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We study a series of the Wess-Zumino actions obtained by repeatedly integrating conformal anomalies with respect to the conformal-factor field that appear at higher loops. We show that they arise as physical quantities required to make…
Convolutional Neural Networks (CNN) offer state of the art performance in various computer vision tasks. Many of those tasks require different subtypes of affine invariances (scale, rotational, translational) to image transformations.…
In classification problems, supervised machine-learning methods outperform traditional algorithms, thanks to the ability of neural networks to learn complex patterns. However, in two-class classification tasks like anomaly or fraud…
Explainable artificial intelligence (XAI) has become increasingly important in decision-critical domains such as healthcare, finance, and law. Counterfactual (CF) explanations, a key approach in XAI, provide users with actionable insights…
Anomaly detection is a ubiquitous and challenging task relevant across many disciplines. With the vital role communication networks play in our daily lives, the security of these networks is imperative for smooth functioning of society. To…
Boolean functions with strong cryptographic properties, such as high nonlinearity and algebraic degree, are important for the security of stream and block ciphers. These functions can be designed using algebraic constructions or…
We analyse the $3+1$ D equilibrium chiral magnetic effect (CME). We apply derivative expansion to the Wigner transform of the two - point Green function. This technique allows us to express the response of electric current to external…
Diffusion effect on chirality selection in a two-dimensional reaction-diffusion model is studied by the Monte Carlo simulation. The model consists of achiral reactants A which turn into either of the chiral products, R or S, in a solvent of…
Let $K$ be any unital commutative $\mathbb Q$-algebra and $z=(z_1, ..., z_n)$ commutative or noncommutative free variables. Let $t$ be a formal parameter which commutes with $z$ and elements of $K$. We denote uniformly by $\kzz$ and…
This paper examines functional equivariance, recently introduced by McLachlan and Stern [Found. Comput. Math. (2022)], from the perspective of backward error analysis. We characterize the evolution of certain classes of observables…
With the increasing interest in applying the methodology of difference-of-convex (dc) optimization to diverse problems in engineering and statistics, this paper establishes the dc property of many well-known functions not previously known…
We present a Riesz integral representation theory in which functions, operators and measures take values in uniform commutative monoids (a commutative monoid with a uniformity making the binary operation of the monoid uniformly continuous).…
We investigate the behaviour of a certain additive function depending on prime divisors of specific integers lying in large gaps between consecutive primes. The result is obtained by a combination of results and ideas related to large gaps…
In this article we show that the inhomogeneous density obtained from a density-functional theory of classical fluids in the canonical ensemble (CE), recently presented by White et al [Phys. Rev. Lett. 84 (2000) 1220], is equivalent to first…
Recent self-supervised contrastive methods have been able to produce impressive transferable visual representations by learning to be invariant to different data augmentations. However, these methods implicitly assume a particular set of…
A wide array of graphical models can be parametrised to have atomic probabilities represented by monomial functions. Such monomial structure has proven very useful when studying robustness under the assumption of a multilinear model where…
In this paper we study some questions in connection with uniform rectifiability and the $L^2$ boundedness of Calderon-Zygmund operators. We show that uniform rectifiability can be characterized in terms of some new adimensional coefficients…
We study the effect of a relevant double-trace deformation on the partition function (and conformal anomaly) of a CFT at large N and its dual picture in AdS. Three complementary previous results are brought into full agreement with each…
The essence of special relativity is hiding in the equal existence of particle and antiparticle, which can be expressed by two discrete symmetries within one inertial frame --- the invariance under the (newly defined) space-time inversion…
We define and study symmetrized and antisymmetrized multivariate exponential functions. They are defined as determinants and antideterminants of matrices whose entries are exponential functions of one variable. These functions are…