arXiv research

Machine learning identifies types of alterations in historical manuscripts.

This manuscript is an introduction to the theory of holomorphic foliations on the complex projective plane. Historically the subject has emerged from the theory of ODEs in the complex domain and various attempts to solve Hilbert's 16th Problem, but with the introduction of complex algebraic geometry, foliation theory a…

Aiming at quantifying and evaluating the regional commercial environment along with the level of economic development among cities in mainland China, the concept of China City Commercial Environment Credit Index(CEI) was first introduced and established in 2010. In this manuscript, a historical review and detailed intr…

The thesis examines stochastic calculus in option pricing with logistic models and numerical methods.

Online leading has disrupted the traditional consumer banking sector with more effective loan processing. Risk prediction and monitoring is critical for the success of the business model. Traditional credit score models fall short in applying big data technology in building risk model. In this manuscript, data with var…

This paper introduces a very challenging dataset of historic German documents and evaluates Fully Convolutional Neural Network (FCNN) based methods to locate handwritten annotations of any kind in these documents. The handwritten annotations can appear in form of underlines and text by using various writing instruments…

The results in the recently posted manuscript arXiv:math/0405153v3 are incorrect. The correct version of the aimed results is not original. The preprint contains material from references that are not properly quoted.

Self-supervised methods learn from noisy data alone, useful for imaging problems.

This is the original manuscript dated March 9th 1983, typeset by the Editors for the Proceedings of the Midwest Geometry Conference 2007 held in memory of Thomas Branson. Stephen Paneitz passed away on September 1st 1983 while attending a conference in Clausthal and the manuscript was never published. For more than 20 …

Proposes a new method for efficient manifold denoising robust to high dimensional noise.

This technical report describes a practical field test on word-image classification in a very large collection of more than 300 diverse handwritten historical manuscripts, with 1.6 million unique labeled images and more than 11 million images used in testing. Results indicate that several deep-learning tests completely…

withdrawn and included in our new manuscript "Abelian subgroups of Garside groups", math.GT/0609683

Generative models create personalized patient health simulations.

Principal component analysis (PCA) is a mainstay of modern data analysis - a black box that is widely used but (sometimes) poorly understood. The goal of this paper is to dispel the magic behind this black box. This manuscript focuses on building a solid intuition for how and why principal component analysis works. Thi…

Recent research connects Hörmander's old work to modern boundary Laplacian analysis.

Domain-general semantic parsing is a long-standing goal in natural language processing, where the semantic parser is capable of robustly parsing sentences from domains outside of which it was trained. Current approaches largely rely on additional supervision from new domains in order to generalize to those domains. We …

We survey some recent results and constructions of almost-Kähler manifolds whose curvature tensors have certain algebraic symmetries. This is an updated and corrected version of the (to be) published manuscript.

This brief manuscript provides an introduction to Lévy processes and their applications in finance as the random process that drives asset models. Characteristic functions and random variable generators of popular Lévy processes are presented in R.

This manuscript develops the theory of agglomerative clustering with Bregman divergences. Geometric smoothing techniques are developed to deal with degenerate clusters. To allow for cluster models based on exponential families with overcomplete representations, Bregman divergences are developed for nondifferentiable co…

In this manuscript, we investigate deep invertible networks for EEG-based brain signal decoding and find them to generate realistic EEG signals as well as classify novel signals above chance. Further ideas for their regularization towards better decoding accuracies are discussed.

Unified HS and related methods with explicit modeling assumptions.

This manuscript presents some new impossibility results on adversarial robustness in machine learning, a very important yet largely open problem. We show that if conditioned on a class label the data distribution satisfies the $W_2$ Talagrand transportation-cost inequality (for example, this condition is satisfied if t…

The purpose of this article is to provide, with the help of a fluctuation identity, a generic link between a number of known identities for the first passage time and overshoot above/below a fixed level of a Levy process and the solution of Gerber and Shiu [Astin Bull. 24 (1994) 195-220], Boyarchenko and Levendorskii […

This paper introduces Bayes Hilbert spaces for efficient posterior approximation.

The link between different psychophysiological measures during emotion episodes is not well understood. To analyse the functional relationship between electroencephalography (EEG) and facial electromyography (EMG), we apply historical function-on-function regression models to EEG and EMG data that were simultaneously r…

Develops a new framework for temporal anchoring in deep embedding spaces.

ArtificialReplay improves data efficiency in bandits using historical data.

Survey of weak form's role in equation learning, parameter estimation, and coarse graining.

ADR helps LLMs find and use historical analogies for foresight analysis.

Proposes dynamic borrowing method for historical data in clinical trials.

In this manuscript we review the construction of the Teichmüller TQFT in [AK1], upgrading it to a theory dependent on an extra odd integer $N$ using results developed in [AK3]. We also describe how this theory is related with quantum Chern--Simons Theory at level $N$ with gauge group $\rm{PSL}(2,\mathbb{C})$.

This manuscript contains a detailed proof of the Poincare Conjecture. The arguments we present here are expanded versions of the ones given by Perelman in his three preprints posted in 2002 and 2003. This is a revised version taking in account the comments of the referees and others. It has been reformatted in the AMS …

Withdrawn and replaced by two related manuscripts: (1) "Stabilization in the braid groups I:MTWS", published in Geometry and Topology Volume 10 (2006), 413-540, arXiv:math.GT/0310279, and (2) "Stabilization in the braid groups II: Transversal simplicity of knots", Geometry and Topology Volume 10 (2006), to appear, arXi…

Data describing historical economic growth are analysed. Included in the analysis is the world and regional economic growth. The analysis demonstrates that historical economic growth had a natural tendency to follow hyperbolic distributions. Parameters describing hyperbolic distributions have been determined. A search …

The study characterizes symmetries in Kaehler manifolds.

Simplicial, piecewise-flat discretizations of manifolds provide a clear path towards curvature analysis on discrete geometries and for solutions of PDE's on manifolds of complex topologies. In this manuscript we review and expand on discrete exterior calculus methods using hybrid domains. We then analyze the geometric …

This study reviews techniques to estimate volatility and price Variance Swaps.

How can we recognise social roles of people, given a completely unlabelled social network? We present a transfer learning approach to network role classification based on feature transformations from each network's local feature distribution to a global feature space. Experiments are carried out on real-world datasets.…

We give a new proof of Markov's classical theorem relating any two closed braid representations of the same knot or link. The proof is based upon ideas in a forthcoming paper by the authors, "Stabilization in the braid groups". The new proof of the classical Markov theorem is used by Nancy Wrinkle in her forthcoming ma…

This manuscript surveys reinforcement learning from the perspective of optimization and control with a focus on continuous control applications. It surveys the general formulation, terminology, and typical experimental implementations of reinforcement learning and reviews competing solution paradigms. In order to compa…

This manuscript contributes a general and practical framework for casting a Markov process model of a system at equilibrium as a structural causal model, and carrying out counterfactual inference. Markov processes mathematically describe the mechanisms in the system, and predict the system's equilibrium behavior upon i…

Extends gradient estimates for heat equation under Finsler geometric flows.

Improved Bayesian inference using power priors with historical data.

This is a facsimile of the circa 1990 unpublished manuscript with the same title. All the original text, figures and tables are included; although text has been reset in \TeX, the original hand-drawn figures have been redrawn digitally, and the parameter $k$ in the original table of lens spaces has been replaced with t…

In this manuscript we analyse the leading statistical properties of fluctuations of (log) 3-month US Treasury bill quotation in the secondary market, namely: probability density function, autocorrelation, absolute values autocorrelation, and absolute values persistency. We verify that this financial instrument, in spit…

We study simple branched coverings of degree d of the 2- and 3- dimensional sphere branched over oriented links. We demonstrate how to use braid charts to develop embeddings of these into $S^k \times D^2$ for $k=2,3 when$d=2,3$. This is an initial part of our study and represents the manuscript submitted to the RIMS w…

Develops a machine learning framework for identifying authorship in texts.

Combines experimental and historical data for robust policy evaluation.