scholarly journals On the distribution of winners’ scores in a round-robin tournament

Author(s):  
Yaakov Malinovsky

In a classical chess round-robin tournament, each of $n$ players wins, draws, or loses a game against each of the other $n-1$ players. A win rewards a player with 1 points, a draw with 1/2 point, and a loss with 0 points. We are interested in the distribution of the scores associated with ranks of $n$ players after ${{n \choose 2}}$ games, that is, the distribution of the maximal score, second maximum, and so on. The exact distribution for a general $n$ seems impossible to obtain; we obtain a limit distribution.

Author(s):  
Guillermo A. Durán ◽  
Mario Guajardo ◽  
Agustina F. López ◽  
Javier Marenco ◽  
Gonzalo A. Zamorano

The first division clubs in Argentinean professional football maintain teams in each of six youth leagues, classed by age as major divisions (Under-20, Under-18, Under-17) and minor divisions (Under-16, Under-15, Under-14). Regular season play in these leagues typically follows a single round-robin format; the minor divisions play the same schedule as the majors but with the home-away status of the matches reversed. This setup can give rise to very significant differences in travel distances between the major and minor division teams of a given club, which is a frustrating situation for club officials, coaches, and players alike but almost impossible to avoid with manual season scheduling techniques. Nor are these methods able to take into account any number of other criteria that go into the design of a satisfactory match calendar. This paper reports on models developed using mathematical programming to simultaneously schedule multiple leagues while also meeting a series of other desirable conditions. The central criterion is a better balance in the travel distances of the various teams, pursued through the application of two alternative solution approaches: one based on regional team clusters and the other on explicit analysis of actual distances between the teams’ home venues. The solutions generated by these approaches have been used by the organizers of the Argentinean youth leagues to draw up their season schedules since 2018, which has resulted in a series of benefits for all stakeholders.


Author(s):  
Marc Scibetta ◽  
Eberhard Altstadt ◽  
Rogelio Herna´ndez Callejas ◽  
Bong-Sang Lee ◽  
Naoki Miura ◽  
...  

There is strong interest from the nuclear industry to use the precracked Charpy single-edge notched bend, SE(B), specimen (PCVN) to enable determination of the reference temperature, T0, with reactor pressure vessel surveillance specimens. Unfortunately, for many different ferritic steels, tests with the PCVN specimen (10×10×55 mm) have resulted in T0 temperatures up to 25°C lower than T0 values obtained using data from compact, C(T), specimens. This difference in T0 reference temperature has often been designated a specimen bias effect, and the primary focus for explaining this effect is loss of constraint in the PCVN specimen. The International Atomic Energy Agency has developed a three-part coordinated research project (CRP) to evaluate various issues associated with the fracture toughness Master Curve for application to light-water reactor pressure vessels. One part of the CRP is focused on the issue of test specimen geometry effects, with emphasis on the PCVN bias. This topic area was organized in two parts, an experimental part and an analytical part with a view towards each part complementing the other. Within the analytical part, elastic plastic finite element methods are extensively used in order to access local stress and strain information that is the basic ingredient for most of the micromodels of cleavage fracture developed to date. In the framework of the international qualification and acceptance of such a tool for actual loss of constraint prediction, the validation of such tool is of prime importance. Therefore, a round robin exercise has been proposed and performed by ten laboratories from nine different countries. The round robin focuses on the modeling of realistic three-dimensional geometries containing shallow and deep crack. This round robin has been useful to qualify different finite element codes and to identify possible errors in the input file. The round robin demonstrates that errors in the input file can be easily introduced. Some remaining differences cannot be attributed to one particular finite element code or to actual errors. Those differences are attributed to the so called “user effect” which can only be reduced through in depth discussion and deep understanding of each finite element code. Independently of the used code and of relatively small user effect differences, it is found that shallow crack specimens are more sensitive to loss of constraint than deep crack specimens for a given specimen size. The difference in terms of reference temperature between the two geometries is evaluated to be about 40 °C. For a deep crack, loss of constraint is identified to appear at M values around 200. This value is larger than the one specified in current standard (M = 30). Increasing the M value to 200 will jeopardize the use of PCVN for the nuclear industry on the other hand bias introduced by M value of 30 is acceptable.


2017 ◽  
Author(s):  
Andysah Putera Utama Siahaan

Task scheduling is needed to maintain every process that comes with a processor in parallel processing. In several conditions, not every algorithm works better on the significant problem. Sometimes FCFS algorithm is better than the other in short burst time while Round Robin is better for multiple processes in every single time. However, it cannot be predicted what process will come after. Average Waiting Time is a standard measure for giving credit to the scheduling algorithm. Several techniques have been applied to maintain the process to make the CPU performance in normal. The objective of this paper is to compare three algorithms, FCFS, SJF, and Round Robin. The target is to know which algorithm is more suitable for the certain process.


Author(s):  
Rupert Freeman ◽  
Evi Micha ◽  
Nisarg Shah

We introduce a new model for two-sided matching which allows us to borrow popular fairness notions from the fair division literature such as envy-freeness up to one good and maximin share guarantee. In our model, each agent is matched to multiple agents on the other side over whom she has additive preferences. We demand fairness for each side separately, giving rise to notions such as double envy-freeness up to one match (DEF1) and double maximin share guarantee (DMMS). We show that (a slight strengthening of) DEF1 cannot always be achieved, but in the special case where both sides have identical preferences, the round-robin algorithm with a carefully designed agent ordering achieves it. In contrast, DMMS cannot be achieved even when both sides have identical preferences.


1988 ◽  
Vol 62 (03) ◽  
pp. 411-419 ◽  
Author(s):  
Colin W. Stearn

Stromatoporoids are the principal framebuilding organisms in the patch reef that is part of the reservoir of the Normandville field. The reef is 10 m thick and 1.5 km2in area and demonstrates that stromatoporoids retained their ability to build reefal edifices into Famennian time despite the biotic crisis at the close of Frasnian time. The fauna is dominated by labechiids but includes three non-labechiid species. The most abundant species isStylostroma sinense(Dong) butLabechia palliseriStearn is also common. Both these species are highly variable and are described in terms of multiple phases that occur in a single skeleton. The other species described areClathrostromacf.C. jukkenseYavorsky,Gerronostromasp. (a columnar species), andStromatoporasp. The fauna belongs in Famennian/Strunian assemblage 2 as defined by Stearn et al. (1988).


1967 ◽  
Vol 28 ◽  
pp. 207-244
Author(s):  
R. P. Kraft

(Ed. note:Encouraged by the success of the more informal approach in Christy's presentation, we tried an even more extreme experiment in this session, I-D. In essence, Kraft held the floor continuously all morning, and for the hour and a half afternoon session, serving as a combined Summary-Introductory speaker and a marathon-moderator of a running discussion on the line spectrum of cepheids. There was almost continuous interruption of his presentation; and most points raised from the floor were followed through in detail, no matter how digressive to the main presentation. This approach turned out to be much too extreme. It is wearing on the speaker, and the other members of the symposium feel more like an audience and less like participants in a dissective discussion. Because Kraft presented a compendious collection of empirical information, and, based on it, an exceedingly novel series of suggestions on the cepheid problem, these defects were probably aggravated by the first and alleviated by the second. I am much indebted to Kraft for working with me on a preliminary editing, to try to delete the side-excursions and to retain coherence about the main points. As usual, however, all responsibility for defects in final editing is wholly my own.)


1967 ◽  
Vol 28 ◽  
pp. 177-206
Author(s):  
J. B. Oke ◽  
C. A. Whitney

Pecker:The topic to be considered today is the continuous spectrum of certain stars, whose variability we attribute to a pulsation of some part of their structure. Obviously, this continuous spectrum provides a test of the pulsation theory to the extent that the continuum is completely and accurately observed and that we can analyse it to infer the structure of the star producing it. The continuum is one of the two possible spectral observations; the other is the line spectrum. It is obvious that from studies of the continuum alone, we obtain no direct information on the velocity fields in the star. We obtain information only on the thermodynamic structure of the photospheric layers of these stars–the photospheric layers being defined as those from which the observed continuum directly arises. So the problems arising in a study of the continuum are of two general kinds: completeness of observation, and adequacy of diagnostic interpretation. I will make a few comments on these, then turn the meeting over to Oke and Whitney.


1966 ◽  
Vol 24 ◽  
pp. 337
Author(s):  
W. Iwanowska

A new 24-inch/36-inch//3 Schmidt telescope, made by C. Zeiss, Jena, has been installed since 30 August 1962, at the N. Copernicus University Observatory in Toruń. It is equipped with two objective prisms, used separately, one of crown the other of flint glass, each of 5° refracting angle, giving dispersions of 560Å/mm and 250Å/ mm respectively.


2020 ◽  
Vol 43 ◽  
Author(s):  
Philip Pettit

Abstract Michael Tomasello explains the human sense of obligation by the role it plays in negotiating practices of acting jointly and the commitments they underwrite. He draws in his work on two models of joint action, one from Michael Bratman, the other from Margaret Gilbert. But Bratman's makes the explanation too difficult to succeed, and Gilbert's makes it too easy.


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