Related papers: Bethe Ansatz in the Bernoulli Matching Model of Ra…
We solve the $A_{2n}^{(2)}$ vertex model with all kinds of diagonal reflecting matrices by using the algebraic Behe ansatz, which includes constructing the multi-particle states and achieving the eigenvalue of the transfer matrix and…
We consider the problem of learning general-purpose, paraphrastic sentence embeddings based on supervision from the Paraphrase Database (Ganitkevitch et al., 2013). We compare six compositional architectures, evaluating them on annotated…
The eigenfunctions and eigenvalues of the master-equation for zero range process with totally asymmetric dynamics on a ring are found exactly using the Bethe ansatz weighted with the stationary weights of particle configurations. The Bethe…
Network alignment has extensive applications in comparative interactomics. Traditional approaches aim to simultaneously maximize the number of conserved edges and the underlying similarity of aligned entities. We propose a novel formulation…
Recent sequential pattern mining methods have used the minimum description length (MDL) principle to define an encoding scheme which describes an algorithm for mining the most compressing patterns in a database. We present a novel…
A time-delay embedding (TDE), grounded in the framework of Takens's Theorem, provides a mechanism to represent and analyze the inherent dynamics of time-series data. Recently, topological data analysis (TDA) methods have been applied to…
While large scale pre-trained language models such as BERT have achieved great success on various natural language understanding tasks, how to efficiently and effectively incorporate them into sequence-to-sequence models and the…
Network representation learning (NRL) methods have received significant attention over the last years thanks to their success in several graph analysis problems, including node classification, link prediction, and clustering. Such methods…
In this proceeding we present the nested Bethe ansatz for open spin chains of XXX-type, with arbitrary representations (i.e. `spins') on each site of the chain and diagonal boundary matrices $(K^+(u),K^-(u))$. The nested Bethe anstaz…
Topological data analysis (TDA) is a fast-growing field that utilizes advanced tools from topology to analyze large-scale data. A central problem in topological data analysis is estimating the so-called Betti numbers of the underlying…
Lattices are an efficient and effective method to encode ambiguity of upstream systems in natural language processing tasks, for example to compactly capture multiple speech recognition hypotheses, or to represent multiple linguistic…
Network representation learning (NRL) methods aim to map each vertex into a low dimensional space by preserving the local and global structure of a given network, and in recent years they have received a significant attention thanks to…
In Bayesian applications, there is a huge interest in rapid and accurate estimation of the posterior distribution, particularly for high dimensional or hierarchical models. In this article, we propose to use optimization to solve for a…
The $A^{(1)}_{n-1}$ trigonometric vertex model with {\it generic non-diagonal} boundaries is studied. The double-row transfer matrix of the model is diagonalized by algebraic Bethe ansatz method in terms of the intertwiner and the…
Summary: Longer sequencing reads, with at least 200 bases per template are now common. While traditional aligners have adopted new strategies to improve the mapping of longer reads, aligners specific to bisulfite-sequencing were optimized…
A new set of DNA base-nucleic acid codes and their hypercomplex number representation have been introduced for taking the probability of each nucleotide into full account. A new scoring system has been proposed to suit the hypercomplex…
We study pattern matching problems on two major representations of uncertain sequences used in molecular biology: weighted sequences (also known as position weight matrices, PWM) and profiles (i.e., scoring matrices). In the simple version,…
Binarization is an attractive strategy for implementing lightweight Deep Convolutional Neural Networks (CNNs). Despite the unquestionable savings offered, memory footprint above all, it may induce an excessive accuracy loss that prevents a…
Building systems with capability of natural language understanding (NLU) has been one of the oldest areas of AI. An essential component of NLU is to detect logical succession of events contained in a text. The task of sentence ordering is…
Variational inference in probabilistic graphical models aims to approximate fundamental quantities such as marginal distributions and the partition function. Popular approaches are the Bethe approximation, tree-reweighted, and other types…