arXiv research

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

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…

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…

New invariant for tied links connects states without resolution dependence.

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-…

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…

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…

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).

We give new examples of 2-component links with linking number one and unknotted components that are topologically concordant to the positive Hopf link, but not smoothly so - in fact they are not smoothly concordant to the positive Hopf link with a knot tied in the first component. Such examples were previously construc…

It was shown by Jim Davis that a 2-component link with Alexander polynomial one is topologically concordant to the Hopf link. In this paper, we show that there is a 2-component link with Alexander polynomial one that has unknotted components and is not smoothly concordant to the Hopf link, answering a question of Jim D…

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

The Yamabe invariant is linked to static potentials and eigenvalues.

Topologically protected vortex knots and links are proposed and proven.

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

The possibility of latency arbitrage in financial markets has led to the deployment of high-speed communication links between distant financial centers. These links are noisy and so there is a need for coding. In this paper, we develop a gametheoretic model of trading behavior where two traders compete to capture laten…

In this paper we first present the construction of the new 2-variable classical link invariants arising from the Yokonuma-Hecke algebras ${\rm Y}_{d,n}(q)$, which are not topologically equivalent to the Homflypt polynomial. We then present the algebra ${\rm FTL}_{d,n}(q)$ which is the appropriate Temperley-Lieb analogu…

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…

Knowledge graphs contain knowledge about the world and provide a structured representation of this knowledge. Current knowledge graphs contain only a small subset of what is true in the world. Link prediction approaches aim at predicting new links for a knowledge graph given the existing links among the entities. Tenso…

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 $\bar A$, …

We establish a theoretical link between adversarial training and operator norm regularization for deep neural networks. Specifically, we prove that $\ell_p$-norm constrained projected gradient ascent based adversarial training with an $\ell_q$-norm loss on the logits of clean and perturbed inputs is equivalent to data-…

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

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

We show how bad and good volatility propagate through forex markets, i.e., we provide evidence for asymmetric volatility connectedness on forex markets. Using high-frequency, intra-day data of the most actively traded currencies over 2007 - 2015 we document the dominating asymmetries in spillovers that are due to bad r…

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…

TransINT embeds KGs by preserving implication rules, outperforming existing methods.

TPM improves medical image segmentation by separating foreground and background.

We derive a new radial link for binary classification under shared elliptical distributions.

Graphs (networks) are ubiquitous and allow us to model entities (nodes) and the dependencies (edges) between them. Learning a useful feature representation from graph data lies at the heart and success of many machine learning tasks such as classification, anomaly detection, link prediction, among many others. Many exi…

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…

This paper examines momentum spillover across multiple asset classes using only pricing data.

We propose a tensor-based model that fuses a more granular representation of user preferences with the ability to take additional side information into account. The model relies on the concept of ordinal nature of utility, which better corresponds to actual user perception. In addition to that, unlike the majority of h…

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 …

Optimized parallel algorithms for identifying strong ties in data.

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

Biological and cellular systems are often modeled as graphs in which vertices represent objects of interest (genes, proteins, drugs) and edges represent relational ties among these objects (binds-to, interacts-with, regulates). This approach has been highly successful owing to the theory, methodology and software that …

The study models and values CAT bonds across multiple regions.

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…

Study shows Bitcoin security tied to mining rewards and prices.

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…

BOtied optimizes multiple objectives using copulas and CDF indicators.

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 …

Paper defines and analyzes mathematical equivalence of periodic tangles.

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