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.
Analyzed writing style changes in Danish high school students.
Research explores how local communities and corporations interact in finance.
New language models improve essay scoring accuracy.
Despite the huge empirical success of deep learning, theoretical understanding of neural networks learning process is still lacking. This is the reason, why some of its features seem "mysterious". We emphasize two mysteries of deep learning: generalization mystery, and optimization mystery. In this essay we review and …
The essay discusses Margulis' theorems and their implications.
Mandelbrot unified diverse fields with scaling concept.
This is an article on the interaction between topology and physics which will appear in 1998 in a book called: A History of Topology, edited by Ioan James and published by Elsevier-North Holland.
Examines scalar curvature results via covariant and contravariant methods.
This mathematical essay brings together ideas from Economics, Geobiodynamics and Thermodynamics. Its purpose is to obtain real models of complex evolutionary systems. More specifically, the essay defines Roegenian Economy and links Geobiodynamics and Roegenian Economy. In this context, we discuss the isomorphism betwee…
In this essay, we study the sufficient and necessary conditions for a Randers metrc to be of constant Ricci curvature without the restriction of strong convexity (regularity). The classification result for the case is provided, which is similar to the famous Bao-Robles-Shen's result for strongly convex Rand…
Explains conformal symmetry with examples in geometry and analysis.
This is an expository essay about systolic geometry. It describes a central theorem in the subject and why the proof is difficult. Then it discusses different metaphors which suggest ways to approach the problem. The metaphors connect the systolic inequality to minimal surfaces, topological dimension, scalar curvature,…
This is not in any way meant to be a complete survey on positive curvature. Rather it is a short essay on the fascinating changes in the landscape surrounding positive curvature. In particular, details and many results and references are not included, and things are not presented in chronological order.
This paper constructs new Einstein metrics from old ones using specific deformation factors.
In this second part of the `essay on the completion of quantum theory' we define the {\em unitary setting of completed quantum mechanics}, by adding as intrinsic data to those from Part I (arXiv:1711.08643) the choice of a north pole N and south pole S in the geometric space. Then we explain that, in the unitary settin…
Study smooth manifolds using disc-presheaves.
AI mirrors modern math's autonomous development, raising interpretive challenges.
In 1981 Edward Witten proved a remarkable result where he derived the classical Morse Inequalities using ideas from Supersymmetric (SUSY) Quantum Mechanics. In this regard, one has an example where a Physical Theory has something to say about the underlying Mathematical Structure. The objective of this essay is to unde…
This essay discusses the advantages of a probabilistic agent-based approach to questions in theoretical economics, from the nature of economic agents, to the nature of the equilibria supported by their interactions. One idea we propose is that "agents" are meta-individual, hierarchically structured objects, that includ…
Deep learning is currently the subject of intensive study. However, fundamental concepts such as representations are not formally defined -- researchers "know them when they see them" -- and there is no common language for describing and analyzing algorithms. This essay proposes an abstract framework that identifies th…
Survey on two non-Kähler geometry conjectures.
A tribute to Norbert A'Campo's life and mathematics.
This essay quantifies convexities in incomplete markets using entropy, adjusting prices for risk and incompleteness.
We describe in this note a new invariant of rooted trees. We argue that the invariant is interesting on it own, and that it has connections to knot theory and homological algebra. However, the real reason that we propose this invariant to readers is that we deal here with an elementary, interesting, new mathematics, an…
This essay, an excerpt of the author's Ph.D. in Philosophy of mathematics (2012) thought of as being a companion to recent discoveries of new explicit Cartan geometry curvatures, analyzes how Gauss, after having devised the isometrically invariant character of curvature, struggled with elimination computations in order…
The study explores how brain development can inspire efficient deep learning models.
This essay suggests that a proper assessment of the presently unfolding financial crisis, and its cure, requires going back at least to the late 1990s, accounting for the cumulative effect of the ITC, real-estate and financial derivative bubbles. We focus on the deep loss of trust, not only in Wall Street, but more imp…
This paper is a sequel to my essay "Distributivity versus associativity in the homology theory of algebraic structures" Demonstratio Math., 44(4), 2011, 821-867 (arXiv:1109.4850 [math.GT]). We start from naive invariants of arc colorings and survey associative and distributive magmas and their homology with relation to…
This essay reviews human observer-based methods employed in shark spotting in Muizenberg Beach. It investigates Machine Learning methods for automated shark detection with the aim of enhancing human observation. A questionnaire and interview were used to collect information about shark spotting, the motivation of the a…
Lie systems form a class of systems of first-order ordinary differential equations whose general solutions can be described in terms of certain finite families of particular solutions and a set of constants, by means of a particular type of mapping: the so-called superposition rule. Apart from this fundamental property…
In this essay we aim to explore the Geometric aspects of the Calabi Conjecture and highlight the techniques of nonlinear Elliptic PDE theory used by S.T. Yau [SY] in obtaining a solution to the problem. Yau proves the existence of a Geometric structure using differential equations, giving importance to the idea that de…
This is an essay on potential theory for geometric plurisubharmonic functions. It begins with a given closed subset G of the Grassmann bundle of tangent -planes to a riemannian manifold . This determines a nonlinear partial differential equation which is convex but never uniformly elliptic (p < dim X). …
Investigates the cost-effectiveness of security features in smart card chips.
The abstract discusses parallels between Galois theory and Stone-Weierstrass theorem in various fields.
Bayesian probability theory is one of the most successful frameworks to model reasoning under uncertainty. Its defining property is the interpretation of probabilities as degrees of belief in propositions about the state of the world relative to an inquiring subject. This essay examines the notion of subjectivity by dr…
This essay examines how what is considered to be artificial intelligence (AI) has changed over time and come to intersect with the expertise of the author. Initially, AI developed on a separate trajectory, both topically and institutionally, from pattern recognition, neural information processing, decision and control …
This article is a follow-up of a short essay that appeared in Nature 455, 1181 (2008) [arXiv:0810.5306]. It has become increasingly clear that the erratic dynamics of markets is mostly endogenous and not due to the rational processing of exogenous news. I elaborate on the idea that spin-glass type of problems, where th…
In this essay, I attempt to provide supporting evidence as well as some balance for the thesis on `Transforming socio-economics with a new epistemology' presented by Hollingworth and Mueller (2008). First, I review a personal highlight of my own scientific path that illustrates the power of interdisciplinarity as well …
Machine learning improves earnings forecasting accuracy and speed.
Behavior of systems that are functions of anticipated behavior of other systems, whose own behavior is also anticipatory but homeostatic and determined by hierarchical ordering, which changes over time, of sets of possible environments that are not co-possible, is proven to be highly non-linear and sensitively dependen…
The relationship between expectation and price is commonly established with two principles: no-arbitrage, which asserts that both maps are positive; and equivalence, which asserts that the maps share the same null events. Constructed from the Arrow-Debreu securities, classical and quantum models of economics are then d…
Episodes of market crashes have fascinated economists for centuries. Although many academics, practitioners and policy makers have studied questions related to collapsing asset price bubbles, there is little consensus yet about their causes and effects. This review and essay evaluates some of the hypotheses offered to …
In this essay, we discuss the notion of optimal transport on geodesic measure spaces and the associated (2-)Wasserstein distance. We then examine displacement convexity of the entropy functional on the space of probability measures. In particular, we give a detailed proof that the Lott-Villani-Sturm notion of generaliz…
Financial markets are not random, but hard to predict due to hidden causes and strategic use.
BSDEs help in financial pricing and utility maximization.
Introduces CHL, a new loss function for continuous similarity learning.
Hierarchical clustering based on pairwise similarities is a common tool used in a broad range of scientific applications. However, in many problems it may be expensive to obtain or compute similarities between the items to be clustered. This paper investigates the hierarchical clustering of N items based on a small sub…
Deconfounds neural network representation similarity metrics to improve consistency and accuracy.