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.
Proves volume conjecture for twist knots using complex analysis.
Unified framework for complex, split-complex, and dual numbers.
The paper finds transformation formulas for quaternionic complex structures.
We study the complexity of the entire regularization path for least squares regression with 1-norm penalty, known as the Lasso. Every regression parameter in the Lasso changes linearly as a function of the regularization value. The number of changes is regarded as the Lasso's complexity. Experimental results using exac…
Improved sample complexity for Gaussian process approximations.
The h-principle helps solve complex geometric problems.
Paper tackles complex risk in deep neural networks.
We apply information-based complexity analysis to support vector machine (SVM) algorithms, with the goal of a comprehensive continuous algorithmic analysis of such algorithms. This involves complexity measures in which some higher order operations (e.g., certain optimizations) are considered primitive for the purposes …
The authors study the method of scaling in the context of the study of automorphism groups of complex domains in multiple dimensions. Various types of scaling techniques are compared and contrasted. Applications are given in a number of areas of complex geometric analysis. Relations with other parts of mathematics are …
Study local and global aspects of complex plane curve embeddings.
Smoothed analysis of complexity bounds and condition numbers has been done, so far, on a case by case basis. In this paper we consider a reasonably large class of condition numbers for problems over the complex numbers and we obtain smoothed analysis estimates for elements in this class depending only on geometric inva…
Paper introduces probabilistic methods to approximate archetypal analysis, reducing complexity.
New TDA approach using Finsler metrics.
Complex network analysis reveals dominant stocks in financial stock returns correlations.
Paper analyzes sample complexity of polynomial neural networks.
The construction of synthetic complex-valued signals from real-valued observations is an important step in many time series analysis techniques. The most widely used approach is based on the Hilbert transform, which maps the real-valued signal into its quadrature component. In this paper, we define a probabilistic gene…
Deep model learns complex latent codes without assuming factor structure.
The extragradient method accelerates convergence in complex game dynamics.
We propose the labeled Čech complex, the plain labeled Vietoris-Rips complex, and the locally scaled labeled Vietoris-Rips complex to perform persistent homology inference of decision boundaries in classification tasks. We provide theoretical conditions and analysis for recovering the homology of a decision boundary fr…
Complex analysis aids in studying minimal surfaces.
Transformers show strengths and weaknesses in complexity analysis.
New complexity analysis for estimating normalizing constants in high dimensions.
Complex analysis techniques link Gaussian RBF kernels to quantum mechanics.
Deep learning improves survival analysis for complex data types.
Study analyzes Echo State Network parameters for Rossler attractor dynamics.
Study compares Bitcoin, gold, and gas price complexity using multifractal and multiscale entropy methods.
We are concerned with bifurcation analysis and control of nonlinear Eulerian flows with non-resonant n-tuple Hopf singularity. The analysis is involved with CW complex bifurcations of flow-invariant Clifford hypertori, where we refer to these toral manifolds by toral CW complexes. We observe from primary to tertiary fl…
Lyapunov-based analysis shows polynomial sample complexity for WCMDPs and RBs.
Paper introduces Simplet Frequency Distribution (SFD) for SCs.
We introduce a simple analysis of the structural complexity of infinite-memory processes built from random samples of stationary, ergodic finite-memory component processes. Such processes are familiar from the well known multi-arm Bandit problem. We contrast our analysis with computation-theoretic and statistical infer…
We carry out a Painlevé analysis to find the cases where the cohomogeneity one steady Ricci soliton equation can be integrable. We concentrate on two classes of solitons: warped products and complex line bundles over a Fano Kähler Einstein base. For warped products, the analysis singles out the case with one factor whe…
The paper analyzes adversarial robustness for linear models and neural networks using Rademacher complexity.
Analyzes the complexity of linear hypothesis sets using Rademacher complexity.
Predicting the runtime complexity of a programming code is an arduous task. In fact, even for humans, it requires a subtle analysis and comprehensive knowledge of algorithms to predict time complexity with high fidelity, given any code. As per Turing's Halting problem proof, estimating code complexity is mathematically…
Classic economic science is reaching the limits of its explanatory powers. Complexity science uses an increasingly larger set of different methods to analyze physical, biological, cultural, social, and economic factors, providing a broader understanding of the socio-economic dynamics involved in the development of nati…
This study analyzes cryptocurrency market crashes using complex network analysis.
Geodesic convexity generalizes the notion of (vector space) convexity to nonlinear metric spaces. But unlike convex optimization, geodesically convex (g-convex) optimization is much less developed. In this paper we contribute to the understanding of g-convex optimization by developing iteration complexity analysis for …
SPCA improves PCA by learning from simple to complex samples.
No nontrivial automorphisms for cubic surfaces moduli space.
A non-Hermitean extension of paradigmatic Wishart random matrices is introduced to set up a theoretical framework for statistical analysis of (real, complex and real quaternion) stochastic time series representing two "remote" complex systems. The first paper in a series provides a detailed spectral theory of non-Hermi…
In this paper, we present a unified analysis of matrix completion under general low-dimensional structural constraints induced by {\em any} norm regularization. We consider two estimators for the general problem of structured matrix completion, and provide unified upper bounds on the sample complexity and the estimatio…
This paper analyzes sampling from heavy-tailed distributions using discretized Itô diffusions.
Quantum Monte Carlo speeds up option pricing for complex payoff functions.
Multifractality is ubiquitously observed in complex natural and socioeconomic systems. Multifractal analysis provides powerful tools to understand the complex nonlinear nature of time series in diverse fields. Inspired by its striking analogy with hydrodynamic turbulence, from which the idea of multifractality originat…
In this paper we give definitions of matrix rates of return which do not depend on the choice of basis describing baskets. We give their economic interpretation. The matrix rate of return describes baskets of arbitrary type and extends portfolio analysis to the complex variable domain. This allows us for simultaneous a…
This note provides a new proof of the real analyticity of the Liouville map.
Performance monitoring, anomaly detection, and root-cause analysis in complex cyber-physical systems (CPSs) are often highly intractable due to widely diverse operational modes, disparate data types, and complex fault propagation mechanisms. This paper presents a new data-driven framework for root-cause analysis, based…
New analysis improves sample complexity for vanilla policy gradient methods.