arXiv research

Pairs of elements in quaternionic hyperbolic space have zero measure of being strongly doubly reversible.

Study identifies prime strongly positive amphicheiral knots with double symmetry.

New invariant measures doubly slice links, disproving previous bounds.

The article enumerates doubly symmetric diagrams for knots up to 18 crossings.

Pairs trading strategy fails to outperform market benchmarks, but performs well during bear markets.

The paper classifies reversible and strongly reversible elements in Hermitian isometry groups.

Classifies reversible and strongly reversible elements in quaternionic groups.

The paper shows some Montesinos links can't be doubly sliced strongly.

This paper classifies reversible and strongly reversible elements in affine groups.

Let $G$ be a group. An element $g$ in $G$ is called reversible if it is conjugate to $g^{-1}$ within $G$, and called strongly reversible if it is conjugate to its inverse by an order two element of $G$. Let $\textbf{H}_{\mathbb H}^n$ be the $n$-dimensional quaternionic hyperbolic space. Let $\mathrm{PSp}(n,1)$ be the i…

We call a closed, connected, orientable manifold in one of the categories TOP, PL or DIFF chiral if it does not admit an orientation-reversing automorphism and amphicheiral otherwise. Moreover, we call a manifold strongly chiral if it does not admit a self-map of degree -1. We prove that there are strongly chiral, smoo…

This work concerns the study of certain finite-energy solutions of the anti-self-dual Yang-Mills equations on Euclidean 4-dimensional space which are periodic in two directions, so-called doubly-periodic instantons. We establish a circle of ideas involving equivalent analytical and algebraic-geometric descriptions of t…

Geometric approach for unsupervised word embedding alignment.

Collective behaviours taking place in financial markets reveal strongly correlated states especially during a crisis period. A natural hypothesis is that trend reversals are also driven by mutual influences between the different stock exchanges. Using a maximum entropy approach, we find coordinated behaviour during tre…

A knot in the 3-sphere is called doubly slice if it is a slice of an unknotted 2-sphere in the 4-sphere. We give a bi-sequence of new obstructions for a knot being doubly slice. We construct it following the idea of Cochran-Orr-Teichner's filtration of the classical knot concordance group. This yields a bi-filtration o…

Established a Hardy inequality on Finsler manifolds.

We study trisections of 4-manifolds obtained by spinning and twist-spinning 3-manifolds, and we show that, given a (suitable) Heegaard diagram for the 3-manifold, one can perform simple local modifications to obtain a trisection diagram for the 4-manifold. We also show that this local modification can be used to conver…

Study of strongly invertible Legendrian links in contact 3-space.

The paper classifies 10 antipodal pairings of self-dual maps.

New knots not rationally concordant to their reverses found.

The paper generalizes a mean value theorem for solutions of the ultrahyperbolic equation.

Study counts and equidistributes geodesic orbits on curved spaces.

The intermarket analysis, in particular the lead-lag relationship, plays an important role within financial markets. Therefore a mathematical approach to be able to find interrelations between the price development of two different financial underlyings is developed in this paper. Computing the differences of the relat…

New method detects inconsistencies in AHP matrices using triadic preference reversals.

In this paper, we study distributed stochastic optimization to minimize a sum of smooth and strongly-convex local cost functions over a network of agents, communicating over a strongly-connected graph. Assuming that each agent has access to a stochastic first-order oracle ($\mathcal{SFO}$), we propose a novel distribut…

A new trading strategy using reinforcement learning for statistical arbitrage.

In this paper, we develop a new accelerated stochastic gradient method for efficiently solving the convex regularized empirical risk minimization problem in mini-batch settings. The use of mini-batches is becoming a golden standard in the machine learning community, because mini-batch settings stabilize the gradient es…

The purpose of these notes is to provide a systematic quantitative framework - in what is intended to be a "pedagogical" fashion - for discussing mean-reversion and optimization. We start with pair trading and add complexity by following the sequence "mean-reversion via demeaning -> regression -> weighted regression ->…

Let {a,b} and {c,d} be two pairs of bounding simple closed curves on an oriented surface which intersect nontrivialy. We prove that if these pairs are invariant under the action of an orientation reversing involution, then the corresponding bounding pair maps generate a free group. This supports the conjecture stated b…

The ropelength of a space curve is usually defined as the quotient of its length by its thickness: the radius of the largest embedded tube around the knot. This idea was extended to space polygons by Eric Rawdon, who gave a definition of ropelength in terms of doubly-critical self-distances (local minima of the distanc…

Defines real link Floer homology for specific types of links.

Proves alternating quasipositive links are positive and strongly quasipositive.

Rotors were introduced in Graph Theory by W.Tutte. The concept was adapted to Knot Theory as a generalization of mutation by Anstee, Przytycki and Rolfsen in 1987. In this paper we show that Tristram-Levine signature is preserved by orientation-preserving rotations. Moreover, we show that any link invariant obtained fr…

A new framework RTK accelerates diffusion inference by breaking down the process into fewer, more efficient subproblems.

Study on the cobordism distance between knots and their reverses.

Proposes a framework for selecting machine learning algorithms in semiparametric models.

We study the profitability of optimal mean reversion trading strategies in the US equity market. Different from regular pair trading practice, we apply maximum likelihood method to construct the optimal static pairs trading portfolio that best fits the Ornstein-Uhlenbeck process, and rigorously estimate the parameters.…

A new method for sparse regression models using graph structure.

The paper introduces a new pairs trading model using nonlinear and non-Gaussian state-space models.

We find an infinite family of Seifert fibered surgeries on strongly invertible knots which do not have primitive/Seifert positions. Each member of the family is obtained from a trefoil knot after alternate twists along a pair of seiferters for a Seifert fibered surgery on a trefoil knot.

The subject of this paper is strongly homotopy (SH) Lie algebras, also known as $L_\infty$-algebras. We extract an intrinsic character, the Atiyah class, which measures the nontriviality of an (SH) Lie algebra $A$ when it is extended to $L$. In fact, given such an SH Lie pair $(L, A)$, and any $A$-module $E$, there ass…

A new algorithm improves regret bounds for contextual bandits.

In a classic paper Zeeman introduced the k-twist spin of a knot K and showed that the exterior of a twist spin fibers over S^1. In particular this result shows that the knot K # -K is doubly slice. In this paper we give a quick proof of Zeeman's result. The k-twist spin of K also gives rise to two metabolizers for K # …

New representations of hyperbolic 3-manifold groups into larger groups.

We study the problem of hypothesis testing between two discrete distributions, where we only have access to samples after the action of a known reversible Markov chain, playing the role of noise. We derive instance-dependent minimax rates for the sample complexity of this problem, and show how its dependence in time is…

The paper examines Einstein doubly warped product manifolds with a semi-symmetric metric connection.

Characterizes spacetimes using doubly torqued vectors.

Sharp inequalities for curved surfaces and cones.