Related papers: Home Spaces and Invariants to Analyze Parameterize…
An analysis of the network defined by the potential energy minima of multi-atomic systems and their connectivity via reaction pathways that go through transition states allows to understand important characteristics like thermodynamic,…
In order to speed up the synthesis of Petri nets from labelled transition systems, a divide and conquer strategy consists in defining decompositions of labelled transition systems, such that each component is synthesisable iff so is the…
In this article, we propose a topological model to encode partial equivariance in neural networks. To this end, we introduce a class of operators, called P-GENEOs, that change data expressed by measurements, respecting the action of certain…
In systems characterized by a rough potential energy landscape, local energetic minima and saddles define a network of metastable states whose topology strongly influences the dynamics. Changes in temperature, causing the merging and…
Gating mechanisms have emerged as an effective strategy integrated into model designs beyond recurrent neural networks for addressing long-range dependency problems. In a broad understanding, it provides adaptive control over the…
The correctness of networks is often described in terms of the individual data flow of components instead of their global behavior. In software-defined networks, it is far more convenient to specify the correct behavior of packets than the…
Classical Petri nets provide a canonical model of concurrency, with unfolding semantics linking nets, occurrence nets, and event structures. No comparable framework exists for quantum concurrency: existing ''quantum Petri nets'' lack…
This study introduces a pore morphology algorithm that emphasizes the central role of topology in multiphase flow through porous media. Analysis of drainage in lattice-based pore networks identifies two key quantities, the percolation…
We recently proposed an approach for the specification and modular formal verification of the interactive (I/O) behavior of programs, based on an embedding of Petri nets into separation logic. While this approach is scalable and modular in…
Inversion techniques are widely used to reconstruct subsurface physical properties (e.g., velocity, conductivity) from surface-based geophysical measurements (e.g., seismic, electric/magnetic (EM) data). The problems are governed by partial…
Comparing weighted networks in neuroscience is hard, because the topological properties of a given network are necessarily dependent on the number of edges of that network. This problem arises in the analysis of both weighted and unweighted…
Solutions proposed for the longstanding problem of automatic decomposition of Petri nets into concurrent processes, as well as methods developed in Grenoble for the automatic conversion of safe Petri nets to NUPNs (Nested-Unit Petri Nets),…
Transformers have emerged as the state of the art neural network architecture for natural language processing and computer vision. In the foundation model paradigm, large transformer models (BERT, GPT3/4, Bloom, ViT) are pre-trained on…
Thresholding--the pruning of nodes or edges based on their properties or weights--is an essential preprocessing tool for extracting interpretable structure from complex network data, yet existing methods face several key limitations.…
Automated verification of living organism models allows us to gain previously unknown knowledge about underlying biological processes. In this paper, we show the benefits to use parametric time Petri nets in order to analyze precisely the…
We study a mean field model of a complex network, focusing on edge and triangle densities. Our first result is the derivation of a variational characterization of the entropy density, compatible with the infinite node limit. We then…
Key features of biological activity can often be captured by transitions between a finite number of semi-stable states that correspond to behaviors or decisions. We present here a broad class of dynamical systems that are ideal for modeling…
We study the finite temperature (FT) phase transitions of two-dimensional (2D) $q$-states Potts models on the square lattice, using the first principles Monte Carlo (MC) simulations as well as the techniques of neural networks (NN). We…
Understanding the topological characteristics of complex networks and how they affect navigability is one of the most important goals in science today, as it plays a central role in various economic, biological, ecological and social…
The reachability semantics for Petri nets can be studied using open Petri nets. For us an "open" Petri net is one with certain places designated as inputs and outputs via a cospan of sets. We can compose open Petri nets by gluing the…