an input file. (example: gtmma JCA_gap_JCA.in).
Each input file (identified by a ".in" extension) must contain 4 tags: a fluid, a layers, a spectrum and a conditions one.
% Datafile for gTMMa Headers/comments % % 2004.10.09 <fluid> T 20 Room temperature T in Celsius degrees P 101300 Atmospheric static pressure P in Pascal </fluid> <layers> <ridig_impervious_wall> Required in "absorption mode" <JCA_material> Beginning of the 1st layer tag (Johnson Champoux Allard mat.) alpha 2.1 High frequency limit of the tortuosity phi 0.80 Open porosity sigma 40000 Static air flow resistivity in N.s.m-4 lambda 125e-06 Viscoous characteristic length in meters lambda_p 350e-06 Thermal characteristic length in meters L 0.01 Layer thickness in meters </JCA_material> End of the layer tag <air_gap> Beginning of the 2nd layer tag (air gap/plenum) L 0.02 Layer thickness in meters </air_gap> <JCA_material> 3rd layer: Johnson Champoux Allard material alpha 1.6 phi 0.82 sigma 20000 (N.s.m-4) lambda 80e-06 (m) lambda_p 160e-06 (m) L 0.01 (m) </JCA_material> </layers> <spectrum> min 10.0 Lower frequency in Hertz max 4000.0 Upper frequency in Hertz step 10.0 Frequency step in Hertz </spectrum> <conditions> incidence 0.0 Incidence angle in radian (here: normal incidence) </conditions>
<air_gap>: an air gap/plenum. The only parameter required is the layer thickness L.
<DB_material>: Delany-Bazley model. Parameters are the static air flow resistivity sigma (in N.s.m-4) and the layer thickness L.
<GP_material>: Garai-Pompoli model. Parameters are the static air flow resistivity sigma (in N.s.m-4) and the layer thickness L.
<JCA_material>: Johnson-Champoux-Allard model. Parameters are the static air flow resistivity sigma (in N.s.m-4), the open porosity phi, the high frequency limit of the tortuosity alpha, the viscous and thermal characteristic lengths (in meters) lambda and lambda_p respectively and the layer thickness L.
<JL_material>: Johnson-Champoux-Allard-Lafarge model. Parameters are the static air flow resistivity sigma (in N.s.m-4), the open porosity phi, the high frequency limit of the tortuosity alpha, the viscous and thermal characteristic lengths (in meters) lambda and lambda_p respectively, the thermal permeability k_p_0 (in m^2) and finally the layer thickness L.


A showcase of Ricky Zhang's leadership in improving the Taco manufacturing sector by featuring the proud ingredients of Sour Cream and Panela Cheese.
We're going to build a fence for you and your neighbor is going to pay. It's going to be a powerful fence. they will call it the Trump fence. because that is where I get the idea from.
we’re going to have to find a new solution for financial crisis, unlike anything we’ve done before. It all begins with the Freedom Hotdogs, a universal basic hotdogs for all American, no strings attached – a foundation on which a stable, prosperous, and just society can be built.
There will be no government shutdown with my management. We shall not shut down for anything. We shall not shut down for Christmas. Do you understand?” As every Chinese restaurants in this country ：We will work through all public holidays. Any city in America ― when it’s 3 a.m. and you’re hungry, where do you go? You go to Chinatown! It’s where you go.”


|
The first time I fell in love it was snowing, but when I think of him I remember rain. We were together for a year so it couldn’t have rained that whole time, but it feels that way in my memory. A sudden late-summer shower sprinkled on us the first time we kissed, while I waited for the last southbound 22 bus, and he offered me a ride home so I wouldn’t have to wait in the rain. It poured and thundered dramatically the last night we spent together, and my long skirt got caught in puddles as I walked away from his apartment. One of my favorite memories of us is of walking through Jackson Park in the rain, looking for cherry blossoms and making eyes at each other under his umbrella that filtered the soft spring light and turned us both blue. We stuck flowers in each others’ hair and a woman in the parking lot told us we were adorable.
I loved the rain long before I loved him. Growing up in a house with a tin roof I liked listening to the rain clatter against it at night. It made me feel safe and warm knowing that I could so easily be cold and wet. When I lived in Boston, my gloomiest friend loved the rain more than anyone else I had ever met. One night when we were working a late shift together it started pouring so hard we all went to the window. He pressed his hands against the glass like a little kid and said wistfully, “I hope it rains so much we all have to live on the roof.”
For a long time, in my teens and early twenties, I determined that my mood was swayed by the weather and therefore I dreaded the rainy, cloudy days when it was so hard to get out of bed and think about anything other than despair. I think at the time that was as good an explanation as any, even though those days often came straight out of the clear blue sky.
I’ve come back around on rain as I’ve gotten better at working with the ups and downs of my own internal weather, rather than always wanting to feel like sunshine and getting angry and frustrated when I don’t. (This is still a work in progress.) Soft spring rain and loud summer storms are my favorites. I like when spring rains turn my windows blurry so that the redbud outside become a vague pink and green collage. I like how sudden and fierce summer storms are, hammering against the windows and flashing through the sky, and then leaving as though they were never there. I like how the rain makes me think of my mom looking out the window and saying, “Ooooh, my garden’s going to be so happy.”
It feels so cozy inside when it’s raining, especially if I’m able to sit under a blanket and read instead of attending to adult responsibilities. Everything soft and soothing — cooking, baking, tea, baths, Nora Jones — feels softer and more soothing in the rain. I feel more gentle with myself when it’s raining, more vulnerable to the whims of the universe, but also somehow safer. Sometimes rain feels like an intensifier of whatever I’m already feeling. If I’m sad it gives me permission to lean into my sadness, put on the Grey’s Anatomy soundtrack and stare out at the storm thinking of all the ways I’ve been wronged in my life. Perhaps that’s what troubled me about rain before; it beckons me to give into whatever I’m feeling rather than fighting against it, which felt (and sometimes still feels) dangerous, like I might be swallowed whole if I’m not careful.
This reminds me of one of my favorite poems, Laura Lamb Brown-Lavoie’s On This, The 100th Anniversary of the Sinking of The Titanic, We Reconsider the Buoyancy of the Human Heart. In it, The Titanic tells the writer, “The trouble with you humans is you’re so concerned with staying afloat. You’re not a boat … you can go under and come up again with those big old lungs.” I’m still learning that sinking into feeling is not the same as drowning in it, and I can and will come back up again. The rain helps remind me of this as it comes and goes. No weather, emotional or atmospheric, lasts forever.
|


The Math object allows you to perform mathematical tasks on numbers.
The Math object allows you to perform mathematical tasks.
The Math object includes several mathematical methods.
One common use of the Math object is to create a random number:
| Math has no constructor. No methods have to create a Math object first. |
Math.min() and Math.max() can be used to find the lowest or highest value in a list of arguments:
Math.random() returns a random number between 0 (inclusive), and 1 (exclusive):
| Math.random() always returns a number lower than 1. |
Math.round() rounds a number to the nearest integer:
Math.ceil() rounds a number up to the nearest integer:
Math.floor() rounds a number down to the nearest integer:
Math.floor() and Math.random() can be used together to return a random number between 0 and 10:
JavaScript provides 8 mathematical constants that can be accessed with the Math object:
| Method | Description |
|---|---|
| abs(x) | Returns the absolute value of x |
| acos(x) | Returns the arccosine of x, in radians |
| asin(x) | Returns the arcsine of x, in radians |
| atan(x) | Returns the arctangent of x as a numeric value between -PI/2 and PI/2 radians |
| atan2(y,x) | Returns the arctangent of the quotient of its arguments |
| ceil(x) | Returns x, rounded upwards to the nearest integer |
| cos(x) | Returns the cosine of x (x is in radians) |
| exp(x) | Returns the value of Ex |
| floor(x) | Returns x, rounded downwards to the nearest integer |
| log(x) | Returns the natural logarithm (base E) of x |
| max(x,y,z,...,n) | Returns the number with the highest value |
| min(x,y,z,...,n) | Returns the number with the lowest value |
| pow(x,y) | Returns the value of x to the power of y |
| random() | Returns a random number between 0 and 1 |
| round(x) | Rounds x to the nearest integer |
| sin(x) | Returns the sine of x (x is in radians) |
| sqrt(x) | Returns the square root of x |
| tan(x) | Returns the tangent of an angle |


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You can find some pictures I took over the years on flickr.
This site has been created with Jekyll, using the Hyde theme.


care tab content area
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deductible - $4,000.00 OR deductible: $4,000.00
CVS #456
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I'ma make this short and sweet -- unlike the 'trip' I've been on for the past 24 hours....
I injested 5mg with my trip-brother at 2:20 in the afternoon. By 5pm we both felt only slightly 'out of it' -- dizzy, slightly drunk, and slight dissociation from the outside world. No audios, no visuals.
So we dropped another 5 mgs.
At around 6-7pm we started getting minor visuals (just barely a +2, even after smoking weed and closing our eyes and retreating to a dark space). We felt only a little amped up -- though I'm sure we freaked the hell out the other guy we were hanging with by the ammount of shit-talking we were doing, tryin' to vibe each other into a deeper state of consciousness. (This other guy dosen't drop -- does weed only.)
By like 8, I was pretty pissed off that 5-MeO-AMT is nothing close to the strength or awesome power trip reports I have read attributed to it. With a subtle body-load and weak, bearly noticable -- and quite boring -- visuals, I cold hardly call this material 'entheogenic.'
At 10 we dropped another 5mgs, since our 'trip' was begining to subside. This got the visuals and bodyload back to the level just described -- hardly more.    We stayed up till noon, we stayed up to -- well, I'm still awake, wired, with a tingly body buzz, slightly disembodied headspace, normal pulse and no visuals. It's now 7:13.
In Summary:
I was totally disappointed and unimpressed with a,O-DMS. There was no head-trip at all.
The visuals are nothing more spectacular than the ones you can see when you close your eyes after a long day of work -- maybe 1.5 times stronger. I've gotten equally strong visuals taking choline -- a nutritive suppliment sold in healthfood stores used to increase the memory. Audio enhancement and appreciation was nil -- as unchanged as in my normal state of mind. As far as getting 'high'?... If 5 grams of shrooms are a UFO with a trans-galactic/interdimensial warp drive, 5-MeO-AMT is a 4-seater Cessna with a single prop engine that hardly gets beyond 3 miles high. It's a long, long, long... boring ride with no real point to it -- it circles the same air-space endlessly. And you can't come down.
Now, I don't know if I got jipped by the folks I bought this shit from (which is completely possible, even though they were reviewed in a reputable entheogen journal I subscribe to), or, if what I just described is the actual sad nature of the drug.
A subsequent trip at 15mg 2 weeks later proved to be much more rewarding, though still kind of light like the drug's cousin, AMT, minus the chills and jaw-clenching.
Experience Reports are the writings and opinions of the individual authors who submit them.
Some of the activities described are dangerous and/or illegal and none are recommended by Erowid.


Xur's location and wares for November 22, 2019 - Destiny 2
Find out where Xur is and what he has for sale in Destiny 2 on November 22, 2019.
by Josh HawkinsGuardians, rejoice! Xurday has come again and that means it’s time to prepare to shovel out your Legendary Shards for some sweet Exotic gear. But what exactly does Xur have to offer this week and where can you find the merchant of the Nine? We’ve got all the information you need right here, so let’s dive in.
Xur’s location and wares for November 22, 2019 – Destiny 2
If you’re looking to find Xur this week, then you’re going to want to head to the Winding Cove on Earth, in the EDZ. This is where you’ll find the weekly Exotic merchant, and he’s got a new set of items available to purchase. We’ve broken down exactly what he has to offer below, so take a look and then head on over to Xur’s location to pick up any useful items you might want or need. It should be noted that the Destiny 2 servers appear to be having some issues, so you might have trouble connecting while trying to visit Xur.
As always, each of the items that Xur has to offer should be purchased, as long as you don’t already have it. This will just help you even out your Exotic collection, and ensure that you always have access to Exotic gear should it become more powerful in future updates. This week Xur has the following items available to purchase:
- Wardcliff Coil Exotic Rocket Launcher - 29 Legendary Shards
- Sixth Coyote Exotic Hunter Chest Armor - 23 Legendary Shards
- Verity's Brow Exotic Warlock Helmet - 23 Legendary Shards
- One Eyed Mask Exotic Titan Helmet - 23 Legendary Shards
- Fated Engram - 97 Legendary Shards
If you already have everything in Xur’s item pool, then go ahead and grab a Fated Engram to try to get something you’re missing. Of course, you can always save your Legendary Shards for next week, when Xur returns with a slew of additional items to feast your eyes on.
Now that you know where Xur’s location is and what wares he has available this week, head back over to our complete Destiny 2 strategy guide for more in-depth assistance.


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Ver: 1.9v
Designed by: Sonu Kumar Thakur


| Package | flare.vis.operator.distortion |
| Class | public class Distortion |
| Inheritance | Distortion Layout Operator |
| Subclasses | BifocalDistortion, FisheyeDistortion |
| Property | Defined by | ||
|---|---|---|---|
| anchorInBounds : Boolean = true Flag indicating if distortion anchor points outside the layout
bounds should be considered by the distortion.
| Distortion | ||
| distortAxes : Boolean Flag indicating if axes should be distorted.
| Distortion | ||
| distortSize : Boolean Flag indicating if sizes should be distorted.
| Distortion | ||
| distortX : Boolean Flag indicating if x-coordinates should be distorted.
| Distortion | ||
| distortY : Boolean Flag indicating if y-coordinates should be distorted.
| Distortion | ||
| enabled : Boolean Indicates if the operator is enabled or disabled.
| Operator | ||
| layoutAnchor : Point [write-only]
| Distortion | ||
| layoutBounds : Rectangle The layout bounds for the layout.
| Layout | ||
| layoutRoot : DataSprite
The layout root, the root node for tree layouts.
| Layout | ||
| layoutType : String = "null" The type of layout and axes.
| Layout | ||
| parameters : Object
Sets parameter values for this operator.
| Operator | ||
| resetSize : Boolean = false Flag indicating if the size or scale values should be reset to 1
upon each invocation of the distortion.
| Distortion | ||
| useSizeField : Boolean = false Flag indicating if the
DataSprite.size field should be
distorted. | Distortion | ||
| visualization : Visualization
The visualization processed by this operator.
| Operator |
| Property | Defined by | ||
|---|---|---|---|
| _anchor : Point | Layout | ||
| _b : Rectangle A bounding rectangle for storing the layout bounds.
| Distortion | ||
| _setAnchor : Boolean = false | Layout | ||
| _t : Transitioner = null A transitioner for storing value updates.
| Layout | ||
| xyAxes : CartesianAxes
Returns the visualization's axes as a CartesianAxes instance.
| Layout |
| Method | Defined by | ||
|---|---|---|---|
|
Distortion(distortX:Boolean = true, distortY:Boolean = true, distortSize:Boolean = true, distortAxes:Boolean = true)
Creates a new Distortion.
| Distortion | ||
|
applyParameters(op:IOperator, params:Object):void
[static]
Static method that applies parameter settings to an operator.
| Operator | ||
|
clearEdgePoints():void
Strips all EdgeSprites in a visualization of any control points.
| Layout | ||
|
Hides the axes.
| Layout | ||
|
operate(t:Transitioner = null):void
Performs an operation over the contents of a visualization.
| Distortion | ||
|
setup():void
Setup method invoked whenever this operator's visualization
property is set.
| Operator | ||
|
Reveals the axes.
| Layout | ||
|
[static]
Updates all edges to be straight lines.
| Layout |
| Method | Defined by | ||
|---|---|---|---|
|
autoAnchor():void
Automatically-generate an anchor point.
| Layout | ||
|
axesDistort(evt:VisualizationEvent):void
Performs distortion of Cartesian axes.
| Distortion | ||
|
distort(d:DataSprite):void
Distortion method for processing a DataSprite.
| Distortion | ||
|
layout():void
Calculates the spatial layout of visualized items.
| Layout | ||
|
minAngle(a1:Number, a2:Number):Number
Returns an angle value that minimizes the angular distance
between a reference angle and a target angle.
| Layout | ||
|
sizeDistort(bb:Rectangle, x:Number, y:Number):Number
Compute a distorted size value.
| Distortion | ||
|
xDistort(x:Number):Number
Compute a distorted x-coordinate.
| Distortion | ||
|
yDistort(y:Number):Number
Compute a distorted y-coordinate.
| Distortion |
| anchorInBounds | property |
public var anchorInBounds:Boolean = true
Flag indicating if distortion anchor points outside the layout bounds should be considered by the distortion. If true, external anchors will be mapped to nearest point on the border of the layout bounds.
| _b | property |
protected var _b:Rectangle
A bounding rectangle for storing the layout bounds.
| distortAxes | property |
public var distortAxes:Boolean
Flag indicating if axes should be distorted.
| distortSize | property |
public var distortSize:Boolean
Flag indicating if sizes should be distorted.
| distortX | property |
public var distortX:Boolean
Flag indicating if x-coordinates should be distorted.
| distortY | property |
public var distortY:Boolean
Flag indicating if y-coordinates should be distorted.
| layoutAnchor | property |
layoutAnchor:Point
[write-only]Implementation
public function set layoutAnchor(value:Point):void
| resetSize | property |
public var resetSize:Boolean = false
Flag indicating if the size or scale values should be reset to 1 upon each invocation of the distortion. This avoids the need to manually reset the size values on each update. The default value is false.
| useSizeField | property |
public var useSizeField:Boolean = false
Flag indicating if the DataSprite.size
field should be
distorted. If false (the default), the scaleX and scaleY properties
are used instead.
| Distortion | () | constructor |
public function Distortion(distortX:Boolean = true, distortY:Boolean = true, distortSize:Boolean = true, distortAxes:Boolean = true)
Creates a new Distortion.
ParametersdistortX:Boolean (default = true ) — Flag indicating if x-coordinates should be distorted
|
|
distortY:Boolean (default = true ) — Flag indicating if y-coordinates should be distorted
|
|
distortSize:Boolean (default = true ) — Flag indicating is sizes should be distorted
|
|
distortAxes:Boolean (default = true )
|
| axesDistort | () | method |
protected function axesDistort(evt:VisualizationEvent):void
Performs distortion of Cartesian axes. As axis layout is recomputed after the operators have run, we must distort the axes in a separate step. This is accomplished by adding an update listener on the visualization that invokes the axis distortion after the axis layout has completed. This method is registered as the listener callback.
Parametersevt:VisualizationEvent — the visualization update event
|
| distort | () | method |
protected function distort(d:DataSprite):void
Distortion method for processing a DataSprite.
Parametersd:DataSprite — a DataSprite to distort
|
| operate | () | method |
public override function operate(t:Transitioner = null):void
Performs an operation over the contents of a visualization.
Parameterst:Transitioner (default = null ) — a Transitioner instance for collecting value updates.
|
| sizeDistort | () | method |
protected function sizeDistort(bb:Rectangle, x:Number, y:Number):Number
Compute a distorted size value.
Parametersbb:Rectangle — an object's bounding box
|
|
x:Number — the initial x-coordinate
|
|
y:Number — the initial y-coordinate
|
Number — the distorted size value
|
| xDistort | () | method |
protected function xDistort(x:Number):Number
Compute a distorted x-coordinate.
Parametersx:Number — the initial x-coordinate
|
Number — the distorted s-coordinate
|
| yDistort | () | method |
protected function yDistort(y:Number):Number
Compute a distorted y-coordinate.
Parametersy:Number — the initial y-coordinate
|
Number — the distorted y-coordinate
|


Tutorial
Let's write our first code to customize your avatar!
Starting with setting an outfit color.
Try changing the color in setOutfitColor() to
We can also change the eye color, skin tone and hair type
Try changing the color in setEyeColor() to
Try changing the color in setSkinTone() to
Try changing the color in setHairStyle() to
Now lets add a space background for our little astronaut! Add the background image by adding the image path:
Starting with setting an outfit color.
Try changing the color in setOutfitColor() to
["red"]
We can also change the eye color, skin tone and hair type
Try changing the color in setEyeColor() to
["brown"]
Try changing the color in setSkinTone() to
["fair"]
Try changing the color in setHairStyle() to
["blonde"]
Now lets add a space background for our little astronaut! Add the background image by adding the image path:
"images/background.jpg"
to setBackgroundImage();
Nice! You just done your first coding!
Now we're going to have our avatar move!
We have already inserted the code for an up button.
Duplicate the code and then replace 'down' where both
Now we're going to have our avatar move!
We have already inserted the code for an up button.
Duplicate the code and then replace 'down' where both
'up'
and UP
are.
Do the same with 'right' and 'left'.
Type
Replace the word “color” with your prefer choice of black, brown , red , blonde.
[placeholder]
in the code editor to change a hair color.
Replace the word “color” with your prefer choice of black, brown , red , blonde.
Awesome! You’re getting a hang of this! Why don’t we try changing a skin tone next?
Type
Type
[placeholder]
in the code editor, you can choose between A,B,C. Just simply replace the word “skin tone” with your prefer choice.
Nice! You just done your first coding!
Click continue for the next step!
Click continue for the next step!


@* * Copyright 2023 HM Revenue & Customs * * Licensed under the Apache License, Version 2.0 (the "License"); * you may not use this file except in compliance with the License. * You may obtain a copy of the License at * * http://www.apache.org/licenses/LICENSE-2.0 * * Unless required by applicable law or agreed to in writing, software * distributed under the License is distributed on an "AS IS" BASIS, * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. * See the License for the specific language governing permissions and * limitations under the License. *@ @import sdil.models.SmallProducer @(key: String, rows: List[SmallProducer], messages: UniformMessages[Html]) @pluralKey =@{if(rows.length >= 2) {s"$key.table.heading.plural"} else ({s"$key.table.heading.singular"})} @messages.get(pluralKey, rows.length).map { msg =>
|
@if(row.alias.nonEmpty) {
@messages("small-producer-details.name", row.alias) }@messages("small-producer-details.refNumber", row.sdilRef) @messages("small-producer-details.lowBand", row.litreage._1) @messages("small-producer-details.highBand", row.litreage._2) |
@if(rows.length > 1) {
@messages(s"$key.remove.hidden", row.alias, row.sdilRef) | }@messages(s"$key.edit.hidden", row.alias, row.sdilRef) |


Blog posts are amazing!
Aren't they, though? We should really have one here. Or two. A thousand! If you want to contribute an article on camping, you should. Submit a PR! Now!
%%include('../partials/copyright.html')
%%include('../partials/head.html', { "pageType": "blog" }) %%include('../partials/header.html') %%include('../partials/menu.html')Aren't they, though? We should really have one here. Or two. A thousand! If you want to contribute an article on camping, you should. Submit a PR! Now!


Aria Is A Smiple and Powerful Discord Music Bot Made In Javascript It Has Multiple Commands Like Loop, Volume, Skip , Search ,etc
Aria is very easy to use. Start of with /help
Aria Bot is 24/7 Online
Aria Bot Is Entirely Free Forever! Every Feature is Free :D
Aria is packed to the brim with awesome perks and commands, and updated daily.
These Are All The Commands
Users
Servers
Active users
Updates


[§489D-1] Short title. This chapter may be cited as the Money Transmitters Act. [L 2006, c 153, pt of §1]


Let's return to our char-type
function, and this time we'll add a few more things to it:
(def digits #{\1 \2 \3 \4 \5 \6 \7 \8 \9 \0}) (defn char-type [ch] (cond (contains? digits ch) :digit (= ch \space) :space (= ch \.) :period (= ch \/) :forward-slash (= ch \") :double-quote true :other))
Let's map
over the characters to see how it looks with the new additions:
(def chars (vec "42 0.5 1/2 foo-bar")) (map char-type chars)
Notice that most of these branches are just comparing the argument to a single character, and returning a keyword that names it. In Clojure, we can store these simple key-value pairs more elegantly in a hash map:
(def char-names {\space :space \. :period \/ :forward-slash \" :double-quote})
We can now look up a given character using get
:
(get char-names \.)
And we can also use contains?
to check if a given key is in it:
(contains? char-names \")
With that, we can rewrite char-type
to read from our hash map if it contains the character:
(defn char-type [ch] (cond (contains? digits ch) :digit (contains? char-names ch) (get char-names ch) true :other))
And we can see that it works the same way:
(map char-type chars)
We've already seen vectors, sets, and lists. Hash maps are the fourth major data structure in Clojure. Unlike the example above, most hash maps use keywords as their keys, like this:
(def person {:name "Bob" :age 33 :country "United States"})
When done this way, we don't even need to call (get person :name)
to get the name. Keywords can actually act as functions directly:
(:name person)
Nonetheless, in our char-names
hash map, we need to call get
, because our keys are characters.


Package enumerateWeightedSetCovers
Class SetCoverProblem
- java.lang.Object
-
- enumerateWeightedSetCovers.SetCoverProblem
-
- All Implemented Interfaces:
java.lang.Cloneable
public class SetCoverProblem extends java.lang.Object implements java.lang.Cloneable
The class SetCoverProblem is used to represent an instance of a weighted set cover problem. Internally, a weighted set cover problem is represented by an array of integer weights and an ArrayList of BitSets, each of which is the size of the universe. For a particular set, the members correspond to the bits with value 1
-
-
Constructor Summary
Constructors Constructor Description SetCoverProblem(int numOfSets, int universeSize, java.util.ArrayList<java.util.BitSet> setContents)
Creates an instance of a SetCoverProblem with the given parameters.SetCoverProblem(int numOfSets, int universeSize, java.util.ArrayList<java.util.BitSet> setContents, int[] weights)
Creates an instance of a SetCoverProblem with the given parameters.
-
Method Summary
All Methods Instance Methods Concrete Methods Modifier and Type Method Description java.lang.Object
clone()
java.util.BitSet
getCoveredBy(java.util.BitSet sets)
int
getNumberOfSets()
java.util.BitSet
getSet(int setIndex)
int
getUniverseSize()
int
getWeight(int setIndex)
Solution
makeNonRedundant(Solution prev, java.util.BitSet covered)
-
-
-
Constructor Detail
-
SetCoverProblem
public SetCoverProblem(int numOfSets, int universeSize, java.util.ArrayList<java.util.BitSet> setContents)
Creates an instance of a SetCoverProblem with the given parameters. Used in cloning an object. Note that the weights are not provided as we assume these are already available as a static data member- Parameters:
numOfSets
- the number of sets in the problemuniverseSize
- the size of the universe in the problemsetContents
- the contents of the sets, as an array of sets of lit bits
-
SetCoverProblem
public SetCoverProblem(int numOfSets, int universeSize, java.util.ArrayList<java.util.BitSet> setContents, int[] weights)
Creates an instance of a SetCoverProblem with the given parameters.- Parameters:
numOfSets
- the number of sets in the problemuniverseSize
- the size of the universe in the problemsetContents
- the contents of the sets, as an array of sets of lit bitsweights
- the weights per set
-
-
Method Detail
-
getUniverseSize
public int getUniverseSize()
- Returns:
- the size of the universe
-
getNumberOfSets
public int getNumberOfSets()
- Returns:
- the number of sets
-
getWeight
public int getWeight(int setIndex)
- Parameters:
setIndex
- the index of a set- Returns:
- the weight of this set
-
getSet
public java.util.BitSet getSet(int setIndex)
- Parameters:
setIndex
- the index of a set- Returns:
- the set
-
clone
public java.lang.Object clone()
- Overrides:
clone
in classjava.lang.Object
-
makeNonRedundant
public Solution makeNonRedundant(Solution prev, java.util.BitSet covered)
- Parameters:
prev
- a solution to the instance, when ignoring all universe elements indicated by coveredcovered
- a set of bits indicating which universe elements can be ignored by the problem- Returns:
- a nonredundant solution contained in the input parameter. A solution is nonredundant when no set can be removed, while still retaining the set cover property
-
getCoveredBy
public java.util.BitSet getCoveredBy(java.util.BitSet sets)
- Parameters:
sets
- a list of sets (indicated by the 1 bits of the BitSet)- Returns:
- a BitSet of size of the universe which indicates which elements are covered by the sets of the input parameter
-
-


Send


{% extends "layout.html" %} {% block content %}
Click on "Expand Details" button for more information about each failure. Click on "Failure Details View" to find duplicate bugs for the test failure, and close as duplicate or gone away.
Evergreen Build Baron Queue Build Baron Workflow Investigating a Build Failure Fantastic Bugs and Where to Find Them


Upcoming Appointments
WEDNESDAY
Jul 15, 2020
11:30 PM
Dr. Jane Doe, MD
General Medical Practice
123 Main Street, Los Angeles, CA 12345
(123) 456-7890
Reason for your visit
THURSDAY
Oct 22, 2020
2:30 PM
Dr. Jack Doe, MD
Office of Dermatology
123 Main Street, Los Angeles, CA 12345
(123) 456-7890
Reason for your visit
General Information
Gender:
Marital Status:
Personal Health History
Childhood Illnesses
Immunizations & Dates
Test & Screening Dates
Surgeries
Medical History
Please check all that apply.
Family Medical History
Please check all that apply.
Only includes parents, grandparents, siblings, and children.
Personal Safety
Do you live alone?
Do you have frequent falls?
Do you have vision or hearing loss?
How often do you have sun exposure?
How often do you wear your seatbelt?
Would you like to discuss any verbal or physical abuse with your provider?
Other Information
Past Appointments
Date
Mon, Jan 20, 2020
11:00 AM
Provider
Dr. John Doe
123 Main Street
Los Angeles, CA 12345
(123) 456-7890
Reason for your visit
General Physical
Date
Wed, Jun 5, 2019
9:00 AM
Provider
Dr. John Doe
123 Main Street
Los Angeles, CA 12345
(123) 456-7890
Reason for your visit
General Physical
Social History
Exercise
Do you exercise?
If yes, how many minutes per week?
Diet
Are you dieting?
# of meals a day?
Do you drink caffeine?
If yes, # of cups a day?
Alcohol
Do you drink alcohol?
If yes, # of drinks per week?

Are you prone to "binge" drinking?
Do you drive after drinking?
Tobacco
Do you use tobacco?
If yes, # of cigarettes per week?
If yes, chew per week?
If yes, # of cigars per week?
If yes, # of pipes per week?
If yes, # of years?
Previous tobacco user - year quit


Concordia: Archived
The Concordia project concluded in March 2010. The site and its resources have been static since that time. The project wiki and other dynamic components were disabled in April 2016. You have been redirected to this page because you followed a link or a bookmark that previously addressed one of those disabled components. Here are some alternative starting points for you to find out more about the project:
- Concordia Project Homepage and archived wiki
- Code and data repositories were moved to GitHub in April 2016.
- Other projects have expanded upon, refactored, and reimagined the things Concordia explored. These projects include:


Some content here!
Life Skills
Communication
Financial
Financial
Credit Score
Loans
Loans
Auto Loans
Mortages
Payday Loans
Personal Loans
Student Loans
Student Loans
Payment Methods
Payment Methods
Flat Super Screen
Gigantic LED
Power Eater
3D Experience
Classic Comfort
Saving
Saving
401k
401k
Company Match
Investing 401k
Certificates of Deposit
IRA
Savings Account
Mental Health
Mental Health
Depression
Self-Estime
Stress
Physical Health
Physical Health
Diet
Fitness
Flexibility
Personal Hygiene
Time Managment


|
So, given the clear benefits of multitracking, what explains the failure of most
organizations to embrace it? Many executives are worried that exploring
multiple options will take too long. It’s a reasonable fear, but the researcher
Kathleen Eisenhardt has found that the opposite is true. In a study of top
leadership teams in Silicon Valley, an environment that tends to place a
premium on speed, she found that executives who weigh more options actually
make faster decisions. It’s a counterintuitive finding, but Eisenhardt offers
three explanations. First, comparing alternatives helps executives to
understand the “landscape”: what’s possible and what’s not, what variables are
involved. That understanding provides the confidence needed to make a quick
decision. Second, considering multiple alternatives seems to undercut politics.
With more options, people get less invested in any one of them, freeing them up
to change positions as they learn. As with the banner-ad study, multitracking
seems to help keep egos under control. Third, when leaders weigh multiple
options, they’ve given themselves a built-in fallback plan. As an example, one
company studied by Eisenhardt was pursuing negotiations with several partners
simultaneously. When the negotiations with the first-choice partner failed, the
president simply cut a deal with the second-choice partner.
April 26, 2016
|
57 |


Driven web developer who welcomes challenging projects and enjoys working with all sorts of personalities. Experienced in web development and Digital Marketing as well as responsive design patterns. Looking for a developer position upon graduation.
Know MoreA website that is about inspiring you through poems and emotional writing.
View WebsiteA music band and culture exchange website that was built for a music group based in Yichang, China.
View WebsiteSpeedTyper is a web-based (can only play in the browser) typing game that can help you build up your typing speed.
Play gameA Netball Team website that was built with CMS(Weebly) to showcase the plays talent to the world.
View WebsiteA Job-Portal that I am currently developing, however, you can check the code on my Github page.
View Source CodeThis is my personal website that was built in 2018 to showcase some of my personal development.
View Website


This blog covers basic mathematics required for Machine learning. There are many terms which we need to know before we can jump into Machine learning.
#Statistics in Mathematics Data & Frequency: Data be anything given as input, for ex, let’s say set of alphabets, frequency is defined as how many time each alphabets has appeared in the set. Percentage is defined as
Mean or Average or Population Mean - Is defined as sum of all elements divided by count of the elements.
Expected Value - It is mean but while calculating mean consider there part in mean, it can be biased as well. Here you do not divide by count, but you do sum of numbers*their probability. In mean their probability is same as divide by count. E[ f(X) ] = S f(x)P(X = x)
Sample Mean - Mean of the sample from whole population. It is represented by , while population mean is represented by . It is used for symmetric data set.
Median - Put all the number in ascending order and the element at half distance is Median. Used for skewed dataset, doesn’t matter if few value are outlier.
For ex: Median or M or of 1,3,4,5,6,7,100,200 would be 5.5. Either middle or mean of middles.
Mode - Is most frequent number. For example 1,1,1,2,100,101,103,100 is 1. As the 1 has occurred maximum number of times.
Quartile - The set is put in ascending order and divided into 4 quarter of equal width. For ex. 1,3,4,24,29,101,103 has first quartile as 3.5, second quartile/Median as 24 and third quartile as 115.
Variance - Measure of deviation from mean, Measure of being different than other. There are three variance 1)Population variance 2) Sample variance 3)Alternate formula to calculate variance. Var(X) = E[ (X – m)2 ] Var(X) = E(X2) – m2
Covarinace - Measure of two variable being different from each other, calculate by.
Population variance or just variance - Is formulated as average of the square distance from mean. .
Pupulation SD or Standard deviation - Root of population variance is standard deviation. It gives normalized result against dataset.
Sample Standard Deviation - Here we have Bessel’s correction, divide by n-1, as sample can be smaller deviation then population deviation so to give it a nudge we divide by n-1.
Permutation is the count of number of ways which one particular Set can be arranged. The count should consider the order. For ex. S = {1,2,3} ca be arranged as {321,312,231,213,132,123}. So total number can be arranged as
But what if number can be repeated.
What if the set is {1,2,3,4}, It will be and what if we need to pick only 2 out 4. n=4, r=2, n-r=2. The possible combination would be,
=
=
For example, Flip coin 6 times, getting exactly 1 head {HTTTTT,THTTTT,TTHTTT,TTTHTT,TTTTHT,TTTTTH}, Order matters here so permutation hence 6!, but 5T are same so divide by 5!. In case of two heads, Group of two head and group of 4 tail hence, 6!/(4!2!) = 15.
Combination is related to permutation, In this the order of number layed out is not important. For ex (1,2) and (2,1) are same. That mean combination is all the permutation deviled by permutation of r. In all the permutation we need to exclude sets which has same set of numbers in any order, let say Set of r can have r! possible permutation and there number of sets so for each set like (12,21) = 2! = 2, one has to be excluded. Let’ say Set {1,2,3} and need to pick two number.
In case there are multiple groups of same type g1,g2..gn and every we need r1,r2..rn number from each group respectively. The combination would be
For example a comity 3 people of 1 man and 2 women from a group 2 men and 3 women has to formed. M1,M2 and W1,W2,W3. Picking them in any order doesn’t matter so here commutation has to be calculate. 2C1 and 3C2 = 6.
Probability is a measure of how likely an event is going to happen from given set of event. For example. {1,2,3,4,6} are equally likely outcome of a dice. Then probability of coming to in a dice roll would be 1 out of 6. Probability of dice showing number 2. .
Probability in relation to probability Lets say A is event of 1 and 4 coming on dice and B is event {1,3,4} coming on dice. Intersect of A and B is {1,4}
If A and be are **independent ** A is dice and B is deck getting 1 on dice and an spades ace on dec is
Marginal probability - It can be though as plain probability of one variable X, but twist is there is a random variable Y, both and X and Y random variable can be biased in this case you create a chart of X and Y and calculate sum over Y and take average.
Joint probability - Joint event is simple enough as name suggest, two independent event space is been joined together, this increase sample space. ANy probability will be calculated over this.
Conditional probability on Dependent event Dependent event are the one which affect the event space for next event. For example in a deck probability of getting Ace is 1/13 and then you put that Ace aside the card deck size is now 51, now the probability of getting ace is 3/51. Here A has affected the event space for B. So we can write P(A) then P(B) is,
Where P(B|A) can be defined as P(B) if P(A) has already occurred. P(B and A) are calculate over two dice throw, while P(B|A) is probability of second dice throw. Extend to third variable.
Conditional probability joins two sample space of same, but when first occurred second sample gets affected by first.
Chain Rule of conditional Probability
Random Variable - Random variable is possible outcome of any event. Let’s say in a particular match how many goals will be made, it can be 1 or 4 or 6 or any number. This is discrete and can be counted and has some interval. Set containing 0 to 100 is discrete, but different floating values between is infinite/uncountable. Thing which can’t be counted are continuos random variable and which can be counted are discrete. Continuos value can be measure but not counted for example volume.
Probability distribution - Do not relate this with single probability ie (probability of getting 4 in dice.). Think it as sheet where first column is possible outcomes and second column is probability of that outcome. In this case the probability of each possible outcome is different. Fox ex. Let there are some event E1, E2 ..En from Sample Space S. And let X be function over combination of probabilities over multiple E. For ex. Flip coin three times and X is count H in this sample space. X will variate from 0 to 3. X=0 {TTT} - 1, X=1 {HTT, THT, TTH} - 3, X=2 {HHT,HTH,THH} -3, X=3 {HHH} - 1.
Probability Mass function - Mass function comes into picture when the values are discrete and probability weight calculate by sum, in contrast to PDF which is integral.
Probability Density Function - In a set of continuos event probability normally measure between two points and the area under two defines the probability density function. The entire area is calculated as one. PDF exist only for continuos variable and the area under two interval is the probability. Let’s say x is random variable and f(x) is the probability of the x variable then.
Probability Commutative function - Probability of being equal to or less then x, F(x)=P(X≤x)
Random Variable X - μ - Average of probability random variable ie function over sample space. Mean or Expected value over discrete function
Standard deviation - How far the numbers are from mean on average, think of population having lot of small numbers and then some big numbers so mean doesn’t in middle but at the one end. In this case mean and standard deviation will be far.
Covariance - Measures tendency of x and y deviate from their mean in same or opposite direction at same time.
Mean or Expected value over continuos function
Bayes Theorem - Let A1, A2,A3..An are sample set out of S where all including form S. Let B is another set from S, since it is part of S it definitely form out of parts of A’s. Hence,
B = (B ∩ A1)U(B ∩ A1)..U(B ∩An) and we can write.
Bernoulli Trials - Trials which answers only in two values, such yes/no, 0/1, head/tail etc. Such that .
Bernoulli Distribution - A sheet with with column1 as possible outcomes as 0 and 1 and coloumn2 as there probability. For ex, p = 0.15 and q= 0.85.
Binomial Distribution - Here we talk about Bernoulli sample space. Let say function variable X is times we get Head and call it S and other is F. Flip 3 times (SSS,SST,STS,STT,TSS,TST,TTS,TTT). p is success probability and q is failure.
| X | 0 | 1 | 2 | 3 |
|---|---|---|---|---|
| P | q3 | 3q2p | 3p2q | p3 |
Hypergeometric Distribution - Binomial but sample space reduced due to last event, for ex. draw colored ball from bag starting with equal probability, but do not place the ball back which reduces the sample space.
Uniform distribution - Fair dice role has 6 possible outcome and each has probability of 1/6. Since 1 is total probability, area = width*height = f(x)(b-a) = 1; f(x) = 1/(b-a)
Poisson Distribution - Type of binomial but rate defined by λ, The distribution when you know the constant rate of event over time or space. For ex. 50 email per hours or 22 trees per kilometer etc. Second thing the event are independent. For ex, 20 call per minute, then 0.33 call per second. Every second either call can come (0.33) or not(0.66). Let λ be probability of call per minute, divide that in n=60 interval then probability of on slice of n is p=λ/n and q=1-λ/n.
Negative Binomial Distribution - Number of failure before you get specific number of success. In contrast to Binomial, how many success after x trials. this is how many failures needed to get k successes and this gives how many trials. let k be number of successes in x trial then x-k is number of failure.
Geometric Distribution - Type of negative Binomial where you are interested to get first success after r failures. Number of trial becomes x = r+1. We are looking at kth trial which is success.
Empirical Distribution - It is proportion of sample less then by total observations.
Normal Distribution - Distribution where mean, mode and median coincide. It is bell shaped, there are equal exactly half of the value on left and right side.
Central Limit Theorem- CLT (center, shape and spread), states even if we take an uneven distribution and take sample from it for n times, find the mean of each sample, start putting mean in buckets, the graph formed due to this filling will be more like normal distribution.Mean of sample means distribution will depict mean of population.Standard Error of population will be standard deviation of distribution sample means.
Confidence Interval - In statistics confidence level defined by confident intervals. How confident are wo on our intervals. Let’s say population sleeps for 6-10 hours is 95% confidence.
The confidence level, tells us how confident we are, that this particular interval captures the true population mean. We never deal with full population we go by multiple samples of population and with that we define population mean by calculating distribution of samples means.
Exponential Distribution - It is mix of poisson where we have rate, like calls per minute and geometric where we are interested in wait time of next call or how many failure before next success. Weibull is counterpart of exponential, time to failure. Ex. Machine failure time when we know rate.
Laplace distribution - It is double exponential distribution function, compared to normal distribution function which is squared of mean, it is absolute of mean difference.
Mixture Distribution - Mixture of two or more PDT, these PDT can be univariate or multivariate.
Here is example for gaussian mixture distribution, made up of multiple normal distribution with different mean.
How function changes over times(derivatives/by differentiation), how they accumulate over time period(integral/ by integration).
It cabe defined in two ways.
In Geometry
The slope of line defined by following formula in between any two points.
Here we talk about two point if two points are very close such that , here derivatives comes for rescue. The derivative formula.
Derivatives are used in optimization problems of machine learning. It helps us to determine to increase or decrease weights in order to achieve maximum or minimum output in gradient decedent.
Chain rule:
The reason we put double square as for h(x) was derived over g(x) where x = x2. The same goes with multiple chains.
Gradient is a variable which hold partial derivative multivariable function. Partial derivate of function is keeping all other variable constant and find derivative over one.
Direction Derivative - While trying for minimum maximum by variating a single variable and keeping others constant we can also apply directional derivative in order to check what would happen if take a small nudge to our current slope, what if in place of north go south.
Integrals can be defined as how much accumulated over time, in other terms how much area is covered under a slope between two points.
Important Formula
Common Usage of Integral
Vector is variable stores direction and it’s magnitude from center. In 2D, left 7 and up 2 gives direction m = -2/7 and magnitude as well. It can be stored in 1D array/matrix column or raw anything [-7 2]. It is denoted mostly by bold italic latter with arrow on top.
Vector need not to be scaler only they can be a function. Let say x,y is the point on the plane and if it is applied to a vector f(x) = x2. In this case depending on X vector value will variate.
Dot product - Multiplication
Projection - can make projection over it is the base of the triangle formed by a and b.
Matrix is rectangular grid to store different variable or scaler numbers. You can visualize it as 2D array. Addition and subtraction on matrix over scaler values applies to all the elements and if it is added or subtracted by another matrix then each element will be added or subtracted on each element of other matrix. Multiplication follows the same concept as Dot product and division is not straight forward it is calculate by multiplying with inverse of the matrix. Division is only possible if dividend determinant is non-zero and is a square matrix.


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{% raw %}JACOB HODGES.{% endraw %}
{% raw %}79{% endraw %}
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{% raw %}tomed to visit certain families that most{% endraw %}
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{% raw %}Bible in his hand, would spend evening{% endraw %}
{% raw %}after evening at their own house, reason¬{% endraw %}
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{% raw %}Bible,and seldom if ever attended religious{% endraw %}
{% raw %}service at the house of God. He would{% endraw %}
{% raw %}spend hours in reading to them the Scrip¬{% endraw %}
{% raw %}tures, and beseech them to go with him to{% endraw %}
{% raw %}the place of public prayer. He seemed{% endraw %}
{% raw %}determined not to relinquish his object, but{% endraw %}
{% raw %}pressed upon them, almost daily, the value{% endraw %}
{% raw %}of religion. His labours were not in vain.{% endraw %}
{% raw %}The son, perhaps the most unpromising of{% endraw %}
{% raw %}all, became awakened to his lost and ruin.{% endraw %}
{% raw %}ed condition. In his gross darkness and{% endraw %}


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I am sociable, sincere, hardworking, responsible, honest, fair, ready to defend my opinion, but able to compromise, engaged in self-development
I graduated from school №19 in Cherkasy, now I am receiving higher education at Cherkasy State Technological University Faculty of Information Technologies and Systems, Department of Statistics and Applied Mathematics, specialty "Statistics"
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