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

This paper investigates a new family of special functions referred to as hypergeometric zeta functions. Derived from the integral representation of the classical Riemann zeta function, hypergeometric zeta functions exhibit many properties…

Contour integral representations for Riemann's Zeta function and Dirichelet's Eta (alternating Zeta) function are presented and investigated. These representations flow naturally from methods developed in the 1800's, but somehow they do not…

Interpretable Multi-Task Learning can be expressed as learning a sparse graph of the task relationship based on the prediction performance of the learned models. Since many natural phenomenon exhibit sparse structures, enforcing sparsity on…

The zeta function of a motive over a finite field is multiplicative with respect to the direct sum of motives. It has beautiful analytic properties, as were predicted by the Weil conjectures. There is also a multiplicative zeta function,…

In this paper we prove that there is a grafting of complete hybrid formula on meta-functional equation. This synergetic formula gives the result of a $\zeta$-chemical reaction between different sets of values of Riemann's zeta-function on…

We introduce a new Lie-algebraic approach to explicitly construct the motivic coaction and single-valued map of multiple polylogarithms in any number of variables. In both cases, the appearance of multiple zeta values is controlled by…

In this note we introduce zeta functions and L-functions for discrete and faithful representations of surface groups in PSL(d, R), for d >= 3. These are natural generalizations of the wellknown classical Selberg zeta function and L-function…

Link prediction with knowledge graphs has been thoroughly studied in graph machine learning, leading to a rich landscape of graph neural network architectures with successful applications. Nonetheless, it remains challenging to transfer the…

Graph neural networks are prominent models for representation learning over graph-structured data. While the capabilities and limitations of these models are well-understood for simple graphs, our understanding remains incomplete in the…

We give an explicit construction of the generating set of a colored operad that implements theta theory in the mathematical model of Minimalism in generative linguistics, in the form of a coloring algorithm for syntactic objects. We show…

We have designed a new logic programming language called LM (Linear Meld) for programming graph-based algorithms in a declarative fashion. Our language is based on linear logic, an expressive logical system where logical facts can be…

In this paper, we investigate new relationships for bilateral series related to two-parameter mock theta functions, which lead to many identities concerning the bilateral mock theta functions. In addition, interesting relations between the…

We survey some recent applications of p-adic cohomology to machine computation of zeta functions of algebraic varieties over finite fields of small characteristic, and suggest some new avenues for further exploration.

Parametric causal modelling techniques rarely provide functionality for counterfactual estimation, often at the expense of modelling complexity. Since causal estimations depend on the family of functions used to model the data, simplistic…

We propose an extension of the Contextual Graph Markov Model, a deep and probabilistic machine learning model for graphs, to model the distribution of edge features. Our approach is architectural, as we introduce an additional Bayesian…

We define a new weighted zeta function for a finite digraph and obtain its determinant expression called the Ihara expression. The graph zeta function is a generalization of the weighted graph zeta function introduced in previous research.…

We consider modular graph functions that arise in the low energy expansion of the four graviton amplitude in type II string theory. The vertices of these graphs are the positions of insertions of vertex operators on the toroidal worldsheet,…

Many complex systems exhibit interactions that depend not only on pairwise connections, but also group structures and memory effects. To capture such effects, we develop a unified tensor framework for modeling higher-order Markov chains…

We introduce the Contextual Graph Markov Model, an approach combining ideas from generative models and neural networks for the processing of graph data. It founds on a constructive methodology to build a deep architecture comprising layers…

The Kac-Baker model describes a 1-dim. classical lattice spin system with exponentially fast decaying two body interaction. The model was introduced by M. Kac and G. Baker to investigate the phenomenon of phase transition in systems with…