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71.
Juan D. Gomez William G. P. Mayner Maggie Beheler-Amass Giulio Tononi Larissa Albantakis 《Entropy (Basel, Switzerland)》2021,23(1)
Integrated information theory (IIT) provides a mathematical framework to characterize the cause-effect structure of a physical system and its amount of integrated information (). An accompanying Python software package (“PyPhi”) was recently introduced to implement this framework for the causal analysis of discrete dynamical systems of binary elements. Here, we present an update to PyPhi that extends its applicability to systems constituted of discrete, but multi-valued elements. This allows us to analyze and compare general causal properties of random networks made up of binary, ternary, quaternary, and mixed nodes. Moreover, we apply the developed tools for causal analysis to a simple non-binary regulatory network model (p53-Mdm2) and discuss commonly used binarization methods in light of their capacity to preserve the causal structure of the original system with multi-valued elements. 相似文献
72.
Clemens G. Raab Georg Regensburger Jamal Hossein Poor 《Journal of Pure and Applied Algebra》2021,225(5):106564
A formal computation proving a new operator identity from known ones is, in principle, restricted by domains and codomains of linear operators involved, since not any two operators can be added or composed. Algebraically, identities can be modelled by noncommutative polynomials and such a formal computation proves that the polynomial corresponding to the new identity lies in the ideal generated by the polynomials corresponding to the known identities. In order to prove an operator identity, however, just proving membership of the polynomial in the ideal is not enough, since the ring of noncommutative polynomials ignores domains and codomains. We show that it suffices to additionally verify compatibility of this polynomial and of the generators of the ideal with the labelled quiver that encodes which polynomials can be realized as linear operators. Then, for every consistent representation of such a quiver in a linear category, there exists a computation in the category that proves the corresponding instance of the identity. Moreover, by assigning the same label to several edges of the quiver, the algebraic framework developed allows to model different versions of an operator by the same indeterminate in the noncommutative polynomials. 相似文献
73.
Mathematical Notes - The paper is devoted to the study of conditional bounds for the expectation of the maximum of independent identically distributed standardized random variables for which the... 相似文献
74.
Mathematical Notes - We consider the problem of the approximation of functions, continuous on the semiaxis $$[0,\infty)$$ and for which the derivatives $$f^{(\nu)}(0)$$ , $$\nu=0,\dots,r-1$$ exist... 相似文献
75.
Mathematical Notes - In the present paper, we propose a new method of derivation of number-theoretic identities which is applied to the proof of the multidimensional analogue of one of the... 相似文献
76.
Mathematical Notes - The notion of a $$\lambda$$ -generalized-search multivalued functional on an $$f$$ -quasimetric space is introduced. An existence theorem for zeros of such functionals is... 相似文献
77.
Mathematical Notes - The main purpose of the paper is to strengthen the results of P. R. Mercer (2003) concerning the comparison of arithmetic, geometric, and harmonic weighted means. 相似文献
78.
79.
Siberian Mathematical Journal - We obtain some new estimates that show the extremality of the Rademacher system in the set of sequences of independent functions considered in rearrangement... 相似文献
80.
Theoretical and Mathematical Physics - We present a one-line closed-form expression for the three-parameter breather of the nonlinear Schrödinger equation. This provides an analytic proof of... 相似文献