Related papers: Backbone decomposition of multitype superprocesses
This paper addresses the decomposition of biochemical networks into functional modules that preserve their dynamic properties upon interconnection with other modules, which permits the inference of network behavior from the properties of…
We study toposes of actions of monoids on sets. We begin with ordinary actions, producing a class of presheaf toposes which we characterize. As groundwork for considering topological monoids, we branch out into a study of supercompactly…
Recent work in machine learning shows that deep neural networks can be used to solve a wide variety of inverse problems arising in computational imaging. We explore the central prevailing themes of this emerging area and present a taxonomy…
A homogeneous mass-fragmentation, as it has been defined in \cite{RFC}, describes the evolution of the collection of masses of fragments of an object which breaks down into pieces as time passes. Here, we show that this model can be…
We consider a branching stable process with positive jumps, i.e. a continuous-time branching process in which the particles evolve independently as stable L{\'e}vy processes with positive jumps. Assuming the branching mechanism is critical…
We propose a new model for multi-token prediction in transformers, aiming to enhance sampling efficiency without compromising accuracy. Motivated by recent work that predicts the probabilities of subsequent tokens using multiple heads, we…
Recurrent neural networks have been the dominant models for many speech and language processing tasks. However, we understand little about the behavior and the class of functions recurrent networks can realize. Moreover, the heuristics used…
We consider general discrete-time multitype branching processes on a countable set $X$. According to these processes, a particle of type $x\in X$ generates a random number of children and chooses their type in $X$, not necessarily…
Deciphering cell type heterogeneity is crucial for systematically understanding tissue homeostasis and its dysregulation in diseases. Computational deconvolution is an efficient approach estimating cell type abundances from a variety of…
We introduce a new computational problem, the BackboneDiscovery problem, which encapsulates both functional and structural aspects of network analysis. While the topology of a typical road network has been available for a long time (e.g.,…
We investigate the limit behavior of supercritical multitype branching processes in random environments with linear fractional offspring distributions and show that there exists a phase transition in the behavior of local probabilites of…
The applicability of computational models to the biological world is an active topic of debate. We argue that a useful path forward results from abandoning hard boundaries between categories and adopting an observer-dependent, pragmatic…
Multivariate Hawkes process provides a powerful framework for modeling temporal dependencies and event-driven interactions in complex systems. While existing methods primarily focus on uncovering causal structures among observed…
We consider a disentanglement process in which local properties of an entangled state are preserved, while the entanglement between the subsystems is erased. Sufficient conditions for a perfect disentanglement (into product states and into…
This paper introduces a new family of reconstruction codes which is motivated by applications in DNA data storage and sequencing. In such applications, DNA strands are sequenced by reading some subset of their substrings. While previous…
In this work we study the bisexual Galton-Watson process with a finite number of types, where females and males mate according to a ''mating function'' and form couples of different types. We assume that this function is superadditive,…
A stretched DNA molecule which is also under- or overwound, undergoes a buckling transition forming intertwined looped domains called plectonemes. Here we develop a simple theory that extends the two-phase model of stretched supercoiled…
Tensor decomposition methods are widely used for model compression and fast inference in convolutional neural networks (CNNs). Although many decompositions are conceivable, only CP decomposition and a few others have been applied in…
A system of a metastable phase with a pseudo continuous set of the heterogeneous centers is considered. An analytical theory for kinetics of decay of the metastable phase in such a system is constructed. The free energy of formation of a…
In large-scale software systems, there are often no fully-fledged bug reports with human-written descriptions when an error occurs. In this case, developers rely on stack traces, i.e., series of function calls that led to the error. Since…