A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Study finds multiple solutions for Van der Waals-Cahn-Hilliard equation on manifolds.
We prove that any limit-interface corresponding to a locally uniformly bounded, locally energy-bounded sequence of stable critical points of the van der Waals--Cahn--Hilliard energy functionals with perturbation parameter tending to 0 is supported by an embedded smooth stable minimal hypersurface in low dimensions and …
We give multiplicity results for the solutions of a nonlinear elliptic equation, with an asymmetric double well potential of Van der Waals-Allen--Cahn--Hilliard type, satisfying a linear volume constraint, on a bounded Lipschitz domain $Ω\subset\mathds R^N$. The number of solutions is estimated in terms of topological …
Proves generic nondegeneracy for solutions under volume constraint in closed manifolds.
Graphs from van der Corput sequence embed into Chamanara surface.
A cubic identity for the Infeld-van der Waerden field is found and its application to verifying an explicit formula for the spinor components of the metric connection is demonstrated.
t-distributed Stochastic Neighborhood Embedding (t-SNE), a clustering and visualization method proposed by van der Maaten & Hinton in 2008, has rapidly become a standard tool in a number of natural sciences. Despite its overwhelming success, there is a distinct lack of mathematical foundations and the inner workings of…
The present paper introduces a majority orienting model in which the dealers' behavior changes based on the influence of the price to show the oscillation of stock price in the stock market. We show the oscillation of the price for the model by applying the van der Pol equation which is a deterministic approximation of…
Novel knot polynomials from Gaussian calculus show half vanish and determine Jones polynomials.
We consider the concept of Stokes-Dirac structures in boundary control theory proposed by van der Schaft and Maschke. We introduce Poisson reduction in this context and show how Stokes-Dirac structures can be derived through symmetry reduction from a canonical Dirac structure on the unreduced phase space. In this way, …
We give a brief review of the definition of the Wang-Yau quasilocal mass and discuss the evaluation of which on surfaces of unit size at null infinity of an axi-symmetric spacetime in Bondi-van der Burg-Metzner coordinates.
Automatically learns summary features from time series data for likelihood-free inference.
A universal rule-based self-learning approach using deep reinforcement learning (DRL) is proposed for the first time to solve nonlinear ordinary differential equations and partial differential equations. The solver consists of a deep neural network-structured actor that outputs candidate solutions, and a critic derived…
Many real-world data sets, especially in biology, are produced by complex nonlinear dynamical systems. In this paper, we focus on brain calcium imaging (CaI) of different organisms (zebrafish and rat), aiming to build a model of joint activation dynamics in large neuronal populations, including the whole brain of zebra…
Motivated by the problem of finding an explicit description of a developable narrow Moebius strip of minimal bending energy, which was first formulated by M. Sadowsky in 1930, we will develop the theory of elastic strips. Recently E.L. Starostin and G.H.M. van der Heijden found a numerical description for an elastic Mo…
Responding to discussions on missing data models.
We have carried out simulations of a financial model of the firm to analyse the validity of the concept of Trade on Equity in dynamics. The results exhibit the ability of the borrowing policy connected to a cautious dividend distribution to inject chaos into the profit motion. The 3D system built with the van der Pol's…
We show that classical thermodynamics has a formulation in terms of Hamilton-Jacobi theory, analogous to mechanics. Even though the thermodynamic variables come in conjugate pairs such as pressure/volume or temperature/entropy, the phase space is odd-dimensional. For a system with n thermodynamic degrees of freedom it …
A submanifold of a Riemannian manifold is called a parallel submanifold if its second fundamental form is parallel with respect to the van der Waerden-Bortolotti connection. From submanifold point of view, parallel submanifolds are the simplest Riemannian submanifolds next to totally geodesic ones. Parallel submanifold…
We study non-degenerate, totally umbilical surfaces of a special class of pseudo-Riemannian manifolds, namely Walker three-manifolds. We show that such surfaces are either one of a totally geodesic family described by Calvaruso and Van der Veken or the ambient manifold must be locally conformally flat (here the surface…
First I will explain my motivation to introduce the -invariants for Riemannian manifolds. I will also recall the notions of ideal immersions and best ways of living. Then I will present a few of the many applications of -invariants to several areas in mathematics. Finally, I will present two optimal inequalities …
We present a deep learning model, DE-LSTM, for the simulation of a stochastic process with an underlying nonlinear dynamics. The deep learning model aims to approximate the probability density function of a stochastic process via numerical discretization and the underlying nonlinear dynamics is modeled by the Long Shor…
Proposes a new method combining Reservoir Computing and Normalizing Flow for predicting stochastic dynamical systems.
Paper proposes robust methods to detect and treat outliers in multivariate loss reserving.
Develops a Gaussian model to compute the Alexander polynomial of knots.
We prove an upper bound for the evaluation of all classical SU(2) spin networks conjectured by Garoufalidis and van der Veen. This implies one half of the analogue of the volume conjecture which they proposed for classical spin networks. We are also able to obtain the other half, namely, an exact determination of the s…
New derivation of knot invariants from universal invariant.
We use Bonahon-Wong's trace map to study character varieties of the once-punctured torus and of the 4-punctured sphere. We clarify a relationship with cluster algebra associated with ideal triangulations of surfaces, and we show that the Goldman Poisson algebra of loops on surfaces is recovered from the Poisson structu…
This paper classifies flat submanifolds with a special type of curvature form.
We study the maximum mean discrepancy (MMD) in the context of critical transitions modelled by fast-slow stochastic dynamical systems. We establish a new link between the dynamical theory of critical transitions with the statistical aspects of the MMD. In particular, we show that a formal approximation of the MMD near …
We use the formalism of Geometrothermodynamics to describe chemical reactions in the context of equilibrium thermodynamics. Any chemical reaction in a closed system is shown to be described by a geodesic in a dimensional manifold that can be interpreted as the equilibrium space of the reaction. We first show this i…
Paper derives closed-form solutions for CEV model using semiclassical approximation.
It was proven in [B.-Y. Chen, F. Dillen, J. Van der Veken and L. Vrancken, Curvature inequalities for Lagrangian submanifolds: the final solution, Differ. Geom. Appl. 31 (2013), 808-819] that every Lagrangian submanifold of a complex space form of constant holomorphic sectional curvature sat…
Study satellite operations on knot invariant θ, proving additivity and distinguishing knots.
A new method ODR-BINDy improves model discovery from noisy data.
New knot invariants derived using quantum cluster algebras.
Study quantifies distribution shifts and uncertainties to improve machine learning model robustness.
The dynamic emulation of non-linear deterministic computer codes where the output is a time series, possibly multivariate, is examined. Such computer models simulate the evolution of some real-world phenomenon over time, for example models of the climate or the functioning of the human brain. The models we are interest…
The CAP slope is Bayes' theorem in cumulative coordinates, unlocking the weight of evidence, Somers' D, and Gini coefficient.
Four-dimensional scanning transmission electron microscopy (4D-STEM) of local atomic diffraction patterns is emerging as a powerful technique for probing intricate details of atomic structure and atomic electric fields. However, efficient processing and interpretation of large volumes of data remain challenging, especi…
Paper proposes a new method for predicting DER adoption with hierarchical guarantees.
Study embeddability of 2-complexes in 4-space, proving Heawood family's excluded minors.
Unified framework identifies nonlinear systems using characteristic curves and neural networks.
We develop an algebraic framework for the description and analysis of financial behaviours, that is, behaviours that consist of transferring certain amounts of money at planned times. To a large extent, analysis of financial products amounts to analysis of such behaviours. We formalize the cumulative interest compliant…
Study of knot invariant growth for twisted knots.
Ensemble learning is a statistical paradigm built on the premise that many weak learners can perform exceptionally well when deployed collectively. The BART method of Chipman et al. (2010) is a prominent example of Bayesian ensemble learning, where each learner is a tree. Due to its impressive performance, BART has rec…
The intention with this paper is to provide all the estimation concepts and techniques that are needed to implement a two-phases approach to the parametric estimation of probability of default (PD) curves. In the first phase of this approach, a raw PD curve is estimated based on parameters that reflect discriminatory p…
Paper introduces -DER for regression tasks using morphological operators and convex-concave procedure.