Connection Games and Sperner’s Lemma

2015 ◽  
Author(s):  
David Molnar
Keyword(s):  
Sperner’S Lemma ◽  
Special Cases ◽  
The Many ◽  
Connection Game

This chapter provides an introduction to connection games in general. It also recounts how Sperner's Lemma, a result about labeling a triangulation of a simplex, can be used to prove that someone must win at Hex—the best-known connection game—as well as The Game of Y®, (or simply, Y) another well-known connection game. Moreover, the chapter proves a generalization of Sperner's Lemma and uses it to show that there is always a winner in the many variations of Atoll and Begird, two connection games which can be played on a variety of boards and include Hex and Y, respectively, as special cases. These “must-win” results have significant strategic implications—if one prevents the opponent from making the desired connection, one would be able to make this connection by necessity.

Computing Cores for Existential Rules with the Standard Chase and ASP

2020 ◽  
Author(s):  
Markus Krötzsch
Keyword(s):  
Large Class ◽  
Data Exchange ◽  
Answer Set Programming ◽  
Query Answering ◽  
Universal Model ◽  
The Core ◽  
Universal Models ◽  
General Terms ◽  
Special Cases ◽  
The Many

To reason with existential rules (a.k.a. tuple-generating dependencies), one often computes universal models. Among the many such models of different structure and cardinality, the core is arguably the “best”. Especially for finitely satisfiable theories, where the core is the unique smallest universal model, it has advantages in query answering, non-monotonic reasoning, and data exchange. Unfortunately, computing cores is difficult and not supported by most reasoners. We therefore propose ways of computing cores using practically implemented methods from rule reasoning and answer set programming. Our focus is on cases where the standard chase algorithm produces a core. We characterise this desirable situation in general terms that apply to a large class of cores, derive concrete approaches for decidable special cases, and generalise these approaches to non-monotonic extensions of existential rules.

scholarly journals Can translocation help wild primates?

Oryx ◽  
1983 ◽  
Vol 17 (3) ◽  
pp. 135-139 ◽  
Author(s):  
Julian Caldecott ◽  
Michael Kavanagh
Keyword(s):  
Special Cases ◽  
The Many

Releasing animals into the wild, especially when they have become extinct there, is an appealing and dramatic conservation technique. It is, however, fraught with risks and often expensive; its success depends upon meticulous planning. The authors discuss the reasons for translocation, the many problems involved and the special cases where such an exercise may be justified.

scholarly journals The Many Formulae for the Number of Latin Rectangles

10.37236/487 ◽  
2010 ◽  
Vol 17 (1) ◽  
Author(s):  
Douglas S. Stones
Keyword(s):  
Closed Form ◽  
Latin Square ◽  
Latin Squares ◽  
Combinatorial Objects ◽  
Special Cases ◽  
Latin Rectangle ◽  
New Equation ◽  
The Many ◽  
Important Milestone

A $k \times n$ Latin rectangle $L$ is a $k \times n$ array, with symbols from a set of cardinality $n$, such that each row and each column contains only distinct symbols. If $k=n$ then $L$ is a Latin square. Let $L_{k,n}$ be the number of $k \times n$ Latin rectangles. We survey (a) the many combinatorial objects equivalent to Latin squares, (b) the known bounds on $L_{k,n}$ and approximations for $L_n$, (c) congruences satisfied by $L_{k,n}$ and (d) the many published formulae for $L_{k,n}$ and related numbers. We also describe in detail the method of Sade in finding $L_{7,7}$, an important milestone in the enumeration of Latin squares, but which was privately published in French. Doyle's formula for $L_{k,n}$ is given in a closed form and is used to compute previously unpublished values of $L_{4,n}$, $L_{5,n}$ and $L_{6,n}$. We reproduce the three formulae for $L_{k,n}$ by Fu that were published in Chinese. We give a formula for $L_{k,n}$ that contains, as special cases, formulae of (a) Fu, (b) Shao and Wei and (c) McKay and Wanless. We also introduce a new equation for $L_{k,n}$ whose complexity lies in computing subgraphs of the rook's graph.

Grand Piano-the Audiovisual Hero of the Soviet Cinema Screen

10.34690/189 ◽  
2021 ◽  
pp. 198-210
Author(s):  
Ольга Яковлевна Каталикова
Keyword(s):  
Film Music ◽  
Film Adaptations ◽  
Soviet Film ◽  
Special Cases ◽  
Soviet Cinema ◽  
Russian Literary ◽  
The Many ◽  
Literary Classics ◽  
Grand Piano ◽  
New Babylon

Статья посвящена особым случаям использования фортепиано в советской киномузыке: не только в составе партитуры, но и как непосредственного «участника» экранного действия. Обычно это происходит в фильмах революционной и исторической тематики, а также в экранизациях русской классики. Среди множества картин, где рояль появляется на экране, нужно выделить ряд шедевров, в которых введение его отмечено уникальными решениями. В статье рассмотрены примеры из фильмов «Новый Вавилон» (музыка Д. Шостаковича), «Строгий юноша» (музыка Г. Попова), «Веселые ребята» (музыка И. Дунаевского). The article is devoted to special cases of the use of the piano in Soviet film music: not only as part of the score, but also as a direct “participant” of the screen action. This usually happens in films with revolutionary and historical themes, as well as in film adaptations of Russian literary classics in scenes of home music. However, among the many films where the instrument appears on the screen, it is necessary to note a number of absolute masterpieces in which the use of the piano is marked by unique solutions. The article considers examples of this kind from the films “New Babylon” (music by D. Shostakovich) “A Strict Young Man” (music by G. Popov), “Funny Guys” (music by I. Dunaevsky).

General theory and comparative anatomy of dip moveout

Geophysics ◽  
1990 ◽  
Vol 55 (5) ◽  
pp. 595-607 ◽  
Author(s):  
Christopher L. Liner
Keyword(s):  
General Formula ◽  
Impulse Response ◽  
Constant Velocity ◽  
Field Data ◽  
Comparative Anatomy ◽  
Two Dimensional ◽  
Time Axis ◽  
Special Cases ◽  
Quality Image ◽  
The Many

It is possible to derive a general formula for constant‐velocity, two‐dimensional dip moveout (DMO). This serves to unify the many published forms of DMO. Known results for common‐offset and shot profile DMO are special cases of the general formula. The analysis is based on the dip‐corrected NMO equation, and thus is a kinematic DMO theory. Using a logarithmic stretch of the time axis, efficient fast Fourier transform (FFT) common‐offset DMO algorithms can be derived. In the published versions, log variables are introduced into the NMO equation. It can be shown that the resulting impulse response departs from the DMO ellipse, which means that some dips have been improperly handled. A new log‐stretch formulation (exact log DMO) which preserves the DMO ellipse can be derived by starting with the analytic impulse response, rather than the NMO equation. Tests on field data indicate that exact log DMO handles shallow, steeply dipping events in agreement with Hale’s DMO, while the other log‐stretch algorithms degrade these events. In situations where constant‐velocity DMO is viable, exact log DMO can be used to create a Hale‐quality image at FFT speed.

The Determination of the Optimum Vulcanization by Means of the Residual Elongation

1935 ◽  
Vol 8 (4) ◽  
pp. 548-553 ◽  
Author(s):  
A. Kusov
Keyword(s):  
Bending Strength ◽  
Mechanical Tests ◽  
Mechanical Method ◽  
Chemical Examination ◽  
Method Of Determination ◽  
Physico Chemical ◽  
Special Cases ◽  
Actual Service ◽  
The Many

Abstract As is well known, various methods have been proposed for determining the optimum vulcanization of rubber. These methods depend either upon physico-chemical examination or upon mechanical tests. In routine control the mechanical method of determination is used for the most part, because it requires but little time, and in addition this method has the advantage of showing directly by mechanical tests whether the vulcanizate being tested passes the requirements or not. The results obtained by this method frequently do not agree with those obtained by other methods. Of the many common methods of testing, determinations of the tensile strength and of the ultimate and residual elongation are the methods most frequently used. These three properties are measured simultaneously by one determination with the apparatus in most widespread use, i. e., the Schopper and the Scott machines. In special cases the resistance to abrasion, bending strength, hardness, and other properties are determined in addition. Considerably less often the hysteresis and Young's modulus of elasticity are determined. All these determinations are of significance in only a limited way, for the conditions under which the tests are carried out in the laboratory are not comparable to the actual service of the products. For basic reasons, this fundamental shortcoming cannot be avoided in the laboratory, though a few of the measurements do approach the true properties found in service. Of course, the results obtained in the laboratory are greatly influenced and made less reliable by other secondary factors, among which are the phenomenon of aging under natural conditions, prolonged stressing, etc.

Identifying suboptimalities with factorial model comparison

2018 ◽  
Vol 41 ◽  
Author(s):  
Wei Ji Ma
Keyword(s):  
Experimental Design ◽  
Model Comparison ◽  
Process Models ◽  
Multiple Forms ◽  
Factorial Experimental Design ◽  
Factorial Model ◽  
Multiple Components ◽  
The Many

AbstractGiven the many types of suboptimality in perception, I ask how one should test for multiple forms of suboptimality at the same time – or, more generally, how one should compare process models that can differ in any or all of the multiple components. In analogy to factorial experimental design, I advocate for factorial model comparison.

Representing utility and deploying the body

2020 ◽  
Vol 43 ◽  
Author(s):  
David Spurrett
Keyword(s):  
Functional Activity ◽  
Degrees Of Freedom ◽  
The Body ◽  
Target Article ◽  
Processing Demands ◽  
The Many

Abstract Comprehensive accounts of resource-rational attempts to maximise utility shouldn't ignore the demands of constructing utility representations. This can be onerous when, as in humans, there are many rewarding modalities. Another thing best not ignored is the processing demands of making functional activity out of the many degrees of freedom of a body. The target article is almost silent on both.

The many faces of obligation

2020 ◽  
Vol 43 ◽  
Author(s):  
Michael Tomasello
Keyword(s):  
Third Party ◽  
The Many ◽  
Sense Of Obligation

Abstract My response to the commentaries focuses on four issues: (1) the diversity both within and between cultures of the many different faces of obligation; (2) the possible evolutionary roots of the sense of obligation, including possible sources that I did not consider; (3) the possible ontogenetic roots of the sense of obligation, including especially children's understanding of groups from a third-party perspective (rather than through participation, as in my account); and (4) the relation between philosophical accounts of normative phenomena in general – which are pitched as not totally empirical – and empirical accounts such as my own. I have tried to distinguish comments that argue for extensions of the theory from those that represent genuine disagreement.

Hydrogen Cyanide Polymers from the Impact of Comet P/Shoemaker-Levy 9 on Jupiter

1997 ◽  
Vol 161 ◽  
pp. 179-187
Author(s):  
Clifford N. Matthews ◽  
Rose A. Pesce-Rodriguez ◽  
Shirley A. Liebman
Keyword(s):  
Amino Acids ◽  
Solar System ◽  
Hydrogen Cyanide ◽  
Nitrogen Heterocycles ◽  
Laboratory Studies ◽  
Heterogeneous Solids ◽  
The Many ◽  
Comet Halley ◽  
The Impact ◽  
By Products

AbstractHydrogen cyanide polymers – heterogeneous solids ranging in color from yellow to orange to brown to black – may be among the organic macromolecules most readily formed within the Solar System. The non-volatile black crust of comet Halley, for example, as well as the extensive orangebrown streaks in the atmosphere of Jupiter, might consist largely of such polymers synthesized from HCN formed by photolysis of methane and ammonia, the color observed depending on the concentration of HCN involved. Laboratory studies of these ubiquitous compounds point to the presence of polyamidine structures synthesized directly from hydrogen cyanide. These would be converted by water to polypeptides which can be further hydrolyzed to α-amino acids. Black polymers and multimers with conjugated ladder structures derived from HCN could also be formed and might well be the source of the many nitrogen heterocycles, adenine included, observed after pyrolysis. The dark brown color arising from the impacts of comet P/Shoemaker-Levy 9 on Jupiter might therefore be mainly caused by the presence of HCN polymers, whether originally present, deposited by the impactor or synthesized directly from HCN. Spectroscopic detection of these predicted macromolecules and their hydrolytic and pyrolytic by-products would strengthen significantly the hypothesis that cyanide polymerization is a preferred pathway for prebiotic and extraterrestrial chemistry.

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