Related papers: Mutually embeddable models of ZFC

The emergence of multicellularity and developmental programs are among the major problems of evolutionary biology. Traditionally, research in this area has been based on the combination of data analysis and experimental work on one hand and…

Basic principles of mathematical modeling are reviewed in this book, with the focus on physics and its practical applications, and examples of selected mathematical methods are presented. Most of the models have been imported from physics…

The primary goal of this paper is to establish a model of $ZFC$ wherein the definable tree property is affirmed for all uncountable regular cardinals. This endeavor commences with the utilization of both a supercompact cardinal and a…

Distributed representations (such as those based on embeddings) and discrete representations (such as those based on logic) have complementary strengths. We explore one possible approach to combining these two kinds of representations. We…

We consider the problem of defining quantum integrability in systems with finite number of energy levels starting from commuting matrices and construct new general classes of such matrix models with a given number of commuting partners. We…

Modeling relations between components of 3D objects is essential for many geometry editing tasks. Existing techniques commonly rely on labeled components, which requires substantial annotation effort and limits components to a dictionary of…

We summarize recent progress on the theory and applications of structural identifiability of compartmental models. On the applications side, we review identifiability analyses undertaken recently for models arising in epidemiology,…

We explore the connection between tasep-like interacting particle systems and last passage percolation type polymer models, focusing on three models: Geometric, Exponential and Brownian last passage percolation and their associated tasep…

We formulate one dimensional many-body integrable systems in terms of a new set of phase space variables involving exchange operators. The hamiltonian in these variables assumes a decoupled form. This greatly simplifies the derivation of…

Despite the flexibility and popularity of mixture models, their associated parameter spaces are often difficult to represent due to fundamental identification problems. This paper looks at a novel way of representing such a space for…

Ensuring the trustworthiness and interpretability of machine learning models is critical to their deployment in real-world applications. Feature attribution methods have gained significant attention, which provide local explanations of…

We study the combinatorial and structural properties of the circle map sequences. We introduce an embedding procedure which gives a map from the hull(closure of the set of translates) to the sequence of embedding operations through which we…

Despite their nearly universal adoption for large language models, the internal workings of transformers are not well understood. We aim to better understand the impact of removing or reorganizing information throughout the layers of a…

Finite mixtures are a flexible modeling tool for irregularly shaped densities and samples from heterogeneous populations. When modeling with mixtures using an exchangeable prior on the component features, the component labels are arbitrary…

We consider the simplest gauge theories given by one- and two- matrix integrals and concentrate on their stringy and geometric properties. We remind general integrable structure behind the matrix integrals and turn to the geometric…

Affine transformations in Euclidean space generates a correspondence between integrable systems on cotangent bundles to the sphere, ellipsoid and hyperboloid embedded in $R^n$. Using this correspondence and the suitable coupling constant…

The neural mechanisms supporting flexible relational inferences, especially in novel situations, are a major focus of current research. In the complementary learning systems framework, pattern separation in the hippocampus allows rapid…

In this note we describe a discrete dynamical system acting on the similarity classes of a plane convex body within the affine class of the body. We find invariant elements in all affine classes, and describe the orbits of bodies in some…

Folding and aggregation of proteins, the interaction between proteins and membranes, as well as the adsorption of organic soft matter to inorganic solid substrates belong to the most interesting challenges in understanding structure and…

Deep Foundation Models (DFMs) offer unprecedented capabilities but their increasing complexity presents profound challenges to understanding their internal workings-a critical need for ensuring trust, safety, and accountability. As we…