Narrow Results

The main concern of this paper is the study of the relationships between the KV-cohomology of Koszul–Vinberg algebras and some properties of various geometrical objects. In particular we show how the scalar KV-cohomology of real or holomorphic Koszul–Vinberg algebroids is closely related to real or holomorphic Poisson manifolds. In the appendix we point out strong relationships between the pioneer work of Nijenhuis [42] and the KV-cohomology.

In the present talk we briefly demonstrate an elegant and effective technique for calculation of the trace expansion in the derivatives of background fields. One of main advantages of the technique is manifestly (super)symmetrical and gauge invariant form of expressions on all stages of calculations. Other advantage is the universality of the calculation method. It shows itself to be good for calculation of one-loop effective action in several well-known models and new results in supersymmetrical models has already been found.

In this paper, using standard pairs, we present a method to construct symbols satisfying the sum rules of order $p$ for any given $p$. It is shown that using matrix polynomial theory symbols, symmetric or non-symmetric, satisfying the sum rules of order $p$ can be constructed efficiently. The construction is illustrated using various examples.

Let G be a finite classical group of characteristic p. In this paper, we give an arithmetic criterion of the primes r ≠ p, for which the Steinberg character lies in the principal r-block of G. The arithmetic criterion is obtained from some combinatorial objects (the so-called partition and symbol).

Brains and computers are both dynamical systems that manipulate symbols, but they differ fundamentally in their architectures and operations. Human brains do mathematics; computers do not. Computers manipulate symbols that humans put into them without grounding them in what they represent. Human brains intentionally direct the body to make symbols, and they use the symbols to represent internal states. The symbols are outside the brain. Inside the brains, the construction is effected by spatiotemporal patterns of neural activity that are operators, not symbols. The operations include formation of sequences of neural activity patterns that we observe by their electrical signs. The process is by neurodynamics, not by logical rule-driven symbol manipulation. The aim of simulating human natural computing should be to simulate the operators. In its simplest form natural computing serves for communication of meaning. Neural operators implement non-symbolic communication of internal states by all mammals, including humans, through intentional actions. The neural operators that implement symbol formation must differ, but how is unknown, so we cannot yet simulate human natural computing. Here, I propose that symbol-making operators evolved from neural mechanisms of intentional action by modification of non-symbolic operators. Both kinds of operators can be investigated by their signs of neuroelectric activity. I propose that the postulated differences should be sought by classification of the spatial textures of the signs in EEG recorded from the scalp overlying those cortical structures unique to humans in the brain that I designate as koniocortex, while the subjects are engaged in elementary arithmetic operations.

Over the $(1,n)$-dimensional real superspace, $n\ge 2$, we study non-trivial deformations of the natural action of the affine Lie superalgebra $𝔞𝔣𝔣(n|1)$ on the direct sum of the superspaces of weighted densities. We compute the necessary and sufficient integrability conditions of a given infinitesimal deformation of this action and we prove that any formal deformation is equivalent to its infinitesimal part. This work is the simplest generalization of a result by Basdouri and Omri [Cohomology and deformation of $𝔞𝔣𝔣(1|1)$ acting on differential operators, Int. J. Geom. Methods Mod. Phys.15 (2018) 1850072].

CBA is a six-layered architecture of consciousness linked to behavior such as reflex action, detour, and ambush. Two emotion-valued criteria are given for behavior selection. While a level of behavior is chosen to maximize the consciousness intensity, an action at the level chosen is selected to increase the pleasure. CBA is efficient for behavior selection because performing a complex task elevates the performer's level of consciousness. Inhibition of behavior triggers an elevation of the level of consciousness and behavior. The model design of detour and ambush was tested using two small mobile robots that had a limited temporal and spatial information of their environments. Emotion-valued criteria for behavior selection explain the meaning of behavior obstruction.