Invites readers to explore higher Teichmüller theory.
problem None explicitly stated; focuses on introduction.
method Description and overview of facets.
result Introduces higher Teichmüller theory to readers.
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Garside groups and geometrymath.GR
Invites geometers to Garside theory for mapping class groups.
problem None explicitly stated, but related to geometric group theory.
method Garside theory applied to mapping class groups.
result No specific key result mentioned in the abstract.
Topological conformal field theories are defined using only basic results from the theory of quasiconformal mappings.
Invites probabilistic approach to Kähler-Einstein metrics via random point processes.
problem Constructing Kähler-Einstein metrics on complex projective algebraic manifolds.
method Large N-limit from random point processes defined by algebro-geometric data; variational approach for positive Ricci curvature.
result Convergence of metrics to Kähler-Einstein metrics under specific conditions.
Lecture notes on singular foliations, smooth and holomorphic.
problem Understanding singular foliations in geometry.
method Review of foundations, recent tools from non-commutative geometry, and homotopic notions.
result Introduction of various homotopic notions and open questions.
Invites study of contact structures and Reeb flows dynamics.
problem Relating dynamics of two Reeb flows of the same contact structure.
method Gathers results and poses many questions and conjectures.
result Many new questions and conjectures posed.
Discussing hybrid models in Bayesian networks.
problem Improving accuracy in network modeling.
method Hybrid semiparametric Bayesian approach.
result Enhanced model performance in complex networks.
This book was intended to serve as supporting material for a mini-course on web geometry delivered at the 27th Brazilian Mathematical Colloquium which took place at IMPA in the last week of July 2009.
The paper contains a geometrization of a time dependent Lagrangian function defined on the 1-jet space J^1(R,M) which identifies with R\times TM. The reader is invited to compare this geometrization with that developped by Miron and Anastasiei.
Introduces dilation surfaces and their geometric and dynamical aspects.
problem None explicitly stated; focuses on introduction.
method Explains geometric and dynamical aspects of dilation surfaces.
result Moduli spaces, directional foliations, and Teichmüller flow are discussed.
Proceedings of the 2016 ICML Workshop on Human Interpretability in Machine Learning (WHI 2016)stat.ML
This is the Proceedings of the 2016 ICML Workshop on Human Interpretability in Machine Learning (WHI 2016), which was held in New York, NY, June 23, 2016. Invited speakers were Susan Athey, Rich Caruana, Jacob Feldman, Percy Liang, and Hanna Wallach.
Tessellations of surfacesmath.HO
Tessellations cover planes without gaps or overlaps.
problem None explicitly stated, focuses on beauty and majesty of tessellations.
method Explains tessellations as tile coverings of a plane.
result Explains the beauty and majesty of tessellations and triangulation of surfaces.
Schervish (1985b) showed that every forecasting system is noncalibrated for uncountably many data sequences that it might see. This result is strengthened here: from a topological point of view, failure of calibration is typical and calibration rare. Meanwhile, Bayesian forecasters are certain that they are calibrated-…
Proceedings of the 2017 ICML Workshop on Human Interpretability in Machine Learning (WHI 2017)stat.ML
ICML workshop on making machine learning models more understandable.
problem Making machine learning models more understandable to humans.
method Various presentations and discussions on interpretability techniques.
result Improved methods for explaining machine learning models.
Proceedings of the 2018 ICML Workshop on Human Interpretability in Machine Learning (WHI 2018)stat.ML
ICML workshop on making machine learning models more understandable.
problem Making machine learning models more understandable to humans.
method Various presentations and discussions on interpretability techniques.
result Advancements in methods to improve model interpretability.
The intention of this article is to give a flavour of some global problems in General Relativity. We cover a variety of topics, some of them related to the fundamental concept of 'Cauchy hypersurfaces': (1) structure of globally hyperbolic spacetimes, (2) the relativistic initial value problem, (3) constant mean curvat…
Explains biharmonic and biconservative submanifolds for beginners.
problem Understanding biharmonic and biconservative submanifolds.
method Explains motivations and key facts, highlights open problems.
result Provides an accessible introduction to these submanifolds.
Likelihood-free Model Choicestat.ME
This document is an invited chapter covering the specificities of ABC model choice, intended for the incoming Handbook of ABC by Sisson, Fan, and Beaumont (2017). Beyond exposing the potential pitfalls of ABC based posterior probabilities, the review emphasizes mostly the solution proposed by Pudlo et al. (2016) on the…
This is neither an elementary introduction to singularity theory nor a specialized treatise containing many new theorems. The purpose of this little book is to invite the reader on a mathematical promenade. We pay a visit to Hipparchus, Newton and Gauss, but also to many contemporary mathematicians. We play with a bit …
Our goal is to show the beauty and power of Alexandrov geometry by reaching interesting applications and theorems with a minimum of preparation. The topics include 1. Reshetnyak's gluing theorem, 2. Estimates on the number of collisions in billiards, 3. Reshetnyak's majorization theorem, 4. Hadamard--Cartan globalizati…
Invited lecture at the XIV-th workshop on geometric methods in physics, Bialowieza, Poland, July 9-15, 1995. In this lecture results are reviewed obtained by the author together with Martin Bordemann and Eckhard Meinrenken on the Berezin-Toeplitz quantization of compact Kaehler manifolds. Using global Toeplitz operator…
Higher Gauge Theoryhep-th
Survey on advanced gauge theory concepts.
problem Understanding higher gauge theory structures.
method Introduction to higher structures and connections on higher principal bundles.
result Summarized applications and principles of higher gauge theories.
Non-existence of orthogonal complex structures on 6-sphere with a metric close to the round onemath.DG
No orthogonal complex structures found on 6-sphere near round metric.
problem Existence of orthogonal complex structures on 6-sphere near round metric.
method Generalized proofs by Bor, Hernandez-Lamoneda, Sekigawa, and Vanhecke.
result Non-existence of orthogonal complex structures for metrics close to the round one.
This paper presents an introduction to the stochastic concepts of \emph{coupling} and \emph{copula}. Coupling means the construction of a joint distribution of two or more random variables that need not be defined on one and the same probability space, whereas a copula is a function that joins a multivariate distributi…
Survey on AI math foundations, focusing on neural networks.
problem Lack of rigorous mathematical foundation for AI.
method Survey and discussion of theoretical directions in AI.
result Discussion of open problems in AI math.
Fashion-Gen dataset offers high-res fashion images and descriptions for research.
problem Lack of high-quality, detailed fashion image datasets for research.
method Created a large dataset of fashion images and descriptions, provided baseline results, and launched a challenge.
result Baseline results on image generation and conditioning on text descriptions.
Econophysics Through Computationphysics.soc-ph
Econophysics uses computer simulations to study financial markets.
problem Understanding financial market dynamics and behaviors.
method Computer simulations and sample programs.
result Exciting new field of econophysics emerged in 1995.
The article explores multisymplectic geometry and its applications in field theories.
problem Understanding the geometry of manifolds with non-degenerate, closed differential forms.
method Describes the transition from Lagrangian to Hamiltonian field theories and reformulates them in multisymplectic terms. Investigates normal forms and symmetries on multisymplectic manifolds.
result Investigates the normal forms of multisymplectic manifolds and the existence of Darboux-type theorems.
This article is the author's contribution to the volume "Problems on mapping class groups and related topics" which will be published in December 2006, with Benson Farb as Editor. Various individuals were invited by Farb to submit open problems which seemed interesting to them about surface mapping class groups. We sin…
Mnay models situated in the current research landscape of modelling and simulating social processes have roots in physics. This is visible in the name of specialties as Econophysics or Sociophysics. This chapter describes the history of knowledge transfer from physics, in particular physics of self-organization and evo…
Overview of 3D TQFTs and 3-manifold invariants.
problem Quantum invariants of 3-manifolds.
method Recall and review of TQFTs, fusion categories, and recent generalizations.
result Overview of various 3D TQFTs and their invariants.
This paper is an exposition of the relationship between Witten's Chern-Simons functional integral and the theory of Vassiliev Invariants of knots and links in three dimensional space. We conceptualize the functional integral in terms of equivalence classes of functionals of gauge fields and we do not use measure theory…
We introduce the south-pointing chariot, an intriguing mechanical device from ancient China. We use its ability to keep track of a global direction as it travels on an arbitrary path as a tool to explore the geometry of curved surfaces. This takes us as far as a famous result of Gauss on the impossibility of a faithful…
Proposes a method to learn fair data representations without requiring fair target data.
problem Achieving fairness in machine learning models, especially for human outcomes.
method Data-to-data translation, learning a mapping from input to a fair target domain using residuals and protected characteristics.
result Enforces fairness (equality of opportunity) by adjusting specific regions in face images and tabular data.
Automatic continuous speech recognition (CSR) is sufficiently mature that a variety of real world applications are now possible including large vocabulary transcription and interactive spoken dialogues. This paper reviews the evolution of the statistical modelling techniques which underlie current-day systems, specific…
Graph Convolutional Networks show promise for AML in Bitcoin transactions.
problem Combining safety and financial inclusion in AML for cryptocurrencies.
method Using Graph Convolutional Networks (GCN) for binary classification of illicit transactions.
result GCN outperforms other methods in binary classification of illicit transactions.
-Bundlesmath.AT
This article reviews -bundles and their applications in geometry and physics.
problem Understanding higher bundles in geometry and physics.
method An -categorical formulation of higher bundles.
result Identification of higher bundles in various contexts.
A textbook on machine learning explaining patterns, predictions, and actions.
problem Understanding patterns in data for predictions and actions.
method Explains foundations of decision making, representation, optimization, and generalization.
result Equips readers with tools to reason about actions and their consequences.
In this lecture results on the Berezin-Toeplitz quantization of arbitrary compact quantizable Kaehler manifolds are presented. These results are obtained in joint work with M. Bordemann and E. Meinrenken. The existence of the Berezin-Toeplitz deformation quantization is also covered. Recent results obtained in joint wo…
Simplified approach to pseudo-Anosov flows on 3-manifolds.
problem Complexity in understanding pseudo-Anosov flows on 3-manifolds.
method Streamlined framework called Anosov-like group actions.
result Unified and simplified presentation of pseudo-Anosov flows.
Networks as Proxies: a relational approach towards economic complexity in the Roman periodphysics.soc-ph
Based on the assumption that economic complexity is characterised by the interactions of economic agents (who) constantly change their actions and strategies in response to the outcome they mutually create, this paper presents how network models can be used a proxies for the mapping, quantification and analysis of Roma…
Population-based learning improves representation of unstructured data.
problem Improving representation of unstructured data.
method Instantiating Lewis signaling games within a population of agents.
result Population-based learning produces better representations than single-agent learning.
AI solutions matched prosthetic control goals in a challenge.
problem Matching time-varying velocity vectors in musculoskeletal models.
method Deep reinforcement learning approaches with various modifications.
result Many solutions used similar techniques but implemented unique modifications.
Deep reinforcement learning models improve musculoskeletal running speed.
problem Optimizing a musculoskeletal model to run as fast as possible through an obstacle course.
method Deep reinforcement learning approaches, including DDPG, PPO, and TRPO, with modifications.
result Various modifications to known algorithms improve running performance.
The book explores analytic properties of groups and their actions.
problem Analytic properties of groups and their actions.
method Analytic approaches to studying groups and their actions, focusing on amenability and Kazhdan's property (T).
result Introduction of useful tricks, ideas, and lemmas in Analytic Group Theory.
Boosting is a general method of generating many simple classification rules and combining them into a single, highly accurate rule. In this talk, I will review the AdaBoost boosting algorithm and some of its underlying theory, and then look at how this theory has helped us to face some of the challenges of applying Ada…
Culler-Shalen theory extended to arbitrary characteristic.
problem Understanding essential surfaces in 3-manifolds over arbitrary fields.
method Using character varieties and group actions on trees over arbitrary algebraically closed fields.
result Examples show changes in the -polynomial and essential surfaces in characteristic 2.
Repelling Random Walksstat.ML
Repelling random walks improve graph-based sampling efficiency.
problem Efficient graph-based sampling and statistical estimation.
method Induces correlations between trajectories of an ensemble of walkers on a graph, maintaining unbiasedness.
result Improves concentration of statistical estimators on graphs.