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We introduce the notion of ''maximal rank type'' for representations of quivers, which requires certain collections of maps involved in the representation to be of maximal rank. We show that real root representations of quivers are of…
Deep generative modeling for biological sequences presents a unique challenge in reconciling the bias-variance trade-off between explicit biological insight and model flexibility. The deep manifold sampler was recently proposed as a means…
For a fixed root of a quiver, it is a very hard problem to construct all or even only one indecomposable representation with this root as dimension vector. We investigate two methods which can be used for this purpose. In both cases we get…
A novel technique based on machine learning is introduced to reconstruct the decays of highly Lorentz-boosted particles. Using an end-to-end deep learning strategy, the technique bypasses existing rule-based particle reconstruction methods…
We present a new third-order, semi-discrete, central method for approximating solutions to multi-dimensional systems of hyperbolic conservation laws, convection-diffusion equations, and related problems. Our method is a high-order extension…
Efficient resource allocation and optical switching promise high key rates, network adaptability, and cost reduction in repeaterless quantum communication networks. However, identifying optimal switching configurations remains a significant…
A hereditary property of quivers is a property preserved by restriction to any full subquiver. Similarly, a mutation-invariant property of quivers is a property preserved by mutation. Using forks, a class of quivers developed by M.…
The reconstruction of phylogenies from DNA or protein sequences is a major task of computational evolutionary biology. Common phenomena, notably variations in mutation rates across genomes and incongruences between gene lineage histories,…
A quiver mutation loop is a sequence of mutations and vertex relabelings, along which a quiver transforms back to the original form. For a given mutation loop, we introduce a quantity called a partition q-series. The partition q-series are…
We introduce new methods for phylogenetic tree quartet construction by using machine learning to optimize the power of phylogenetic invariants. Phylogenetic invariants are polynomials in the joint probabilities which vanish under a model of…
A proper subsemigroup of a semigroup is maximal if it is not contained in any other proper subsemigroup. A maximal subsemigroup of a finite semigroup has one of a small number of forms, as described in a paper of Graham, Graham, and Rhodes.…
This paper explores the ability of the Chinese Remainder Theorem formalism to model Montgomery-type algorithms. A derivation of CRT based on Qin's Identity gives Montgomery reduction algorithm immediately. This establishes a unified…
Materials discovery is decisive for tackling urgent challenges related to energy, the environment, health care and many others. In chemistry, conventional methodologies for innovation usually rely on expensive and incremental strategies to…
Although deep learning has demonstrated remarkable capability in learning from unstructured data, modern tree-based ensemble models remain superior in extracting relevant information and learning from structured datasets. While several…
First-order applicative term rewriting systems provide a natural framework for modeling higher-order aspects. In earlier work we introduced an uncurrying transformation which is termination preserving and reflecting. In this paper we…
Ensemble models refer to methods that combine a typically large number of classifiers into a compound prediction. The output of an ensemble method is the result of fitting a base-learning algorithm to a given data set, and obtaining diverse…
In the recent research of data mining, frequent structures in a sequence of graphs have been studied intensively, and one of the main concern is changing structures along a sequence of graphs that can capture dynamic properties of data. On…
A minimal (by inclusion) generating set for the algebra of semi-invariants of a quiver of dimension (2,...,2) is established over an infinite field of arbitrary characteristic. The mentioned generating set consists of the determinants of…
A method of prediction is presented to aid compression of sequences of complex-valued samples. The focus is on using prediction to reduce the average magnitude of residual values after prediction (not on the subsequent compression of the…
Conservation laws are time-invariant properties that constrain many physical systems. For systems of chemical reactions, the law of mass conservation constrains how atoms flow between chemical species. Chemical reaction networks can display…