arXiv research

In this paper we introduce the tied links, i.e. ordinary links provided with some ties between strands. The motivation for introducing such objects originates from a diagrammatical interpretation of the defining generators of the so-called algebra of braids and ties; indeed, one half of such generators can be interpret…

Tied links and the tied braid monoid were introduced recently by the authors and used to define new invariants for classical links. Here, we give a version purely algebraic-combinatoric of tied links. With this new version we prove that the tied braid monoid has a decomposition like a semi--direct group product. By usi…

Study tied links in various 3-manifolds, introducing new groups and proving theorems.

New invariant for tied links connects states without resolution dependence.

New monoids tied to symmetric group and Jones/Brauer monoids discovered.

Paper derives explicit formulas for AJ-bracket of tied links.

Study of pseudo knots, links, and knotoids with braiding and L-moves.

We introduce the concept of tied links in the solid torus, which generalize naturally the concept of tied links in $S^3$ previously introduced by Aicardi and Juyumaya. We also define an invariant of these tied links by using skein relations, and subsequently we recover this invariant by using Jones' method over the bt-…

Let $M$ be a closed symplectic manifold of dimension $2n$ with non-ellipticity. We can define an almost Kähler structure on $M$ by using the given symplectic form. Hence, we have a $\G=π_1(M)$-invariant almost Kähler structure on the universal covering, $\ti M$, of $M$. Using Darboux coordinate charts, we globally defo…

We define two new invariants for tied links. One of them can be thought as an extension of the Kauffman polynomial and the other one as an extension of the Jones polynomial which is constructed via a bracket polynomial for tied links. These invariants are more powerful than both the Kauffman and the bracket polynomials…

Suppose $S$ is a surface of genus $\ge 2$, $f: S \to S$ is a surface homeomorphism isotopic to a pseudo-Anosov map $α$ and suppose $\ti S$ is the universal cover of $S$ and $F$ and $A$ are lifts of $f$ and $α$ respectively. We show there is a semiconjugacy $Θ: \ti S \to \bar Ł^s \times \bar Ł^u$ from $F$ to $\bar A$, …

NFT art market shows strong preferential ties among sellers and buyers.

Paper discusses extending Gini score for tied rankings and case weights.

In this paper we extend the concept of Competitivity Graph to compare series of rankings with ties ({\em partial rankings}). We extend the usual method used to compute Kendall's coefficient for two partial rankings to the concept of evolutive Kendall's coefficient for a series of partial rankings. The theoretical frame…

TPM improves medical image segmentation by separating foreground and background.

We prove that the so-called t algebra of braids and ties supports a Markov trace. Further, by using this trace in the Jones' recipe, we define invariant polynomials for classical knots and singular knots. Our invariants have three parameters. The invariant of classical knots is an extension of the Homflypt polynomial a…

Thermodynamic integration (TI) for computing marginal likelihoods is based on an inverse annealing path from the prior to the posterior distribution. In many cases, the resulting estimator suffers from high variability, which particularly stems from the prior regime. When comparing complex models with differences in a …

We introduce a two-parameters bt-algebra which, by specialization, becomes the one-parameter bt-algebra, introduced by the authors, as well as another one-parameter presentation of it; the invariant for links and tied links, associated to this two-parameter algebra via Jones recipe, contains as specializations the inva…

Optimized parallel algorithms for identifying strong ties in data.

Study framizations of algebras using Schur--Weyl duality and tied braids.

In this paper we research the differential geometric and algebro-geometric proper- ties of the noncollasping limit in the conical continuity equation.

We give a simple characterization of braids that can be unplaited keeping separately their upper ends and their lower ends tied together

MultiDendrograms is a Java-written application that computes agglomerative hierarchical clusterings of data. Starting from a distances (or weights) matrix, MultiDendrograms is able to calculate its dendrograms using the most common agglomerative hierarchical clustering methods. The application implements a variable-gro…

Numerous studies have been carried out to measure wind pressures around circular cylinders since the early 20th century due to its engineering significance. Consequently, a large amount of wind pressure data sets have accumulated, which presents an excellent opportunity for using machine learning (ML) techniques to tra…

Gating is a key technique used for integrating information from multiple sources by long short-term memory (LSTM) models and has recently also been applied to other models such as the highway network. Although gating is powerful, it is rather expensive in terms of both computation and storage as each gating unit uses a…

In this paper we propose a method to model speaker and session variability and able to generate likelihood ratios using neural networks in an end-to-end phrase dependent speaker verification system. As in Joint Factor Analysis, the model uses tied hidden variables to model speaker and session variability and a MAP adap…

Finding the most probable assignment (MAP) in a general graphical model is known to be NP hard but good approximations have been attained with max-product belief propagation (BP) and its variants. In particular, it is known that using BP on a single-cycle graph or tree reweighted BP on an arbitrary graph will give the …

Notes based on lessons given at {\sc Escuela " Fico González Acuña" de Nudos y 3-variedades}, Mérida Yucatán, México, 7--10 (2015) and {\sc Encuentro de nudos, trenzas y álgebras}, Oaxaca--México, 3--10 October (2018).

Paper uses referenced thermodynamic integration for Bayesian model selection in a complex COVID-19 transmission model.

FastCPH efficiently predicts survival times using neural networks.

It is well known that the twisters, section of twister space, classify the almost complex structure on even dimensional Riemannian manifold $X$. In this paper, it will be proved that a harmonic and anti-holomorphic twister is equivalent ti a symplectic structure on $X$.

Representation learning is an essential problem in a wide range of applications and it is important for performing downstream tasks successfully. In this paper, we propose a new model that learns coupled representations of domains, intents, and slots by taking advantage of their hierarchical dependency in a Spoken Lang…

The recently introduced dropout training criterion for neural networks has been the subject of much attention due to its simplicity and remarkable effectiveness as a regularizer, as well as its interpretation as a training procedure for an exponentially large ensemble of networks that share parameters. In this work we …

A manifold's discreteness is tied to its number of ends.

Classifies 85 tie knots into mathematical categories.

A review of the parallel transport (translation) in fibre bundles is presented. The connections between transports along paths and parallel transports in fibre bundles are examined. It is proved that the latter ones are special cases of the former.

We relate the existence of many infinite geodesics on Alexandrov spaces to a statement about the average growth of volumes of balls. We deduce that the geodesic flow exists and preserves the Liouville measure in several important cases. The developed analytic tool has close ties to integral geometry.

Many important forms of data are stored digitally in XML format. Errors can occur in the textual content of the data in the fields of the XML. Fixing these errors manually is time-consuming and expensive, especially for large amounts of data. There is increasing interest in the research, development, and use of automat…

Graph comparison ties to Alexandrov's theorems.

DEQs converge to optimal solutions with mild over-parameterization.

We explore the geometry of the Nahm-Schmid equations, a version of Nahm's equations in split signature. Our discussion ties up different aspects of their integrable nature: dimensional reduction from the Yang--Mills anti-self-duality equations, explicit solutions, Lax-pair formulation, conservation laws and spectral cu…

Researchers study how teachers' advising relationships influence their perceptions of satisfaction and students, not policy influence.

This paper compares rank aggregation methods for partial label ranking.

New spaces at infinity identified for Minkowski spacetime.

For a long time, designing neural architectures that exhibit high performance was considered a dark art that required expert hand-tuning. One of the few well-known guidelines for architecture design is the avoidance of exploding gradients, though even this guideline has remained relatively vague and circumstantial. We …

The Yamabe invariant is linked to static potentials and eigenvalues.

There is an implicit assumption that traditional hybrid approaches for automatic speech recognition (ASR) cannot directly model graphemes and need to rely on phonetic lexicons to get competitive performance, especially on English which has poor grapheme-phoneme correspondence. In this work, we show for the first time t…

Suppose (X,ω) is a compact Kähler manifold. In the present work we propose a simple construction for weak geodesic rays in the space of Kähler metrics that seems to be tied together with properties of the class E(X,ω). As an application of our construction, we prove a characterization of E(X,ω) in terms of envelopes.