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 examines boundedness of oscillating singular integrals on specific Lie groups.
We study geometric quantization of the harmonic oscillator in terms of a singular real polarization given by fibres of the energy momentum map.
We consider a closed Willmore surface properly immersed in (m>2) with square-integrable second fundamental form, and with one point-singularity of finite arbitrary integer order. Using the "conservative" reformulation of the Willmore equation introduced in a previous paper by the second author, we show that, i…
Study on black hole interiors with matter fields, showing oscillation condition impacts blow-up.
To overcome the oscillation problem in the classical momentum-based optimizer, recent work associates it with the proportional-integral (PI) controller, and artificially adds D term producing a PID controller. It suppresses oscillation with the sacrifice of introducing extra hyper-parameter. In this paper, we start by …
Study of harmonic oscillators on singular geometries using supersymmetry.
It is shown that the estimates obtained by Manfredo P. do Carmo and Detang Zhou, in their paper "Eigenvalue estimate on complete noncompact Riemannian manifolds and applications", for the first eigenvalue of the Laplace-Beltrami operator on open manifolds, via an oscillation theorem, can be naturally extended for the s…
The paper studies the smoothness of critical points of variational integrals on Hessian spaces.
New integral transforms solve multilayer heat equations.
Deep linear networks oscillate beyond the edge of stability in a predictable manner.
We prove well-posedness and regularity results for elliptic boundary value problems on certain domains with a smooth set of singular points. Our class of domains contains the class of domains with isolated oscillating conical singularities, and hence they generalize the classical results of Kondratiev on domains with c…
We study a generalization of Hodge structures which first appeared in the work of Cecotti and Vafa. It consists of twistors, that is, holomorphic vector bundles on P^1, with additional structure, a flat connection on C^*, a real subbundle and a pairing. We call these objects TERP-structures. We generalize to TERP-struc…
The Black-Scholes model anticipates rather well the observed prices for options in the case of a strike price that is not too far from the current price of the underlying asset. Some useful extensions can be obtained by an adequate modification of the coefficients in the Black-Scholes equation. We investigate from a ma…
The Sornette-Ide differential equation of herding and rational trader behaviour together with very small random noise is shown to lead to crashes or bubbles where the price change goes to infinity after an unpredictable time. About 100 time steps before this singularity, a few predictable roughly log-periodic oscillati…
The paper focuses on various properties and applications of the homotopy operator, which occurs in the Poincaré lemma. In the first part, an abstract operator calculus is constructed, where the exterior derivative is an abstract derivative and the homotopy operator plays the role of an abstract integral. This operator …
Proposes a new method combining Reservoir Computing and Normalizing Flow for predicting stochastic dynamical systems.
We introduce tools to capture the dynamics of three different pathways, in which the synchronization of human decision-making could lead to turbulent periods and contagion phenomena in financial markets. The first pathway is caused when stock market indices, seen as a set of coupled integrate-and-fire oscillators, sync…
A challenging problem in physics concerns the possibility of forecasting rare but extreme phenomena such as large earthquakes, financial market crashes, and material rupture. A promising line of research involves the early detection of precursory log-periodic oscillations to help forecast extreme events in collective p…
The Planck mass can be derived from gravitational potential behavior in compactifications.
In this paper we are interested in term structure models for pricing zero coupon bonds under rapidly oscillating stochastic volatility. We analyze solutions to the generalized Cox-Ingersoll-Ross two factors model describing clustering of interest rate volatilities. The main goal is to derive an asymptotic expansion of …
A new oscillator measures trending behavior of financial instruments.
Minimal vector fields on oscillator groups studied, with specific conditions for minimality.
Integrates singular subalgebroids using diffeological groupoids.
The harmonic oscillator as a distinguished dynamical system can be defined not only on the Euclidean plane but also on the sphere and on the hyperbolic plane, and more generally on any configuration space with constant curvature and with a metric of any signature, either Riemannian (definite positive) or Lorentzian (in…
Log-periodic oscillations have been used to predict price trends and crashes on financial markets. So far two types of log-periodic oscillations have been associated with the real markets. The first type are oscillations which accompany a rising market and which ends in a crash. The second type oscillations, called "an…
Estimates box dimension of fractal interpolation surfaces using oscillation vectors.
Researchers classify lattices in a specific four-dimensional group.
The paper proves stability of certain singularities in integrable systems.
Proves singular set of certain integral hypercurrents has measure zero.
Novel method for solving ODEs on k-polysymplectic manifolds.
TDA detects financial bubbles through early warning signals.
Study oscillatory integrals with degenerate singular points in multivariable phase functions.
The Duffing oscillator's parameters are identified online using variational message passing.
New method linearizes nonlinear coupled oscillators on graphs.
The study classifies singularities in curved 3D shapes.
We consider the problem of adaptive stratified sampling for Monte Carlo integration of a differentiable function given a finite number of evaluations to the function. We construct a sampling scheme that samples more often in regions where the function oscillates more, while allocating the samples such that they are wel…
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…
Symplectic classification for a specific type of singularity in integrable systems.
We compare the homology groups of the chain complex of integral currents with compact support of a metric space with the singular Lipschitz homology and with ordinary singular homology. If satisfies certain cone inequalities all these homology theories coincide. On the other hand, for…
Gradient and Laplacian estimates for complex Monge-Ampère equations found.
Builds torus fibrations over singular manifolds with specific features.
The study derives generalization bounds for neural oscillators, improving their performance with regularization.
The paper defines singular evolutoids and uses them to derive an integral equality.
Study finds the spectrum of a cubic Dirac operator on specific oscillator group manifolds.
The paper explores hidden torus symmetries in integrable systems and their stability.
We discuss normal forms and symplectic invariants of parabolic orbits and cuspidal tori in integrable Hamiltonian systems with two degrees of freedom. Such singularities appear in many integrable systems in geometry and mathematical physics and can be considered as the simplest example of degenerate singularities. We a…
We describe the geometry of geodesics on a Lorentz ellipsoid: give explicit formulas for the first integrals (pseudo-confocal coordinates), curvature, geodesically equivalent Riemannian metric, the invariant area-forms on the time- and space-like geodesics and invariant 1-form on the space of null geodesics. We prove a…
The purpose of this paper is to study the validity of Stokes' Theorem for singular submanifolds and differential forms with singularities in Euclidean space. The results are presented in the context of Lebesgue Integration, but their proofs involve techniques from gauge integration in the spirit of R.~Henstock, J.~Kurz…