The paper proves regularity for varifolds with bounded anisotropic mean curvature.
problem Regularity of varifolds with bounded anisotropic mean curvature.
method Local anisotropic regularity theorem and touching balls approach.
result Varifolds can be covered by countably many C2-regular submanifolds. The paper generalizes TQFTs to fermionic systems and classifies SPTs and SETs.
problem Classifying fermionic SPTs and SETs with finite group symmetries.
method Formulating fermionic TQFTs, gauging SPTs, using bordism groups, and constructing anomalous boundary states.
result Explicit classification of fermionic SPTs and SETs, including new anomalous boundary states.
In this paper we propose a novel application of Gaussian processes (GPs) to financial asset allocation. Our approach is deeply rooted in Stochastic Portfolio Theory (SPT), a stochastic analysis framework introduced by Robert Fernholz that aims at flexibly analysing the performance of certain investment strategies in st…
SPT predicts age and mass of red giants from spectra.
problem Challenges in age and mass estimation of red giants using traditional methods.
method SPT framework with Multi-head Hadamard Self-Attention and Mahalanobis distance-based loss function.
result Remarkable age and mass estimations with low errors and uncertainties.
We classify higher-SPTs and their anomalies via cobordism theory.
problem Understanding higher symmetries and anomalies in quantum field theories.
method Developed a generalized cobordism theory using advanced mathematical tools.
result Classified higher-SPTs and their boundary anomalies.
This paper extends Euclidean theorems to anisotropic settings for varifolds.
problem Anisotropic mean curvature of codimension-one varifolds.
method Proves perpendicularity and locality of mean curvature for bounded anisotropic mean curvature varifolds.
result Anisotropic mean curvature agrees with the approximate mean curvature on the rectifiable part of the varifold.
The study extends SPT to account for real-world transaction costs, improving portfolio performance.
problem Real-world transaction costs affect portfolio performance, especially during market stress.
method Developed a continuous-time model with stochastic transaction costs and derived lower bounds for cost-adjusted wealth.
result Functionally generated portfolios can still achieve relative arbitrage after accounting for transaction costs.
Constructs rank-based continuous semimartingales for financial markets.
problem Model financial markets using rank-based diffusions.
method Uses Dirichlet forms and Feller property to construct semimartingales.
result Establishes nonexistence of triple collisions and simplified rank process dynamics.
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.
Study optimizes decay estimates for minimizing currents in submanifolds.
problem Optimizing decay estimates for minimizing currents in submanifolds.
method Proves excess-decay estimate for codimension 1 currents mod 2Q.
result Optimal dependence of estimates upon second fundamental form of submanifold.
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.
Constructs a path integral for fermionic SPTs, solving anomalies in 2+1D topological orders.
problem Anomalies in (2+1)D fermionic topological phases and their computation.
method Combining (2+1)D fermionic topological order with symmetry fractionalization data to construct a (3+1)D path integral.
result Reproduces the Z16 anomaly indicator for time-reversal symmetric topological superconductors. Study SKK groups of manifolds to classify non-unitary TQFTs.
problem Classify non-unitary invertible topological quantum field theories.
method Apply Galatius-Madsen-Tillman-Weiss and Genauer-Schommer-Pries results to compute SKK groups.
result Complete classification of non-unitary invertible TQFTs in dimensions 1-5.
This paper proposes SPT to generate diverse and transferable adversarial examples.
problem Limitations of recent adversarial examples in diversity and transferability.
method Structure-preserving transformation (SPT) to generate natural and diverse adversarial examples.
result Adversarial examples generated by SPT transfer well to other models with high success rate.
Topological Quantum Field Theories (TQFTs) pertinent to some emergent low energy phenomena of condensed matter lattice models in 2+1 and 3+1D are explored. Many of our field theories are highly-interacting without free quadratic analogs. Some of our bosonic TQFTs can be regarded as the continuum field theory formulatio…
The Clifford torus minimizes Willmore energy closely for small perturbations.
problem Finding the closest shape to the Clifford torus under small perturbations of Willmore energy.
method Analyzing integral 2-varifolds with specific properties and showing quantitative closeness to the Clifford torus.
result The support of the varifold is quantitatively close to the Clifford torus after a conformal transformation.
Paper provides estimates for varifolds with critical mean curvature.
problem Estimating tilt-excess on varifolds with critical mean curvature.
method Generalizing Lipschitz approximation and Sobolev-Poincaré estimates to almost-integral rectifiable varifolds.
result VMO-type estimates for quadratic tilt-excess on varifolds with critical mean curvature.
New insights into 4d YM and 5d topological field theories with higher symmetries.
problem Exploring new topological field theories with higher symmetries.
method Dynamic gauging of 1-form symmetry, higher anomalies, and lattice simplicial complex regularizations.
result Discovery of new higher-form gauge fields and exotic anyonic statistics.
The paper studies the behavior of Möbius-invariant Willmore flow in 3-sphere, proving convergence to Clifford torus.
problem Investigating the behavior of Möbius-invariant Willmore flow in 3-sphere.
method Analyzing flow lines of the Möbius-invariant Willmore flow in 3-sphere, constructing divergent and convergent flow lines, and identifying limit surfaces.
result The flow lines of the Möbius-invariant Willmore flow in 3-sphere converge to parametrizations of the Clifford torus, up to Möbius transformations.
Study optimizes growth rate for investors with long-only constraints.
problem Maximizing growth rate under drift uncertainty and long-only constraints.
method Developed a finite dimensional approximation for concave functionally generated portfolios.
result Proved uniqueness and existence for optimal portfolios under long-only constraints.
Novel PCA method for high-dimensional inverse problems.
problem Optimizing large-scale random fields with gradient information.
method Gradient-Sensitive Principal Component Analysis (Gradient-SPCA) that modifies PCA using objective function gradients.
result Improvements in encoding quality for objective function minimization and field distribution.
Paper proves minimal surfaces near quadratic cones have specific smooth structure.
problem Characterize minimal surfaces near quadratic cones.
method Analyzes n-varifolds in the unit ball close to a minimizing quadratic cone. result Singularities modeled on these cones determine the local structure of nearby minimal surfaces.
Unified approach to equity markets with open and hybrid Jacobi models.
problem Stochastic Portfolio Theory problems in equity markets.
method Combining open markets and hybrid Jacobi processes.
result Stability of capital distribution curve and growth optimal strategies.
The paper models market crashes as phase transitions, finding dynamic transitions offer better predictions.
problem Understanding and predicting extreme financial events like market crashes.
method Employing phase transition theory, focusing on endogenous crashes, and comparing DPT, CPT, and SPT.
result Dynamic phase transitions provide more accurate predictions of market crashes compared to critical and stochastic models.
This paper generalizes two facts about oriented 3d TFTs to the unoriented case. On one hand, it is known that oriented 3d TFTs having a topological boundary condition admit a state-sum construction known as the Turaev-Viro construction. This is related to the string-net construction of fermionic phases of matter. We sh…
Bayesian inference calibrates Hall thruster model uncertainty at varying pressures.
problem Quantifying uncertainty in a multi-component Hall thruster model at different facility pressures.
method Bayesian inference applied to calibrate and quantify prediction uncertainty in a coupled multi-component Hall thruster model.
result Model reduces predictive errors in thrust and discharge current by more than 50% compared to a previous model.
This paper compares modern portfolio theories and applies them to real-world portfolio selection.
problem Balancing risk and return in financial investments.
method Introduction of Markowitz's MPT and Fernholz's SPT, application of four models (Markowitz, Constant Correlation, Single Index, Multi-Factor), and use of Portfolio Algorithm and time series models for prediction.
result Comparison and evaluation of portfolio performance and risk management strategies.
Study on singularities of area-minimizing currents, focusing on frequency and branch points.
problem Understanding the nature of singular points in area-minimizing currents.
method Intrinsic frequency function and decomposition theorem for singular set.
result Established properties of the planar frequency function and decomposition of singular set.