arXiv research

Study $G_2$ skein algebra elements using Kuperberg webs and threading operations.

Quantum Frobenius map for $SL_3$ skein modules constructed and described.

We discuss Darboux-Staude type of thread configurations for the ellipsoid similar to Chasles-Graves type of thread configurations for the ellipse. These threads are formed by rectilinear segments, geodesic and line of curvature segments on the considered ellipsoid and with tangents tangent to the given ellipsoid and a …

Online discussion forums are complex webs of overlapping subcommunities (macrolevel structure, across threads) in which users enact different roles depending on which subcommunity they are participating in within a particular time point (microlevel structure, within threads). This sub-network structure is implicit in m…

Study on bit threads and their locking properties in holographic spacetimes.

Bit threads provide an alternative description of holographic entanglement, replacing the Ryu-Takayanagi minimal surface with bulk curves connecting pairs of boundary points. We use bit threads to prove the monogamy of mutual information (MMI) property of holographic entanglement entropies. This is accomplished using t…

Closed formulas for η-corrections in the once-punctured torus identified.

(NOTE: per referee comments, this article has been split; it is now superseded by "Existence of thread-wire minimizers" and "Near-wire thread-wire minimizers"; please see http://www.bkstephens.net.) Alt's thread problem asks for least-area surfaces bounding a fixed "wire" curve and a movable "thread" curve of length L.…

Study identifies stable configurations of intertwined threads with repulsive interactions.

Given a knot diagram $D$, we construct a semi-threading circle for it which can be an axis of $D$ as a closed braid depending on knot diagrams. In particular, we consider semi-threading circles for minimal diagrams of a knot with respect to overpasses which give us some information related to the braid index. By this n…

A deep-learning inference accelerator is synthesized from a C-language software program parallelized with Pthreads. The software implementation uses the well-known producer/consumer model with parallel threads interconnected by FIFO queues. The LegUp high-level synthesis (HLS) tool synthesizes threads into parallel FPG…

A new deep metric learning method for defect classification in threaded pipe connections.

Stochastic gradient descent (SGD) is an immensely popular approach for online learning in settings where data arrives in a stream or data sizes are very large. However, despite an ever-increasing volume of work on SGD, much less is known about the statistical inferential properties of SGD-based predictions. Taking a fu…

This paper describes our system submitted to SemEval 2019 Task 7: RumourEval 2019: Determining Rumour Veracity and Support for Rumours, Subtask A (Gorrell et al., 2019). The challenge focused on classifying whether posts from Twitter and Reddit support, deny, query, or comment a hidden rumour, truthfulness of which is …

We address the issue of speeding up the training of convolutional neural networks by studying a distributed method adapted to stochastic gradient descent. Our parallel optimization setup uses several threads, each applying individual gradient descents on a local variable. We propose a new way of sharing information bet…

New central elements found in a quantum algebra related to knot theory.

Based on a general $(1+3)$ threading of the spacetime $(M,g)$, we obtain a new and simple splitting of a both the Einstein field equations (EFE) and the conservation laws in $(M,g)$. As an application we obtain the splitting of (EFE) in an almost FLRW universe with energy-momentum tensor of a perfect fluid. In particul…

The Ryu-Takayanagi (RT) formula relates the entanglement entropy of a region in a holographic theory to the area of a corresponding bulk minimal surface. Using the max flow-min cut principle, a theorem from network theory, we rewrite the RT formula in a way that does not make reference to the minimal surface. Instead, …

We develop a new approach on the (1+3) threading of spacetime $(M, g)$ with respect to a congruence of curves defined by an arbitrary timelike vector field. The study is based on spatial tensor fields and on the Riemannian spatial connection $\nabla^{\star}$, which behave as $3D$ geometric objects. We obtain new formul…

DeepTraderX learns from other strategies to place market orders.

We address the issue of speeding up the training of convolutional networks. Here we study a distributed method adapted to stochastic gradient descent (SGD). The parallel optimization setup uses several threads, each applying individual gradient descents on a local variable. We propose a new way to share information bet…

We continue our research work started in "Kinematic Quantities and Raychaudhuri Equations in a $5D$ Universe" (Eur. Phys. J. C, 2015), and obtain in a covariant form, the equations of motion with respect to the $(1+1+3)$ threading of a $5D$ universe $(\bar{M}, \bar{g})$. The natural splitting of the tangent bundle of $…

We present a numerical model for the dynamics of thin viscous threads based on a discrete, Lagrangian formulation of the smooth equations. The model makes use of a condensed set of coordinates, called the centerline/spin representation: the kinematical constraints linking the centerline's tangent to the orientation of …

New simulation shows trading algorithms' performance varies with parallelism.

We expect manifolds obtained by Dehn filling to inherit properties from the knot manifold. To what extent does that hold true for the Heegaard structure? We study four changes to the Heegaard structure that may occur after filling: (1) Heegaard genus decreases, (2) a new Heegaard surface is created, (3) a non-stabilize…

Self-Organizing Maps (SOM) are popular unsupervised artificial neural network used to reduce dimensions and visualize data. Visual interpretation from Self-Organizing Maps (SOM) has been limited due to grid approach of data representation, which makes inter-scenario analysis impossible. The paper proposes a new way to …

Frobenius homomorphisms for SL_n skein modules generalize knot theory results.

AI agents on social networks rarely engage in extended conversations.

Stochastic gradient descent (SGD) is a well known method for regression and classification tasks. However, it is an inherently sequential algorithm at each step, the processing of the current example depends on the parameters learned from the previous examples. Prior approaches to parallelizing linear learners using SG…

This paper optimizes object tracking on edge devices with small matrices.

This paper proposes SplitSGD, a new dynamic learning rate schedule for stochastic optimization. This method decreases the learning rate for better adaptation to the local geometry of the objective function whenever a stationary phase is detected, that is, the iterates are likely to bounce at around a vicinity of a loca…

This paper classifies a specific weave type by their crossing number.

We present a generic framework for parallel coordinate descent (CD) algorithms that includes, as special cases, the original sequential algorithms Cyclic CD and Stochastic CD, as well as the recent parallel Shotgun algorithm. We introduce two novel parallel algorithms that are also special cases---Thread-Greedy CD and …

Algorithm of construction of all knots, links with given number of crosses on diagram of knot, link is offered. This algorithm is based on simple proposition, that there is a representation of knot (link) as closure of braid with n threads and length of this braid does not exceed n(4n-5)+2.

BBE simulates sports betting exchanges for data generation.

This paper classifies periodic weaves and their universal cover, extending Tait's conjectures.

This paper surveys work on generalized Johnson homomorphisms and tools for studying them. The goal is to unite several related threads in the literature and to clarify existing results and relationships among them using Hodge theory. We survey the work of Alekseev, Kawazumi, Kuno and Naef on the Goldman--Turaev Lie bia…

The present work has as principal objective analyze the evolution of the process of privatization, mergers and acquisitions of the big companies in the country in the last decades, to understand the conductive threads that formed the structural changes of the economy, in order world oligopólicas to insert it to the glo…

We first review the notion of a $G_2$-manifold, defined in terms of a principal $G_2$ ("gauge") bundle over a $7$-dimensional manifold, before discussing their relation to supergravity. In a second thread, we focus on associative submanifolds and present their deformation theory. In particular, we elaborate on a deform…

We establish that first-order methods avoid saddle points for almost all initializations. Our results apply to a wide variety of first-order methods, including gradient descent, block coordinate descent, mirror descent and variants thereof. The connecting thread is that such algorithms can be studied from a dynamical s…

The study of topological properties of random smooth maps, focusing on Kac-Rice formula and Betti numbers.

Post-quantum cryptography needed for blockchain security.

Training neural network often uses a machine learning framework such as TensorFlow and Caffe2. These frameworks employ a dataflow model where the NN training is modeled as a directed graph composed of a set of nodes. Operations in neural network training are typically implemented by the frameworks as primitives and rep…

Linear algebra algorithms are used widely in a variety of domains, e.g machine learning, numerical physics and video games graphics. For all these applications, loop-level parallelism is required to achieve high performance. However, finding the optimal way to schedule the workload between threads is a non-trivial prob…

liquidSVM is a package written in C++ that provides SVM-type solvers for various classification and regression tasks. Because of a fully integrated hyper-parameter selection, very carefully implemented solvers, multi-threading and GPU support, and several built-in data decomposition strategies it provides unprecedented…

Paper characterizes isotopies and hyperbolicity of weaves using geodesics.

We exploit the link between the transport equation and derivatives of expectations to construct efficient pathwise gradient estimators for multivariate distributions. We focus on two main threads. First, we use null solutions of the transport equation to construct adaptive control variates that can be used to construct…

Unified view of improving tree model interpretability and debiasing feature importance.