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.
Study geodesics on neck-degenerate manifolds, focusing and winding behavior observed.
A very brief history of relative valuation in neoclassical finance since 1973 is presented, with attention to core currency issues for emerging economies. Price formation is considered in the context of hierarchical causality, with discussion focussed on identifying mathematical modelling challenges for robust and tran…
We review basic facts on the structure of nearly Kähler manifolds, focussing in particular on the six-dimensional case. A self-contained proof that nearly Kähler six-manifolds are Einstein is given by combining different known results. We finally rephrase the definition of nearly Kähler six-manifold in terms of a pair …
We present updates to the problems on Hirzebruch's 1954 problem list focussing on open problems, and on those where substantial progress has been made in recent years. We discuss some purely topological problems, as well as geometric problems about (almost) complex structures, both algebraic and non-algebraic, about co…
When approximating a black-box function, sampling with active learning focussing on regions with non-linear responses tends to improve accuracy. We present the FLOLA-Voronoi method introduced previously for deterministic responses, and theoretically derive the impact of output uncertainty. The algorithm automatically p…
This is an expository article which describes one approach to the construction and classification of harmonic tori "of finite type", namely, via their ring of polynomial Killing fields. To keep the discussion focussed, the first section is devoted entirely to non-conformal harmonic tori in the 2-sphere. The second sect…
This is a problem list in the theory of foliations and laminations of 3-manifolds. The focus is on the relationship of foliations and laminations with other aspects of 3-manifold topology, especially with the Thurston theory of geometric structures. This problem list is not meant to be comprehensive; rather it focusses…
Estimates ends of Ricci shrinkers, focusing on smooth and singular cases.
This paper focusses on "safe" screening techniques for the LASSO problem. Motivated by the need for low-complexity algorithms, we propose a new approach, dubbed "joint" screening test, allowing to screen a set of atoms by carrying out one single test. The approach is particularized to two different sets of atoms, respe…
Learning the parameters of a (potentially partially observable) random field model is intractable in general. Instead of focussing on a single optimal parameter value we propose to treat parameters as dynamical quantities. We introduce an algorithm to generate complex dynamics for parameters and (both visible and hidde…
This article describes various moduli spaces of pseudoholomorphic curves on the symplectization of a particular overtwisted contact structure on S^1 x S^2. This contact structure appears when one considers a closed self dual form on a 4-manifold as a symplectic form on the complement of its zero locus. The article is f…
A Poincaré-Hopf Theorem for line fields with point singularities on orientable surfaces can be found Hopf's 1956 Lecture Notes on Differential Geometry. In 1955 Markus presented such a theorem in all dimensions, but Markus' statement only holds in even dimensions . In 1984 Jänich presented a Poincaré-Hopf th…
We discuss two generalizations of the inverse problem of the calculus of variations, one in which a given mechanical system can be brought into the form of Lagrangian equations with non-conservative forces of a generalized Rayleigh dissipation type, the other leading to Lagrangian equations with so-called gyroscopic fo…
Record companies invest billions of dollars in new talent around the globe each year. Gaining insight into what actually makes a hit song would provide tremendous benefits for the music industry. In this research we tackle this question by focussing on the dance hit song classification problem. A database of dance hit …
While statistics focusses on hypothesis testing and on estimating (properties of) the true sampling distribution, in machine learning the performance of learning algorithms on future data is the primary issue. In this paper we bridge the gap with a general principle (PHI) that identifies hypotheses with best predictive…
Classifies charge-3 monopoles with symmetry, identifying new spectral curves.
Matrix factorisation methods decompose multivariate observations as linear combinations of latent feature vectors. The Indian Buffet Process (IBP) provides a way to model the number of latent features required for a good approximation in terms of regularised reconstruction error. Previous work has focussed on latent fe…
Research on the multi-armed bandit problem has studied the trade-off of exploration and exploitation in depth. However, there are numerous applications where the cardinal absolute-valued feedback model (e.g. ratings from one to five) is not suitable. This has motivated the formulation of the duelling bandits problem, w…
We analyze (the harmonic map representation of) static solutions of the Einstein Equations in dimension three from the point of view of comparison geometry. We find simple monotonic quantities capturing sharply the influence of the Lapse function on the focussing of geodesics. This allows, in particular, a sharp estima…
We study quasi-isometry invariants of Gromov hyperbolic spaces, focussing on the l_p-cohomology and closely related invariants such as the conformal dimension, combinatorial modulus, and the Combinatorial Loewner Property. We give new constructions of continuous l_p-cohomology, thereby obtaining information about the l…
The extreme event statistics plays a very important role in the theory and practice of time series analysis. The reassembly of classical theoretical results is often undermined by non-stationarity and dependence between increments. Furthermore, the convergence to the limit distributions can be slow, requiring a huge am…
In recent years, a rapidly growing literature has focussed on the construction of wavelet systems to analyze functions defined on the sphere. Our purpose in this paper is to generalize these constructions to situations where sections of line bundles, rather than ordinary scalar-valued functions, are considered. In part…
This article reviews -bundles and their applications in geometry and physics.
Bayesian Optimization (BO) has become a core method for solving expensive black-box optimization problems. While much research focussed on the choice of the acquisition function, we focus on online length-scale adaption and the choice of kernel function. Instead of choosing hyperparameters in view of maximum likelihood…
Improved Gaussian Process model for predicting trajectories without independence assumption errors.
Study on harmonic spinors on specific Lie groups.
Enhances time-series regression trees with latent factors for robust financial analysis.
Online class imbalance learning constitutes a new problem and an emerging research topic that focusses on the challenges of online learning under class imbalance and concept drift. Class imbalance deals with data streams that have very skewed distributions while concept drift deals with changes in the class imbalance s…
Recent work (Cohen & Welling, 2016) has shown that generalizations of convolutions, based on group theory, provide powerful inductive biases for learning. In these generalizations, filters are not only translated but can also be rotated, flipped, etc. However, coming up with exact models of how to rotate a 3 x 3 filter…
Paper uses SLT to improve model selection for SHM.
Explains how surfaces can have hyperbolic geometries and connects them to Higgs bundles.
In this survey, we study three different notions of curvature that are defined on graphs, namely, combinatorial curvature, Bakry-Émery curvature, and Ollivier's Ricci curvature. For each curvature notion, the definition and its motivation from Riemannian geometry will be explained. Moreover, we bring together some glob…
Dictionaries are collections of vectors used for representations of elements in Euclidean spaces. While recent research on optimal dictionaries is focussed on providing sparse (i.e., -optimal,) representations, here we consider the problem of finding optimal dictionaries such that representations of samples of …
Using quantum field-theoretic arguments, Witten has established a relation between the Donaldson and Seiberg-Witten invariants of smooth four-manifolds. In this survey article, we describe the program to prove this relation using a moduli space of PU(2) = SO(3) monopoles as a cobordism between the Donaldson moduli spac…
Two firms compete in a financial market, choosing dividend strategies to avoid default and maximize profits.
The target space geometry of abelian vector multiplets in theories in four and five space-time dimensions is called special geometry. It can be elegantly formulated in terms of Hessian geometry. In this review, we introduce Hessian geometry, focussing on aspects that are relevant for the special geometrie…
In this paper, we propose a new algorithm for exploratory projection pursuit. The basis of the algorithm is the insight that previous approaches used fairly narrow definitions of interestingness / non interestingness. We argue that allowing these definitions to depend on the problem / data at hand is a more natural app…
A review of statistical SSL methods showing improved classifier performance.
We describe the induced geometry on several classes of Kodaira moduli spaces of rational curves in twistor spaces. By constructing connections and frames on the moduli spaces we build and review twistor theories pertaining to relativistic and non-relativistic geometries. Focussing on the cases of three- and five-dimens…
In this paper, we explore the fixed point theory of -valued maps using configuration spaces and braid groups, focussing on two fundamental problems, the Wecken property, and the computation of the Nielsen number. We show that the projective plane (resp.\ the -sphere ) has the Wecken property for …
In de novo drug design, computational strategies are used to generate novel molecules with good affinity to the desired biological target. In this work, we show that recurrent neural networks can be trained as generative models for molecular structures, similar to statistical language models in natural language process…
This paper explores sequential modelling of polyphonic music with deep neural networks. While recent breakthroughs have focussed on network architecture, we demonstrate that the representation of the sequence can make an equally significant contribution to the performance of the model as measured by validation set loss…
Hydroxyurea (HU) has been shown to be effective in alleviating the symptoms of Sickle Cell Anemia disease. While Hydroxyurea reduces the complications associated with Sickle Cell Anemia in some patients, others do not benefit from this drug and experience deleterious effects since it is also a chemotherapeutic agent. T…
We consider model-based reinforcement learning in finite Markov De- cision Processes (MDPs), focussing on so-called optimistic strategies. In MDPs, optimism can be implemented by carrying out extended value it- erations under a constraint of consistency with the estimated model tran- sition probabilities. The UCRL2 alg…
Advocates focusing on utility functions to avoid unfair outcomes.
The Gaussian process state space model (GPSSM) is a non-linear dynamical system, where unknown transition and/or measurement mappings are described by GPs. Most research in GPSSMs has focussed on the state estimation problem, i.e., computing a posterior of the latent state given the model. However, the key challenge in…
Bayesian networks are probabilistic graphical models widely employed to understand dependencies in high dimensional data, and even to facilitate causal discovery. Learning the underlying network structure, which is encoded as a directed acyclic graph (DAG) is highly challenging mainly due to the vast number of possible…
This paper goes beyond the optimal trading Mean Field Game model introduced by Pierre Cardaliaguet and Charles-Albert Lehalle in [Cardaliaguet, P. and Lehalle, C.-A., Mean field game of controls and an application to trade crowding, Mathematics and Financial Economics (2018)]. It starts by extending it to portfolios of…