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.
Non-Euclidean number rings have non-integral Steinberg modules.
Proves cohomology vanishing for SL_n Z and GL_n Z.
We prove a new structural result for the spherical Tits building attached to SL_n(K) for many number fields K, and more generally for the fraction fields of many Dedekind domains O: the Steinberg module St_n(K) is generated by integral apartments if and only if the ideal class group cl(O) is trivial. We deduce this int…
We propose definitions of homogeneity and projective equivalence for systems of ordinary differential equations of order greater than two, which allow us to generalize the concept of a spray (for systems of order two). We show that the Euler-Lagrange fields of parametric Lagrangians of order greater than one which are …
Flat subsets in Euclidean buildings are contained within apartments.
An obstruction theory for representing homotopy classes of surfaces in 4-manifolds by immersions with pairwise disjoint images is developed, using the theory of non-repeating Whitney towers. The accompanying higher-order intersection invariants provide a geometric generalization of Milnor's link-homotopy invariants, an…
Study finds apartment owners can set Airbnb policies to be socially efficient.
We show that if the Hempel distance of a Heegaard splitting is larger than three then the mapping class group of the Heegaard splitting is isomorphic to a subgroup of the mapping class group of the ambient 3-manifold. This implies that given two handlebody sets in the curve complex for a surface that are distance at le…
New method prevents class collapse in metric learning with margin-based losses.
Diameters of ball intersections decrease as centers move apart.
Paper presents a neural network for open set recognition.
Study of spacetimes with timelike boundaries, proving their orthogonal product structure.
A strategy for constructing an embedded sphere in a 4-manifold realizing a given homology class which has been successfully applied in the past is to represent the class as a first step stably by an embedded sphere, i.e. after adding products of 2-spheres, and to move that sphere back into the original manifold. In thi…
New method interpolates high-dimensional scattered data using kernel theory.
The study explores using unlabeled data to improve survival time predictions.
The study approximates option prices using Hermite polynomials without assuming a specific distribution.
We study integrable geodesic flows on Stiefel varieties given by the Euclidean, normal (standard), Manakov-type, and Einstein metrics. We also consider natural generalizations of the Neumann systems on with the above metrics and proves their integrability in the non-commutative sense b…
Paper explores activity recognition and prediction in real homes using sensor data and video.
We model the dynamics of asset prices and associated derivatives by consideration of the dynamics of the conditional probability density process for the value of an asset at some specified time in the future. In the case where the price process is driven by Brownian motion, an associated "master equation" for the dynam…
We give three infinite families of examples of nonhyperbolic Dehn fillings on hyperbolic manifolds. A manifold in the first family admits two Dehn fillings of distance two apart, one of which is toroidal and annular, and the other is reducible and -reducible. A manifold in the second family has boundary consi…
Study compares Kriging and DNN for apartment rent price prediction accuracy.
Paper tackles medieval Latin sequence tagging using deep learning.
Autoencoder reduces memory overhead in incremental class learning.
The paper explores mapping class groups of simply connected Kaehler manifolds, highlighting a significant difference from curves.
In this note, we show that the asymptotic dimension of any building is finite and equal to the asymptotic dimension of an apartment in that building.
New method tells apart parents and children in causal graphs.
Geodesics in R^n configuration spaces for points apart by epsilon.
The paper improves probabilistic herding methods using Gibbs distributions.
Let X be a symmetric space of non-compact type or a locally finite, strongly transitive Euclidean building, and let B denote the geodesic boundary of X. We reduce the study of visual limits of maximal flats in X to the study of limits of apartments in the spherical building B: this defines a natural, geometric compacti…
This paper includes an original self contained proof of well-posedness of an initial-boundary value problem involving a non-local parabolic PDE which naturally arises in the study of derivative pricing in a generalized market model. We call this market model a semi-Markov modulated market. Although a wellposedness resu…
A Heegaard diagram for a 3-manifold is regarded as a pair of simplexes in the complex of curves on a surface and a Heegaard splitting as a pair of subcomplexes generated by the equivalent diagrams. We relate geometric and combinatorial properties of these subcomplexes with topological properties of the manifold and/or …
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…
We reinvestigate the "rockets and feathers" effect between retail gasoline and crude oil prices in a new framework of fractional integration, long-term memory and borderline (non-)stationarity. The most frequently used error-correction model is examined in detail and we find that the prices return to their equilibrium …
We begin by considering several properties commonly (but not universally) possessed by Bäcklund transformations between hyperbolic Monge-Ampère equations: wavelike nature of the underlying equations, preservation of independent variables, quasilinearity of the transformation, and autonomy of the transformation. We show…
We classify the polar actions on the complex hyperbolic plane up to orbit equivalence. Apart from the trivial and transitive polar actions, there are five polar actions of cohomogeneity one and four polar actions of cohomogeneity two.
A new DR formulation improves metric learning for faster and more stable performance.
New unsupervised method selects hard negative samples for contrastive learning.
We show that any number of disjointly embedded 2-spheres in 4-space can be pulled apart by a link homotopy, ie, by a motion in which the 2-spheres stay disjoint but are allowed to self-intersect.
Study shows Futaki invariant vanishes on most Fano threefolds.
A probabilistic method for deep embedding that improves classification accuracy and interpretability.
CAST improves spectral clustering for multi-scale data by integrating reachability similarity.
New framework classifies generated images into finer categories.
The first author conjectured certain relations for Morita-Mumford classes and Newton classes in the integral cohomology of mapping class groups (integral Riemann-Roch formulae). In this paper, the conjecture is verified for cyclic subgroups of mapping class groups.
Paper analyzes stability of discrete-time hypercomplex-valued Hopfield neural networks.
New parallelisms of 3D projective space found and classified.
Fine-grained visual categorization (FGVC) is to categorize objects into subordinate classes instead of basic classes. One major challenge in FGVC is the co-occurrence of two issues: 1) many subordinate classes are highly correlated and are difficult to distinguish, and 2) there exists the large intra-class variation (e…
Generalizes Frobenius theorem to quasiconformal deformations.
A moduli space is constructed for affine homogeneous spaces using their local geometry.