arXiv research

Let $X$ be a compact complex Calabi-Yau 4-fold. Under certain assumptions, we define Donaldson-Thomas type deformation invariants ($DT_{4}$ invariants) by studying moduli spaces of solutions to the Donaldson-Thomas equations on $X$. We also study sheaves counting problems on local Calabi-Yau 4-folds. We relate $DT_{4}$…

The article finds non-Abelian DT-instantons on non-Kähler manifolds.

We discuss Donaldson-Thomas (DT) invariants of torsion sheaves with 2 dimensional support on a smooth projective surface in an ambient non-compact Calabi Yau fourfold given by the total space of a rank 2 bundle on the surface. We prove that in certain cases, when the rank 2 bundle is chosen appropriately, the universal…

We study orientability issues of moduli spaces from gauge theories on Calabi-Yau manifolds. Our results generalize and strengthen those for Donaldson-Thomas theory on Calabi-Yau manifolds of dimensions 3 and 4. We also prove a corresponding result in the relative situation which is relevant to the gluing problem in DT …

Proof of wall-crossing formula using spectral networks.

New rule reduces exploration regret to logarithmic, improving bad episode handling.

Records of the traded value f_i(t) of stocks display fluctuation scaling, a proportionality between the standard deviation sigma(i) and the average <f(i)>: sigma(i) ~ f(i)^alpha, with a strong time scale dependence alpha(dt). The non-trivial (i.e., neither 0.5 nor 1) value of alpha may have different origins and provid…

New method builds hyperbolic spheres with controlled holonomy.

Study evaluates digital transformation impact on financial performance using LLMs.

The identification of novel drug-target (DT) interactions is a substantial part of the drug discovery process. Most of the computational methods that have been proposed to predict DT interactions have focused on binary classification, where the goal is to determine whether a DT pair interacts or not. However, protein-l…

Mathematical structures link Gromov-Witten to Donaldson-Thomas invariants.

Given a complex 4-fold $X$ with an (Calabi-Yau 3-fold) anti-canonical divisor $Y$, we study relative Donaldson-Thomas invariants for this pair, which are elements in the Donaldson-Thomas cohomologies of $Y$. We also discuss gluing formulas which relate relative invariants and $DT_{4}$ invariants for Calabi-Yau 4-folds.

This research assesses uncertainty quantification and sensitivity analysis for DTs in nuclear fuel performance.

Variational autoencoder is a powerful deep generative model with variational inference. The practice of modeling latent variables in the VAE's original formulation as normal distributions with a diagonal covariance matrix limits the flexibility to match the true posterior distribution. We propose a new transformation, …

The paper connects Legendrian links to cluster algebras via microlocal methods.

Mathematical advances needed for Digital Twins, differing from traditional models.

Boosted DT classifiers become DP with new calibrated loss.

We consider differential operators on a supermanifold of dimension $1|1$. We define non-degenerate operators as those with an invertible top coefficient in the expansion in the "superderivative" $D$ (which is the square root of the shift generator, the partial derivative in an even variable, with the help of an odd ind…

Generative dynamic texture models (GDTMs) are widely used for dynamic texture (DT) segmentation in the video sequences. GDTMs represent DTs as a set of linear dynamical systems (LDSs). A major limitation of these models concerns the automatic selection of a proper number of DTs. Dirichlet process mixture (DPM) models w…

DeepONet accelerates nuclear DT inference with high accuracy and efficiency.

The paper constructs Darboux transforms for a specific hierarchy and its related flows.

GDT improves reinforcement learning by matching future state information efficiently.

DTS improves inference-time alignment of diffusion models with less compute.

The paper extends orientability results for DT invariants on Calabi-Yau 4-folds.

Growth of monetary assets and debts is commonly described by the formula of compound interest which for the case of continuous compounding is the exponential growth law. Its differential form is dc/dt = i c where dc/dt describes the rate of monetary growth, i the compounded interest rate and c the actual principal. Exp…

Paper proposes DG-ETC for online submodular maximization with stochastic bandit feedback.

DTS improves robustness of bandit algorithms in nonstationary environments.

For a given time horizon DT, this article explores the relationship between the realized volatility (the volatility that will occur between t and t+DT), the implied volatility (corresponding to at-the-money option with expiry at t+DT), and several forecasts for the volatility build from multi-scales linear ARCH process…

Given a knot $K$ parametrized by $r: [0,2π] \to \mathbb{R}^3$, we can define the electric potential on its complement by $Φ(x) = \int_0^{2π} \frac{|r'(t)|}{|x - r(t)|}dt$. Physicists and knot theorists want to understand the critical points of the potential and their behavior. The tunneling number $t(K)$ of a knot is t…

We aim at developing and improving the imbalanced business risk modeling via jointly using proper evaluation criteria, resampling, cross-validation, classifier regularization, and ensembling techniques. Area Under the Receiver Operating Characteristic Curve (AUC of ROC) is used for model comparison based on 10-fold cro…

The popular cubic smoothing spline estimate of a regression function arises as the minimizer of the penalized sum of squares $\sum_j(Y_j - μ(t_j))^2 + λ\int_a^b [μ"(t)]^2 dt$, where the data are $t_j,Y_j$, $j=1,..., n$. The minimization is taken over an infinite-dimensional function space, the space of all functions wi…

Researchers use DT to transfer policies from one environment to another using causal reasoning.

Enhances RL in target domains with limited data using augmented return.

The paper proves a comparison principle for complex Monge-Ampère flows and solves a uniqueness problem.

Paper defines new risk measures for elliptical distributions.

Transform ANNs into interpretable decision trees.

Study computes isoperimetric profiles in low-dimensional Riemannian products.

Let $Σ_{g,p}$ be the genus--$g$ oriented surface with $p$ punctures, with either $g>0$ or $p>3$. We show that $MCG(Σ_{g,p})/DT$ is acylindrically hyperbolic where $DT$ is the normal subgroup of the mapping class group $MCG(Σ_{g,p})$ generated by $K^{th}$ powers of Dehn twists about curves in $Σ_{g,p}$ for suitable $K$.…

Domestic violence (DV) is a global social and public health issue that is highly gendered. Being able to accurately predict DV recidivism, i.e., re-offending of a previously convicted offender, can speed up and improve risk assessment procedures for police and front-line agencies, better protect victims of DV, and pote…

Proposes DTS framework to predict CTR by tracking user interest evolution over time.

In this paper we propose the use of Generative Adversarial Networks (GAN) to generate artificial training data for machine learning tasks. The generation of artificial training data can be extremely useful in situations such as imbalanced data sets, performing a role similar to SMOTE or ADASYN. It is also useful when t…

Study biharmonic submanifolds in warped product structures.

The main purpose in the present paper is to build a Hamiltonian theory for fields which is consistent with the principles of relativity. For this we consider detailed geometric pictures of Lepage theories in the spirit of Dedecker and try to stress out the interplay between the Lepage-Dedecker (LP) description and the …

In this paper, we give a general time-varying parameter model, where the multidimensional parameter possibly includes jumps. The quantity of interest is defined as the integrated value over time of the parameter process $Θ= T^{-1} \int_0^T θ_t^* dt$. We provide a local parametric estimator (LPE) of $Θ$ and conditions u…

In this paper we propose a synergistic melting of neural networks and decision trees (DT) we call neural decision trees (NDT). NDT is an architecture a la decision tree where each splitting node is an independent multilayer perceptron allowing oblique decision functions or arbritrary nonlinear decision function if more…

Let $X$ be a complex four-dimensional compact Calabi-Yau manifold equipped with a Kähler form $ω$ and a holomorphic four-form $Ω$. Under certain assumptions, we define Donaldson-Thomas type deformation invariants by studying the moduli space of the solutions of Donaldson-Thomas equations on the given Calabi-Yau manifol…

We study the origins of the $\sqrt{dt}$ effect in finance and SDE. In particular, we show, in the game-theoretic framework, that market volatility is a consequence of the absence of riskless opportunities for making money and that too high volatility is also incompatible with such opportunities. More precisely, riskles…

We present an empirical study of the subordination hypothesis for a stochastic time series of a stock price. The fluctuating rate of trading is identified with the stochastic variance of the stock price, as in the continuous-time random walk (CTRW) framework. The probability distribution of the stock price changes (log…