Related papers: Backbone decomposition of multitype superprocesses
Retrosynthesis consists of breaking down a chemical compound recursively step-by-step into molecular precursors until a set of commercially available molecules is found with the goal to provide a synthesis route. Its two primary research…
We consider an indecomposable Galton-Watson branching process with countably infinitely many types. Assuming that the process is critical and allowing for infinite variance of the offspring sizes of some (or all) types of particles we…
A multi-type neutral Cannings population model with mutation and fixed subpopulation sizes is analyzed. Under appropriate conditions, as all subpopulation sizes tend to infinity, the ancestral process, properly time-scaled, converges to a…
To understand the real world using various types of data, Artificial Intelligence (AI) is the most used technique nowadays. While finding the pattern within the analyzed data represents the main task. This is performed by extracting…
Designing novel proteins with desired functions is crucial in biology and chemistry. However, most existing work focus on protein sequence design, leaving protein sequence and structure co-design underexplored. In this paper, we propose…
The joint task of bug localization and program repair is an integral part of the software development process. In this work we present DeepDebug, an approach to automated debugging using large, pretrained transformers. We begin by training…
The goal of this document is to provide a pedagogical introduction to the main concepts underpinning the training of deep neural networks using gradient descent; a process known as backpropagation. Although we focus on a very influential…
A system of a metastable phase with several sorts of the heterogeneous centers is considered. An analytical theory for the process of decay in such a system has been constructed. The free energy of formation of the critical embryo is…
While entanglement is believed to be an important ingredient in understanding quantum many-body physics, the complexity of its characterization scales very unfavorably with the size of the system. Finding super-sets of the set of separable…
Bilevel optimization formulates hierarchical decision-making processes that arise in many real-world applications such as in pricing, network design, and infrastructure defense planning. In this paper, we consider a class of bilevel…
This paper proposes bimorphic recursion, which is restricted polymorphic recursion such that every recursive call in the body of a function definition has the same type. Bimorphic recursion allows us to assign two different types to a…
Proteins must fold quickly to acquire their biologically functional three-dimensional native structures. Hence, these are mainly stabilized by local contacts, while intricate topologies such as knots are rare. Here, we reveal the existence…
Massive networks have shown that the determination of dense subgraphs, where vertices interact a lot, is necessary in order to visualize groups of common interest, and therefore be able to decompose a big graph into smaller structures. Many…
We present an understandable, efficient, and streamlined proof of the Holonomy Decomposition for finite transformation semigroups and automata. This constructive proof closely follows the existing computational implementation. Its novelty…
The central problem of concern to Serrano, Boguna and Vespignani ("Extracting the multiscale backbone of complex weighted networks", Proc Natl Acad Sci 106:6483-6488 [2009]) can be effectively and elegantly addressed using a…
Parameter-efficient tuning has become a trend in transferring large-scale foundation models to downstream applications. Existing methods typically embed some light-weight tuners into the backbone, where both the design and the learning of…
Knotted proteins, when forced through the pores, can get stuck if the knots in their backbone tighten under force. Alternatively, the knot can slide off the chain, making translocation possible. We construct a simple energy landscape model…
In mechanical manipulation experiments, a single DNA molecule overwound at constant force undergoes a discontinuous drop in extension as it buckles and forms a superhelical loop (a plectoneme). Further overwinding the DNA, we observe an…
A mesoscopic model for heterogeneous DNA denaturation is developed in the framework of the path integral formalism. The base pair stretchings are treated as one-dimensional, time dependent paths contributing to the partition function. The…
We study the topological types of pants decompositions of a surface by associating to any pants decomposition $P,$ in a natural way its pants decomposition graph, $\Gamma(P).$ This perspective provides a convenient way to analyze the…