arXiv research

We consider in this paper a class of composite optimization problems whose objective function is given by the summation of a general smooth and nonsmooth component, together with a relatively simple nonsmooth term. We present a new class of first-order methods, namely the gradient sliding algorithms, which can skip the…

This paper provides a framework to analyze stochastic gradient algorithms in a mean squared error (MSE) sense using the asymptotic normality result of the stochastic gradient descent (SGD) iterates. We perform this analysis by taking the asymptotic normality result and applying it to the finite iteration case. Specific…

We propose a sliding surface for systems on the Lie group $SO(3)\times \mathbb{R}^3$ . The sliding surface is shown to be a Lie subgroup. The reduced-order dynamics along the sliding subgroup have an almost globally asymptotically stable equilibrium. The sliding surface is used to design a sliding-mode controller for t…

Constrained second-order convex optimization algorithms are the method of choice when a high accuracy solution to a problem is needed, due to their local quadratic convergence. These algorithms require the solution of a constrained quadratic subproblem at every iteration. We present the \emph{Second-Order Conditional G…

Improved complexity for machine learning optimization methods.

New algorithms improve distributed optimization under specific conditions.

The paper analyzes the sliding regret of stochastic bandit algorithms.

Presentations for involutions on non-orientable surfaces up to genus 5.

We determine all critical configurations for the Area function on polygons with vertices on a circle or an ellipse. For isolated critical points we compute their Morse index, resp index of the gradient vector field. We relate the computation at an isolated degenerate point to an eigenvalue question about combinations. …

We present a new operation to be performed on elements in a Garside group, called cyclic sliding, which is introduced to replace the well known cycling and decycling operations. Cyclic sliding appears to be a more natural choice, simplifying the algorithms concerning conjugacy in Garside groups and having nicer theoret…

Novel time series forecasting method using sliding window signatures.

Proposes a sliding window method for better portfolio trading.

Paper simplifies proof of slide-equivalence in crown diagrams.

Optimizes sliding window approach for tracking Gaussian densities.

Let $N_{g}$ denote a closed nonorientable surface of genus $g$. For $g \geq 2$ the mapping class group $\mathcal{M}(N_{g})$ is generated by Dehn twists and one crosscap slide ($Y$-homeomorphism) or by Dehn twists and a crosscap transposition. Margalit and Schleimer observed that Dehn twists have nontrivial roots. We gi…

Small bubbles sliding on a boundary maintain half-spherical shape.

We show that reducible braids which are, in a Garside-theoretical sense, as simple as possible within their conjugacy class, are also as simple as possible in a geometric sense. More precisely, if a braid belongs to a certain subset of its conjugacy class which we call the stabilized set of sliding circuits, and if it …

If a variational problem comes with no boundary conditions prescribed beforehand, and yet these arise as a consequence of the variation process itself, we speak of a free boundary values variational problem. Such is, for instance, the problem of finding the shortest curve whose endpoints can slide along two prescribed …

A theorem of Kirby states that two framed links in the 3-sphere produce orientation-preserving homeomorphic results of surgery if they are related by a sequence of stabilization and handle-slide moves. The purpose of the present paper is twofold: First, we give a sufficient condition for a sequence of handle-slides on …

Kirby color defined in Khovanov homology for 4D handlebodies.

A new method SLIDE ensures fairness in AI models.

We analyze higher-dimensional sliding puzzles, finding solvability patterns.

Crosscap slide is a homeomorphism of a nonorientable surface of genus at least 2, which was introduced under the name Y-homeomorphism by Lickorish as an example of an element of the mapping class group which cannot be expressed as a product of Dehn twists. We prove that the subgroup of the mapping class group of a clos…

New algorithms achieve optimal regret in sliding window model with limited memory.

We present a novel approach to train pixel resolution segmentation models on whole slide images in a weakly supervised setup. The model is trained to classify patches extracted from slides. This leads the training to be made under noisy labeled data. We solve the problem with two complementary strategies. First, the pa…

In many applications, monitoring area under the ROC curve (AUC) in a sliding window over a data stream is a natural way of detecting changes in the system. The drawback is that computing AUC in a sliding window is expensive, especially if the window size is large and the data flow is significant. In this paper we propo…

We propose a means by which some categorifications can be evaluated at a root of unity. This is implemented using a suitable localization in the context of prior work by the authors on categorification of the Jones-Wenzl projectors. Within this construction we define objects, invariant under handle slides, which decate…

TAKDE optimizes kernel density estimation for real-time dynamic processes.

Bedside monitors in Intensive Care Units (ICUs) frequently sound incorrectly, slowing response times and desensitising nurses to alarms (Chambrin, 2001), causing true alarms to be missed (Hug et al., 2011). We compare sliding window predictors with recurrent predictors to classify patient state-of-health from ICU multi…

Study predicts cryptocurrency trends using LSTM model.

A new method for real-time CCA on streaming data.

New robustness certificates for streaming models with a sliding window.

Bordered Heegaard Floer homology is an invariant for three-manifolds with boundary. In particular, this invariant associates to a handle decomposition of a surface F a differential graded algebra, and to an arc slide between two handle decompositions, a bimodule over the two algebras. In this paper, we describe these b…

Garside-theoretical solutions to the conjugacy problem in braid groups depend on the determination of a characteristic subset of the conjugacy class of any given braid, e.g. the sliding circuit set. It is conjectured that, among rigid braids with a fixed number of strands, the size of this set is bounded by a polynomia…

A knot K in the 3-sphere is said to have Property nR if, whenever K is a component of an n-component link L and some integral surgery on L produces the connected sum of n copies of S^1 x S^2, there is a sequence of handle slides on L that converts L into a 0-framed unlink. The Generalized Property R Conjecture is that …

Let N_{g,s} denote the nonorientable surface of genus g with s boundary components. Recently Paris and Szepietowski obtained an explicit finite presentation for the mapping class group M(N_{g,s}) of the surface N_{g,s}, where s\in{0,1} and g+s>3. Following this work we obtain a finite presentation for the mapping class…

Study examines asset pricing using various attention models, finding global self-attention and sliding window sparse attention models perform well.

A new PGA algorithm ensures stable, robust, and noise-immune solutions for non-negative inverse problems.

In this paper we introduce a new technique based on high-dimensional Chebyshev Tensors that we call \emph{Orthogonal Chebyshev Sliding Technique}. We implemented this technique inside the systems of a tier-one bank, and used it to approximate Front Office pricing functions in order to reduce the substantial computation…

We consider reinforcement learning in changing Markov Decision Processes where both the state-transition probabilities and the reward functions may vary over time. For this problem setting, we propose an algorithm using a sliding window approach and provide performance guarantees for the regret evaluated against the op…

We present a new algorithm for the 2D Sliding Window Discrete Fourier Transform (SWDFT). Our algorithm avoids repeating calculations in overlapping windows by storing them in a tree data-structure based on the ideas of the Cooley- Tukey Fast Fourier Transform (FFT). For an $N_0 \times N_1$ array and $n_0 \times n_1$ wi…

Task-specific scores are often used to optimize for and evaluate the performance of conditional text generation systems. However, such scores are non-differentiable and cannot be used in the standard supervised learning paradigm. Hence, policy gradient methods are used since the gradient can be computed without requiri…

We present the classical Wagner construction from 1935 of the curvature tensor for completely nonholonomic manifolds in both invariant and coordinate way. The starting point is the Shouten curvature tensor for nonholonomic connection introduced by Vranceanu and Shouten. We illustrate the construction on two mechanical …

Paper studies simplified trisections and their equivalence classes.

We give an example of two JSJ decompositions of a group that are not related by conjugation, conjugation of edge-inclusions, and slide moves. This answers the question of Rips and Sela stated in "Cyclic splittings of finitely presented groups and the canonical JSJ decomposition," Ann. of Math. 146 (1997), 53-109. On th…

The increased availability of the multi-view data (data on the same samples from multiple sources) has led to strong interest in models based on low-rank matrix factorizations. These models represent each data view via shared and individual components, and have been successfully applied for exploratory dimension reduct…

In this paper we study the reduction curves of a braid, and how they can be used to decompose the braid into simpler ones in a precise way, which does not correspond exactly to the decomposition given by Thurston theory. Then we study how a cyclic sliding (which is a particular kind of conjugation) affects the normal f…

We study the multi-player stochastic multiarmed bandit (MAB) problem in an abruptly changing environment. We consider a collision model in which a player receives reward at an arm if it is the only player to select the arm. We design two novel algorithms, namely, Round-Robin Sliding-Window Upper Confidence Bound\# (RR-…