arXiv research

Minimal stretch factors for certain pseudo-Anosov maps are bounded.

This study compares Bitcoin and Litecoin using cryptocurrency metrics and trading strategies.

There are many industrial situations where rods are used to stir a fluid, or where rods repeatedly stretch a material such as bread dough or taffy. The goal in these applications is to stretch either material lines (in a fluid) or the material itself (for dough or taffy) as rapidly as possible. The growth rate of mater…

Binary PheNorm extends phenotype labeling for EHRs using binary silver labels.

Improved MF-DFA model analyzes precious metals market efficiency and multifractality.

Study assesses weakly-supervised methods for rare outcomes in medical records.

The main result of this paper, Simon's conjecture for fibered knots, was previously proven by Silver and Whitten math.GT/0405462 with essentially the same proof. This paper is therefore being withdrawn. The author would like to apologize for having missed this.

Given a TQFT in dimension d+1, and an infinite cyclic covering of a closed (d+1)-dimensional manifold M, we define an invariant taking values in a strong shift equivalence class of matrices. The notion of strong shift equivalence originated in R. Williams' work in symbolic dynamics. The Turaev-Viro module associated to…

We show that a group presented by a labelled oriented tree presentation in which the tree has diameter at most three is an HNN extension of a finitely presented group. From results of Silver, it then follows that the corresponding higher dimensional ribbon knots admit minimal Seifert manifolds.

We consider the space of all representations of the commutator subgroup of a knot group into Z/p, p is prime. As proven by D. Silver and S. Williams, this space can be completely described by a finite oriented graph. We describe the lengths of cycles in this graph.

It follows from earlier work of Silver-Williams and the authors that twisted Alexander polynomials detect the unknot and the Hopf link. We now show that twisted Alexander polynomials also detect the trefoil and the figure-8 knot, that twisted Alexander polynomials detect whether a link is split and that twisted Alexand…

We define a family of virtual knots generalizing the classical twist knots. We develop a recursive formula for the Alexander polynomial $Δ_0$ (as defined by Silver and Williams) of these virtual twist knots. These results are applied to provide evidence for a conjecture that the odd writhe of a virtual knot can be obta…

We give a new interpretation of the Alexander polynomial $Δ_0$ for virtual knots due to Sawollek and Silver and Williams, and use it to show that, for any virtual knot, $Δ_0$ determines the writhe polynomial of Cheng and Gao (equivalently, Kauffman's affine index polynomial). We also use it to define a second-order wri…

Correlation matrices of foreign exchange rate time series are investigated for 60 world currencies. Minimal Spanning Tree (MST) graphs for the gold, silver and platinum are presented. Inverse power like scaling is discussed for these graphs as well as for four distinct currency groups (major, liquid, less liquid and no…

A birack is an algebraic structure with axioms encoding the blackboard-framed Reidemeister moves, incorporating quandles, racks, strong biquandles and semiquandles as special cases. In this paper we extend the counting invariant for finite racks to the case of finite biracks. We introduce a family of biracks generalizi…

The astonishing success of AlphaGo Zero\cite{Silver_AlphaGo} invokes a worldwide discussion of the future of our human society with a mixed mood of hope, anxiousness, excitement and fear. We try to dymystify AlphaGo Zero by a qualitative analysis to indicate that AlphaGo Zero can be understood as a specially structured…

In this paper we present a sequence of link invariants, defined from twisted Alexander polynomials, and discuss their effectiveness in distinguish knots. In particular, we recast and extend by geometric means a recent result of Silver and Williams on the nontriviality of twisted Alexander polynomials for nontrivial kno…

We show that (under mild assumptions) the generating function of log homology torsion of a knot exterior has a meromorphic continuation to the entire complex plane. As corollaries, this gives new proofs of (a) the Silver-Williams asymptotic, (b) Fried's theorem on reconstructing the Alexander polynomial (c) Gordon's th…

We consider the space of all representations of the commutator subgroup of a knot group into a finite abelian group Σ, together with a shift map σ_x. This is a finite dynamical system, introduced by D.Silver and S. Williams. We describe the lengths of its cycles in terms of the roots of the Alexander polynomial of the …

New groups defined from knot diagrams, invariant under Reidemeister moves.

Fox coloring provides a combinatorial framework for studying dihedral representations of the knot group. The less well-known concept of Dehn coloring captures the same data. Recent work of Carter-Silver-Williams clarifies the relationship between the two focusing on how one transitions between Fox and Dehn colorings. I…

Maximizes mixing efficiency in surface braids.

Many real world learning tasks involve complex or hard-to-specify objectives, and using an easier-to-specify proxy can lead to poor performance or misaligned behavior. One solution is to have humans provide a training signal by demonstrating or judging performance, but this approach fails if the task is too complicated…

CheXpert++ improves CheXpert's accuracy and usability for medical radiology reports.

Predicts short-term futures contract direction using neural networks and order flow data.

This study examines torsion homology in Oeljeklaus-Toma manifolds, extending knot theory concepts.

We show that the behaviour of Bitcoin has interesting similarities to stock and precious metal markets, such as gold and silver. We report that whilst Litecoin, the second largest cryptocurrency, closely follows Bitcoin's behaviour, it does not show all the reported properties of Bitcoin. Agreements between apparently …

The Tong-Yang-Ma representations are extended to string links and welded string links.

We prove a conjecture of K. Schmidt in algebraic dynamical system theory on the growth of the number of components of fixed point sets. We also generalize a result of Silver and Williams on the growth of homology torsions of finite abelian covering of link complements. In both cases, the growth is expressed by the Mahl…

The present paper aims at locating the breakings of the integration process of an international system observed during about 50 years in the 19th century. A historical study could link them to special events, which operated as exogenous shocks on this process. The indicator of integration used is the spread between the…

Joint state and parameter estimation is a core problem for dynamic Bayesian networks. Although modern probabilistic inference toolkits make it relatively easy to specify large and practically relevant probabilistic models, the silver bullet---an efficient and general online inference algorithm for such problems---remai…

Study shows post-COVID commodity futures returns and volatility changed for different products.

A Coxeter $n$-orbifold is an $n$-dimensional orbifold based on a polytope with silvered boundary facets. Each pair of adjacent facets meet on a ridge of some order $m$, whose neighborhood is locally modeled on ${\mathbb R}^n$ modulo the dihedral group of order $2m$ generated by two reflections. For $n \geq 3$, we study…

Recurrent Neural Networks (RNN) have become competitive forecasting methods, as most notably shown in the winning method of the recent M4 competition. However, established statistical models such as ETS and ARIMA gain their popularity not only from their high accuracy, but they are also suitable for non-expert users as…

This paper proves that every oriented non-disk Seifert surface $F$ for a knot $K$ in $S^3$ is smoothly concordant to a Seifert surface $F^{\prime}$ for a hyperbolic knot $K^{\prime}$ of arbitrarily large volume. This gives a new and simpler proof of the result of Friedl and of Kawauchi that every knot is $S$-equivalent…

Given a virtual knot $K$, we construct a group $VG_K$ called the virtual knot group, and we use the elementary ideals of $VG_K$ to define invariants of $K$ called the virtual Alexander invariants. For instance, associated to the $k=0$ ideal is a polynomial $H_K(s,t,q)$ in three variables which we call the virtual Alexa…

We discuss - in what is intended to be a pedagogical fashion - generalized "mean-to-risk" ratios for portfolio optimization. The Sharpe ratio is only one example of such generalized "mean-to-risk" ratios. Another example is what we term the Fano ratio (which, unlike the Sharpe ratio, is independent of the time horizon)…

TabPFN doesn't outperform GLM and XGBoost for motor insurance pricing.

FORE evaluates occupancy ratios without requiring Bellman completeness.

Optimal option portfolios under Sharpe Ratio maximization with skew-elliptical t-distributed returns

Omega ratio, defined as the probability-weighted ratio of gains over losses at a given level of expected return, has been advocated as a better performance indicator compared to Sharpe and Sortino ratio as it depends on the full return distribution and hence encapsulates all information about risk and return. We comput…

We present a new methodology of computing incremental contribution for performance ratios for portfolio like Sharpe, Treynor, Calmar or Sterling ratios. Using Euler's homogeneous function theorem, we are able to decompose these performance ratios as a linear combination of individual modified performance ratios. This a…

New method combines deep learning and quantum mechanics for efficient molecular statistics.

New algorithm accelerates optimization on Riemannian manifolds, including Wasserstein space.

We analyze structure of the world foreign currency exchange (FX) market viewed as a network of interacting currencies. We analyze daily time series of FX data for a set of 63 currencies, including gold, silver and platinum. We group together all the exchange rates with a common base currency and study each group separa…

Study compares deep learning models for volatility prediction using multivariate data.

The paper proposes an asset allocation strategy using the Sortino ratio for better performance.

A new ratio, the Hansen ratio, simplifies mean-variance portfolio theory.