arXiv research

Two-parameter models can learn high-dimensional targets via gradient flow.

We introduce a noncommutative differential calculus on the two-parameter $h$-superplane via a contraction of the (p,q)-superplane. We manifestly show that the differential calculus is covariant under $GL_{h_1,h_2}(1| 1)$ transformations. We also give a two-parameter deformation of the (1+1)-dimensional phase space alge…

We construct a two-parameter covariant differential calculus on the quantum $h$-exterior plane. We also give a deformation of the two-dimensional fermionic phase space.

Capital distribution curve is defined as log-log plot of normalized stock capitalizations ranked in descending order. The curve displays remarkable stability over periods of time. Theory of exchangeable distributions on set partitions, developed for purposes of mathematical genetics and recently applied in non-parametr…

New invariant for singular links via bt-algebra.

We introduce a two-parameters bt-algebra which, by specialization, becomes the one-parameter bt-algebra, introduced by the authors, as well as another one-parameter presentation of it; the invariant for links and tied links, associated to this two-parameter algebra via Jones recipe, contains as specializations the inva…

We model non-stationary volume-price distributions with a log-normal distribution and collect the time series of its two parameters. The time series of the two parameters are shown to be stationary and Markov-like and consequently can be modelled with Langevin equations, which are derived directly from their series of …

Constructs non-abelian G2-instantons on ALC members of B7 family.

In this paper, we formulate a method for minimising the expectation value of the procurement cost of electricity in two popular spot markets: {\it day-ahead} and {\it intra-day}, under the assumption that expectation value of unit prices and the distributions of prediction errors for the electricity demand traded in tw…

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…

The object of investigations are almost hypercomplex structures with Hermitian-Norden metrics on 4-dimensional Lie groups considered as smooth manifolds. There are studied both the basic classes of a classification of 4-dimensional indecomposable real Lie algebras depending on two parameters. Some geometric characteris…

Constructs a unique surface in a ball with specific properties.

Study biharmonic functions on vector bundles with spherical symmetry.

In the context of the Dragulescu-Yakovenko (2000) model, we show that empirical income distribution with truncated datasets, cannot be properly modeled by the one-parameter exponential distribution. However, a truncated version characterized by an exponential distribution with two parameters gives an accurate fit.

We explore Jaeger's state model for the HOMFLYPT polynomial. We reformulate this model in the language of Gauss diagrams and use it to obtain Gauss diagram formulas for a two-parameter family of Vassiliev invariants coming from the HOMFLYPT polynomial. These formulas are new already for invariants of degree 3.

In this paper is studied the behavior of lines of curvature near umbilic points that appear generically on surfaces depending on two parameters.

In this note, we study a class of stochastic control problems where the optimal strategies are described by two parameters. These include a subset of singular control, impulse control, and two-player stochastic games. The parameters are first chosen by the two continuous/smooth fit conditions, and then the optimality o…

Advanced forecasting models outperform Holt-Winters and ARIMA for stock market data.

The paper proposes a neural network model for estimating conditional mixture Weibull distributions with right-censored data.

A new logit model derived from the Weibull manifold.

Refines Hurwitz numbers with a two-parameter theory.

The paper characterizes biconservative surfaces in hyperbolic 4-space.

We propose an elementary model to price European physical delivery swaptions in multicurve setting with a simple exact closed formula. The proposed model is very parsimonious: it is a three-parameter multicurve extension of the two-parameter Hull-White (1990) model. The model allows also to obtain simple formulas for a…

New model predicts implied volatility using past asset price paths.

The paper extends Bour's theorem to BCV spaces with constant mean curvature helicoids.

New bounds on continuous random variables' right-tail probabilities.

We construct the universal sl(2)-tangle cohomology using an approach with webs and dotted foams. This theory depends on two parameters, and for the case of links it is a categorification of the unnormalized Jones polynomial of the link.

Weibull framework diagnoses transformer weight distributions, revealing distinct patterns across modules.

We investigate projective spherically symmetric Finsler metrics with constant flag curvature in $R^n$ and give the complete classification theorems. Furthermore, a new class of Finsler metrics with two parameters on n-dimensional disk are found to have constant negative flag curvature.

We investigate the curvature properties of a two-parameter family of Hermitian structures on the product of two Sasakian manifolds, as well as intermediate relations. We give a necessary and sufficient condition for a Hermitian structure belonging to the family to be Einstein and provide concrete examples.

We generalize the Khovanov-Rozansky cohomology for n=2 by means of a homogeneous potential that depends on two parameters, to obtain the universal Khovanov-Rozansky sl(2) link cohomology. This theory is equivalent to the universal foam sl(2) link cohomology, after tensoring both theories with appropriate rings.

We propose an algorithm which allows to derive the generalized Alexander polynomial invariants of knots and links with the help of the q,p-numbers, appearing in bosonic two-parameter quantum algebra. These polynomials turn into HOMFLY ones by applying special parametrization. The Jones polynomials can be also obtained …

Many popular random partition models, such as the Chinese restaurant process and its two-parameter extension, fall in the class of exchangeable random partitions, and have found wide applicability in model-based clustering, population genetics, ecology or network analysis. While the exchangeability assumption is sensib…

We review a construction of a new class of algebraic curves, called super-A-polynomials, and their quantum generalizations. The super-A-polynomial is a two-parameter deformation of the A-polynomial known from knot theory or Chern-Simons theory with SL(2,C) gauge group. The two parameters of the super-A-polynomial encod…

Researchers found explicit solutions to a complex equation in advanced geometry.

In this note we describe the recursion relations between two parameter HOMLFY and Kauffman polynomials of framed links These relation correspond to embeddings of quantized universal enveloping algebras. The relation corresponding to embeddings $g_{n}\supset g_{k}\times sl_{n-k}$ where $g_{n}$ is either $so_{2n+1}$, $so…

Non-compact G_2 holonomy metrics that arise from a T^2 bundle over a hyper-Kahler space are discussed. These are one parameter deformations of the metrics studied by Gibbons, Lu, Pope and Stelle in hep-th/0108191. Seven-dimensional spaces with G_2 holonomy fibered over the Taub-Nut and the Eguchi-Hanson gravitational i…

An unobstructedness theorem is proved for deformations of compact holomorphic Poisson manifolds and applied to a class of examples. These include certain rational surfaces and Hilbert schemes of points on Poisson surfaces. We study in particular the Hilbert schemes of the projective plane and show that a generic deform…

An array system of coupled maps is proposed as a model for economy evolution. The local dynamics of each map or agent is controlled by two parameters. One of them represents the growth capacity of the agent and the other one is a control term representing the local environmental pressure which avoids an exponential gro…

We consider a financial market model driven by an R^n-valued Gaussian process with stationary increments which is different from Brownian motion. This driving noise process consists of $n$ independent components, and each component has memory described by two parameters. For this market model, we explicitly solve optim…

The problem to accurately and parsimoniously characterize random series of events (RSEs) present in the Web, such as e-mail conversations or Twitter hashtags, is not trivial. Reports found in the literature reveal two apparent conflicting visions of how RSEs should be modeled. From one side, the Poissonian processes, o…

Study models weather index insurance pricing by insurers and farmers, finding flexible pricing kernels boost profits.

We derive representations of local risk-minimization of call and put options for Barndorff-Nielsen and Shephard models: jump type stochastic volatility models whose squared volatility process is given by a non-Gaussian rnstein-Uhlenbeck process. The general form of Barndorff-Nielsen and Shephard models includes two par…

A deterministic system of coupled maps is proposed as a model for economic activity among interacting agents. The values of the maps represent the wealth of the agents. The dynamics of the system is controlled by two parameters. One parameter expresses the growth capacity of the agents and the other describes the local…

We document and analyze the empirical facts concerning one of the clearest evidence of speculation in financial trading as observed in the postage collection stamp market. We unravel some of the mechanisms of speculative behavior which emphasize the role of fancy and collective behavior. In our conclusion, we propose a…

Inspired by the concept of evolutoids of planar curves, we present the concept of evolutoids for regular surfaces as an envelope of a two-parameter family of lines in Euclidean 3-space. We give an explicit parametrization for such evolutoids. Besides, we used the theory of singularities to study the local behavior of r…

The paper models and deforms A-infinity structures for bordered knot algebras.

Clustering ensemble is one of the most recent advances in unsupervised learning. It aims to combine the clustering results obtained using different algorithms or from different runs of the same clustering algorithm for the same data set, this is accomplished using on a consensus function, the efficiency and accuracy of…