It is shown that a fundamental question of revealed preference theory, namely whether the weak axiom of revealed preference (WARP) implies the strong axiom of revealed preference (SARP), can be reduced to a Hamiltonian cycle problem: A set of bundles allows a preference cycle of irreducible length if and only if the convex monotonic hull of these bundles admits a Hamiltonian cycle. This leads to a new proof to show that preference cycles can be of arbitrary length for more than (...) two but not for two commodities. For this, it is shown that a set of bundles satisfying the given condition exists if and only if the dimension of the commodity space is at least three. Preference cycles can be constructed by embedding a cyclic $(L-1)$ -polytope into a facet of a convex monotonic hull in $L$ -space, because cyclic polytopes always admit Hamiltonian cycles. An immediate corollary is that WARP only implies SARP for two commodities. The proof is intuitively appealing as this gives a geometric interpretation of preference cycles. (shrink)

Localizing content in neural networks provides a bridge to understanding the way in which the brain stores and processes information. In this paper, I propose the existence of polytopes in the state space of the hidden layer of feedforward neural networks as vehicles of content. I analyze these geometrical structures from an information-theoretic point of view, invoking mutual information to help define the content stored within them. I establish how this proposal addresses the problem of misclassification and provide a (...) novel solution to the disjunction problem, which hinges on the precise nature of the causal-informational framework for content advocated herein. (shrink)

Let be n events in a probability space, and suppose that we have only partial information about the distribution: The probabilites of the events themselves, and their pair intersections. With this partial information we cannot, usually, deternine the probability of an event B in the algebra generated by the 's, but we can obtain lower and upper bounds. This is done by a linear program related to the correlation polytope c(n), a structure introduced in [3], [4]. In the first part (...) of the paper I demonstrate how laws of large numbers (for sequences of events which are not necessarily independent) can be proved, using only the duality theorem of linear programming. These include the weak law of large numbers (necessary and sufficient condition) and various sufficient conditions for strong laws. The connection between these laws and the facet structure of the correlation polytope is established. In the second part of the paper I consider a more general case. Assume that our information consists of the values of the probabilities of all intersections of the 's up to size k, k < n. The techniques of linear programming lead naturally to an application of the theory of polynomial approximation in estimating the size of various events. In particular, I prove an approximate version of the central limit theorem. (shrink)

Probably many people have cyclic preferences: they prefer A to B, B to C and C to A for some objects of choice A, B and C. Recent work has resurrected the objection to cyclic preference that agents possessing them are open to exploitation by means of ‘money pumps’. The paper briefly reviews this work and proposes a general approach to problems of sequential choice that makes cyclic preference immune to exploitation by means of these new mechanisms.

Cyclic mechanic is intended as a suitable generalization both of quantum mechanics and general relativity apt to unify them. It is founded on a few principles, which can be enumerated approximately as follows: 1. Actual infinity or the universe can be considered as a physical and experimentally verifiable entity. It allows of mechanical motion to exist. 2. A new law of conservation has to be involved to generalize and comprise the separate laws of conservation of classical and relativistic mechanics, (...) and especially that of conservation of energy: This is the conservation of action or information. 3. Time is not a uniformly flowing time in general. It can have some speed, acceleration, more than one dimension, to be discrete. 4. The following principle of cyclicity: The universe returns in any point of it. The return can be only kinematic, i.e. per a unit of energy (or mass), and thermodynamic, i.e. considering the universe as a thermodynamic whole. 5. The kinematic return, which is per a unit of energy (or mass), is the counterpart of conservation of energy, which can be interpreted as the particular case of conservation of action “per a unit of time”. The kinematic return per a unit of energy (or mass) can be interpreted in turn as another particular law of conservation in the framework of conservation of action (or information), namely conservation of wave period (or time). These two counterpart laws of conservation correspond exactly to the particle “half” and to the wave “half” of wave-particle duality. 6. The principle of quantum invariance is introduced. It means that all physical laws have to be invariant to discrete and continuous (smooth) morphisms (motions) or mathematically, to the axiom of choice. The list is not intended to be exhausted or disjunctive, but only to give an introductory idea. (shrink)

We introduce a path-based cyclic proof system for first-order $\mu $-calculus, the extension of first-order logic by second-order quantifiers for least and greatest fixed points of definable monotone functions. We prove soundness of the system and demonstrate it to be as expressive as the known trace-based cyclic systems of Dam and Sprenger. Furthermore, we establish cut-free completeness of our system for the fragment corresponding to the modal $\mu $-calculus.

A connected graph is called Hamilton-connected if there exists a Hamiltonian path between any pair of its vertices. Determining whether a graph is Hamilton-connected is an NP-complete problem. Hamiltonian and Hamilton-connected graphs have diverse applications in computer science and electrical engineering. The detour index of a graph is defined to be the sum of lengths of detours between all the unordered pairs of vertices. The detour index has diverse applications in chemistry. Computing the detour index for a graph is also (...) an NP-complete problem. In this paper, we study the Hamilton-connectivity of convex polytopes. We construct three infinite families of convex polytopes and show that they are Hamilton-connected. An infinite family of non-Hamilton-connected convex polytopes is also constructed, which, in turn, shows that not all convex polytopes are Hamilton-connected. By using Hamilton connectivity of these families of graphs, we compute exact analytical formulas of their detour index. (shrink)

This paper proposes an architecture for the mapping between syntax and phonology — in particular, that aspect of phonology that determines ordering. In Fox and Pesetsky (in prep.), we will argue that this architecture, when combined with a general theory of syntactic domains ("phases"), provides a new understanding of a variety of phenomena that have received diverse accounts in the literature. This shorter paper focuses on two processes, both drawn from Scandinavian: the familiar process of Object Shift and the less (...) well-known process of Quantifier Movement. We will argue that constraints on these operations can be seen as instances of the same property of grammar that explains the fact that movement is local and successive cyclic. We begin by sketching a model in which locality and successive cyclicity are consequences of the architecture that we propose, rather than specific facts about movement itself. We next present our proposal in somewhat greater detail, and show how it can account for a wide range of apparent limitations on movement — in particular, superficially contradictory restrictions on Object Shift and Quantifier Movement. The restrictions on Object Shift include those grouped under the rubric of Holmberg's Generalization, which Quantifier Movement does not seem to obey. We will argue that Quantifier Movement instead obeys a near mirror-image of Holmberg's Generalization (an "Inverse Holmberg Effect"), but that both Holmberg's Generalization and its mirror image are expected if our proposed architecture is correct. (shrink)

In 1976, the Genetics Society of America published a document entitled “Resolution of Genetics, Race, and Intelligence.” This document laid out the Society’s position in the IQ controversy, particularly that on scientific and ethical questions involving the genetics of intellectual differences between human populations. Since the GSA was the largest scientific society of geneticists in the world, many expected the document to be of central importance in settling the controversy. Unfortunately, the Resolution had surprisingly little influence on the discussion. In (...) 1979, William Provine analyzed the possible factors that decreased the impact of the Resolution, among them scientists’ limited understanding of the relationship between science and ethics. Through the analysis of unpublished versions of the Resolution and exchanges between GSA members, I will suggest that the limited impact of the statement likely depended on a shift in the aims of the GSA due to the controversies that surrounded the preparation of the document. Indeed, the demands of the membership made it progressively more impartial in both scientific and political terms, decreasing its potential significance for a wider audience. Notably, the troubled history of the Resolution raises the question of what can make effective or ineffective the communication between scientists and the public—a question with resonance in past and present discussions on topics of social importance. (shrink)

Cyclic nucleotides can regulate the sensitivity of retinal rods to light through phosducin. The phosphorylation state of phosducin determines the amount of G available for activation by Rho*. Phosducin phosphorylation is regulated by cyclic nucleotides through their activation of cAMP-dependent protein kinase. The regulation of phosphodiesterase activity by the noncatalytic cGMP binding sites as well as Ca2+/calmodulin dependent regulation of cGMP binding to the cation channel are also discussed.

More than a decade of experimental research confirms that external linguistic information provided in the form of word labels can induce a "mutually exclusive" bias against double naming and lead children to infer the name of novel objects and parts. Linguistic labels have also been shown to encourage more sophisticated reasoning, particularly with respect to superordinate and atypical object categorization. By contrast, however, the inverse possibility that the linguistic labeling of basic-level objects may also developmentally support the kind of "phonological (...) reorganization" observed within infant speech categorization has yet to be theoretically isolated and experimentally explored. Yet the dynamic of relying on labels to inform object categorization clearly presupposes that potential word labels themselves have already been classified into language-specific phonemic categories. However, a two-staged strategy of first relying on basic-level object categories to refine speech categorization, and then exploiting such learned speech categories to fine tune object categorization would reveal a cyclically opportunistic learner. A uniform assumption of a one to one pairing between words and objects allows bootstrapping not only from language to object classification, but also from basic object categorization to phonemic speech classification. (shrink)

In this paper we characterize the MV-algebras containing as subalgebras Post algebras of finitely many orders. For this we study cyclic elements in MV-algebras which are the generators of the fundamental chain of the Post algebras.

Guns, slug-throwing weapons, have evolved as humans have increased their grasp of the mechanical arts. In the near future, however, it seems likely that soldiers' rifles operating at punishing cyclic rates of fire face the limits of physics and materials science— heat and speed will cost accuracy and distance. This article considers not only the near future of the personal weapon carried by soldiers in battlespace but also the rifle's evolution as an index of alterations in 20th-and 21st-century war (...) fighting. The arc traced by multiple-fire weapons, from the Gatling to the laser rifle, is a narrative of humans, machinery, and their cocreative symbiotic relationship. This article begins by examining some current examples of late-generation rifles and their imagined futures, continues by pursuing the linkages between guns and soldiers, and finally asks what new guns will mean for soldiers being born now. (shrink)

It is well known that in Sluicing constructions wh-dependencies can cross certain projections that are otherwise barriers to movement (Ross (1969), Chomsky (1972)). This fact would follow under the assumption that the relevant barriers are somehow deactivated when phonologically deleted ('island repair'). The problem, however, is that another form of phonological deletion (VP Ellipsis, VPE) seems to be impossible in certain contexts where Sluicing allows for island repair (Chung et al. (1995), Merchant (1999)).

The jaw movements of speech are most probably derived from jaw movements associated with vocalisation. Cyclicity does not argue strongly for derivation from a cyclic pattern, because it arises readily in any system with feedback control. The appearance of regular repetition as a part of ritualisation of a display may have been important.

This paper proposes an architecture for the mapping between syntax and phonology — in particular, that aspect of phonology that determines ordering. In Fox and Pesetsky (in prep.), we will argue that this architecture, when combined with a general theory of syntactic domains ("phases"), provides a new understanding of a variety of phenomena that have received diverse accounts in the literature. This shorter paper focuses on two processes, both drawn from Scandinavian: the familiar process of Object Shift and the less (...) well-known process of Quantifier Movement. We will argue that constraints on these operations can be seen as instances of the same property of grammar that explains the fact that movement is local and successive cyclic. We begin by sketching a model in which locality and successive cyclicity are consequences of the architecture that we propose, rather than specific facts about movement itself. We next present our proposal in somewhat greater detail, and show how it can account for a wide range of apparent limitations on movement — in particular, superficially contradictory restrictions on Object Shift and Quantifier Movement. The restrictions on Object Shift include those grouped under the rubric of Holmberg's Generalization, which Quantifier Movement does not seem to obey. We will argue that Quantifier Movement instead obeys a near mirror-image of Holmberg's Generalization (an "Inverse Holmberg Effect"), but that both Holmberg's Generalization and its mirror image are expected if our proposed architecture is correct. (shrink)

Recursive linear structural equation models can be represented by directed acyclic graphs. When represented in this way, they satisfy the Markov Condition. Hence it is possible to use the graphical d-separation to determine what conditional independence relations are entailed by a given linear structural equation model. I prove in this paper that it is also possible to use the graphical d-separation applied to a cyclic graph to determine what conditional independence relations are entailed to hold by a given non-recursive (...) linear structural equation model. I also give a causal intepretation to the linear coefficients in a non- recursive structural equation models, and explore the relationships between cyclic graphs and undirected graphs, directed acyclic graphs with latent variables, and chain independence graphs. (shrink)

An example shows that 'pairwise preferences' (certain hypothetical choices) can cycle even when rational. General considerations entail that preferences tout court (certain relations of actual valuations) cannot cycle. A world-bayesian theory is explained that accommodates these two kinds of preference, and a theory for rational actions that would have them maximize and be objects of ratifiable choices. It is observed that choices can be unratifiable either because of troublesome credences or because of troublesome preferences. An appendix comments on a third (...) way in which efforts to maximize can be frustrated. (shrink)

The mechanistic perspective has dominated biological disciplines such as biochemistry, physiology, cell and molecular biology, and neuroscience, especially during the 20th century. The primary strategy is reductionist: organisms are to be decomposed into component parts and operations at multiple levels. Researchers adopting this perspective have generated an enormous body of information about the mechanisms of life at scales ranging from the whole organism down to genetic and other molecular operations.

The idea that certain troubadours may have anthologized their own songs into compilations and even books has tantalized scholars ever since Gustav Gröber published his bold monograph on the question in 1877. Gröber's hypothesis about the prevalence of such compilations and books is now often put in doubt. It remains plausible, though uncertain, that several troubadours did put together collections of their own works — among them, Peire Vidal , Ponç de la Guardia , and Cerveri de Girona . There (...) is, however, one highly convincing case of a troubadour who acted as his own anthologist, and that is Guiraut Riquier. (shrink)

Our synthetic review of the relevant and related literatures on the ethics and effects of using AI in education reveals five qualitatively distinct and interrelated divides associated with access, representation, algorithms, interpretations, and citizenship. We open our analysis by probing the ethical effects of algorithms and how teams of humans can plan for and mitigate bias when using AI tools and techniques to model and inform instructional decisions and predict learning outcomes. We then analyze the upstream divides that feed into (...) and fuel the algorithmic divide, first investigating access and then representation. After that, we analyze the divides that are downstream of the algorithmic divide associated with interpretation and citizenship. At present, lacking ongoing reflection and action by learners, educators, educational leaders, designers, scholars, and policymakers, the five divides collectively create a vicious cycle and perpetuate structural biases in teaching and learning. However, increasing human responsibility and control over these divides can create a virtuous cycle that improves diversity, equity, and inclusion in education. We conclude the article by looking forward and discussing ways to increase educational opportunity and effectiveness for all by mitigating bias through a cycle of progressive improvement. (shrink)

Relativistic models of an expanding universe followed by contraction, or a big bang followed by a big crunch, were first proposed by A. Friedmann in 1922 and nine years later by A. Einstein. In the period ca. 1922–1960, the more speculative idea of a large and possibly infinite number of cycles was discussed by R. Tolman in particular. To some cosmologists, the idea was philosophically appealing because it seemed to justify an eternal yet dynamic universe without an absolute beginning in (...) time. During the 1950s models of this kind, sometimes known as Phoenix models, were investigated by a few cosmologists of whom the most important were A. Dauvillier, W. Bonnor, and H. Zanstra. (shrink)

Many models of evolution are implicitly causal processes. Features such as causal feedback between evolutionary variables and evolutionary processes acting at multiple levels, though, mean that conventional causal models miss important phenomena. We develop here a general theoretical framework for analyzing evolutionary processes drawing on recent approaches to causal modeling developed in the machine-learning literature, which have extended Pearls do-calculus to incorporate cyclic causal interactions and multilevel causation. We also develop information-theoretic notions necessary to analyze causal information dynamics in (...) our framework, introducing a causal generalization of the Partial Information Decomposition framework. We show how our causal framework helps to clarify conceptual issues in the contexts of complex trait analysis and cancer genetics, including assigning variation in an observed trait to genetic, epigenetic and environmental sources in the presence of epigenetic and environmental feedback processes, and variation in fitness to mutation processes in cancer using a multilevel causal model respectively, as well as relating causally-induced to observed variation in these variables via information theoretic bounds. In the process, we introduce a general class of multilevel causal evolutionary processes which connect evolutionary processes at multiple levels via coarse-graining relationships. Further, we show how a range of fitness models can be formulated in our framework, as well as a causal analog of Prices equation, clarifying the relationships between realized/probabilistic fitness and direct/indirect selection. Finally, we consider the potential relevance of our framework to foundational issues in biology and evolution, including supervenience, multilevel selection and individuality. Particularly, we argue that our class of multilevel causal evolutionary processes, in conjunction with a minimum description length principle, provides a conceptual framework in which identification of multiple levels of selection may be reduced to a model selection problem. (shrink)

In the post-Soviet context, various cyclical models of recurrent Russian “Times of Troubles” have become increasingly popular. This perspective emerged first in Soviet dissident circles, who used it as a means to expose as mistaken the Soviet belief in continual historical progress on Russian soil. In post-Soviet Russia this critical approach has been continued by members of the “Akhezier circle,” the economist Egor Gaidar, and others. Meanwhile it was given an affirmative, conservative reinterpretation by Aleksandr Panarin, according to whom Russia (...) has always managed to overcome its phases of devastating Westernization and state collapse. This idea of Russian history has become influential; even Vladimir Putin has talked about Russia as a strong state able to survive various “Times of Troubles” from the early seventeenth century to the early post-Soviet period. It also figures prominently among members of the neoconservative Izborsk Club. This article analyzes different conceptions of Russian history as cyclical and their prominent place in the prevailing civilizational discourse of post-Soviet Russia. By means of postcolonial perspectives, this discourse is seen on the one hand as an attempt to question and reject Western hegemony, attempts that on the other hand nevertheless seem unable to liberate themselves from a normative dependence on the West. (shrink)

Women’s preferences for several male traits, including voices, change over the menstrual cycle, but the proximate causes of these changes are unknown. This paper explores relationships between levels of estradiol, progesterone, luteinizing hormone, follicle stimulating hormone, prolactin, and testosterone (estimated using menstrual cycle information) and women’s preferences for male vocal masculinity in normally cycling and hormonally contracepting heterosexual females. Preferences for vocal masculinity decreased with predicted progesterone levels and increased with predicted prolactin levels in normally cycling—but not hormonally contracepting—women. Adaptive (...) explanations for menstrual variation in women’s preferences for masculine traits are discussed and evaluated in light of these findings. (shrink)

Bermúdez describes the extensionality principle as being “almost unquestioned.” This claim might come as a surprise to philosophers who work on agency and ethics. In Kantian deontological ethics and in Platonic or Aristotelian virtue ethics, our preferences for outcomes can be rationally affected by how those outcomes are framed in terms of maxims and character traits.

The dynamics inherent to the life activity of all living systems presents itself in the form of regular patterns viewed by the observer as taking place in an extended timeline. Routines, rituals and celebrations, each in their own way, are defined by the typical cyclical behavioural patterns exhibited by individuals embedded in specific semiospheres. The particular nature of these semiospheres will determine the distinct patterns of behaviour to be adopted in different life contexts so that existential functions are fulfilled. The (...) restricted and protected family circle normally provides the initial learning environment where the definition of the individual’s Umwelt (von Uexküll 1909, 1934; Ferreira, Biosemiotics 3(1):107–130, 2010, 2011) his/her meaningful world, starts to take shape. This learning process comprehends the progressive identification of distinct physical entities, the development of basic patterns of physical and social behaviour- the incorporation of basic routines and the assignment of meaning to particular events. (shrink)

This paper is concerned with techniques for identifying simple and quantified lattice points in 2SAT polytopes. 2SAT polytopes generalize the polyhedra corresponding to Boolean 2SAT formulas, Vertex-Packing and Network flow problems; they find wide application in the domains of Program verification and State-Space search . Our techniques are based on the symbolic elimination strategy called the Fourier-Motzkin elimination procedure and thus have the advantages of being extremely simple and incremental. We also provide a characterization of a 2SAT polytope (...) in terms of its extreme points and derive some interesting hardness results for associated optimization problems. Finally, we provide a brief discussion on the maximum size of a subdeterminant of the linear system representing a 2SAT polytope; this parameter plays a vital role in deriving analytical bounds on the size of the search space for checking whether the polyhedron includes a lattice point. (shrink)

Our proposal is concerned with the relation between an aspect of phonology (linearization) and syntax.1 In the picture that we had in mind, the syntax is autonomous — "it does what it does" — but sometimes the result maps to an unusable phonological representation. In this sense, linearization acts logically as a filter on derivations. We know of no evidence that the syntax can predict which syntactic objects will be usable by the phonology, and we know of no clear evidence (...) that the phonology communicates this information to the syntax. In this sense, our proposal fits squarely into the tradition that Svenonius characterizes as the "mainstream".2 We thus attempted to identify certain deviant configurations that are not plausibly excluded for syntax-internal reasons, but are filtered out in the linearization process. (shrink)

• Why does wh-movement proceed through the left edge of CP? • Logic of a common answer: Things would go wrong otherwise.

Nikolay Kondratieff is known primarily for his theory of long cycles. However, it is worth recalling that he was among the first who started to investigate the nature of different economic cycles and their systematic interaction. Actually the primary classification of cycles into short, medium and long belongs to Kondratieff.

This paper considers the Hellenistic poets' attitude towards pre-Trojan war myths; in particular, it examines the Hellenistic reception of six narratives from the Cypria: the marriage of Peleus and Thetis; the duel between the Dioscuri and Idas and Lynceus; the story of Telephus; the love affair between Achilles and Deidameia; the abandonment of Philoctetes on Lemnos; and the involvement of the Achaeans with the priest Anius and his daughters, the Oenotropae. Furthermore, it is argued that the reception of these stories (...) from the Cypria may be seen as a metaliterary comment upon epic poetry, firstly because narratives from the Epic Cycle are adapted to fit epic subgenres, such as the elegy, the epyllion, the hymn and the idyll, and secondly because the neoteric versions of these narratives put particular emphasis on certain motifs, types of hero and narrative techniques which are typical of Hellenistic poetics. (shrink)