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.
A new method generates MAX-2-SAT instances with adjustable hardness.
Deep networks show less disorder and more monotonic behavior.
Definition of frustration is expressed by transitivity of binary entanglement relation in considered complex system. Extending this definition into n-ary relation a hierarchy of frustrations is derived. As a complex system the U.S. Intermarket is chosen where the correlation coefficient of intermarket sectors plays the…
Geometric framework detects concept frustration between human concepts and machine representations.
We introduce a minimal agent-based model to qualitatively conceptualize the allocation of limited wealth among more abundant opportunities. We study the interplay of power, satisfaction and frustration in distribution, concentration, and inequality of wealth. Our framework allows us to compare subjective measures of fr…
Frustration causes buckling-like behavior in tubular foldable mechanisms.
We study some aspects of conformal transformations in the context of twistor theory, leading to the definition of a frustrated conformal transformation. This equation relies on two instantons for the left and right copies of , one being self-dual and the other anti-self-dual. Solutions to this equation naturally…
Dual decomposition provides a tractable framework for designing algorithms for finding the most probable (MAP) configuration in graphical models. However, for many real-world inference problems, the typical decomposition has a large integrality gap, due to frustrated cycles. One way to tighten the relaxation is to intr…
We show that the emergence of systemic risk in complex systems can be understood from the evolution of functional networks representing interactions inferred from fluctuation correlations between macroscopic observables. Specifically, we analyze the long-term collective dynamics of the New York Stock Exchange between 1…
Symmetry-electronic fingerprints reveal competing magnetic phases in two-dimensional materials.
Combinatorial auctions are formulated as frustrated lattice gases on sparse random graphs, allowing the determination of the optimal revenue by methods of statistical physics. Transitions between computationally easy and hard regimes are found and interpreted in terms of the geometric structure of the space of solution…
Model tracks structural changes in Brownian particle configurations on a sphere.
Unsupervised learning techniques in computer vision often require learning latent representations, such as low-dimensional linear and non-linear subspaces. Noise and outliers in the data can frustrate these approaches by obscuring the latent spaces. Our main goal is deeper understanding and new development of robust ap…
AI threatens financial stability through misuse and stealth adoption.
We have studied here the self-organising features of the dynamics of a model market, where the agents `trade' for a single commodity with their money. The model market consists of fixed numbers of economic agents, money supply and commodity. We demonstrate that the model, apart from showing a self-organising behaviour,…
The search of unconventional magnetic and nonmagnetic states is a major topic in the study of frustrated magnetism. Canonical examples of those states include various spin liquids and spin nematics. However, discerning their existence and the correct characterization is usually challenging. Here we introduce a machine-…
We propose a frustrated and disordered many-body model of a stockmarket in which independent adaptive traders can trade a stock subject to the economic law of supply and demand. We show that the typical scaling properties and the correlated volatility arise as a consequence of the collective behavior of agents: With th…
This paper introduces a new specialized algorithm for equilibrium Monte Carlo sampling of binary-valued systems, which allows for large moves in the state space. This is achieved by constructing self-avoiding walks (SAWs) in the state space. As a consequence, many bits are flipped in a single MCMC step. We name the alg…
We examine the effect of clamping variables for approximate inference in undirected graphical models with pairwise relationships and discrete variables. For any number of variable labels, we demonstrate that clamping and summing approximate sub-partition functions can lead only to a decrease in the partition function e…
Machine Learning (ML) and Deep Learning (DL) innovations are being introduced at such a rapid pace that model owners and evaluators are hard-pressed analyzing and studying them. This is exacerbated by the complicated procedures for evaluation. The lack of standard systems and efficient techniques for specifying and pro…
Study loop ensembles on graphs, linking group theory and topology.
Study smooth loops and loop bundles, relating to -structures.
Estimates graph curvature and diameter using Laplacian eigenvalues.
DeepDIVA simplifies reproducible deep learning experiments.
We produce skew loops -- loops having no pair of parallel tangent lines -- homotopic to any loop in a flat torus or other quotient of R^n. The interesting case here is n=3. More subtly for any n, we characterize the homotopy classes that will contain a skew loop having a specified loop in the unit sphere as tangent ind…
The paper proves T-duality and Hori formulae for winding loop spaces.
Paper establishes loop space T-duality formulae and refines earlier work.
The 2-loop polynomial is a polynomial presenting the 2-loop part of the Kontsevich invariant of knots. We show a cabling formula for the 2-loop polynomial of knots. In particular, we calculate the 2-loop polynomial for torus knots.
Rational loops played a central role in Uhlenbeck's construction of harmonic maps into U(n) (chiral model in physics), and they are generated by simple elements with one pole and one zero constructed from Hermitian projections. It has been believed for long time that nilpotent loops should be added to generate rational…
Kähler manifold loop space inherits Kähler structure and is complete.
New structure found in loops on quasi-surfaces.
Using the relations between the theory of differentiable Bol loops and the theory of affine symmetric spaces we classify all connected differentiable Bol loops having an at most -dimensional semi-simple Lie group as the group topologically generated by their left translations. We show that all these Bol loops are is…
A skew loop is a closed curve without parallel tangent lines. We prove: The only complete surfaces in euclidean 3-space with a point of positive curvature and no skew loops are the quadrics. In particular, ellipsoids are the only closed surfaces without skew loops. We also prove results about skew loops on cylinders an…
Introduces string structures linking to loop spaces.
Study shows looping a 6-manifold over a 4-manifold results in a product of loops on spheres.
The Dynamic Chain Event Graph (DCEG) is able to depict many classes of discrete random processes exhibiting asymmetries in their developments and context-specific conditional probabilities structures. However, paradoxically, this very generality has so far frustrated its wide application. So in this paper we develop an…
New theory defines invariants for framed 3-manifolds using trivalent graphs with self-loops.
Method calculates loop intersections on surfaces.
Geodesic loops on tetrahedra are studied in spherical and hyperbolic spaces.
New definition of twisted 1-loop invariant using Ptolemy coordinates.
Training-free looped transformers improve model performance without additional training.
Study path spaces and their homology, extending loop products and coproducts.
Study the topology of loops of contactomorphisms and Legendrians in non-orderable manifolds.
This paper reformulates the -adic Littlewood Conjecture using infinite loops.
Complex surfaces show non-simply connected diffeomorphism groups with non-homotopic loops.
New basis and Schur-Weyl duality for loop Hecke algebra defined.
A central extension of the loop group of a Lie group is called transgressive, if it corresponds under transgression to a degree four class in the cohomology of the classifying space of the Lie group. Transgressive loop group extensions are those that can be explored by finite-dimensional, higher-categorical geometry ov…
Study finds loops with specific curvature exist using Hardy's inequality.