Two new versions of a master formula in portfolio theory proven using pathwise Itô calculus.
problem Proving strictly pathwise versions of a master formula in portfolio theory.
method Pathwise Itô calculus, Föllmer's pathwise Itô calculus, Dupire's functional pathwise Itô calculus, Cont & Fournié's functional pathwise Itô calculus.
result Two new versions of the master formula in stochastic portfolio theory proven.
Unified approach to time-inconsistent problems with distribution-dependent rewards.
problem Time-inconsistent problems with distribution-dependent rewards in behavioral finance and economics.
method Equilibrium master equation on Wasserstein space, refined derivatives, Itô's formula.
result Unified approach to find equilibrium solutions for time-inconsistent problems.
Using technique of wheeled props we establish a correspondence between the homotopy theory of unimodular Lie 1-bialgebras and the famous Batalin-Vilkovisky formalism. Solutions of the so called quantum master equation satisfying certain boundary conditions are proven to be in 1-1 correspondence with representations of …
Formula for Milnor triple linking number in link diagrams with multiple crossings.
problem Calculating Milnor triple linking number for complex link diagrams.
method Polyak-Viro type formula with explicit computation of configuration space integral.
result Formula applicable to diagrams with triple or more crossings.
A theory for cellular BF models on decomposed spaces.
problem Constructing invariant partition functions for cellular BF models.
method Construction of cellular BF theory on cobordisms with cellular decompositions.
result Invariants under subdivisions and gluing formulas.
Characterizes points in Thurston's Master Teapot and tests their membership.
problem Characterizing points in Thurston's Master Teapot.
method Explicit characterization and algorithmic implementation.
result Intersection of Master Teapot with unit cylinder is not symmetrical.
Study of Thurston's Master Teapot and its properties.
problem Characterize geometric and topological properties of Thurston's Master Teapot.
method Establish basic geometric and topological properties through analysis of self-maps and intersections.
result The Master Teapot is connected, contains the unit cylinder, and its intersection with Dimes{c} grows monotonically with c. Master algorithm fails to detect non-stationarity in practical settings.
problem Non-Stationary Reinforcement Learning without prior knowledge.
method Master algorithm tested under various conditions, including piecewise stationary multi-armed bandits.
result Master's non-stationarity detection is ineffective for practical horizons, leading to performance similar to random restarting.
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.
problem Developing a mathematical framework for non-acyclic Chern-Simons theory.
method Introduces a DG Lie algebra of uni-trivalent graphs with loops satisfying a Maurer-Cartan equation.
result Arithmetic analogue of effective action and quantum master equation.
Two neural network methods solve the master equation for MFGs.
problem Approximating Nash equilibria in stochastic, finite-agent games.
method Backward induction and direct PDE tackling neural networks.
result Neural networks can approximate the master equation's solution.
Master-slave architecture tackles combinatorial multi-armed bandits with diversity constraints.
problem Solving top-K combinatorial multi-armed bandits with non-linear feedback and diversity constraints. method Master-slave architecture with six slave models, teacher learning, and policy co-training.
result Significantly outperforms existing algorithms in synthetic and real datasets.
New algorithm outperforms existing ones by focusing on mastering rate.
problem Low sample efficiency in learning progress-based algorithms.
method Proposes a new algorithm based on mastering rate.
result Significantly outperforms learning progress-based algorithms.
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…
Develops SPT with price impact, deriving formulas for wealth and arbitrage conditions.
problem Tackles price impact in high-dimensional markets.
method Incorporates nonlinear price impact and impact decay models.
result Derives master formula for trading strategies and wealth dynamics.
Deep neural networks improve sEMG-based hand gesture classification.
problem Accurate classification of hand gestures from sEMG signals.
method Master-slave architecture with DNNs and synthetic feature data.
result Up to 9% improvement in accuracy with synthetic data.
Optimizes master faces for 2D and 3D face verification using evolutionary algorithms and neural networks.
problem Impersonation attacks using master faces for face-based identity authentication.
method Evolutionary algorithm in latent space of StyleGAN, neural network to direct search, 2D and 3D face reconstruction.
result Obtains high impersonation rates with fewer master faces for 2D and 3D face verification.
The paper explores geometric calculations on probability manifolds derived from master equations.
problem Understanding geometric properties of probability manifolds from master equations.
method Deriving geometric quantities like Levi-Civita connection, gradient, Hessian, parallel transport, and curvatures on probability manifolds.
result Calculation of geometric quantities in probability manifolds, including curvatures and connections.
Small trades show unexpected price impact after fee changes.
problem Anomaly in price impact for small transaction volumes post-fee restructuring.
method Reviewed existing master curve for price impact, re-estimated after fee reductions, found anomalies, and rescaled by liquidity proxy.
result Master curve for price impact can be approximated using a liquidity proxy, providing a practical method for practitioners.
In this master thesis, I present a new family of knots in the solid torus called lassos, and their properties. Given a knot K with Alexander polynomial ΔK(t), I then use these lassos as patterns to construct families of satellite knots that have Alexander polynomial ΔK(td) where d∈N∪{0}. In …
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.
problem Proving incidence theorems over C and R using the master theorem.
method Formalizes tiling proofs and introduces a hierarchy of theorems based on topological spaces.
result Identifies which theorems can or cannot be proved over C and R.
Master thesis proves Bergman kernel asymptotics for positive line bundles.
problem Proving asymptotic expansion of Bergman kernel for positive line bundles.
method Introduced a semi-classical symbol space and symbolic calculus.
result Established pointwise asymptotic expansion on positive parts of certain semi-positive line bundles.
Unified model explains income inequality across countries.
problem Understanding and explaining income inequality across different countries.
method Analytical model based on a master equation with growth and reset terms, tested on real data.
result Income distributions collapse on a master-curve when normalized, suggesting a universal pattern.
Study of supersymmetric AdS solutions using fibred GK geometries.
problem Understanding flux quantization and supersymmetric Killing vectors in AdS solutions.
method Analysis of GK geometries that fibre over Kähler bases, using master volume and global data.
result Quantum mechanical and SCFT central charges and entropy can be computed without explicit geometry.
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…
Combines multiple bandit algorithms to create a master algorithm.
problem Creating a master algorithm that performs well despite less feedback for base algorithms.
method Developed an Online Mirror Descent with a special mirror map and learning rate scheme.
result Achieved superior regret bounds by balancing exploitation and exploration.
LocalNewton reduces communication in distributed learning.
problem Communication bottleneck in distributed optimization.
method LocalNewton is a distributed second-order algorithm with local averaging, updating models locally and communicating once every few iterations.
result LocalNewton reduces communication rounds and end-to-end running time compared to state-of-the-art algorithms.
Researchers create a teapot model for Mandelbrot set, proving connectedness.
problem Understanding the connectedness of the outside part of the Mandelbrot set.
method Defined a 'Master teapot' model and generalized kneading theory for principal veins.
result Outside part of the 'Thurston set' is path connected.
Teaches advanced differential topology to master students with minimal background.
problem Teaching complex differential topology concepts to students with limited mathematical background.
method Cut-and-paste procedures, transversality, cobordism rings.
result Topics can be treated with 'bare hands' using simple mathematical tools.
Study linearized Schwarzschild spacetimes, proving decay of master quantities.
problem Linear stability of higher-dimensional Schwarzschild spacetimes.
method Hodge decomposition, gauge-invariant master quantities, wave equations.
result Uniform boundedness and decay estimates for master quantities in 6 or fewer dimensions.
A novel MCMC method clusters data faster and more accurately.
problem Efficiently clustering large datasets with unknown number of clusters.
method Master/Worker architecture for distributed MCMC inference.
result Significant improvement in clustering accuracy and speed.
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 explore homotopies in quantum field theory formalism.
problem Constructing homotopies in Batalin-Vilkovisky formalism.
method Review and construction of homotopies from renormalization group flow and gauge fixing changes.
result Constructing spans of quantum master actions with isomorphic effective actions using homotopies.
Develops a new model-free approach to portfolio theory using rough paths.
problem Handles more general portfolios without probabilistic assumptions.
method Rough path theory for stochastic portfolio theory (SPT).
result Asymptotic growth rates of various portfolios match.
Master's thesis reviews bundle gerbe theory and introduces new isomorphic gerbe.
problem Understanding bundle gerbe theory and its applications.
method Introduced cup product bundle gerbe and showed its isomorphism to the pullback of the basic bundle gerbe by the Weyl map.
result Stable isomorphism between cup product bundle gerbe and pullback of basic bundle gerbe by the Weyl map.
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…
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…
A new algorithm reduces worker workload in parallel optimization.
problem Solving large-scale machine learning problems efficiently.
method Decoupled asynchronous proximal stochastic gradient descent (DAP-SGD).
result Achieves faster convergence rates compared to existing methods.
Unified analytical tool for non-Markovian jump processes.
problem Analyzing history-dependent jump processes with non-Markovian behavior.
method Developed a standard form of master equations using Laplace-space embedding and asymptotic solution.
result Unified analytical toolset for general non-Markovian processes, leading to the GLE approximation.
New approach models sustained growth leading to stationary distributions.
problem Understanding stationary distributions in fast-growing systems.
method Applied discrete and continuous master equations, derived rates from stationary distributions.
result Reconstructed distributions for various growing systems.
Efficiently bootstraps massive distributed data without over-resampling.
problem Statistical inference for massive distributed data.
method Distributed Bootstrap applied to gradients from worker machines.
result Proves optimal statistical efficiency with minimal communication.
Study proves non-degeneracy of certain metrics in linearized gravity.
problem Proving non-degeneracy of Riemannian Schwarzschild-anti de Sitter metrics.
method Analyzing solutions of the linearized Einstein equations around Kottler metrics.
result Linearized Einstein operator is non-degenerate for open ranges of mass parameter.
ProductNet curates high-quality product datasets for better product understanding.
problem Lack of high-quality product datasets for product representation learning.
method Curated high-quality product datasets with a multi-modal deep neural network and active learning.
result Master model yields high categorization accuracy (94.7% top-1 accuracy for 1240 classes).
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 …
Efficiently approximates first-passage time distributions in reaction processes.
problem Computing first-passage time distributions for reaction processes modelled by master equations.
method Equivalent to a sequential Bayesian inference problem, solved by coupled ordinary differential equations for low-order moments.
result Good agreement with stochastic simulations in epidemic and trimerization models.