arXiv research

Paper explores conditions for constructing new quasi-alternating links.

Paper proposes an alternative method to price American options using HJM approach.

An alternative method is described for determining the hyperbolic structure on a link complement, and some of its elementary consequences are examined. The method is particularly suited to alternating links.

Alternating minimization represents a widely applicable and empirically successful approach for finding low-rank matrices that best fit the given data. For example, for the problem of low-rank matrix completion, this method is believed to be one of the most accurate and efficient, and formed a major component of the wi…

New theory connects geometry without relying on connections.

New invariant for prime alternating knots from error-correcting codes

Given a dataset and an existing clustering as input, alternative clustering aims to find an alternative partition. One of the state-of-the-art approaches is Kernel Dimension Alternative Clustering (KDAC). We propose a novel Iterative Spectral Method (ISM) that greatly improves the scalability of KDAC. Our algorithm is …

Pairwise Choice Markov Chains (PCMC) have been recently introduced to overcome limitations of choice models based on traditional axioms unable to express empirical observations from modern behavior economics like context effects occurring when a choice between two options is altered by adding a third alternative. The i…

Alternative metric defined on vector bundles, proving vanishing theorem.

Investigates optimal consumption and investment using alternative data sources.

We propose an alternative approach on the existence of affine realizations for HJM interest rate models. It is applicable to a wide class of models, and simultaneously it is conceptually rather comprehensible. We also supplement some known existence results for particular volatility structures and provide further insig…

We show that quasi-alternating links arise naturally when considering surgery on a strongly invertible L-space knot (that is, a knot that yields an L-space for some Dehn surgery). In particular, we show that for many known classes of L-space knots, every sufficiently large surgery may be realized as the two-fold branch…

Alternative construction of Rumin complex on Lie groups.

Efficiently completes low-rank matrices with nearly linear time complexity.

The paper studies alternating links in thickened surfaces using flow lattices and disc mutations.

Characterizes a specific type of neural network for alternating group equivariance.

The floating body approach to affine surface area is adapted to a holomorphic context providing an alternate approach to Fefferman's invariant hypersurface measure.

This paper presents a model to describe contractual dispute resolution by mediation in situations where a defaulting supplier is near insolvent. While each party has internal constraints, and if alternate performances are available, such as more costly alternative goods, the proposed approach allows the mediator to fin…

Zero Emission Vehicles (ZEV) play an important role in the decarbonization of the transportation sector. For a wider adoption of ZEVs, providing a reliable infrastructure is critical. We present a machine learning approach that uses unsupervised temporal clustering algorithm along with survey analysis to determine infr…

Study optimizes sampling to avoid extreme tail risks in unknown heavy-tailed distributions.

Checkerboard surfaces in alternating link complements are used frequently to determine information about the link. However, when many crossings are added to a single twist region of a link diagram, the geometry of the link complement stabilizes (approaches a geometric limit), but a corresponding checkerboard surface in…

Link invariants fail to detect most links with high probability.

Model analyzes cooccurrence data for recommender systems and item relevance.

A meta-learning approach improves the performance of alternating minimization for non-convex optimization problems.

Alternative neural network training using monotone variational inequality.

Introduces a new geometric method for optimal experimental design.

A new method constrains PARAFAC2 for better pattern recovery.

New method improves predictive systems with better theoretical guarantees.

It is well known that the braid index of a link equals the minimum number of Seifert circles among all link diagrams representing it. For a link with a reduced alternating diagram $D$, $s(D)$, the number of Seifert circles in $D$, equals the braid index $\textbf{b}(D)$ of $D$ if $D$ contains no {\em lone crossings} (a …

Two new methods for option pricing without or with a riskless asset.

This thesis is concerned with the question of when the double branched cover of an alternating knot can arise by Dehn surgery on a knot in $S^3$. We approach this problem using a surgery obstruction, first developed by Greene, which combines Donaldson's Diagonalization Theorem with the $d$-invariants of Ozsv{á}th and S…

Recent success in deep reinforcement learning for continuous control has been dominated by model-free approaches which, unlike model-based approaches, do not suffer from representational limitations in making assumptions about the world dynamics and model errors inevitable in complex domains. However, they require a lo…

Matrix Factorization is a popular non-convex optimization problem, for which alternating minimization schemes are mostly used. They usually suffer from the major drawback that the solution is biased towards one of the optimization variables. A remedy is non-alternating schemes. However, due to a lack of Lipschitz conti…

This article gives an alternative approach to the self-shrinking and self-expanding solutions of the curve shortening flow, which are related to singularity formation of the mean curvature flow. The motivation for the self-similar solutions arises from natural area preserving rescaling. Further we describe the self-sim…

Paper proposes an algorithm for PARAFAC2-based CMTF models with various constraints.

Alternative proof of weak solutions to mean curvature flow using minimizing movements.

Alternative approach to rigidity of high-dimensional isometric immersions.

This paper studies a stylized, yet natural, learning-to-rank problem and points out the critical incorrectness of a widely used nearest neighbor algorithm. We consider a model with $n$ agents (users) $\{x_i\}_{i \in [n]}$ and $m$ alternatives (items) $\{y_j\}_{j \in [m]}$, each of which is associated with a latent feat…

Random utility theory models an agent's preferences on alternatives by drawing a real-valued score on each alternative (typically independently) from a parameterized distribution, and then ranking the alternatives according to scores. A special case that has received significant attention is the Plackett-Luce model, fo…

In the field of structural reliability, the Monte-Carlo estimator is considered as the reference probability estimator. However, it is still untractable for real engineering cases since it requires a high number of runs of the model. In order to reduce the number of computer experiments, many other approaches known as …

This paper determines the braid indices for non-alternating pretzel links.

Alternative discrete Dirac mechanics using Dirac structures.

Derives FACT, an alternative to NFA for neural networks, explaining feature learning.

Choice functions accept a set of alternatives as input and produce a preferred subset of these alternatives as output. We study the problem of learning such functions under conditions of context-dependence of preferences, which means that the preference in favor of a certain choice alternative may depend on what other …

A new Euclidean approach reveals the pentagram map's beauty.

Alternating Minimization is a widely used and empirically successful heuristic for matrix completion and related low-rank optimization problems. Theoretical guarantees for Alternating Minimization have been hard to come by and are still poorly understood. This is in part because the heuristic is iterative and non-conve…

Self-reinforcing feedback loops in personalization systems are typically caused by users choosing from a limited set of alternatives presented systematically based on previous choices. We propose a Bayesian choice model built on Luce axioms that explicitly accounts for users' limited exposure to alternatives. Our model…

We give an explicit solution of robust mean-variance hedging problem in the single period model for some type of contingent claims. The alternative approach is also considered.