arXiv research

DDGM generates realistic ECG signals for clinical use.

Quantum time evolution exhibits rich physics, attributable to the interplay between the density and phase of a wave function. However, unlike classical heat diffusion, the wave nature of quantum mechanics has not yet been extensively explored in modern data analysis. We propose that the Laplace transform of quantum tra…

Two-dimensional transition rates improve life insurance reserve calculations.

Developed accurate empirical potentials for Si:H nanowires using multi-fidelity Gaussian process.

Paper calculates Torelli group's cohomology second group.

There are many studies about twisted Alexander invariants for knots and links, but calculations of twisted Alexander invariants for spatial graphs, handlebody-knots, and surface-links have not been demonstrated well. In this paper, we give some remarks to calculate the twisted Alexander ideals for spatial graphs, handl…

New algorithm calculates $S$-invariants for links efficiently.

Method calculates function integrals on complex manifolds.

We calculate the volumes of the hyperbolic twist knot cone-manifolds using the Schläfli formula. Even though general ideas for calculating the volumes of cone-manifolds are around, since there is no concrete calculation written, we present here the concrete calculations. We express the length of the singular locus in t…

This thesis builds a real-time VaR calculation workflow for crypto derivatives.

Quantum method calculates risk contributions in credit portfolios efficiently.

We describe financial systems as condensates, similar to Bose-Einstein condensates, and calculate statistical distributions following from the model. The calculated distributions of investments into speculated financial assets are found equivalent to a Pareto distribution, and the calculated distributions of the price …

The study proves a localization theorem and calculates volumes for superspaces.

We calculate the Hirzebruch $χ_y$ and $\hatχ_y$-genera of symmetric products of closed complex manifolds by the holomorphic Lefschetz formula of Atiyah and Singer \cite{Ati-Sin}. Such calculation rederive some formulas proved in an earlier paper \cite{Zho} by a different method.

AD-HOC simplifies high-order derivative calculations in C++.

Proposes a fix for IRS calculation of Obamacare tax credits.

We model the quantities appearing in Internal Revenue Service (IRS) tax guidance for calculating the health insurance premium tax credit created by the Patient Protection and Affordable Care Act, also called Obamacare. We ask the question of whether there is a procedure, computable by hand, which can calculate the appr…

Ownership cost calculation plays an important role in optimal operation of distributed energy resources (DERs) and microgrids (MGs) in the future power system, known as smart grid. In this paper, a general framework for ownership cost calculation is proposed using uncertainty and risk analyses. Four ownership cost calc…

The calculation of minimum energy paths for transitions such as atomic and/or spin re-arrangements is an important task in many contexts and can often be used to determine the mechanism and rate of transitions. An important challenge is to reduce the computational effort in such calculations, especially when ab initio …

Calculates knot $X$-torsion order using spectral sequences.

During reactive transport modeling, the computational cost associated with chemical reaction calculations is often 10-100 times higher than that of transport calculations. Most of these costs results from chemical equilibrium calculations that are performed at least once in every mesh cell and at every time step of the…

Algorithm calculates genus of embedded graphs on surfaces.

The paper calculates automorphisms of Weil algebras, focusing on one-component groups.

Infinitesimal calculations link fundamental groups to Lie algebras.

The importance of counterparty credit risk to the derivative contracts was demonstrated consistently throughout the financial crisis of 2008. Accurate valuation of Credit value adjustment (CVA) is essential to reflect the economic values of these risks. In the present article, we reviewed several different approaches f…

We develop a general framework for applying the Kelly criterion to stock markets. By supplying an arbitrary probability distribution modeling the future price movement of a set of stocks, the Kelly fraction for investing each stock can be calculated by inverting a matrix involving only first and second moments. The fra…

A new method calculates risk loadings in classification ratemaking without subjective parameters.

We extend the definition of algebraic entropy to endomorphisms of affine varieties. We calculate algebraic entropy of the action of elements of mapping class groups on various character varieties, and show that it is equal to a quantity we call the spectral radius, a generalization of the dilatation of a Pseudo-Anosov …

Unified method to calculate Gromov norm for Kähler classes of bounded symmetric domains.

For $4 \nmid L$ and $g$ large, we calculate the integral Picard groups of the moduli spaces of curves and principally polarized abelian varieties with level $L$ structures. In particular, we determine the divisibility properties of the standard line bundles over these moduli spaces and we calculate the second integral …

Study calculates Floer homology for binary polyhedral spaces.

New polynomials defined for virtual knots, calculated up to crossing 4.

A new method calculates implied volatilities without using option prices.

We provide methods to compute the colored HOMFLY polynomials of knots and links with symmetric representations based on the linear skein theory. By using diagrammatic calculations, several formulae for the colored HOMFLY polynomials are obtained. As an application, we calculate some examples for hyperbolic knots and li…

We calculate the Euler characteristics of all of the Teichmuller curves in the moduli space of genus two Riemann surfaces which are generated by holomorphic one-forms with a single double zero. These curves can all be embedded in Hilbert modular surfaces and our main result is that the Euler characteristic of a Teichmu…

This paper calculates the derivative of surface holonomy for non-abelian gerbes.

We carry out calculations of Orlicz cohomology for some basic Riemannian manifolds (the real line, the hyperbolic plane, the ball). Relationship between Orlicz cohomology and Poincaré--Sobolev--Orlicz-type inequalities is discussed.

We calculate the rational equivariant cohomology of the spaces of non-contractible loops in compact space forms and show how to apply these calculations for proving the existence of closed geodesics.

Homology groups of spaces of nonsingular polynomial embeddings ${\bf R}^1 \to {\bf R}^n$ of degrees $\le 4$ are calculated. A general algebraic technique of such calculations for spaces of polynomial knots of arbitrary degrees is described.

We present a method to compensate statistical errors in the calculation of correlations on asynchronous time series. The method is based on the assumption of an underlying time series. We set up a model and apply it to financial data to examine the decrease of calculated correlations towards smaller return intervals (E…

Speeds up complex portfolio exposure calculations.

Quasi-Monte Carlo speeds up option Greeks calculation on GPUs.

We give a formula to calculate the indices of special (non-totally geodesic) minimal orbits of Hermann actions. Also, we give examples of such minimal orbits of Hermann actions and calculate their indices by using the formula.

We define a Floer-homology invariant for knots in an oriented three-manifold, closely related to the holomorphic disk Floer homologies for three-manifolds defined in an earlier paper. We set up basic properties of these invariants, including an Euler characteristic calculation, behaviour under connected sums. Then, we …

Recently, Mullins calculated the Casson-Walker invariant of the 2-fold cyclic branched cover of an oriented link in S^3 in terms of its Jones polynomial and its signature, under the assumption that the 2-fold branched cover is a rational homology 3-sphere. Using elementary principles, we provide a similar calculation f…

Minimum energy paths for transitions such as atomic and/or spin rearrangements in thermalized systems are the transition paths of largest statistical weight. Such paths are frequently calculated using the nudged elastic band method, where an initial path is iteratively shifted to the nearest minimum energy path. The co…

Study calculates fundamental groups of torus knots using algebraic topology.

Calculates twist in Teichmüller space using cross ratios.