It was shown by Cholak, Jockusch, and Slaman that every computable 2-coloring of pairs admits an infinite low₂ homogeneous set H. We answer a question of the same authors by showing that H may be chosen to satisfy in addition $C\,\not \leqslant _T \,H$, where C is a given noncomputable set. This is shown by analyzing a new and simplified proof of Seetapun's cone avoidance theorem for Ramsey's theorem. We then extend the result to show that every computable 2-coloring of (...) pairs admits a pair of low₂ infinite homogeneous sets whose degrees form a minimal pair. (shrink)

We study the effective and proof-theoretic content of the polarized Ramsey’s theorem, a variant of Ramsey’s theorem obtained by relaxing the definition of homogeneous set. Our investigation yields a new characterization of Ramsey’s theorem in all exponents, and produces several combinatorial principles which, modulo bounding for ${\Sigma^0_2}$ formulas, lie (possibly not strictly) between Ramsey’s theorem for pairs and the stable Ramsey’s theorem for pairs.

The stable Ramsey's theorem for pairs has been the subject of numerous investigations in mathematical logic. We introduce a weaker form of it by restricting from the class of all stable colorings to subclasses of it that are nonnull in a certain effective measure-theoretic sense. We show that the sets that can compute infinite homogeneous sets for nonnull many computable stable colorings and the sets that can compute infinite homogeneous sets for all computable stable colorings agree below $\emptyset'$ but not (...) in general. We also answer the analogs of two well-known questions about the stable Ramsey's theorem by showing that our weaker principle does not imply COH or WKL 0 in the context of reverse mathematics. (shrink)

We present an overview of the topics in the title and of some of the key results pertaining to them. These have historically been topics of interest in computability theory and continue to be a rich source of problems and ideas. In particular, we draw attention to the links and connections between these topics and explore their significance to modern research in the field.

Sorites is an ancient piece of paradoxical reasoning pertaining to sets with the following properties: elements of the set are mapped into some set of “attributes”; if an element has a given attribute then so are the elements in some vicinity of this element; and such vicinities can be arranged into pairwise overlapping finite chains connecting two elements with different attributes. Obviously, if Superveneince is assumed, then Tolerance implies lack of Connectedness, and Connectedness implies lack of Tolerance. Using a very (...) general but precise definition of “vicinity”, Dzhafarov & Dzhafarov offered two formalizations of these mutual contrapositions. Mathematically, the formalizations are equally valid, but in this paper, we offer a different basis by which to compare them. Namely, we show that the formalizations have different proof-theoretic strengths when measured in the framework of reverse mathematics: the formalization of is provable in$RC{A_0}$, while the formalization of is equivalent to$AC{A_0}$over$RC{A_0}$. Thus, in a certain precise sense, the approach of is more constructive than that of. (shrink)

Journal of Mathematical Logic, Volume 22, Issue 03, December 2022. Hirschfeldt and Jockusch (2016) introduced a two-player game in which winning strategies for one or the other player precisely correspond to implications and non-implications between [math] principles over [math]-models of [math]. They also introduced a version of this game that similarly captures provability over [math]. We generalize and extend this game-theoretic framework to other formal systems, and establish a certain compactness result that shows that if an implication [math] between two (...) principles holds, then there exists a winning strategy that achieves victory in a number of moves bounded by a number independent of the specific run of the game. This compactness result generalizes an old proof-theoretic fact noted by H. Wang (1981), and has applications to the reverse mathematics of combinatorial principles. We also demonstrate how this framework leads to a new kind of analysis of the logical strength of mathematical problems that refines both that of reverse mathematics and that of computability-theoretic notions such as Weihrauch reducibility, allowing for a kind of fine-structural comparison between [math] principles that has both computability-theoretic and proof-theoretic aspects, and can help us distinguish between these, for example by showing that a certain use of a principle in a proof is “purely proof-theoretic”, as opposed to relying on its computability-theoretic strength. We give examples of this analysis to a number of principles at the level of [math], uncovering new differences between their logical strengths. (shrink)

In many simple integral domains, such as Z or Z[i], there is a straightforward procedure to determine if an element is prime by simply reducing to a direct check of finitely many potential divisors. Despite the fact that such a naive approach does not immediately translate to integral domains like Z[x] or the ring of integers in an algebraic number field, there still exist computational procedures that work to determine the prime elements in these cases. In contrast, we will show (...) how to computably extend Z in such a way that we can control the ordinary integer primes in any Π20 way, all while maintaining unique factorization. As a corollary, we establish the existence of a computable unique factorization domain such that the set of primes is Π20-complete in every computable presentation. (shrink)

We formulate a polarized version of Ramsey’s theorem for trees. For those exponents greater than 2, both the reverse mathematics and the computability theory associated with this theorem parallel that of its linear analog. For pairs, the situation is more complex. In particular, there are many reasonable notions of stability in the tree setting, complicating the analysis of the related results.

An abstract mathematical theory is presented for a common variety of soritical arguments, treated here in terms of responses of a system, say, a biological organism, a gadget, or a set of normative linguistic rules, to stimuli. Any characteristic of the system's responses which supervenes on stimuli is called a stimulus effect upon the system. Classificatory sorites is about the identity of or difference between the effects of stimuli that differ 'only microscopically'. We formulate the classificatory sorites on arguably the (...) highest possible level of generality and show that the 'paradox' is dissolved on grounds unrelated to vague predicates or other linguistic issues traditionally associated with it. If stimulus effects are properly defined (i.e., they are uniquely determined by stimuli), and if the space of the stimuli is endowed with appropriate (not necessarily metric) closeness and connectedness properties, then this space must contain points in every vicinity of which, 'however small', the stimulus effect is not constant. The effects can only be 'tolerant' to very small differences between stimuli if the closeness structure that is used to define very close stimuli does not render the space of stimuli appropriately connected: in this case the 'paradox' cannot be formulated. Nor can it be formulated if the response properties considered are not true effects, i.e., if they do not supervene on stimuli. (shrink)

We develop a mathematical theory for comparative sorites, considered in terms of a system mapping pairs of stimuli into a binary response characteristic whose values supervene on stimulus pairs and are interpretable as the complementary relations 'are the same' and 'are not the same' (overall or in some respect). Comparative sorites is about hypothetical sequences of stimuli in which every two successive elements are mapped into the relation 'are the same', while the pair comprised of the first and the last (...) elements of the sequence is mapped into 'are not the same'. Although soritical sequences of this kind are logically possible, we argue that their existence is grounded in no empirical evidence and show that it is excluded by a certain psychophysical principle proposed for human comparative judgements in a context unrelated to soritical issues. We generalize this principle to encompass all conceivable situations for which comparative sorites can be formulated. (shrink)

We define the notion of a completely determined Borel code in reverse mathematics, and consider the principle $CD - PB$, which states that every completely determined Borel set has the property of Baire. We show that this principle is strictly weaker than $AT{R_0}$. Any ω-model of $CD - PB$ must be closed under hyperarithmetic reduction, but $CD - PB$ is not a theory of hyperarithmetic analysis. We show that whenever $M \subseteq {2^\omega }$ is the second-order part of an ω-model (...) of $CD - PB$, then for every $Z \in M$, there is a $G \in M$ such that G is ${\rm{\Delta }}_1^1$-generic relative to Z. (shrink)

Kernthema der »Skitze einer Geschichte der Lehre vom Idealen und Realen« ist die angemessene Verortung und Bestimmung des Realen. Dieses Vorhaben ist durchaus komplex und anspruchsvoll wegen der Doppeldeutigkeit des Wortes ›real‹: Es kann sich auf das ausgedehnte und physische Reale innerhalb der Vorstellung beziehen.

La lumière et l’ombre constituent un couple conceptuel qui, également dans la cadre de la philosophie, induit de nombreuses allusions . La lumière se présente, historiquement parlant, comme un paradigme des lumières . Typiquement dans ce paradigme apparaît l’hésitation dans le tournant des lumières au romantisme : l’ombre se voit revalorisée dans le sillage de la transformation romantique du côté sombre de l’existence humaine. Sur l’exemple de la nouvelle L’histoire merveilleuse de Peter Schlemihl d’Adelbert von Chamisso, il est possible d’illustrer (...) de façon prégnante ce tournant de la lumière vers l’ombre. Cet article présente une interprétation philosophique de l’aliénation de l’ombre en tant que perte d’identité, comme illustré dans le conte. Après cette interprétation, suivra une tentative de déterminer la structure du rapport entre le corps et l’ombre comme lien avec l’identité. En aucun cas l’ombre ne doit être réduite à un simple phénomène secondaire, mais doit être observée en tant qu’élément important de la constellation formant l’identité. . Bien que son apparition soit caractérisée par l’éphémère, l’ombre fait essentiellement/proprement partie de l’identité du corps, le corps étant défini justement par le fait qu’il produit l’ombre lorsqu’il est éclairé. Le rapport de la lumière, du corps et de l’ombre se rapproche par conséquent de l’exemplification d’un modèle alternatif de l’identité, d’après quoi une simple caractéristique potentielle devient indispensable dans une occasion particulière . Avec le concept d’identité occasionnelle, il est possible de corriger la rigide notion ontologique de l’identité. (shrink)

One can often encounter claims that classical (Kolmogorovian) probability theory cannot handle, or even is contradicted by, certain empirical findings or substantive theories. This note joins several previous attempts to explain that these claims are unjustified, illustrating this on the issues of (non)existence of joint distributions, probabilities of ordered events, and additivity of probabilities. The specific focus of this note is on showing that the mistakes underlying these claims can be precluded by labeling all random variables involved contextually. Moreover, contextual (...) labeling also enables a valuable additional way of analyzing probabilistic aspects of empirical situations: determining whether the random variables involved form a contextual system, in the sense generalized from quantum mechanics. Thus, to the extent the Wang-Busemeyer QQ equality for the question order effect holds, the system describing them is noncontextual. The double-slit experiment and its behavioral analogues also turn out to form a noncontextual system, having the same probabilistic format (cyclic system of rank 4) as the one describing spins of two entangled electrons. (shrink)

The book explores the variety of meanings of contextuality across different disciplines, with the emphasis on quantum physics and on psychology. Keywords: Contextuality; Quantum Physics; Psychology.

Allowing pupils to choose the content of their learning is an important step towards individualized development. Despite the need proclaimed by society for the development of competences in STEM area, educational cycles in this field are the least represented in the Croatian general education curriculum. This research was conducted in order to gain insight into pupils’ interests in the contents of technical culture and for school activities. The research was conducted on a stratified sample of primary school pupils in Croatia (...) aged 11 to 15 years. The analysis of the research results showed that the activities from ICT, robotics, programming and woodworking are the most attractive. When it comes to school activities, pupils most prefer sports activities, computer activities, experiments in science subjects and then technical activities. This result suggests that the school curricula needs to be redesigned so that pupils can develop according to their interests. Učenikova mogućnost izbora sadržaja učenja tijekom općeg obveznog obrazovanja važan je korak ka individualiziranom razvoju. Unatoč proklamiranim potrebama društva za razvojem kompetencija u tzv. STEM području, u hrvatskom su obrazovnom sustavu aktivnosti iz ovog područja najmanje zastupljene u kurikulumu općeg obrazovanja. Stoga je provedeno istraživanje interesa učenika za izbornu nastavu tehničke kulture te za aktivnosti koje bi odabrali kad bi mogli birati što će u školi učiti i raditi. Istraživanje je provedeno na stratificiranom uzorku učenika osnovnih škola u Hrvatskoj u dobi od 11. do 15. godine života. Analizom rezultata istraživanja ustanovljeno je da su aktivnosti iz IKT-a, robotike, programiranja i modelarstva najatraktivnija područja za izbornu nastave tehničke kulture. Kad je riječ o aktivnostima u školi, učenici bi najradije odabrali sportske aktivnosti, a potom slijede informatičke, prirodoznanstvene i tehničke aktivnosti. Ovakav nalaz ukazuje na nužnu preobrazbu školskog kurikuluma koji će učenicima omogućiti razvoj u skladu s njihovim interesima. (shrink)

Učenikova mogućnost izbora sadržaja učenja tijekom općeg obveznog obrazovanja važan je korak ka individualiziranom razvoju. Unatoč proklamiranim potrebama društva za razvojem kompetencija u tzv. STEM području, u hrvatskom su obrazovnom sustavu aktivnosti iz ovog područja najmanje zastupljene u kurikulumu općeg obrazovanja. Stoga je provedeno istraživanje interesa učenika za izbornu nastavu tehničke kulture te za aktivnosti koje bi odabrali kad bi mogli birati što će u školi učiti i raditi. Istraživanje je provedeno na stratificiranom uzorku učenika osnovnih škola u Hrvatskoj u (...) dobi od 11. do 15. godine života. Analizom rezultata istraživanja ustanovljeno je da su aktivnosti iz IKT-a, robotike, programiranja i modelarstva najatraktivnija područja za izbornu nastave tehničke kulture. Kad je riječ o aktivnostima u školi, učenici bi najradije odabrali sportske aktivnosti, a potom slijede informatičke, prirodoznanstvene i tehničke aktivnosti. Ovakav nalaz ukazuje na nužnu preobrazbu školskog kurikuluma koji će učenicima omogućiti razvoj u skladu s njihovim interesima. (shrink)

We present a proof for a conjecture previously formulated by Dzhafarov et al.. The conjecture specifies a measure for the degree of contextuality and a criterion for contextuality in a broad class of quantum systems. This class includes Leggett–Garg, EPR/Bell, and Klyachko–Can–Binicioglu–Shumovsky type systems as special cases. In a system of this class certain physical properties \ are measured in pairs \ \); every property enters in precisely two such pairs; and each measurement outcome is a binary random variable. (...) Denoting the measurement outcomes for a property \ in the two pairs it enters by \ and \, the pair of measurement outcomes for \ \) is \ \). Contextuality is defined as follows: one computes the minimal possible value \ for the sum of \ ) that is allowed by the individual distributions of \ and \; one computes the minimal possible value \ for the sum of \ across all possible couplings of the entire set of random variables \ in the system; and the system is considered contextual if \ ). This definition has its justification in the general approach dubbed Contextuality-by-Default, and it allows for measurement errors and signaling among the measured properties. The conjecture proved in this paper specifies the value of \ in terms of the distributions of the measurement outcomes \ \). (shrink)

The Bell/CHSH inequalities of quantum physics are identical with the inequalities derived in mathematical psychology for the problem of selective influences in cases involving two binary experimental factors and two binary random variables recorded in response to them. The following points are made regarding cognitive science applications: (1) compliance of data with these inequalities is informative only if the data satisfy the requirement known as marginal selectivity; (2) both violations of marginal selectivity and violations of the Bell/CHSH inequalities are interpretable (...) as indicating that at least one of the two responses is influenced by both experimental factors. (shrink)

Licht und Schatten bilden ein Begriffspaar, welches auch innerhalb der Philosophie Anlass zu vielen Anspielungen gegeben hat . Licht gilt, geschichtlich gesehen, als Paradigma der Aufklärung . Bezeichnenderweise gerät dieses Paradigma am Übergang vom Zeitalter der Aufklärung zur Romantik ins Wanken: Es kommt zu einer Aufwertung des Schattens im Zuge der romantischen Verklärung der dunklen Seiten der menschlichen Existenz. Am Beispiel von Adelbert von Chamissos Novelle Peter Schlemihls wundersame Geschichte lässt sich diese Abwendung vom Licht zum Schatten prägnant illustrieren. Im (...) vorliegenden Text soll eine philosophische Interpretation des in ihr geschilderten Schattenraubs als Identitätsverlust gegeben werden. Im Anschluss an diese Interpretation soll eine Strukturbestimmung des Verhältnisses von Körper und Schatten als Identitätsbeziehung versucht werden. Keineswegs darf der Schatten zur bloßen Begleiterscheinung degradiert werden, sondern muss als wesentliches Element einer identitätsbildenden Konstellation angesehen werden . Obwohl seine Erscheinung nur flüchtigen Charakter hat, gehört der Schatten wesentlich zur Identität des Körpers, da sich ein Körper gerade dadurch definieren lässt, dass er bei Beleuchtung Schatten wirft. Das Licht-Körper-Schatten-Verhältnis kann daher zur Exemplifizierung eines alternativen Identitätsmodells herangezogen werden, demzufolge ein bloß potentielles Merkmal eines Gegenstandes bei einer bestimmten Gelegenheit zu einem notwendigen wird. Mit dem Konzept einer okkasionellen Identität lässt sich ein ontologisch rigides Identitätsverständnis korrigieren. (shrink)

Svjetlo i sjena tvore pojmovni par koji i u okviru filozofije daje povoda za brojne aluzije . Svjetlost vrijedi, povijesno sagledano, kao paradigma prosvjetiteljstva . Karakteristično, u ovoj se paradigmi javlja kolebanje na prijelazu iz razdoblja prosvjetiteljstva u romantizam: dolazi do uzvisivanja sjene u jeku romantičnog preobraženja tamne strane ljudske egzistencije. Na primjeru novele Adelberta von Chamissa Čudnovata pripovijest Petra Schlemihla moguće je pregnantno ilustrirati spomenuti zaokret od svjetla ka sjeni. U ovom tekstu će biti predstavljena filozofska interpretacija otuđenja sjene (...) kao gubitka identiteta, kako je oslikano u pripovijesti. Nadovezujući se na tu interpretaciju, uslijedit će pokušaj određivanja strukture odnosa tijela i sjene kao poveznice s identitetom. Ni u kom slučaju sjena ne smije biti degradirana na puku popratnu pojavu, već smo je dužni promatrati kao ozbiljan element konstelacije u tvorbi identiteta . Iako njezinu pojavu obilježava kratkotrajnost, sjena je značajno implementirana u identitet tijela, s obzirom da je tijelo definirano upravo činjenicom da pri osvjetljivanju stvara sjenu. Uzajamnost se svjetla, tijela i sjene stoga primiče egzemplifikaciji alternativnog modela identiteta, analogno čemu jedno tek potencijalno obilježje predmeta u određenoj prilici postaje neophodno. Konceptom okazionalnog identiteta moguće je korigirati ontološki rigidno poimanje identiteta. (shrink)

Light and shadow create a conceptual pair which gives rise to a number of allusions in philosophy . Historically speaking, light is the paradigm of the Enlightenment . Significantly, in this paradigm certain vacillations appeared at the transition from the Age of Enlightenment to Romanticism: an appreciation of the shadow in the wake of the Romantic idealization of the dark side of human existence rises. Using the example of Adelbert von Chamisso’s work Peter Schlemihl’s Remarkable Story, the point of turn (...) from light to shadow can be fruitfully illustrated. This paper is a philosophical interpretation of the shadow alienation as loss of identity. Following this interpretation an attempt to define the structure of relationship between body and shadow as an identity relationship will be presented. By no means should shadow be degraded to a mere concomitant, it must be considered as an essential element of an identity-forming constellation . Although its appearance is characterised by short duration, the shadow belongs to the essential identity of the body, given that the body is defined exactly by the fact that it casts shadows when illuminated. The reciprocity of the light, the body and the shadow is therefore used to exemplify an alternative identity model, according to which a potential feature of an object on a particular occasion becomes necessary. With the concept of occasional identity it becomes possible to correct an ontologically rigid understanding of identity. (shrink)

U članku se pokušava odrediti svjetonazorno polazište bioetike, posebno one »integrativne «. Prvo će biti istaknut značaj tzv. pogleda na svijet za obrazovanje filozofskih pozicija. Zatim se pokreće pitanje o svjetonazornoj pozadini bioetičkih pozicija, pri čemu se kao njihov zajednički nazivnik pokazuje »bioprotekcionizam« kao vrsta umjerenog biocentrizma. Naposljetku se preispituje osnova integrativne bioetike koja inače ima zadatak promišljati svjetonazorne pretpostavke bioetičkih učenja. U tu svrhu će se ponuditi dvije interpretacije koje će rezultirati ukazivanjem na perspektivizam odnosno pluriperspektivizam kao onaj pogled (...) na svijet koji do izražaja dolazi upravo u integrativnoj bioetici.Im Aufsatz wird der Versuch unternommen, den weltanschaulichen Ausgangspunkt der Bioethik zu ermitteln, vor allem der „integrativen Bioethik“. Zuallererst wird die Bedeutung der sog. Weltanschauungen für die Bildung der philosophischen Positionen hervorgehoben. Des Weiteren wird die Frage nach dem weltanschaulichen Hintergrund der bioethischen Positionen aufgeworfen, wobei sich „Bioprotektionismus“, eine gemäßigte Variante des Biozentrismus, als ihr gemeinsamer Nenner erweist. Schließlich wird die Grundlage der integrativen Bioethik überprüft, die ansonsten die Aufgabe hat, die weltanschaulichen Voraussetzungen der bioethischen Lehren zu reflektieren. Zu diesem Zweck werden zwei Interpretationen angeboten, die zum Perspektivismus bzw. Pluriperspektivismus hinführen, als jener Weltanschauung, welche gerade in der integrativen Bioethik zur Geltung kommt. (shrink)

We present a formal theory of contextuality for a set of random variables grouped into different subsets corresponding to different, mutually incompatible conditions. Within each context the random variables are jointly distributed, but across different contexts they are stochastically unrelated. The theory of contextuality is based on the analysis of the extent to which some of these random variables can be viewed as preserving their identity across different contexts when one considers all possible joint distributions imposed on the entire set (...) of the random variables. We illustrate the theory on three systems of traditional interest in quantum physics. These are systems of the Klyachko–Can–Binicioglu–Shumovsky-type, Einstein–Podolsky–Rosen–Bell-type, and Suppes–Zanotti–Leggett–Garg-type. Listed in this order, each of them is formally a special case of the previous one. For each of them we derive necessary and sufficient conditions for contextuality while allowing for experimental errors and contextual biases or signaling. Based on the same principles that underly these derivations we also propose a measure for the degree of contextuality and compute it for the three systems in question. (shrink)

According to event-causal libertarianism, an action is free in the sense relevant to moral responsibility when it is caused indeterministically by an agent’s beliefs, desires, intentions, or by their occurrences. This paper attempts to clarify one of the major objections to this theory: the objection that the theory cannot explain the relevance of indeterminism to this kind of freedom (known as free will). Christopher Evan Franklin (2011, 2018) has argued that the problem of explaining the relevance of indeterminism to free (...) will (which he calls “the problem of enhanced control”) arises because it is difficult to see how indeterminism could enhance our abilities, and disappears when we realize that beside the relevant abilities free will requires opportunities. In this paper, I argue that the problem occurs not because of the focus on abilities, but because of the difficulty to explain how indeterminism could contribute to the satisfaction of the sourcehood condition of free will in the framework of event-causal theory of action. (shrink)

The paper starts with Jaspers’ comprehensive principle of faith which states that man is finite and imperfectible. Man’s finality is peculiar because it is marked by unclosedness. Man is conscious of his finality, so Jaspers concludes that inconclusiveness is a signum of man’s freedom. In this sense, the paper is dedicated to man as determined by freedom, Existenz determined by freedom which eludes investigation. In Jaspers, it is a matter of freedom which is at the same time a matter of (...) the relation of Existenz and transcendence: finality as Existenz for him means that man is gifted to himself thanks to transcendence, and he becomes conscious of transcendence thanks to freedom. The freedom of Existenz is in a dialectic of independence and dependence. Freedom leads Existenz beyond the world by way of ciphers to transcendence. For Jaspers, humanness is a matter of freedom in which lies the source of man’s action and self-consciousness. Humanness is not exhausted in knowledge but philosophical faith comes to the fore, the faith of man in his openness of possibilities by way of philosophy. The paper concludes with the view that a demand for meaning is made out to man as Existenz out of freedom as postulated by Jaspers. (shrink)

There is an evident lack of studies examining the pursuit of excellence in futsal. The aims of this study were to evaluate anthropometric and physiological variables that may contribute to distinguishing among performance levels in professional futsal players and to evaluate correlates of those variables. The participants were 75 male professionals (age = 25.1 ± 5.1 years, body height = 182.3 ± 6.2 cm, body mass = 80.8 ± 10.4 kg), who were divided into performance levels using two criteria: (i) (...) starters (first teams) vs. non-starters (substitutes) and (ii) top-level players (members of the national team and players who participated in top-level team competition in Europe) vs. high-level players (team players competing at the highest national competitive rank). Variables included anthropometrics (body height and mass, BMI, body fat percentage), generic tests of physiological capacities [5- and 10-m sprints, countermovement jump, broad jump, 20-yard test, reactive strength index (RSI)], and futsal-specific fitness tests [kicking speed by dominant and non-dominant leg, futsal-specific tests of change of direction speed, and reactive agility (FSRAG) involving/not involving dribbling the ball]. Top-level players outperformed high-level players in RSI, broad jump, kicking speed, and FSRAG involving dribbling. Starters achieved better results than non-starters in fewer variables, including kicking speed and RSI. Body fat percentage negatively influenced FSRAG involving dribbling, and RSI. FSRAG, RSI, and kicking speed were significantly correlated, indicating the similar physiological background of these capacities. The findings suggest that enhanced reactive strength and the ability to rapidly change direction speed in response to external stimulus while executing futsal-specific motor tasks (e.g., dribbling), along with players’ ability to kick the ball speedily, can be considered essential qualities required for advanced performance in futsal. Consequently, futsal strength and conditioning training should be targeted toward lowering relative body fat, maximizing lower-body reactive strength and including futsal-specific skills (e.g., dribbling, shooting) in reactive agility drills. (shrink)

Correlations of spins in a system of entangled particles are inconsistent with Kolmogorov’s probability theory (KPT), provided the system is assumed to be non-contextual. In the Alice–Bob EPR paradigm, non-contextuality means that the identity of Alice’s spin (i.e., the probability space on which it is defined as a random variable) is determined only by the axis $\alpha _{i}$ chosen by Alice, irrespective of Bob’s axis $\beta _{j}$ (and vice versa). Here, we study contextual KPT models, with two properties: (1) Alice’s (...) and Bob’s spins are identified as $A_{ij}$ and $B_{ij}$ , even though their distributions are determined by, respectively, $\alpha _{i}$ alone and $\beta _{j}$ alone, in accordance with the no-signaling requirement; and (2) the joint distributions of the spins $A_{ij},B_{ij}$ across all values of $\alpha _{i},\beta _{j}$ are constrained by fixing distributions of some subsets thereof. Of special interest among these subsets is the set of probabilistic connections, defined as the pairs $\left( A_{ij},A_{ij'}\right) $ and $\left( B_{ij},B_{i'j}\right) $ with $\alpha _{i}\not =\alpha _{i'}$ and $\beta _{j}\not =\beta _{j'}$ (the non-contextuality assumption is obtained as a special case of connections, with zero probabilities of $A_{ij}\not =A_{ij'}$ and $B_{ij}\not =B_{i'j}$ ). Thus, one can achieve a complete KPT characterization of the Bell-type inequalities, or Tsirelson’s inequalities, by specifying the distributions of probabilistic connections compatible with those and only those spin pairs $\left( A_{ij},B_{ij}\right) $ that are subject to these inequalities. We show, however, that quantum-mechanical (QM) constraints are special. No-forcing theorem says that if a set of probabilistic connections is not compatible with correlations violating QM, then it is compatible only with the classical–mechanical correlations. No-matching theorem says that there are no subsets of the spin variables $A_{ij},B_{ij}$ whose distributions can be fixed to be compatible with and only with QM-compliant correlations. (shrink)