Related papers: On the Counting of Fully Packed Loop Configuration…
Protein-protein interactions (PPIs) are fundamental to numerous cellular processes, and their characterization is vital for understanding disease mechanisms and guiding drug discovery. While protein language models (PLMs) have demonstrated…
We use finite-time Lyapunov exponent (FTLE) distributions to probe transition mechanisms in high-dimensional reservoir maps trained on low-dimensional chaotic dynamics across multiple regimes. While trained reservoirs accurately predict…
This is a technical report, containing all the theorem proofs in the following two papers: (1) Liang Ma, Ting He, Kin K. Leung, Ananthram Swami, and Don Towsley, "Identifiability of Link Metrics Based on End-to-end Path Measurements," in…
We discuss one-dimensional stochastic processes defined through the Temperley-Lieb algebra related to the Q=1 Potts model. For various boundary conditions, we formulate a conjecture relating the probability distribution which describes the…
We discuss in this paper combinatorial aspects of boundary loop models, that is models of self-avoiding loops on a strip where loops get different weights depending on whether they touch the left, the right, both or no boundary. These…
We study combinatorial configurations with the associated point and line graphs being strongly regular. Examples not belonging to known classes such as partial geometries and their generalizations or elliptic semiplanes are constructed.…
In this work a field theoretical model is constructed to describe the statistical mechanics of an arbitrary number of topologically linked polymers in the context of the analytical approach of Edwards. As an application, the effects of the…
The threshold, or saturation phenomenon of spatially coupled systems is revisited in the light of Lyapunov's theory of dynamical systems. It is shown that an application of Lyapunov's direct method can be used to quantitatively describe the…
The pair distribution function and the static structure factor are computed for composite fermions. Clear and robust evidence for a $2k_F$ structure is seen in a range of filling factors in the vicinity of the half-filled Landau level.…
The paper investigates the properties of a fuzzy logic of typicality. The extension of fuzzy logic with a typicality operator was proposed in recent work to define a fuzzy multipreference semantics for Multilayer Perceptrons, by regarding…
It is increasingly common to model, simulate, and process complex materials based on loopy structures, such as in yarn-level cloth garments, which possess topological constraints between inter-looping curves. While the input model may…
Large-scale language models (LLMs) operate in extremely high-dimensional state spaces, where both token embeddings and their hidden representations create complex dependencies that are not easily reduced to classical Markov structures. In…
Link prediction in complex networks has attracted increasing attention from both physical and computer science communities. The algorithms can be used to extract missing information, identify spurious interactions, evaluate network evolving…
In this paper we study various properties of finite stochastic systems or hidden Markov chains as they are alternatively called. We discuss their construction following different approaches and we also derive recursive filtering formulas…
The traditional setup of link prediction in networks assumes that a test set of node pairs, which is usually balanced, is available over which to predict the presence of links. However, in practice, there is no test set: the ground-truth is…
We present a braided circuit topology framework for investigating topology and structural phase transitions in aggregates of semiflexible polymers. In the conventional approach to circuit topology, which specifically applies to single…
We consider the observability model in networks with arbitrary topologies. We introduce a system of coupled nonlinear equations, valid under the locally tree-like ansatz, to describe the size of the largest observable cluster as a function…
In order to obtain functional limit theorems for heavy tailed stationary processes arising from dynamical systems, one needs to understand the clustering patterns of the tail observations of the process. These patterns are well described by…
Logarithmic Conformal Field Theories (LCFT) play a key role, for instance, in the description of critical geometrical problems (percolation, self avoiding walks, etc.), or of critical points in several classes of disordered systems…
A principled approach to understand network structures is to formulate generative models. Given a collection of models, however, an outstanding key task is to determine which one provides a more accurate description of the network at hand,…