arXiv research

New methods evaluate stock market anomalies for prospect investors.

Differentiable clustering method using perturbed spanning forests.

Weighted SVM (or fuzzy SVM) is the most widely used SVM variant owning its effectiveness to the use of instance weights. Proper selection of the instance weights can lead to increased generalization performance. In this work, we extend the span error bound theory to weighted SVM and we introduce effective hyperparamete…

We derive properties of the cdf of random variables defined as saddle-type points of real valued continuous stochastic processes. This facilitates the derivation of the first-order asymptotic properties of tests for stochastic spanning given some stochastic dominance relation. We define the concept of Markowitz stochas…

Refines knot defect measurement in 3D and 4D.

The paper identifies the minimum mean-variance spanning set and its importance in asset evaluation.

We use the methods of Hedden, Juhasz, and Sarkar to exhibit a set of arborescent knots that bound large numbers of non-isotopic minimal genus spanning surfaces. In particular, we describe a sequence of prime knots K_{n} which will bound at least 2^{2n-1} non-isotopic minimal spanning surfaces of genus n.

New spanning tree model connects knot homology, s-invariant, and exotic discs.

Plateau's problem is to find a surface with minimal area spanning a given boundary. In 1960, Reifenberg and Adams developed a definition for "span" using Čech homology, and variants of this definition have been used ever sense. However, limitations of Čech homology resulted in the lack of a natural definition for a bou…

For a given boundary set consisting of arcs and vertices, with two or more arcs meeting at each vertex, we treat the problem of estimating the area density of a soap film-like surface spanning the boundary.

New algorithms find optimal policies without knowing MDP span.

Study Kauffman bracket skein modules of Seifert fibered spaces.

Traditional automatic speech recognition (ASR) systems often use an acoustic model (AM) built on handcrafted acoustic features, such as log Mel-filter bank (FBANK) values. Recent studies found that AMs with convolutional neural networks (CNNs) can directly use the raw waveform signal as input. Given sufficient training…

Plateau's soap film problem is to find a surface of least area spanning a given boundary. We begin with a compact orientable $(n-2)$-dimensional submanifold $M$ of $\R^n$. If $M$ is connected, we say a compact set $X$ "spans" $M$ if $X$ intersects every Jordan curve whose linking number with $M$ is 1. Picture a soap fi…

Let X and Y be infinite graphs, such that the automorphism group of X is nonamenable, and the automorphism group of Y has an infinite orbit. We prove that there is no automorphism-invariant measure on the set of spanning trees in the direct product X times Y. This implies that the minimal spanning forest corresponding …

New spanning 3-disks found for unlink in 4-sphere.

We introduce the notion of a "state function" for framed tangles in a disk. After choosing a finite set of states for each marked disk, a state function is a projection from the vector space spanned by all tangles to the vector space spanned by the states, that is local, and topologically invariant. Given the states fo…

New dataset and models detect cryptocurrency bubbles using social media data.

By using a suitable triple cover we show how to possibly model the construction of a minimal surface with positive genus spanning all six edges of a tetrahedron, working in the space of BV functions and interpreting the film as the boundary of a Caccioppoli set in the covering space. After a question raised by R. Hardt…

New methods show sparse portfolios offer no advantage over mean-variance in diversification.

Sharp bounds for spanning tree entropy in planar lattices.

Totally geodesic surfaces found in knots and links.

New complexity measure helps in agnostic reinforcement learning with or without access to MDP dynamics.

The Jones polynomial can be expressed in terms of spanning trees of the graph obtained by checkerboard coloring a knot diagram. We show there exists a complex generated by these spanning trees whose homology is the reduced Khovanov homology. The spanning trees provide a filtration on the reduced Khovanov complex and a …

A new classification method based on Minimum Spanning Trees

We study reinforcement learning in non-episodic factored Markov decision processes (FMDPs). We propose two near-optimal and oracle-efficient algorithms for FMDPs. Assuming oracle access to an FMDP planner, they enjoy a Bayesian and a frequentist regret bound respectively, both of which reduce to the near-optimal bound …

Ancient curves span halfplanes via flow.

Spanning attack improves black-box attacks with unlabeled data.

Proves bounds on spanning two-forests and random cut sizes.

Alexander polynomial equals spanning tree count at t=1.

We introduce the warping polynomial of an oriented knot diagram. In this paper, we characterize the warping polynomial, and define the span of a knot to be the minimal span of the warping polynomial for all diagrams of the knot. We show that the span of a knot is one if and only if it is non-trivial and alternating, an…

Non-spanning identification of scheduled event risk in option pricing.

We address the problem of computing reliable policies in reinforcement learning problems with limited data. In particular, we compute policies that achieve good returns with high confidence when deployed. This objective, known as the \emph{percentile criterion}, can be optimized using Robust MDPs~(RMDPs). RMDPs general…

New invariants measure how far spanning surfaces are from being compressible.

Let $M$ be an $n$-dimensional complete simply connected Riemannian manifold with sectional curvature bounded above by a nonpositive constant $-κ^2$. Using the cone total curvature $TC(Γ)$ of a graph $Γ$ which was introduced by Gulliver and Yamada Math. Z. 2006, we prove that the density at any point of a soap film-like…

A behavior of extreme networks under deformations of their boundary sets is investigated. It is shown that analyticity of a deformation of boundary set guarantees preservation of the networks types for minimal spanning trees, minimal fillings and so-called stable shortest trees in the Euclidean space.

Study Murasugi sum in 4D for knotted surfaces, defining arborescent surfaces.

Nonorientable spanning surfaces of periodic knots can have arbitrarily high first Betti number.

For a spanning tree T of a connected graph G and for a labelling φ: E(T) \rightarrow {+, -}, φis called an alternating sign on a spanning tree T of a graph G if for any cotree edge e \in E(G)-E(T), the unique path in T joining both end vertices of e has alternating signs. In the present note, we prove that any graph ha…

We investigate the time series of the degree of minimum spanning trees obtained by using a correlation based clustering procedure which is starting from (i) asset return and (ii) volatility time series. The minimum spanning tree is obtained at different times by computing correlation among time series over a time windo…

This paper proposes a new method to adapt ROMs for new parameter settings.

The Plateau-Douglas problem asks to find an area minimizing surface of fixed or bounded genus spanning a given finite collection of Jordan curves in Euclidean space. In the present paper we solve this problem in the setting of proper metric spaces admitting a local quadratic isoperimetric inequality for curves. We more…

Estimates tree-based density from random vectors.

We show that any twisted Dijkgraaf-Witten representation of a mapping class group of an orientable, compact surface with boundary has finite image. This generalizes work of Etingof, Rowell and Witherspoon showing that the braid group images are finite. In particular, our result answers their question regarding finitene…

We define a geometric flow that is designed to change surfaces of cylindrical type spanning two disjoint boundary curves into solutions of the Douglas-Plateau problem of finding minimal surfaces with given boundary curves. We prove that also in this new setting and for arbitrary initial data, solutions of the Teichmüll…

The mixed braid groups $B_{2,n}, \ n \in \mathbb{N}$, with two fixed strands and $n$ moving ones, are known to be related to the knot theory of certain families of $3$-manifolds. In this paper we define the mixed Hecke algebra $\mathrm{H}_{2,n}(q)$ as the quotient of the group algebra ${\mathbb Z}\, [q^{\pm 1}] \, B_{2…

In this paper we provide the first examples of non-flat soap films proven to span tetrahedra. These are members of a continuous two parameter family of soap films with tetrahedral boundaries. Of particular interest is a two parameter subfamily where each spanning soap film has the property that two minimal surfaces mee…

We use a spanning tree model to prove a result of E. S. Lee on the support of Khovanov homology of alternating knots.