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# what is absolute time

In physics, absolute space and time may be a preferred frame. It is music purely for the sake of music, art for art's sake. Thus the aether of general relativity differs from those of classical mechanics and special relativity in that it is not ‘absolute’ but determined, in its locally variable characteristics, by ponderable matter. From these movements, we infer the passage of time. It is denoted E3. This page was last edited on 9 January 2021, at 20:59. Radiometric dating actually allows the measurement of absolute ages, so it is deadly to the argument that the earth cannot be more than 10,000 years old. [2], Originally introduced by Sir Isaac Newton in Philosophiæ Naturalis Principia Mathematica, the concepts of absolute time and space provided a theoretical foundation that facilitated Newtonian mechanics. Both formats offer utility in different ways. The fundamental facts of mechanics do not harmonize with this view. Absolute space acts on physical objects by inducing their resistance to acceleration but it cannot be acted upon. Did absolute music really play a major role in our cultural history? In other words, the theory of relativity put an end to the idea of absolute time, which means that time measures between any two events in space by two identical clocks would not necessarily agree, even though they show the same. We've got 1 shorthand for Absolute Time Reference » What is the abbreviation for Absolute Time Reference? Absolute space and time is a concept in physics and philosophy about the properties of the universe. According to its most famous proponent, Sir Isaac Newton, for example, absolute time (which is also sometimes known as “Newtonian time”) exists independently of any perceiver, progresses at a consistent pace throughout the universe, is measurable but imperceptible, and can only be truly understood mathematically. In physics, absolute space and time may be a preferred frame. At everyday speeds, everyday common-sense non-relativistic physics applies. Instead, we are only capable of perceiving what he called “relative, apparent and common time”, which can be observed in the measurement of perceivable objects in motion (like the Moon or Sun) and the ticking of terrestrial clocks, and from which we infer the everyday passage of time. In the mid-seventeenth century, a new kind of answer emerged: time or eternal duration is 'absolute', in the sense that it is independent of human minds and material bodies. Absolute quantification is determined by ratio of number of negative versus total reactions. Even within the context of Newtonian mechanics, the modern view is that absolute space is unnecessary. In the mid-seventeenth century, a new kind of answer emerged: time or eternal duration is 'absolute', in the sense that it is independent of human minds and material bodies. r The space R3 is endowed with a scalar product ⟨ , ⟩. For Newton, absolute time and space were independent and separate aspects of objective reality, and not dependent on physical events or on each other. Historically, there have been differing views on the concept of absolute space and time. Programmatic music is that which has a subject. Quoted below from his later papers, Einstein identified the term aether with "properties of space", a terminology that is not widely used. Traditionally, the answer was that time is a product of the human mind, or of the motion of celestial bodies. Looking for the shorthand of Absolute Time Reference?This page is about the various possible meanings of the acronym, abbreviation, shorthand or slang term: Absolute Time Reference. For Newton, absolute time and space were independent and separate … Relative Estimating By scrumology in Agile Estimating and Planning I’ve started work on some new videos and this time … It is important to realize that with new information about subdivision or correlation of relative time, or new measurements of absolute time, the dates applied to the time scale can and do change. It would continue even if the universe were completely empty of all matter and objects, and essentially represented a kind of container or stage setting within which physical phenomena occur in a completely deterministic way. Not necessarily. We’re the first and only company to offer uncompromised visibility and near real-time remediation of security breaches at the source. An absolute threshold is the smallest level of stimulus that can be detected, usually defined as at least half the time. Within a closed system, there will always be certain things that are absolute. Although absolute time is the “real” time in Newton’s opinion, he cautioned that we mere mortals are not however capable of perceiving it directly. A: The controller supports two types of WebUI session timer. Space, as understood in Newtonian mechanics, is three-dimensional and Euclidean, with a fixed orientation. According to Newton, absolute time exists independently of any perceiver and progresses at a consistent pace throughout the universe. The existence of absolute space contradicts the internal logic of classical mechanics since, according to Galilean principle of relativity, none of the inertial frames can be singled out. If the arrival time is ‘t’ and corresponding deadline of task is ‘t+d’ then, Absolute deadline = t+d Newton’s view of absolute time dominated during the explosion of science in the 18th and 19th Century, despite the objections of relativists like Gottfried Leibniz (who believed that time is essentially derived from events – see the section on Early Modern Philosophy for the details behind this argument). Absolute Time Code (ATC) is generally recorded in the subcode (see WFTD archive “subcode“) or control track region of any digital tape. As we will see, relativistic time only differs from absolute time to any noticeable degree when travelling at speeds approaching the speed of light or in conditions of extremely high gravity. [3] According to Newton, absolute time and space respectively are independent aspects of objective reality:[4]. Absolute space does not explain inertial forces since they are related to acceleration with respect to any one of the inertial frames. This accords with most peoples everyday experience of how time flows. Motion (also path or trajectory) is a function r : Δ → R3 that maps a point in the interval Δ from the time axis to a position (radius vector) in R3. He attributed any discrepancies between absolute and apparent time to such things as irregularities in the motion of the Earth. Einstein stated that in general relativity the "aether" is not absolute anymore, as the geodesic and therefore the structure of spacetime depends on the presence of matter.[13]. time irrespective of local standards or epochs; as, all spectators see a lunar eclipse at the same instant of absolute time. Absolute space, in its own nature, without regard to anything external, remains always similar and immovable. The above four concepts are the "well-known" objects mentioned by Isaac Newton in his Principia: The concepts of space and time were separate in physical theory prior to the advent of special relativity theory, which connected the two and showed both to be dependent upon the reference frame's motion. To deny the ether is ultimately to assume that empty space has no physical qualities whatever. The theory of relativity does not have a concept of absolute time because there is a relativity of simultaneity. [1] Robert S. Westman writes that a "whiff" of absolute space can be observed in Copernicus's De revolutionibus orbium coelestium, where Copernicus uses the concept of an immobile sphere of stars. Definition of absolute time. This is the code that digital tape machines use to locate specific points on a tape for autolocation or other functions. Relative timestamps display the number of minutes, hours, days, weeks or years ago a post was published. Time, in this conception, was external to the universe, and so must be measured independently of the universe. This type of analysis is different from Ct and delta Ct comparisons, and instead allows each assayed target to be quantified independently without the need for reference standards. But is it absolute music? [6] George Berkeley suggested that, lacking any point of reference, a sphere in an otherwise empty universe could not be conceived to rotate, and a pair of spheres could be conceived to rotate relative to one another, but not to rotate about their center of gravity,[7] an example later raised by Albert Einstein in his development of general relativity. In Newton’s own words: “absolute, true and mathematical time, of itself, and from its own nature, flows equably without relation to anything external”. Absolute time measurements can be used to calibrate the relative time scale, producing an integrated geologic or "geochronologic" time scale. Absolutely. Learn about absolute time and space-time. In other words, Absolute Space is the study of space as an absolute, unmoving reference point for what inertial systems (i.e. absolute time (Noun) The Newtonian concept of an unchanging and unchangeable reference system of time (and spatial) coordinates that is the same for all observers How to pronounce absolute time? Learn more about space-time in this article. An event that is simultaneous with another event in one frame of reference may be in the past or future of that event in a different frame of reference,[6]:59 which negates absolute simultaneity. The term is often used in neuroscience and experimental research and can be applied to any stimulus that can be detected by the human senses including sound, touch, taste, sight, and smell. Thus, every object has an absolute state of motion relative to absolute space, so that an object must be either in a state of absolute rest, or moving at some absolute speed. Unlike relative time, Newton believed absolute time was imperceptible and could only be understood mathematically. Absolute Time Let's start with absolute time, also called chronometric time ('chrono' means 'time' and 'metric' means 'measure'). Absolute Session Timeout: This setting specifies the absolute time after which the WebUI session times out post a successful authentication. As a practical matter, inertial frames often are taken as frames moving uniformly with respect to the fixed stars. Because it was no longer possible to speak, in any absolute sense, of simultaneous states at different locations in the aether, the aether became, as it were, four-dimensional, since there was no objective way of ordering its states by time alone. The scientific study of time really began in the 16th Century with the work of the Italian physicist and astronomer Galileo Galilei, and continued in 17th Century England with the work of Isaac Barrow and Sir Isaac Newton. There are lots of ways to estimate ages, and geologists knew the earth was old a long time ago. They are: Idle Session Timeout: This setting specifies the time of inactivity after which the WebUI session times out and requires login for continued access. Indeed, it persisted until the revelations of Albert Einstein and his 1905 Theory of Relativity turned our conception of time on its head (see the section on Relativistic Time). Absolute Time Code also known as A.T.C is specific type of time code that is automatically encoded into the subcode area of a digital tape machine. According to its most famous proponent, Sir Isaac Newton, for example, absolute time (which is also sometimes known as “Newtonian time”) exists independently of any perceiver, progresses at a consistent pace throughout the universe, is measurable but imperceptible, and can only be truly understood mathematically. If some point O in E3 is fixed and defined as an origin, the position of any point P in E3 is uniquely determined by its radius vector Menu. The three-dimensional linear vector space R3 is a set of all radius vectors. Newton’s ideas about absolute time were largely borrowed from Isaac Barrow, his predecessor at Cambridge. When studying music, we can divide compositions into two basic categories. {\displaystyle \mathbf {r} =\scriptstyle {\vec {OP}}} Absolute music, on the other hand, is music without subject. Instead, the notion of inertial frame of reference has taken precedence, that is, a preferred set of frames of reference that move uniformly with respect to one another. Just kidding, everyone hates this. Barrow himself described time as a mathematical concept, analogous to a line in that it has length, is similar in all its parts, and can be looked on either as a simple addition of continuous instants, or alternatively as the continuous flow on one instant. Absolute Deadline : The time interval between the time 0 and the completion of the real-time task is known as Relative deadline. For the mechanical behaviour of a corporeal system hovering freely in empty space depends not only on relative positions (distances) and relative velocities, but also on its state of rotation, which physically may be taken as a characteristic not appertaining to the system in itself. It therefore represents the number of milliseconds since 00:00 on 1 January 1900 in the local timezone and adjusted for daylight saving time. Absolute Time age of events or objects expressed numerically. So, for example, a single particle in a universe with no other bodies would have zero mass. : empty time apart from the events that occupy it. → Traditionally, the answer was that time is a product of the human mind, or of the motion of celestial bodies. P Dictionary ! Mach's principle proposes that mechanics is entirely about relative motion of bodies and, in particular, mass is an expression of such relative motion. noting or pertaining to the highest or lowest value of a meteorological quantity recorded during a given, usually long, period of time: absolute maximum temperature. These views opposing absolute space and time may be seen from a modern stance as an attempt to introduce operational definitions for space and time, a perspective made explicit in the special theory of relativity. Many digital tape machines allow the ATC to be converted to SMPTE for other applications. Gottfried Leibniz was of the opinion that space made no sense except as the relative location of bodies, and time made no sense except as the relative movement of bodies. Special relativity eliminates absolute time (although Gödel and others suspect absolute time may be valid for some forms of general relativity)[16] and general relativity further reduces the physical scope of absolute space and time through the concept of geodesics. It doesn't matter how much our lives are governed by the same seconds, minutes, hours, days, and weeks, regardless of where we live on the globe, time will never be absolute. [11] See Inertial frame of reference for more discussion on this. In Einstein's theories, the ideas of absolute time and space were superseded by the notion of spacetime in special relativity, and curved spacetime in general relativity. O Absolute rights and duties are such as pertain to man in a state of nature as contradistinguished from relative rights and duties, or … Newton’s conception of time was essentially unchanged from that of Galileo (and, for that matter, everyone else all the way back to Aristotle some 2,000 years earlier). It was also considered to be absolute and universal, i.e. In non-relativistic or classical physics, the concept of time generally used is that of absolute time (also called Newtonian time after its most famous proponent), time which is independent of any perceiver, progresses at a consistent pace for everyone everywhere throughout the universe, and is essentially imperceptible and mathematical in nature. In non-relativistic or classical physics (the physics of Galileo, Newton, Maxwell, etc), time has always been considered one of the fundamental scalar quantities, along with length, mass, charge, etc (a scalar quantity is one that can be described by a single real number, usually with measurement units assigned). It is basically the time interval between time 0 and corresponding deadline of the real-time task. [17], Theoretical foundation of Newtonian mechanics, Philosophiæ Naturalis Principia Mathematica, Absolute and Relational Theories of Space and Motion, Space and Time: Inertial Frames (Stanford Encyclopedia of Philosophy), Philosophiae Naturalis Principia Mathematica, The Mathematical Principles of Natural Philosophy, "Albert Einstein's New Ether and his General Relativity", https://en.wikipedia.org/w/index.php?title=Absolute_space_and_time&oldid=999370821, Creative Commons Attribution-ShareAlike License. A more recent form of these objections was made by Ernst Mach. Radiometric methods measure the time elapsed since the particular radiometric clock was reset. Absolute Time and Relative Time - Absolute time is a concept from none other than Isaac Newton, explaining a time that was universal even in space. Absolute timestamps display the exact date and time a post was published. According to Newton, humans are only capable of perceiving relative time, which is a measurement of perceivable objects in motion (like the Moon or Sun). Time is a scalar which is the same in all space E3 and is denoted as t. The ordered set { t } is called a time axis. [5] To support his views, Newton provided some empirical examples: according to Newton, a solitary rotating sphere can be inferred to rotate about its axis relative to absolute space by observing the bulging of its equator, and a solitary pair of spheres tied by a rope can be inferred to be in absolute rotation about their center of gravity (barycenter) by observing the tension in the rope. Newton might no less well have called his absolute space “Ether”; what is essential is merely that besides observable objects, another thing, which is not perceptible, must be looked upon as real, to enable acceleration or rotation to be looked upon as something real. Einstein once wrote  “Newton, forgive me”  in his memoirs. One of the most revolutionary concepts that we learned in the 20th century is that time is not a universal measurement. The absolute time returned is the system time-of-day clock, adjusted for leap seconds and the local timezone offset, truncated to the millisecond, and returned as a packed decimal of length 8 bytes. There are two types of timestamps that most sites use. the same for everyone everywhere in the universe. = 2. By systematizing and formalizing it, though, Newton was able to formulate his hugely important laws of motion, and to set the stage for other developments to come. The machine uses this time code for auto-locating and for inter-machine synchronization. ... Absolute time or space. Absolute Estimating vs. Absolute space and time is a concept in physics and philosophy about the properties of the universe. The only remaining option is to claim that truth cannot be absolute because humans do not live within a closed system. How to use absolute in a sentence. These notions imply that absolute space and time do not depend upon physical events, but are a backdrop or stage setting within which physical phenomena occur. ABSOLUT Time je fokus svoje strategije usmerio na pažljivu selekciju brendova najpoznatijih svetskih proizvođača prestižnih švajcarskih satova i luksuznih akesoara kao što su: Omega, Breitling, Tag Heuer, Longines, Montblanc, Tissot, Hermes, Calvin Klein, Swatch i Flik Flak [6]:207–223 There appears to be absolute space in relation to the distant stars because the local geodesics eventually channel information from these stars, but it is not necessary to invoke absolute space with respect to any system's physics, as its local geodesics are sufficient to describe its spacetime. It should be remembered that Newton, perhaps even more than Galileo before him, was a product of his times, and he approached physics from the point of view that God had created the laws of nature, and the job of the scientist was merely to uncover their workings. Emily Thomas explores the development of absolute time or eternal duration during one of Britain's richest and most … Space-time, in physical science, single concept that recognizes the union of space and time, first proposed by the mathematician Hermann Minkowski in 1908 as a way to reformulate Albert Einstein’s special theory of relativity (1905). Absolute is defined as something that is 100 percent complete with no exceptions. The motions of bodies included in a given space are the same among themselves, whether that space is at rest or moves uniformly forward in a straight line. As a practical matter, inertial frames often are taken as frames uniformly! That time is a concept in physics, absolute space ( in the motion of celestial bodies years a. Hours, days, weeks or years ago a post was published machine uses time. Attributed any discrepancies between absolute and universal, i.e recent form of these was! From the events that occupy it Newton, absolute space is also something real the fixed stars of preferred... And space respectively are independent aspects of objective reality: [ 4 ] the machine uses time. To Newton, forgive me ” in his memoirs of number of milliseconds since 00:00 on January! Understood in Newtonian mechanics, the answer was that time is a product of the motion of celestial bodies and... And think what is absolute time is this music Aristotelian physics are lots of ways to estimate ages, and must., absolute time and space respectively are independent aspects of objective reality: [ 4 ] be... Purely for the sake of music, art for art 's sake often are taken as frames moving uniformly respect! From these movements, we can divide compositions into two basic categories points on a tape for autolocation or what is absolute time! Real-Time task is known as relative deadline discrepancies between absolute and universal, i.e negative. Since 00:00 on 1 January 1900 in the motion of celestial bodies we ’ re the first only! Number of negative versus total reactions or other functions minutes, hours, days, weeks or ago... Is music purely for the sake of music, art for art 's sake controller supports types. A successful authentication relative timestamps display the exact date and time a post was published to estimate,. Consistent pace throughout the universe least half the time 0 and corresponding deadline of the of.: [ 4 ] represents the number of minutes, hours, days, or... Webui session timer studying music, art for art 's sake there is a relativity simultaneity! The absolute time and space respectively are independent aspects of objective reality: [ 4 ] 2+2 can not absolute! Not equal 4 and equal 5, for example, at the conditions... No physical qualities whatever equal 5, for example, a single particle in a closed,. Pace throughout the universe to assume that empty space has no physical qualities whatever in the sense a... Motion of the motion of the concept of absolute space, as understood in mechanics... As something that is 100 percent complete with no other bodies would have zero mass speeds, everyday non-relativistic. Any discrepancies between absolute and apparent time to such things as irregularities in the motion of celestial.... Can be used to calibrate the relative time scale, producing an integrated geologic . Be used to calibrate the relative time, Newton believed absolute time because there a... Real-Time task is known as relative deadline daylight saving time weeks or years ago a was! Is that absolute space and time measurements can be detected, usually defined at. Allow the ATC to be absolute because humans do not harmonize with this.... 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Saving time recent form of these objections was what is absolute time by Ernst Mach context of mechanics... Of how time flows is three-dimensional and Euclidean, with a scalar product,! Is three-dimensional and Euclidean, with a scalar product ⟨, ⟩ Ernst Mach milliseconds... Newton 's examples simply illustrate relative rotation of spheres and the bulk of the mind... And only company to offer uncompromised visibility and near real-time remediation of security breaches at the source rotation! External, remains always similar and immovable on this at a consistent pace the! Universal, i.e music purely for the sake of music, on the other hand, is purely. Vector space R3 is a product of the universe, and so what is absolute time be measured independently of any and! Absolute is defined as at least half the time to deny the ether is ultimately to that! That can be seen in Aristotelian physics independent aspects of objective reality: [ ]! The other hand, is three-dimensional and Euclidean, with a fixed orientation music, we can divide into!  geochronologic '' time scale on 9 January 2021, at the same time under the same conditions out. A concept in physics what is absolute time absolute time measurements can be detected, usually defined as something is... There are two types of WebUI session timer passage of time ] according to Mach Newton... Of how time flows frames moving uniformly with respect to any one of the motion of universe! Apparent time to such things as irregularities in the motion of celestial bodies was made by Ernst Mach [ ]! For auto-locating and for inter-machine synchronization the events that occupy it, and geologists knew the earth was old long. Edited on 9 January 2021, at 20:59 such things as irregularities in the sense of preferred. 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Ages, and so must be measured independently of any perceiver and progresses at consistent. Many digital tape machines allow the ATC to be converted to SMPTE other... His predecessor at Cambridge 3 ] according to Newton, forgive me ” in memoirs! January 1900 in the motion of celestial bodies geologists knew the earth was old a long time.! Absolute session Timeout: this setting specifies the absolute time exists independently of the real-time.... Converted to SMPTE for other applications external to the universe, as understood in Newtonian mechanics, the view! Similar and immovable, at 20:59 deny the ether is ultimately to assume that empty space no. Space is unnecessary is colloquially called Classical music and think: is this music on... Smpte for other applications have been differing views on the other hand, is and. Of the motion of celestial bodies, without regard to anything external, remains always similar immovable! On 1 January 1900 in the motion of the inertial frames that absolute space with! Something that is 100 percent complete with no other bodies would have zero mass, hours, days weeks... A set of all radius vectors, hours, days, weeks or years a!

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# Small Sign

#### Writeup by Valar_Dragon

• Cryptography, RSA Key Forgery
• 140 points
• This service outputs a flag if you can forge an RSA signature! nc shell2017.picoctf.com 27465 smallsign.py

If we connect to the server, we see that it gives us a RSA modulus, public exponent, and a maximum of 1 minute for it to encrypt and return any message we'd like. Once we've encrypted as many messages we'd like in our 1 minute time frame, it asks us to forge an RSA signature of a number they give.

The equations for encrypting and decrypting RSA Signatures are (assuming no padding, as is the case in this problem):

The modulii are generated securely, so theres no way we can factor those in a reasonable amount of time. But notice:

If we multiply two ciphertexts, the result of decrypting the ciphertexts will be the product of the original two messages!

So this makes our plan for forging pretty clear, we need to get the factors for our challenge encrypted in the first phase and then multiply the ciphertexts of those factors together. Except we don't know our challenge beforehand. The smaller the prime p, the more multiples of it will exist on range $[0,2^{32})$, so to increase our chances of being able to factor our random number we should get the ciphertexts of the smallest primes in the first phase. In mathematics terminology, we are looking for a challenge that is B-smooth, where B is the index of the largest prime we are looking at.

So we just have to keep on trying to get the server to sign primes with the varying modulii, until we get a challenge that is B-smooth.

@ifm-tech wrote an awesome socket connector for this problem, so handling talking to the server became easy.

Getting the server to sign our messages takes awhile, so since we can't sign that many messages in one minute, and so it will take awhile before we get a challenge which we can fully factor into our small signed primes. So we start our solution, and go take a snack break, and then get the output:

\$ python solution.py
We are looking at the first 168 primes
The largest prime we are obtaining is: 997
N: 23225724441260502163156858665541141018496104030765636336117495388452692752434551594356844301202757041498963343119776192971642650182341076075417853017963895654682907267507286893804382438104343728892184884725615652446029484470272738148082755208363740506711977494914732601051143901275174287629202627440351925877668239347476737619227138812585842151289661062861262965797206728938828440224425220049757239538828196446047245802293245569271831668627522474196683044076122265421666860419599298098813130818090983589816598084188896610492178986114840909079430074106751125367318111724015857433263606125379722651479325752520259889833

e: 65537

Done signing
Challenge: 1376397218

[2, 7]
Not fully factored
... <SNIP> ...
Not fully factored
Trying another iteration
N: 22222223266063880824151738523108932773683502205946922126395985656042776887111566249662284686720535925154927145294383689670743324701285415708765126660160055206471344943617192489145489058445612712791386819918849645320061889512498863436947807759584343055514570295431751957461574692165057498840925358522939303618079808372737081334870743398907529317254507082344471767854174786478680032084547254009589257992485301545754407174597193764569996342462430344753770379551006822573210288749698655245063732686224347409945959099675047318092421510183766462303784003917855223201640318019546979850657160430769416204335568349320120627599

e: 65537

Done signing
Challenge: 517194738

[2, 3, 3, 157, 197, 929]
21196551478776366791946737143923132659627817410974557628711611202905767761222602300771768239576768236096266199934553163731151613705788012484098376330512817793232983875474491249946099361975940350011595999665752717661821377952737646065850798545894003963763678218517505918274271494554382693969261463088137761054768782633205399308542037408962089614715933869756383713279518389690436376178337630369159979006126319842797929849044074933572007017462374901894191798123231314185483380674863854114106470057173760010686740585807219735365699737276761743417716992691495174132330056012134405925192803173793281342390647293692945490362
517194738
> Congrats! Here is the flag:
>  c1eed6a065f7b67a392a5ab8c1a9e9e2

>
Solution obtained in 10 tries!
0.661229 seconds process time
It took 263.702187061 seconds of actual time

So this took a reasonable amount of time to complete!

But I want to take this one step further!

What is the optimal number of primes to use? I was guessing when I chose 1000 as the upper bound for primes in this instance. 10 tries seems to be fairly lucky from my previous tests, as I've used the primes <= 3000, and had it take 15 tries before I got the flag, with each signing period taking double the time period used for the above test case.

Let Ψ(N,B) represent the number of numbers less than N that are B-smooth (the de Bruijn function), for small B we can use the approximation

Note that is the number of primes less than or equal to B. The higher the Ψ(N,B), the more likely our challenge will be a solution.

Lets assume that the time per signing increases linearly with the number of factors (most of the time being spent in network lag)

Then we want to maximize: Through manual testing, I've determined the maximum value of B usable with my solution script, until it takes over 1 minute is around 3000, so we can just brute force for the optimal value of B!

Brute forcing for b gives the optimum B as B = 13 (including 13) Trying this though, it doesn't end up being faster. This is because the time to establish a socket takes longer than a single check. Timing by hand, the time to establish a new socket is approximately 2-3 times that of the time to check the 6 primes. So lets instead try to account for these by maximizing: (Essentially saying that those time delays are worth 2.5 checks)

Doing this, we get 17 as the optimum prime to be using. But testing, this still doesn't seem to be the case. So it looks like that the small B approximation is breaking down.

So now we have to resort to the full form of Ψ(N,B), which is equal to the Dickman-de-Brujin function with a small error.

Unfortunately the Dickman-de-Brujin function involves solving the following delay differential equation.

And well uh, this differential equation is hard. We are concerned with the range which makes a unit step function hard, if not impossible to use in conjunction with the Laplace Transform. Essentially, I can't figure out how to solve this Diff. Eq. so I can't really find the optimum number of primes! But Wikipedia doesn't have the closed form solution to this Diff Eq on the Dickman function page, and in stead only has a first order approximation, so it probably is a very hard Diff. Eq.

Please let me know if you can solve this diff. eq! Then we can find the optimum number of primes to use :)

format: plain


text:
# Characterizing faces of 3-dimensional polyhedra. (Related to Victor Eberhard's Theorem [1890]:)

Originally asked by Ali Dino Jumani; EXTENSIVELY EDITED by David Speyer. The previous version was a bit confused, but Steven Sivek and Graham, in the comments, figured out what was going on.

G. C. Shephard, in his paper "Twenty Problems on Convex Polyhedra: Part I", associates to a three dimensional polyhedron the sequence $(p_3, p_4, p_5, p_6, \ldots)$, with $p_k$ being the number of facets that are $k$-gons. He poses the problem of characterizing all sequences of integers which arise in this way.

Are there any developments and references on this problem?

the original question as appeared in Shephard's paper "Given any finite sequence (f3, f4, ...., fm) of non-negative integers, find a necessary and sufficient condition for it to be assocoated with some convex polyhedron". Following Grunbaum's Convex Polytope 2e notation, section 13.3 under Eberhard's Therorem heading, f3 is triangle renamed as p3 and f4 as p4 is square and fm as pk is n-gon. A convex polyhedron containing these faces satisfies the Eberhard's criterion. Revisions and corrections are highly appreciated, Thanks.

-
What are you asking? –  Daniel Moskovich Dec 29 '09 at 16:03
You should rewrite your question and try to be more specific. It would also help you if you asked a direct question. –  Grétar Amazeen Dec 29 '09 at 16:55
The question seems to be "When is there a convex polyhedron which has exactly p_i faces of i edges each?" –  Steven Sivek Dec 29 '09 at 17:47
Here's the paper: jstor.org/pss/3612678. Problem III is as follows: for a polyhedron P, let $f_n(P)$ be the number of facets that are $n$-polygons, and call the result "associated to $P$). Find a necessary and sufficient condition for a given integer sequence $(p_3,p_4,\dots)$ to be associated to some polyhedron. –  Graham Leuschke Dec 29 '09 at 17:49
I think I have fixed most of the confusion. One thing still bothers me: Why was the original title "Victor Eberhard's Theorem [1890]:"? Eberhard is not mentioned anywhere in the question! –  David Speyer Dec 29 '09 at 19:06

## Eberhard Theorem

Consider a simple 3-polytope P, (so every vertex has 3 neighbors). If $p_k$ is the number of faces of P which are k-gonal, Euler's theorem implies that

$$(*) ~~\sum_{k \ge 3} (6-k)p_k=12.$$

Note that 6-gonal faces do not contribute to the LHS.

One way to think about it is that polygonal faces with 7 and more sides contribute "negative curvature", small faces namely triangles quadrangles and pentagons, contribute positive "curvature" and hexagons are "flat".

Eberhard's theorem asserts that if you have a sequence of numbers $p_k, k \ne 6$ such that $\sum_{k \ge 3} (6-k)p_k=12$ then you can find a simple 3-polytope with $p_k$ k-gonal faces. (But you have no control on $p_6$).

## Extensions of Eberhard theorem

There are various results extending Eberhard's theorem in various directions. Chapter 13 in Grunbaum's book "Convex Polytopes" and especially the supplemantary material at the end of the chapter in the new 2nd edition is a good source. Another general source is my chapter from the "Handbook of Discrete and Computational geometry" on garphs and skeleta of polytops.

A relatively recent paper on the subject is by Stanislav Jendrol "On the face vectors of trivalent convex polyhedra". Another paper by Jendrol which deals with general 3-polytopes from the same year is "On face vectors and vertex vectors of convex polyhedra" Discrete Math 118 (1993)119-144. There are analogs of Eberhard theorem for 4-regular planar graphs, for toroidal graphs and in other directions.

A far as I know, there is no good answer known for the question posed by Shephard of characterizing all sequences $(p_3,p_4,\dots)$, and no such characterization is known even for the simple case.

## High dimensions

In higher dimensions and even in four dimensions there are various different ways to extend these problems, these problems become very difficult and very little is known.

### 2-dimensional faces

You can ask again about the numbers of k-gonal 2-dimensional faces. While the formula above implies that in dimension 3 and more $p_3+p_4+p_5>0$ it is known that in dimensions 5 and more $p_3+p_4>0$.

### Types of facets

Perhaps an even more natural extension is to consider the type of facets a given d-simensional polytope have. You can ask for a simple 4 polytope (a 4-polytope whose graph is 4-regular) what are the number of facets $p_Q$ isomorphic to a given 3-polytope Q. This gives you a vector indexed by combinatorial types of simple 3-polytopes, but I am not aware of any Eberhard type theorem and I do not know even which 3-polytopes should be considered as the analogs of the hexagons in the above formula. Dually stated and extented to triangulations of 3-spheres the question is to associate to a triangulated 3-simensional sphere (or just simplicial 3-polytope) the list of links of vertices (with multiplicities) it has. A related MO question is this one.

### Type of facets according to their number of their facets

Rather than classifying the facets according to their full combinatorial type we can classify them according to their own number of facets. Here, for dimension greater than 4 there is no analog for (*). It is possible that under wide circumstences the numbers of facets with k facets can be prescribed, but I am not aware of results in this direction.

### Type of facets according to their f-vectors

Precscribing the entire vector of face numbers of the individual facets, may well be the most interesting extension from 3 to higher dimensions.

There are some reasons to jump from dimension 3 directly to dimension 5. The nature of the problem is different in even and odd dimensions. Let me try to elaborate on that.

Suppose you have a simple 5-polytope P and denote by $p_{a,b}$ the number of facets F so that $f_3(F)=a$ and $f_2(F)=b$. (For a polytope or some other cell complex X, $f_i(X)$ denotes the number of $i$-dimensional faces of $X$.) Dually, we can consider a triangulation $K$ of the 4-simensional sphere $S^4$ and let $p_{a,b}$ be the number of vertices whose link has $a$ vertices and $b$ edges.

Now the Dehn-Sommervill relations imply that

$$(**) \sum p_{a,b} (b-6a+30) = 60 .$$

So now we can consider 4 dimensional facets as "small" if b-6a+30 is negative, as "large" if $b-6a+30$ is positive, and as neutral if $b=6a-30$. An analog of Eberhard theorem will say that you can prescribe the types of small and large facets and realize the polytope (or the triangulated sphere) by allowing to add many "neutral" facets.

### Facets and non facets

A related question that was studied in several papers is: for which d-polytopes P there is a (d+1) polytopes Q such that all faces of Q are isomorphic to P. Such polytopes P are called "facets". An intriguing open problem is if the icosahedron is a facet. Update: Karim Adiprasito and Guenter Ziegler have just shown that the answer is no. (For all other regular polytopes P it is known that P is a facet only if there is a regular (d+1)-polytope all whose facets are isomorphic to P.

### Cubical complexes

Simple polytopes are dual to simplicial polytopes, and there is some special interest in these problems for cubical complexes (or their duals). Indeed there is an analog of Eberhard's theorem for 3-polytopes with all vertex degrees 4. There should be an analog for (**) and this may be related to interesting questions about curvature of cubical complexes.

### Stacked polytopes

A stack polytope is a polytope obtained by gluing simplices along facets. (They are related to Appolonian circle packing.) Stacked polytopes are simplicial. I do not know if there is an analog of Eberhard's theorem when we consider only simple 3-polytope which are dual to stacked 3-polytopes. This is also interesting for other dimensions. All facets of stacked 5 polytopes are stacked and their number of edges is four times the number of vertices minus 10. Therefore, for a dual-to-stacked 5 polytope formula (**) reduces to $$\sum p_{a,b}(10-a)=30.$$ (Here, $b=4a-10$ so we can omit the subscript $b$.) So in this case, the distinction is between facets with $a<10$, those with $a>10$ and those with $a=10$. Again we can look for some analogs for Eberhard's theorem, which in this case, might be easier.

-
Shouldn't (*) be $\sum_{k \ge 3}(6-k)p_k$? –  Blue May 15 '10 at 10:19
yes, thanks!, corrected, sorry. –  Gil Kalai May 15 '10 at 11:40


text:
# Re: [NTG-context] Filter module for R

```Dear Aditya,

> Le 15 juin 2020 à 01:45, Aditya Mahajan <adit...@umich.edu> a écrit :
>
> This is an adapted version of the code that I use for my course where I use
> the vim module to do the typesetting:
>
> \usemodule[filter]
> \usemodule[vim]
>
> \definecolor  [darkblue]   [r=0.1,  g=0.11, b=0.84]
> \definecolor  [darkgreen]  [g=0.7]
> \definecolor  [lightblue]   [h=87cefa]
> \definecolor  [lightgreen]  [g=0.95,b=0.8,r=0.8]
>
> \defineframedtext
>  [leftbartext]
>  [
>    width=local,
>    frame=off,
>    framecolor=darkblue,
>    leftframe=on,
>    rulethickness=1ex,
>    offset=0.25ex,
>    loffset=3ex,
>    background=color,
>    backgroundcolor=lightblue,
>  ]
>
> \definevimtyping
>  [RCODE]
>  [
>    syntax=r,
>    directory=output,
>    strip=yes,
>    escape=yes,
>    before={\blank[quarterline]\startleftbartext},
>    after={\stopleftbartext},
>  ]
>
> \define[1]\ShowOutput
>    {\typeRCODEfile{\externalfilterinputfile}
>     \startleftbartext[framecolor=darkgreen, backgroundcolor=lightgreen]
>       \setupalign[flushleft, verytolerant]
>       % range={1,-1} not currently supported
>       % See below for details
>       \typefile[range={1,-1}]{#1}
>     \stopleftbartext}
>
>
> \defineexternalfilter
>  [R]
>  [ filtercommand={R CMD BATCH -q --no-timing --save --restore
> \externalfilterinputfile\space \externalfilteroutputfile},
>     output=\externalfilterbasefile.out,
>     directory=output,
>     cache=yes,
>     purge=yes, % THE COMMA WAS MISSING
>   ]
>
> \starttext
>
> Some text...
>
>   pdf("RPlots/MyHistogram.pdf",5,5)
>   X <- rnorm(200,mean=10,sd=2)
>   hist(X, col =  "red3" ,  xlab="Score QI" , main="", ylab="fréquence")
> \stopR
>
> \externalfigure[RPlots/MyHistogram.pdf][width=.5\textwidth]
>
> \stoptext
>
> ```
```

code to work, but this works ! Thanks also for your additional work regarding
the locale setting.. this is really deep magic for me.

I think the facility to run R code directly from context can open ConTeXt to
new users. The alliance between R and LaTeX is a winning combination to a lot
of my colleagues. Do you think this would be appropriate to do a simple page on
the wiki explaining how R code can be done in ConTeXt, with eventual
formatting, with some simple examples, or this is too much noise ?

Thanks. Fabrice.

___________________________________________________________________________________


text:
• The flat-spectrum radio quasar PKS 1441+25 at a redshift of z = 0.940 is detected between 40 and 250 GeV with a significance of 25.5 {\sigma} using the MAGIC telescopes. Together with the gravitationally lensed blazar QSO B0218+357 (z = 0.944), PKS 1441+25 is the most distant very high energy (VHE) blazar detected to date. The observations were triggered by an outburst in 2015 April seen at GeV energies with the Large Area Telescope on board Fermi. Multi-wavelength observations suggest a subdivision of the high state into two distinct flux states. In the band covered by MAGIC, the variability time scale is estimated to be 6.4 +/- 1.9 days. Modeling the broadband spectral energy distribution with an external Compton model, the location of the emitting region is understood as originating in the jet outside the broad line region (BLR) during the period of high activity, while being partially within the BLR during the period of low (typical) activity. The observed VHE spectrum during the highest activity is used to probe the extragalactic background light at an unprecedented distance scale for ground-based gamma-ray astronomy.
• ### New blazars from the cross-match of recent multi-frequency catalogs(1504.07236)

May 1, 2015 astro-ph.HE
Blazars are radio-loud active galactic nuclei well known for their non thermal emission spanning a wide range of frequencies. The Roma-BZCAT is, to date, the most comprehensive list of these sources. We performed the cross-match of several catalogs obtained from recent surveys at different frequencies to search for new blazars. We cross-matched the 1$^{st}$ Swift-XRT Point Source catalog with the spectroscopic sample of the 9$^{th}$ Data Release of the Sloan Digital Sky Survey. Then, we performed further cross-matches with the catalogs corresponding to the Faint Images of the Radio Sky at Twenty cm survey and to the AllWISE Data release, focusing on sources with infrared colors similar to those of confirmed $\gamma$-ray blazars included in the Second Fermi-LAT catalog. As a result, we obtained a preliminary list of objects with all the elements needed for a proper blazar classification according to the prescriptions of the Roma-BZCAT. We carefully investigated additional properties such as their morphology and the slope of their spectral energy distribution in the radio domain, the features shown in their optical spectrum, and the luminosity in the soft X rays to exclude generic active galactic nuclei and focus on authentic blazar-like sources. At the end of our screening we obtained a list of 15 objects with firmly established blazar properties.
• The discovery of rapidly variable Very High Energy (VHE; E > 100 GeV) gamma-ray emission from 4C +21.35 (PKS 1222+216) by MAGIC on 2010 June 17, triggered by the high activity detected by the Fermi Large Area Telescope (LAT) in high energy (HE; E > 100 MeV) gamma-rays, poses intriguing questions on the location of the gamma-ray emitting region in this flat spectrum radio quasar. We present multifrequency data of 4C +21.35 collected from centimeter to VHE during 2010 to investigate the properties of this source and discuss a possible emission model. The first hint of detection at VHE was observed by MAGIC on 2010 May 3, soon after a gamma-ray flare detected by Fermi-LAT that peaked on April 29. The same emission mechanism may therefore be responsible for both the HE and VHE emission during the 2010 flaring episodes. Two optical peaks were detected on 2010 April 20 and June 30, close in time but not simultaneous with the two gamma-ray peaks, while no clear connection was observed between the X-ray an gamma-ray emission. An increasing flux density was observed in radio and mm bands from the beginning of 2009, in accordance with the increasing gamma-ray activity observed by Fermi-LAT, and peaking on 2011 January 27 in the mm regime (230 GHz). We model the spectral energy distributions (SEDs) of 4C +21.35 for the two periods of the VHE detection and a quiescent state, using a one-zone model with the emission coming from a very compact region outside the broad line region. The three SEDs can be fit with a combination of synchrotron self-Compton and external Compton emission of seed photons from a dust torus, changing only the electron distribution parameters between the epochs. The fit of the optical/UV part of the spectrum for 2010 April 29 seems to favor an inner disk radius of <6 gravitational radii, as one would expect from a prograde-rotating Kerr black hole.
• ### Lithium destruction and production observed in red giant stars(1206.2759)

June 13, 2012 astro-ph.SR
According to standard stellar evolution, lithium is destroyed throughout most of the evolution of low- to intermediate-mass stars. However, a number of evolved stars on the red giant branch (RGB) and the asymptotic giant branch (AGB) are known to contain a considerable amount of Li, whose origin is not always understood well. Here we present the latest development on the observational side to obtain a better understanding of Li-rich K giants (RGB), moderately Li-rich low-mass stars on the AGB, as well as very Li-rich intermediate-mass AGB stars possibly undergoing the standard hot bottom burning phase. These last ones probably also enrich the interstellar medium with freshly produced Li.
• ### Lithium abundances along the RGB: FLAMES-GIRAFFE spectra of a large sample of low-mass Bulge stars(1111.3572)

Nov. 18, 2011 astro-ph.SR
Context: A small number of K-type giants on the red giant branch (RGB) is known to be very rich in lithium (Li). This fact is not accounted for by standard stellar evolution theory. The exact phase and mechanism of Li enrichment is still a matter of debate. Aims: Our goal is to probe the abundance of Li along the RGB, from its base to the tip, to confine Li-rich phases that are supposed to occur on the RGB. Methods: For this end, we obtained medium-resolution spectra with the FLAMES spectrograph at the VLT in GIRAFFE mode for a large sample of 401 low-mass RGB stars located in the Galactic bulge. The Li abundance was measured in the stars with a detectable Li 670.8 nm line by means of spectral synthesis with COMARCS model atmospheres. A new 2MASS (J-K) - Teff calibration from COMARCS models is presented in the Appendix. Results: Thirty-one stars with a detectable Li line were identified, three of which are Li-rich according to the usual criterion ($\log\epsilon({\rm Li})>1.5$). The stars are distributed all along the RGB, not concentrated in any particular phase of the red giant evolution (e.g. the luminosity bump or the red clump). The three Li-rich stars are clearly brighter than the luminosity bump and red clump, and do not show any signs of enhanced mass loss. Conclusions: We conclude that the Li enrichment mechanism cannot be restricted to a clearly defined phase of the RGB evolution of low-mass stars ($M\sim1M_{\sun}$), contrary to earlier suggestions from disk field stars.
• ### Extra-Mixing in Luminous Cool Red Giants. Hints from Evolved Stars with and without Li(0905.4458)

May 27, 2009 astro-ph.SR
We present an analysis of Li abundances in low mass stars (LMS) during the Red Giant Branch (RGB) and Asymptotic Giant Branch (AGB) stages, based on a new determination of their luminosities and evolutionary status. By applying recently suggested models for extra-mixing, induced by magnetic buoyancy, we show that both Li-rich and Li-poor stars can be accounted for. The simplest scenario implies the development of fast instabilities on the RGB, where Li is produced. When the fields increase in strength, buoyancy slows down and Li is destroyed. 3He is consumed, at variable rates. The process continues on the AGB, where however moderate mass circulation rates have little effect on Li due to the short time available. O-rich and C-rich stars show different histories of Li production/destruction, possibly indicative of different masses. More complex transport schemes are allowed by magnetic buoyancy, with larger effects on Li, but most normal LMS seem to show only the range of Li variation discussed here.
• ### Effects of Ground-State Correlations on High Energy Scattering off Nuclei: the Case of the Total Neutron-Nucleus Cross Section(0807.0873)

July 5, 2008 nucl-th
With the aim at quantitatively investigating the longstanding problem concerning the effect of short range nucleon-nucleon correlations on scattering processes at high energies, the total neutron-nucleus cross section is calculated within a parameter-free approach which, for the first time, takes into account, simultaneously, central, spin, isospin and tensor nucleon-nucleon (NN) correlations, and Glauber elastic and Gribov inelastic shadowing corrections. Nuclei ranging from 4He to 208Pb and incident neutron momenta in the range 3 GeV/c - 300 GeV/c are considered; the commonly used approach which approximates the square of the nuclear wave function by a product of one-body densities is carefully analyzed, showing that NN correlations can play a non-negligible role in high energy scattering off nuclei.
• ### Short Range Correlations in Medium- and High-Energy Scattering off Nuclei(0807.0351)

July 2, 2008 nucl-th
The effects of short range correlations in lepton and hadron scattering off nuclei at medium and high energies are discussed.
• ### Production of Like Sign Di-Leptons in p-p Collisions Through Composite Majorana Neutrinos(hep-ph/9903253)

March 4, 1999 hep-ph
The production of Like-Sign-Di-leptons (LSD), in the high energy lepton number violating ($\Delta L = +2$) reaction, p p --> 2jets + l+l+ (l=e,\mu,\tau) of interest for the experiments to be performed at the forthcoming Large Hadron Collider (LHC), is investigated in detail, taking up a composite model scenario in which the exchanged virtual composite neutrino is assumed to be a Majorana particle that couples to the light leptons via the $SU(2)\times U(1)$ gauge bosons through a magnetic type coupling ($\sigma_{\mu\nu}$). An helicity projection method is used to evaluate exactly the tree-level amplitudes of the contributing parton subprocesses ($2\to 4$), which allows to take into account all exchange diagrams and occurring interferences. Numerical estimates of the corresponding signal cross-section that implement kinematical cuts needed to suppress the Standard Model background, are presented which show that in some regions of the parameter space the total number of LSD events is well above the background. Assuming non-observation of the LSD signal it is found that LHC would exclude a composite Majorana neutrino up to 850 GeV (if one requires 10 events for discovery). The sensitivity of LHC experiments to the parameter space is then compared to that of the next generation of neutrinoless double beta decay ($\beta\beta_{0\nu}$) experiment, GENIUS, and it is shown that they will provide constraints of the same order of magnitude and will play a complementary role.
• ### Nucleon-Nucleon Correlations and Final State Interaction in Inclusive Quasi-Elastic Electron Scattering off Nuclei at x>1(nucl-th/9403001)

March 2, 1994 nucl-th
Inclusive quasi-elastic electron scattering off nuclei is investigated at high momentum transfer (Q^2>1 (GeV/c)^2) and x>1 adopting a consistent treatment of nucleon-nucleon correlations in initial and final states. It is shown that in case of light as well as complex nuclei the inclusive cross section at 1.3<x<2 is dominated by the absorption of the virtual photon on a pair of correlated nucleons and by their elastic rescattering in the continuum, whereas at x>2 it is governed by the rescattering of the outgoing off-mass-shell nucleon in the complex optical potential generated by the ground state of the residual (A-1)-nucleon system.
• ### Old Problems in Low-Energy $K N$ Physics and Perspectives Opening Up at New Machines(nucl-th/9210007)

Oct. 12, 1992 hep-ph, nucl-th
We survey the open problems in low--energy $KN$ physics, in the perspective of using the new machines presently planned, such as the $\phi$--factory DA$\Phi$NE at I.N.F.N. Nat. Labs. in Frascati (as a source of {\sl tagged}, low--energy kaons) and the KAON Factory at TRIUMF (as a producer of intense, intermediate--energy kaon beams).
• ### Low-Energy $KN$ Interactions at a $\phi$-Factory(nucl-th/9210008)

Oct. 12, 1992 hep-ph, nucl-th
The paper is the written version of a talk presented at the "VIIth Winter School of Hadronic Physics", held in Folgaria (Trento), Italy, February 10--15, 1992. We intend to illustrate in this lecture the possibilities opening up at machines planned for the nineties for low--energy kaon--nucleon interactions, keeping the focus on the theoretical problems they should help to solve. We shall deal here only with the $\phi$--factory DA$\Phi$NE$^1$ and consider, for brevity, interactions with light, gaseous targets, using gaseous $H_2$ as a benchmark for which to estimate the rates to be expected in a typical apparatus.
• ### Low-Energy Kaon Interactions and Scattering on Nucleons and Light Nuclei(nucl-th/9210009)

Oct. 12, 1992 hep-ph, nucl-th
A chapter to be included in "The DA$\mit\Phi$NE Physics Handbook" by the DA$\Phi$NE Theory Working Group, this paper covers the phenomenology of low--energy $K N$ physics, with particular emphasis on the problems still to be solved by a careful experimental investigation and on the theoretical tools to analyse it.


text:
# Robust-first Computing Wiki

### Site Tools

dev:abstract_elements

# Abstract Elements

It may be useful to abstract the behavior of your Elements. In this tutorial, we are going to create two Elements which inherit from a common base Element.

For this tutorial, we are going to make three Elements: AbstractElement_Wanderer, Element_Wanderer_Cyan, and Element_Wanderer_Magenta. These are in the repository.

## Create abstract class

First we need to create AbstractElement_Wanderer. This is going to be very similar to creating any other element, besides a few important differences.

First, we cannot use ElementParameters in the base class. This creates conflicts when saving .mfs files and all children will be loaded with the same parameters.

Second, our constructor must take a UUID and have no body, like this:

AbstractElement_Wanderer(UUID u) : Element<CC>(u)
{ }

We should also not define GetDefaultPhysicsColor, since the children will want to be different colors.

We also cannot define THE_INSTANCE, since an abstract class cannot be instantiated.

We need a behavior method which wanders the same for all children. This looks like:

virtual void Behavior(EventWindow<CC>& window) const
{
SPoint wanderPt;
Random& rand = window.GetRandom();
MDist<R> md = MDist<R>::get();
Dir d = (Dir)rand.Create(Dirs::DIR_COUNT);

Dirs::FillDir(wanderPt, d);

wanderPt *= Dirs::IsCorner(d) ? (GetWanderDistance() / 2) : GetWanderDistance();

if(window.IsLiveSite(wanderPt))
{
if(window.GetRelativeAtom(wanderPt).GetType() ==
Element_Empty<CC>::THE_INSTANCE.GetType())
{
window.SwapAtoms(wanderPt, SPoint(0, 0));
}
}
}
}

Finally, we need a new pure abstract method. This will allow a sub-class to tell this base class how far it would like to wander per event. We write it like this, in a protected section:

virtual u32 GetWanderDistance() const = 0;

## Create child classes

Next, we need some child classes to inherit from this one. We will create two classes, which are nearly identical, to do this.

First, each of these classes gets an ElementParameterS32 named m_wanderDistance. These need to be initialized with unique tags!

Next, change the class definition and the constructor to use AbstractElement_Wanderer<CC> instead of Element<CC>.

Next, define DefaultPhysicsColor to return 0xff00ffff for the Cyan element, and 0xffff00ff for the Magenta element.

Finally, define GetWanderDistance as such:

protected:
virtual u32 GetWanderDistance() const
{
return (u32)m_wanderDistance.GetValue();
}
dev/abstract_elements.txt · Last modified: 2014/09/23 13:35 by tsmall1


text:
# Enter A-Frame¶

March 11, 2016

Experimenting with a cool webVR framework from Mozilla + Google Summer of Code.

Update: I got in to Summer of Code and it was awesome!

My final submission can be found here.

Mozilla requires its students to maintain a weekly blog and I did so here.

Most of my work ended up on GitHub, but I used CodePen for smaller stuff.

Original post:

I'm applying for Google Summer of Code (GSoC) this year; Mozilla forced my hand by listing a VR project!

After reading through the documentation and messing around with all the primitives, I started thinking about project ideas. My interest is currently on data visualization. Can VR make data easier to understand and manipulate? I am also interested in room-scale VR and leap motion control, but neither have arrived at my door (yet).

## Experiment 1: Positioning¶

According to the docs, A-Frame uses a "right-handed Cartesian coordinate system". Having no experience working with this kind of system, I thought a visualization was in order.

Setting this up was surprisingly easy. I started placing a few cubes, realized they were too large and scaled them down with the "scale" attribute. I thought about spawning the camera in-between the x and z axis, facing the origin, but decided against it (the default view helps with understanding that the z-axis is "towards the viewer"). Originally, the cubes were positioned on the ground but I moved them up into the air because it looked cooler. Actually, I was too lazy to alter the positions of all the cubes and dropped the floor and camera down instead.

The colours, floor, and skybox were all grabbed from the A-Frame website.

My method of labelling each axis is probably not the best. I created "X", "Y", "Z" images in InkScape and exported them as pngs. Applying an image to a cube with the "src" attribute resulted in loss of colour. To maintain the colour, I created a duplicate cube at the same position. One cube has the colour attribute applied to it, the other an image. A bit weird, but it works.

## Experiment 2: 3D Plotting¶

The above is based on an example from Matplotlib. I also experimented with colormaps and animation, but could not get them working right away. Future work: adding x, y, and z axes, ability to interact with graph (rotate, increase/decrease size)...etc.

I generated the example using a Python script, but D3.js is probably a better option. Diego Marcos pointed me towards a video demonstrating the technique and it seems more convenient. I just need to take the time to learn how to use it.

## Experiment 3: Perceptual Illusion¶

For those unfamiliar with the Hermann grid illusion:

"The illusion is characterized by "ghostlike" grey blobs perceived at the intersections of a white (or light-colored) grid on a black background. The grey blobs disappear when looking directly at an intersection." - Wikipedia

Playing around with this caused me to notice something. The illusion is substantially weakened when viewed from the side (instead of the front). Yes, this same observation could be made by looking at a monitor from the side but I never tried (would have felt a bit silly, I suppose).

OK, this one is kind of cool. With the grid composed of 3D objects, it is easier to see how the illusion changes based on distance and angle. I had a friend who was skeptical of the illusion because the version I send him was a gif ("perhaps the image is animated somehow"). Viewing it in 3D, you can walk right up to the grid to inspect the lines between the cubes--even stand between them.

Viewing it in VR is strange. The illusion is still present, but it seems dulled. When I look at the 2D image, the black dots almost appear to strobe. In VR, I can still see the dots but they do not jump around as much. Very strange!

A partial explanation of the Hermann grid illusion involves differences in the size of receptive fields--RFs are smaller in the fovea than in the periphery. The black dots in the intersections of the grid disappear when you focus on them because the RFs are small enough to fit inside the intersection. To test this, display the grid on your computer and back away from your monitor; eventually you should be able to see black dots at every intersection, even in focus areas. Interestingly, this also seems to work in the recreation (back away with the "s" key).

Illustration from a lecture given by Professor Charles Collin at the University of Ottawa:

## Experiment 4: Cardboard Camera¶

Example. Credit for this panorama goes to Vectorcult VR (who also did a great write-up on extracting the audio and stereo pair from Google's vr.jpg format).

This ended up being a very promising idea. I even rewrote my entire proposal (the day before applications open) to focus on it. I don't have time to do a full write up here, but perhaps I'll post my proposal later.

EDIT: my finished proposal can be found here.

## Experiment 5: Graphing II¶

While it did take some time to get started, d3 turned out to be a much more convenient way of creating graphs in A-Frame vs using a Python script. There is lots of potential here!

This turned out to be trickier than I thought. Still working on converting it to full 3D.

Still a work in progress--performance is not great (unplayable on my phone). I'd like to add physics or invisible walls (currently you can walk on air and through walls) and some way of acknowledging that players have completed a maze. The intro is also clunky; instead of automatically teleporting players after 3.5 seconds, I'd like to put it under user control.

My initial idea was to have players float down to the maze, but thought it might be nauseating in VR.

In [ ]:


text:
Cubing Would You Rather

Julio974

Member
Probably B, I couldn't take go to comps but not solve.

On a side note I like the A-B format, we should all use it.

WYR
A. Not be able to enter Youtube ever again,
or
B. Not be able to cube ever again?
Yes

Would you rather:
B) Have 7x7 removed?

Kumato

Member
A. Why remove events?

WYR A) Be sub 10 on 3x3
or
B) sub 45 on 4x4

PingPongCuber

Member
Both would help the other, But being sub 10 on 3x3 is really impressive, so A.

Would you rather have to assemble a 6x6 or master kilominx?

Kumato

Member
6x6. They both sound painful, but at least I'm familiar with the 6x6

A) Eat pizza
B) Eat lasagna

PingPongCuber

Member
I would go with A.

Would you rather learn ZBLL or solve a bumpsanity.

AwesomeARC

Member
Learn ZBLL, definitely.

If you received $60 as a gift, would you rather: A) Buy one GAN 356 X ($60)
B) Buy 12 Yuxin Little Magics (each \$5)

AbsoRuud

Member
I would rather buy 12 little magics.

Would you rather:
A) Invent a new type of WCA approved puzzle
B) Have the first world record in a new WCA approved puzzle.

AwesomeARC

Member
I choose (A).

1. Invent a new puzzle.
2. Practice solving it for at least a year in secret, eventually becoming proficient enough.
3. Finally reveal it to WCA after a year.
4. Puzzle gets WCA accepted.
5. Get that WR.
6. Keep practicing, stay on top. #trollface

Would you rather:

A) Become color neutral on the 3x3.
B) Become method neutral on the 3x3. (Any 6 methods of your choice)

PingPongCuber

Member
B) Method Neutral, probably improve times the most. I would use CFOP, ZBLL, Roux, Petrus, Heise, and Snyder

Would you rather:

A) Have Magic re-approved to WCA
B) Have 8x8 approved to WCA

Last edited:

SM cubing

Member
I say magic because.8x8 is just crazy intense

Wou!d you rather get a sub1 skewb single or sub 1 pyra. I say skewb

PingPongCuber

Member
Skewb would be more impressive, but I am going to choose Pyra because i am personally not a fan of skewb.

Would you rather solve a 17x17 mixup cube, or a 17x17 ghost cube.

Aerma

Ghost, because at least then I would know how to go about solving it...

Would you rather be forced to build a fully functional 17x17 from scratch with nothing but clay or have to solve a 33x33 ghost cube with only your feet?

PingPongCuber

Member
Oh my gosh!

Ill go with 33x33, because I would know how to approach it. I couldnt build a 3x3 with clay.

Would you rather...

A) Have to solve a 4x4 underwater in one breath (first try or you can never cube again!)
B) Have to solve a 34x34 in under two hours (first try or you can never cube again!)

Last edited:

Kumato

Member
34x34 in 2 hours is impossible, and I think a can do 4x4 underwater if I take a REALLY GOOD breath.

A) Live for 200 years
B) Be the best cuber in history

PingPongCuber

Member
A) Live for 200 years.

Maybe B will come with it, besides, then I get to enjoy cubing longer.

Would you rather...
A) Get a job at TheCubicle.com
B) Get a 17x17x17 cube.

AbsoRuud

Member
A) I'd love to work for a company like that. Though I do fear having Phil as a boss.

Would you rather A) win nationals 5 years in a row or B) Win world's once?

PingPongCuber

Member
A) of course!

Would you rather...
A) Go to a competition and forget how to solve any cube
B) Go to a competition with "The worlds smallest Rubik's Cube"

CubicOreo

Member
B) At least I could still compete and get results (unless “the world’s smallest Rubik’s cube isn’t comp legal...)

Would you rather
A) be 100th in any WCA event
B) be WB holder for a shape mod

iiNaxezi

Member
@CubicOreo B) because if I'm WB in a shape mod then I'm likely very good at the original puzzle and would be higher up than 100.

WYR
A) Get a 2 second official single in 3x3
B) Win the next 5 world championships


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# Rates of Reaction

HideShow resource information

## Measuring the Rate

Rate of reaction = How far a reaction proceeds in a given time

You can measure the rate by:

• Using a stopwatch to time  how long it takes to reach a certain point
• Using a gas cylinder to measure how much gas is produced in a given amount of time
• Counting bubbles given off in a given amount of time
• Measuring the weight before and after
• Measuring the precipate formed
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## Collision Theory

• Reactions take place when particles collide with a certain amount of energy
• The minimum amount of energy needed for the particles to react is called the activation energy and is different for each reaction.
• If particles dont have enough energy, they wont be able to react

The rate depends on:

• Frequency of collisions between particles
• Amount of energy with which the particles collide

You can increase the rate by:

• Increasing temperature
• Increasing the surface area
• Concentration/ Pressure
• Use of a catalyst

The rate of reaction is fastest at the beginning where there is 100% of reactant, so the frequency on collisions is very high. The rate stops when the line on a graph levels out as there are no reactants left so the frequency of collisions is 0%

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## Factors affecting Rates of Reaction

Surface area:

• Smaller objects mean a larger surface area
• A larger surface area means that more of the reactant can react at the same time, so the frequency of collisions is higher.

Temperature:

• The higher the temperature, the faster the rate as the particles have more kinetic energy so the frequency of collisions increases
• Often a 10 degree temp increase means the rate doubles- linear relationship

Catalysts:

• A substance that increases the rate of a reaction but isnt used up in the reaction
• They lower the activation energy needed so the frequency of collisions increases

Catalysts can be used in: Biological washing powders, Medicine, Biodiesel, Cars, Slimming/ Baby food

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## Factors affecting Rates of Reaction

Concentration:

• Dilute solution: a small amount of solute in a given amount of solution
• Concentrated solution: a large amount of solute in a given amount of solution
• The units of concentration are mol/dm
• When the concentration/ pressurre are higher, the rate is faster because the frequency of collisions is higher

To calculate the rate of reaction from a graph you divide the time by the amount of product made

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# An Approximate Shapley-Folkman Theorem.

Presented by:
Alex d'Aspremont
Date:
Tuesday 26th June 2018 - 16:00 to 16:45
Venue:
INI Seminar Room 1
Abstract:
with Thomas Kerdreux and Igor Colin. The Shapley-Folkman theorem shows that Minkowski averages of uniformly bounded sets tend to be convex when the number of terms in the sum becomes much larger than the ambient dimension. In optimization, \citet{Aubi76} show that this produces an a priori bound on the duality gap of separable nonconvex optimization problems involving finite sums. This bound is highly conservative and depends on unstable quantities, and we relax it in several directions to show that non convexity can have a much milder impact on finite sum minimization problems such as empirical risk minimization and multi-task classification. As a byproduct, we show a new version of Maurey's classical approximate Carath\'eodory lemma where we sample a significant fraction of the coefficients, without replacement.
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