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.
The study establishes bounds for Schrödinger operators on Riemannian manifolds.
Abstract notes on generative modeling techniques.
Paper introduces a new generative learning model using Schrödinger bridge diffusion in latent space.
Graphs from van der Corput sequence embed into Chamanara surface.
Study finds multiple solutions for Van der Waals-Cahn-Hilliard equation on manifolds.
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 …
Unified framework for robust, stable, and efficient density ratio estimation.
In this paper, we partially settle down the long standing open problem of the finite time blow-up property about the nonlinear Schrdinger equations on some Riemannian manifolds like the standard 2-sphere and the hyperbolic 2-space . Using the similar idea, we establish such blow-up results on…
Characterizes Schrödinger operator boundedness on weighted Riemannian manifolds.
Paper proposes a new method for predicting DER adoption with hierarchical guarantees.
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…
Paper introduces -DER for regression tasks using morphological operators and convex-concave procedure.
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.
The implementation of optimal power flow (OPF) methods to perform voltage and power flow regulation in electric networks is generally believed to require extensive communication. We consider distribution systems with multiple controllable Distributed Energy Resources (DERs) and present a data-driven approach to learn c…
We give a new lower bound for the first gap of the Dirichlet eigenvalues of the Schr{ö}dinger operator on a bounded convex domain in R or S and greatly sharpens the previous estimates. The new bound is explicit and computable.
Suppose that is a finite graph with the vertex set and the edge set . Let be the usual graph Laplacian. Consider the following nonlinear Schrdinger type equation of the form on graph , where $f(x…
New method selects critical DER scenarios for distribution grid investment planning.
X-DER improves continual learning by revising replay memory and learning unseen classes.
Mnay models situated in the current research landscape of modelling and simulating social processes have roots in physics. This is visible in the name of specialties as Econophysics or Sociophysics. This chapter describes the history of knowledge transfer from physics, in particular physics of self-organization and evo…
Study shows observability for Schrödinger equations on product manifolds with specific conditions.
ProbFM provides principled uncertainty quantification for financial forecasting.
New method identifies distribution grid outages using smart meter data.
For the spherical Laplacian on the sphere and for the Dirichlet Laplacian in the square}, Antonie Stern claimed in her PhD thesis (1924) the existence of an infinite sequence of eigenvalues whose corresponding eigenspaces contain an eigenfunction with exactly two nodal domains. These results were given complete proofs …
We solved the Schr{ö}dinger equation for a particle in a uniform magnetic field in the n-dimensional torus. We obtained a complete set of solutions for a broad class of problems; the torus T^n = R^n / Λ is defined as a quotient of the Euclidean space R^n by an arbitrary n-dimensional lattice Λ. The lattice is not neces…
The goal of this article is twofold: in a first part, we prove Gaussian estimates for the heat kernel of Schr{ö}dinger operators delta + V whose potential V is "small at infinity" in an integral sense. In a second part, we prove sharp boundedness result for the associated Riesz transform with potential d(delta+V) --1/2…
The growing integration of distributed energy resources (DERs) in urban distribution grids raises various reliability issues due to DER's uncertain and complex behaviors. With a large-scale DER penetration, traditional outage detection methods, which rely on customers making phone calls and smart meters' "last gasp" si…
Generative model for time series using Schrödinger bridge.
Proves generic nondegeneracy for solutions under volume constraint in closed manifolds.
DKULENOVO team improves speech diarization by 27.5% and 31.7% in DIHARD II.
This is a commentary on Teichm{ü}ller's paper Ein Verschiebungssatz der quasikonformen Abbildung (A displacement theorem of quasiconformal mapping), published in 1944. We explain in detail how Teichm{ü}ller solves the problem of finding the quasiconformal mapping from the unit disc to itself, sending 0 to a strictly ne…
We comment on the paper Über Extremalprobleme der konformen Geometrie (On extremal problems in conformal geometry) by Teichmüller, published in 1941. This paper contains ideas on a wide generalization of his previous work on the solution of extremal problems in conformal geometry. The generalization concerns at the sam…
We characterize the derivation $d:A\to Ω^1_{\der}(A)$ by a universal property introducing a new class of bimodules.
New internal symmetry found for Lie pair algebra.
We comment on Teichm{ü}ller 's paper ''Vollst{ä}ndige L{ö}sung einer Extremalaufgabe der quasikonformen Abbildung'' (Complete solution of an ex-tremal problem of the quasiconformal mapping),, published in 1941. In this paper, Teichm{ü}ller gives a proof of the existence of extremal quasiconformal mappings in the case o…
Recent innovations in Information and Communication Technologies (ICT) provide new opportunities and challenges for integration of distributed energy resources (DERs) into the energy supply system as active market players. By increasing integration of DERs, novel market platform should be designed for these new market …
Novel knot polynomials from Gaussian calculus show half vanish and determine Jones polynomials.
In this paper, the Dirac, twistor and Killing equations on Weyl manifolds with CSpin structures are investigated. A conformal Schr"odinger-Lichnerowicz formula is presented and used to show integrability conditions for these equations. By introducing the Killing equation for spinors of arbitrary weight, the result of A…
In this paper, for a Lie 2-algebra $\g$, we construct the automorphism 2-group $\Aut(\g)$, which turns out to be an integration of the derivation Lie 2-algebra $\Der(\g)$.
For a transitive Lie algebroid A on a connected manifold M and its a representation on a vector bundle F, we study the localization map Y^1: H^1(A,F)-> H^1(L_x,F_x), where L_x is the adjoint algebra at x in M. The main result in this paper is that: Ker Y^1_x=Ker(p^{1*})=H^1_{deR}(M,F_0). Here p^{1*} is the lift of H^1(…
New inequalities for spectral zeta kernels on spheres and manifolds.
Optimal Volt/VAR control rules designed using deep learning.
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.
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 …
Many real-world decision problems are characterized by multiple conflicting objectives which must be balanced based on their relative importance. In the dynamic weights setting the relative importance changes over time and specialized algorithms that deal with such change, such as a tabular Reinforcement Learning (RL) …
DER uses neural nets to better handle uncertainty in machine learning.
Automatically learns summary features from time series data for likelihood-free inference.
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…
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…