Related papers: Zeta Functions and the (Linear) Logic of Markov Pr…

In this paper we study spectral zeta functions associated to finite and infinite graphs. First we establish a meromorphic continuation of these functions under some general conditions. Then we study special values in the case of standard…

We give an overview of the theory of functional relations for zeta-functions of root systems, and show some new results on functional relations involving zeta-functions of root systems of types $B_r$, $D_r$, $A_3$ and $C_2$. To show those…

Zeta functions of periodic cubical lattices are explicitly derived by computing all the eigenvalues of the adjacency operators and their characteristic polynomials. We introduce cyclotomic-like polynomials to give factorization of the zeta…

Human beings are fundamentally sociable -- that we generally organize our social lives in terms of relations with other people. Understanding social relations from an image has great potential for intelligent systems such as social chatbots…

In this paper we introduce new class of multiplicative interactions of the $\zeta$-oscillating systems generated by a subset of power functions. The main result obtained expresses an analogue of prime decomposition (without the property of…

Time-continuous dynamical systems defined on graphs are often used to model complex systems with many interacting components in a non-spatial context. In the reverse sense attaching meaningful dynamics to given 'interaction diagrams' is a…

Many continuous reaction-diffusion models on $\mathbb{Z}$ (annihilating or coalescing random walks, exclusion processes, voter models) admit a rich set of Markov duality functions which determine the single time distribution. A common…

An analytic representation with Theta functions on a torus, for systems with variables in Z(d), is considered. Another analytic representation with Theta functions on a strip, for systems with positions in a circle S and momenta in Z, is…

The theory of geometric zeta functions for locally symmetric spaces as initialized by Selberg and continued by numerous mathematicians is generalized to the case of higher rank spaces. We show analytic continuation, describe the divisor in…

This work presents the use of graph learning for the prediction of multi-step experimental outcomes for applications across experimental research, including material science, chemistry, and biology. The viability of geometric learning for…

The notion of the Jacob's ladders, reversely iterated integrals and the $\zeta$-factorization is used in this paper in order to obtain new results in study of the function $\arg\zf$. Namely, we obtain new formulae for non-local and…

Inductive link prediction -- where entities during training and inference stages can be different -- has been shown to be promising for completing continuously evolving knowledge graphs. Existing models of inductive reasoning mainly focus…

This paper presents a speculation on a fictive co-creation scenario that extends classical interaction patterns with generative models. While existing interfaces are restricted to the input and output layers, we suggest hidden layer…

In [19] it was explained how one can naturally associate a Deitmar scheme (which is a scheme defined over the field with one element, $\mathbb{F}_1$) to a so-called "loose graph" (which is a generalization of a graph). Several properties of…

We establish the quaternionic weighted zeta function of a graph and its Study determinant expressions. For a graph with quaternionic weights on arcs, we define a zeta function by using an infinite product which is regarded as the Euler…

Real-world scenarios demand reasoning about process, more than final outcome prediction, to discover latent causal chains and better understand complex systems. It requires the learning algorithms to offer both accurate predictions and…

Mathematical models and algorithms are an essential part of mathematical research data, as they are epistemically grounding numerical data. In order to represent models and algorithms as well as their relationship semantically to make this…

We present a theorem which elucidates the connection between self-duality of Markov processes and representation theory of Lie algebras. In particular, we identify sufficient conditions such that the intertwining function between two…

Graphs are commonly used in mathematics to represent some relationships between items. However, as simple objects, they sometimes fail to capture all relevant aspects of real-world data. To address this problem, we generalize them and model…

We apply to logic programming some recently emerging ideas from the field of reduction-based communicating systems, with the aim of giving evidence of the hidden interactions and the coordination mechanisms that rule the operational…