The smallest bimolecular mass action reaction networks admitting Andronov–Hopf bifurcation

We address the question of which small, bimolecular, mass action chemical reaction networks (CRNs) are capable of Andronov–Hopf bifurcation (from here on abbreviated to ‘Hopf bifurcation’). It is easily shown that any such network must have at least three species and at least four irreversible reactions, and one example of such a network with exactly three species and four reactions was previously known due to Wilhelm. In this paper, we develop both theory and computational tools to fully classify three-species, four-reaction, bimolecular CRNs, according to whether they admit or forbid Hopf bifurcation. We show that there are, up to a natural equivalence, 86 minimal networks which admit nondegenerate Hopf bifurcation. Amongst these, we are able to decide which admit supercritical and subcritical bifurcations. Indeed, there are 25 networks which admit both supercritical and subcritical bifurcations, and we can confirm that all 25 admit a nondegenerate Bautin bifurcation. A total of 31 networks can admit more than one nondegenerate periodic orbit. Moreover, 29 of these networks admit the coexistence of a stable equilibrium with a stable periodic orbit. Thus, fairly complex behaviours are not very rare in these small, bimolecular networks. Finally, we can use previously developed theory on the inheritance of dynamical behaviours in CRNs to predict the occurrence of Hopf bifurcation in larger networks which include the networks we find here as subnetworks in a natural sense

Tiny Alice by Edward Albee: A Production Record and Analysis with Emphasis on Dynamic Theatrical Symbolism

Man is distinguished from the beasts by his deliberate use of faculties of the mind. He has the ability to think, reason, and imagine at will. He is a being of supreme intelligence and creativity. Yet, because of his very powers of mentality, he is forced to face the pain of mentality. He must make decisions. He experiences frustration, anxiety, and mental torment. Physical man may completely give way to mental man, creating a world based upon imagination. In this circumstance, the life of illusion, man finds it impossible to adjust to the real world. He can only attempt to make reality a part of his illusion or make his illusions a part of his reality. It is this thesis which is developed in Edward Albee\u27s drama TINY ALICE. The presentation of TINY ALICE which is the basis of this project, was directed to exhibit the merging of the real with the illusionary. It was a project which included such technical problems as finding solutions to the difficulties involved in the personification of abstractions, and translating the subjective into the objective in language and action. It also demanded the implementation of directing techniques which required the manipulation of people and ideas toward the goal of achieving objective believability as characters and motivations on the physical stage. The three performances. of TINY ALICE which evidenced the results of the creative work on this project, were held in the Gray Campus Laboratory School Auditorium on the campus of St. Cloud State College, St. Cloud, Minnesota, on Thursday, Friday, and Saturday, April 13, 14, and 15, 1967. The facilities included a proscenium stage, extended five feet into the auditorium house. The seating capacity of the auditorium was 270 persons, although each performance necessitated the inclusion of additional seating. The project was undertaken solely by students, although it was advised by theatre staff members. It proceeded from a five hundred dollar working budget. From this allotment were built three stage settings plus the majority of the costumes. It also included funds for royalties, promotion, the rental of miscellaneous set items, and the rebuilding of major property units. This production of TINY ALICE was experimental in every respect. Because of the ambiguity, subjectivity, and heavy symbolism of the play, no single definite approach was dictated. Innovation and trial of new methods of staging and genera! production techniques was possible. Every aspect of production was prepared in this free spirit. TINY ALICE is a difficult drama to produce. It is filled with vaguery and ambiguity; yet, it contains an element of thought which continues long after the final performance. It is immodestly believed that TlNY ALICE required creative freedom, controlled and concentrated toward a goal of believability, and quality of production. Such a goal demanded the application of the many severe disciplines of this complex art form

Towards Understanding Spontaneous Speech: Word Accuracy vs. Concept Accuracy

In this paper we describe an approach to automatic evaluation of both the speech recognition and understanding capabilities of a spoken dialogue system for train time table information. We use word accuracy for recognition and concept accuracy for understanding performance judgement. Both measures are calculated by comparing these modules' output with a correct reference answer. We report evaluation results for a spontaneous speech corpus with about 10000 utterances. We observed a nearly linear relationship between word accuracy and concept accuracy.Comment: 4 pages PS, Latex2e source importing 2 eps figures, uses icslp.cls, caption.sty, psfig.sty; to appear in the Proceedings of the Fourth International Conference on Spoken Language Processing (ICSLP 96

The smallest bimolecular mass-action system with a vertical Andronov–Hopf bifurcation

We present a three-dimensional differential equation, which robustly displays a degenerate Andronov–Hopf bifurcation of infinite codimension, leading to a center, i.e., an invariant two-dimensional surface that is filled with periodic orbits surrounding an equilibrium. The system arises from a three-species bimolecular chemical reaction network consisting of four reactions. In fact, it is the only such mass-action system that admits a center via an Andronov–Hopf bifurcation

Lambda Polarization in Polarized Proton-Proton Collisions at RHIC

We discuss Lambda polarization in semi-inclusive proton-proton collisions, with one of the protons longitudinally polarized. The hyperfine interaction responsible for the $\Delta$-$N$ and $\Sigma$-$\Lambda$ mass splittings gives rise to flavor asymmetric fragmentation functions and to sizable polarized non-strange fragmentation functions. We predict large positive Lambda polarization in polarized proton-proton collisions at large rapidities of the produced Lambda, while other models, based on SU(3) flavor symmetric fragmentation functions, predict zero or negative Lambda polarization. The effect of $\Sigma^0$ and $\Sigma^*$ decays is also discussed. Forthcoming experiments at RHIC will be able to differentiate between these predictions.Comment: 18 pages, 5 figure

Production mechanisms and single-spin asymmetry for kaons in high energy hadron-hadron collisions

Direct consequences on kaon production of the picture proposed in a recent Letter and subsequent publications are discussed. Further evidence supporting the proposed picture is obtained. Comparison with the data for the inclusive cross sections in unpolarized reactions is made. Quantitative results for the left-right asymmetry in single-spin processes are presented.Comment: 10 pages, 2 Postscript figure

Single spin asymmetries in QCD

Measurements of single transverse spin asymmetries in high energy inclusive processes have always shown unexpected and challenging results. Several cases are considered and discussed within a QCD approach which couples perturbative dynamics to new non perturbative partonic information; the aim is that of developing a consistent phenomenological description of these unusual single spin phenomena, based on a generalized QCD factorization scheme.Comment: 14 pages, lectures delivered at School on "Symmetries and Spin", Praha-SPIN-2001, Prague, July 15 - July 28, 200

How Much Is Winning a Matter of Luck? A Comparison of 3 × 3 and 5v5 Basketball

Background: The comparison of team sports based on luck has a long tradition and remains unsolved. A contrast between the new Olympic format three-on-three (3 × 3) and five-on-five (5v5) forms of basketball has never been analyzed and provides a comparison within the same form of sports. Methods: We developed a new method to calculate performance indicators for each team and invented the Relative Score Difference Index, a new competitive balance indicator that allows the comparison of luck in the two basketball forms for both men and women. We collected game-level data about 3 × 3 and 5v5 from the World Cups held between 2010 and 2019 (N = 666). Luck was defined as the difference between the expected and the actual outcomes of games. Using the basketball World Cup data, we applied the Surprise Index, ran probit regression models, and compared the basketball forms on the goodness-of-fit of the models. Results: As we predicted, there are differential effects of luck between game formats and sex, such that the 3 × 3 form depends more on luck and women’s games are less influenced by luck when compared to men’s games. Conclusion: Coaches may better understand the differences between the two forms and sexes regarding luck if they are aware that the 3 × 3 and men’s competitions are usually more influenced by luck. The findings provide a leverage point for testing new performances and competition balance indicators and will acknowledge the number of games we enjoy watching