arXiv research

Study linearized Schwarzschild spacetimes, proving decay of master quantities.

In this paper, we study the theory of linearized gravity and prove the linear stability of Schwarzschild black holes as solutions of the vacuum Einstein equations. In particular, we prove that solutions to the linearized vacuum Einstein equations centered at a Schwarzschild metric, with suitably regular initial data, r…

The paper explores geometric calculations on probability manifolds derived from master equations.

We analyze a monetary system of random money transfer on the basis of double entry bookkeeping. Without boundary conditions, we do not reach a price equilibrium and violate text-book formulas of economists quantity theory (MV=PQ). To match the resulting quantity of money with the model assumption of a constant price, w…

We simplify supergravity in 10D using geometric insights.

Characterizes points in Thurston's Master Teapot and tests their membership.

MuZero learns models to master complex games without domain knowledge.

Study of Thurston's Master Teapot and its properties.

Master algorithm fails to detect non-stationarity in practical settings.

We extend the Chern-Simons perturbative invariant of Axelrod and Singer to non-acyclic connections. We construct a solution of the quantum master equation on the space of functions on the cohomology of the connection. We prove that this solution is well defined up to master homotopy. We discuss also invariants of links…

We construct master spaces for oriented torsion free sheaves coupled with morphisms into a fixed reference sheaf. These spaces are projective varieties endowed with a natural $\C^*$-action. The fixed point set of this action contains the moduli space of semistable oriented torsion free sheaves and the quot scheme assoc…

Generalizes Hodge correlators using quantum master equation concepts.

Two neural network methods solve the master equation for MFGs.

Master-slave architecture tackles combinatorial multi-armed bandits with diversity constraints.

New algorithm outperforms existing ones by focusing on mastering rate.

A master equation approach to the numerical solution of option pricing models is developed. The basic idea of the approach is to consider the Black--Scholes equation as the macroscopic equation of an underlying mesoscopic stochastic option price variable. The dynamics of the latter is constructed and formulated in term…

Deep neural networks improve sEMG-based hand gesture classification.

Optimizes master faces for 2D and 3D face verification using evolutionary algorithms and neural networks.

In his lectures at College de France, P.L. Lions introduced the concept of Master equation, see [5] for Mean Field Games. It is introduced in a heuristic fashion, from the system of partial differential equations, associated to a Nash equilibrium for a large, but finite, number of players. The method, also explained in…

Investigates proving geometric theorems over complex and real numbers using tilings.

Master thesis proves Bergman kernel asymptotics for positive line bundles.

Unified model explains income inequality across countries.

We construct a solution of the master equation by means of standard tools from homological perturbation theory under just the hypothesis that the ground field be of characteristic zero, thereby avoiding the formality assumption of the relevant Lie algebra. To this end we endow the homology H(g) of any differential grad…

LocalNewton reduces communication in distributed learning.

Researchers create a teapot model for Mandelbrot set, proving connectedness.

Teaches advanced differential topology to master students with minimal background.

We report on the occurrence of an anomaly in the price impacts of small transaction volumes following a change in the fee structure of an electronic market. We first review evidence for the existence of a master curve for price impact on the Johannesburg Stock Exchange (JSE). On attempting to re-estimate a master curve…

A novel MCMC method clusters data faster and more accurately.

We explore homotopies in quantum field theory formalism.

Master's thesis reviews bundle gerbe theory and introduces new isomorphic gerbe.

The quantum master equation is usually formulated in terms of functionals of the components of mappings from a space-time manifold M into a finite-dimensional vector space. The master equation is the sum of two terms one of which is the anti-bracket (odd Poisson bracket) of functionals and the other is the Laplacian of…

Asynchronous parallel optimization algorithms for solving large-scale machine learning problems have drawn significant attention from academia to industry recently. This paper proposes a novel algorithm, decoupled asynchronous proximal stochastic gradient descent (DAP-SGD), to minimize an objective function that is the…

We analyze an ideal gas like model of a trading market with quenched random saving factors for its agents and show that the steady state income ($m$) distribution $P(m)$ in the model has a power law tail with Pareto index $ν$ exactly equal to unity, confirming the earlier numerical studies on this model. The analysis s…

Unified analytical tool for non-Markovian jump processes.

Efficiently bootstraps massive distributed data without over-resampling.

ProductNet curates high-quality product datasets for better product understanding.

This is my master thesis. Unfortunately it is written in Italian, but maybe somebody will find it helpful when it comes to Evans Potentials

In this lecture I review how a matrix/Azumaya-type noncommutative geometry arises for D-branes in string theory and how such a geometry serves as an origin of the master nature of D-branes; and then highlight an abundance conjecture on D0-brane resolutions of singularities that is extracted and purified from a work of …

We use pathwise Itô calculus to prove two strictly pathwise versions of the master formula in Fernholz' stochastic portfolio theory. Our first version is set within the framework of Föllmer's pathwise Itô calculus and works for portfolios generated from functions that may depend on the current states of the market port…

We study the problem of combining multiple bandit algorithms (that is, online learning algorithms with partial feedback) with the goal of creating a master algorithm that performs almost as well as the best base algorithm if it were to be run on its own. The main challenge is that when run with a master, base algorithm…

Solves portfolio optimization with cardinality constraints using column generation.

We revisit our earlier work on the AKSZ formulation of topological sigma model on generalized complex manifolds, or Hitchin model. We show that the target space geometry geometry implied by the BV master equations is Poisson--quasi--Nijenhuis geometry recently introduced and studied by Stiénon and Xu (in the untwisted …

An introductory course on hyperbolic geometry for advanced students.

Study improves $L^{\infty}$ estimates and extreme value behavior in stochastic differential games.

New algorithm tackles adversarial bandits with arbitrary strategies.

In three dimensions, a `master theory' for all Thurston geometries requires imaginary flux. However, these geometries can be obtained from physical three-dimensional theories with various additional scalar fields, which can be interpreted as moduli in various compactifications of a higher-dimensional `master theory'. T…

Equations of dispersionless Hirota type have been thoroughly investigated in the mathematical physics and differential geometry literature. It is known that the parameter space of integrable Hirota type equations in 3D is 21-dimensional and the action of the natural equivalence group Sp(6, R) on the parameter space has…

Unified approach to time-inconsistent problems with distribution-dependent rewards.