Related papers: Zeta Functions and the (Linear) Logic of Markov Pr…
Discovering causal relationship using multivariate functional data has received a significant amount of attention very recently. In this article, we introduce a functional linear structural equation model for causal structure learning when…
Causal relationships play a fundamental role in understanding the world around us. The ability to identify and understand cause-effect relationships is critical to making informed decisions, predicting outcomes, and developing effective…
Owing to their versatility, graph structures admit representations of intricate relationships between the separate entities comprising the data. We formalise the notion of connection between two vertex sets in terms of edge and vertex…
Subgraph matching in logic circuits is foundational for numerous Electronic Design Automation (EDA) applications, including datapath optimization, arithmetic verification, and hardware trojan detection. However, existing techniques rely…
As a supplement to my talk at the workshop, this extended abstract motivates and summarizes my work with co-authors on problems in two separate areas: first, in the lambda-calculus with letrec, a universal model of computation, and second,…
In this paper, we analyze the complexity of functional programs written in the interaction-net computation model, an asynchronous, parallel and confluent model that generalizes linear-logic proof nets. Employing user-defined sized and…
Topology identification and inference of processes evolving over graphs arise in timely applications involving brain, transportation, financial, power, as well as social and information networks. This chapter provides an overview of graph…
Deep learning has been shown to achieve impressive results in several tasks where a large amount of training data is available. However, deep learning solely focuses on the accuracy of the predictions, neglecting the reasoning process…
Using an information theoretic point of view, we investigate how a dynamics acting on a network can be coarse grained through the use of graph partitions. Specifically, we are interested in how aggregating the state space of a Markov…
This is an expository paper on the meromorphic continuation of zeta functions with Euler products (for example zeta functions of groups and height zeta functions) or without (for example the Goldbach zeta function). As an application we…
Using a scheme involving a lifting of a row contraction we introduce a toy model of repeated interactions between quantum systems. In this model there is an outgoing Cuntz scattering system involving two wandering subspaces. We associate to…
We define the rank-metric zeta function of a code as a generating function of its normalized $q$-binomial moments. We show that, as in the Hamming case, the zeta function gives a generating function for the weight enumerators of rank-metric…
Large-scale knowledge graphs provide structured representations of human knowledge. However, as it is impossible to collect all knowledge, knowledge graphs are usually incomplete. Reasoning based on existing facts paves a way to discover…
We present a novel methodology to jointly perform multi-task learning and infer intrinsic relationship among tasks by an interpretable and sparse graph. Unlike existing multi-task learning methodologies, the graph structure is not assumed…
We introduce the Hadamard topology on the Witt ring of rational functions, giving a simultaneous refinement of the weight and point-counting topologies. Zeta functions of algebraic varieties over finite fields are elements of the rational…
Calculi of string diagrams are increasingly used to present the syntax and algebraic structure of various families of circuits, including signal flow graphs, electrical circuits and quantum processes. In many such approaches, the semantic…
The theory of Ihara zeta functions is extended to non-compact arithmetic quotients of Bruhat-Tits trees. This new zeta function turns out to be a rational function, despite the infinite-dimensional setting. In general it has zeros and…
We study zeta functions enumerating subalgebras or ideals of Lie algebras over finite field of prime order $\mathbb{F}_p$. We first develop a general blueprint method for computing zeta functions of $\mathbb{F}_p$-Lie algebras, and…
Network Models with couplings between link pairs are the simplest models for a class of networks with Higher Order interactions. In this paper we give an analytic, general solution to this family of Random Graph Models extending previous…
We define motivic analogues of Igusa's local zeta functions. These functions take their values in a Grothendieck group of Chow motives. They specialize to p-adic Igusa local zeta functions and to the topological zeta functions we introduced…