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.
Develops a new family of signature-changing models on metric manifolds.
A theorem transforms Lorentzian to signature-changing metrics.
Study shows non-orientable manifolds restrict signature-changing metrics globally.
Study explores embedding signature-changing manifolds into higher-dimensional spaces.
Detects graph topology changes from noisy signals using prior spectral information.
We discuss and investigate the problem of existence of metric-compatible linear connections for a given space-time metric which is, generally, assumed to be semi-pseudo-Riemannian. We prove that under sufficiently general conditions such connections exist iff the rank and signature of the metric are constant. On this b…
New concept of Lorentzian-Euclidean black holes and metric transitions explored.
The paper extends graph signatures to Klein graphs and foams, linking signatures to knot properties.
A bound on knot unknotting using equivariant signature.
We refine prior bounds on how the multivariable signature and the nullity of a link change under link cobordisms. The formula generalizes a series of results about the 4-genus having their origins in the Murasugi-Tristram inequality, and at the same time extends previously known results about concordance invariance of …
New loops found in universe's timeline, challenging traditional time direction.
We present a survey on generic singularities of geodesic flows in smooth signature changing metrics (often called pseudo-Riemannian) in dimension 2. Generically, a pseudo-Riemannian metric on a 2-manifold changes its signature (degenerates) along a curve , which locally separates into a Riemannian () an…
We derive the topological obstruction to spin-Klein cobordism. This result has implications for signature change in general relativity, and for the superstring.
Detects changes in brain signal topology to predict epileptic seizures.
We use Morse theoretical arguments to study algebraic curves in C^2. We take an algebraic curve C in C^2 and intersect it with a family of spheres with fixed origin and varying radii. We explain in detail how does the resulting link change when we cross a singular point of C. Applying link invariants as Murasugi's sign…
Rotors were introduced in Graph Theory by W.Tutte. The concept was adapted to Knot Theory as a generalization of mutation by Anstee, Przytycki and Rolfsen in 1987. In this paper we show that Tristram-Levine signature is preserved by orientation-preserving rotations. Moreover, we show that any link invariant obtained fr…
We consider the problem of modeling cardiovascular responses to physical activity and sleep changes captured by wearable sensors in free living conditions. We use an attentional convolutional neural network to learn parsimonious signatures of individual cardiovascular response from data recorded at the minute level res…
Methods for learning feature representations for Offline Handwritten Signature Verification have been successfully proposed in recent literature, using Deep Convolutional Neural Networks to learn representations from signature pixels. Such methods reported large performance improvements compared to handcrafted feature …
The divergence theorem in its usual form applies only to suitably smooth vector fields. For vector fields which are merely piecewise smooth, as is natural at a boundary between regions with different physical properties, one must patch together the divergence theorem applied separately in each region. We give an elegan…
A hybrid framework for American option pricing under time-varying rough volatility.
A flat complete causal Lorentzian manifold is called {\it strictly causal} if the past and the future of each its point are closed near this point. We consider strictly causal manifolds with unipotent holonomy groups and assign to a manifold of this type four nonnegative integers (a signature) and a parabola in the con…
Generative model prices basket options efficiently.
SPECTRE defends against backdoor attacks by amplifying corrupted data's spectral signature.
Study sharpens unlinking number bounds for special alternating links.
We consider a pseudo-Riemannian metric that changes signature along a smooth curve on a surface, called the discriminant curve. The discriminant curve separates the surface locally into a Riemannian and a Lorentzian domain. We study the local behaviour and properties of geodesics at a point on the discriminant where th…
Derives functional Itô formula for non-anticipative maps of rough paths.
Assuming minimal regularity assumptions on the data, we revisit the classical problem of finding isometric immersions into the Minkowski spacetime for hypersurfaces of a Lorentzian manifold. Our approach encompasses metrics having Sobolev regularity and Riemann curvature defined in the distributional sense, only. It ap…
Rough Transformers improve time series modeling with lower costs and better performance.
The Weyl principle is extended from the Riemannian to the pseudo-Riemannian setting, and subsequently to manifolds equipped with generic symmetric -tensors. More precisely, we construct a family of generalized curvature measures attached to such manifolds, extending the Riemannian Lipschitz-Killing curvature mea…
We start with a disk with vertices along its boundary where pairs of vertices are connected with strips with certain restrictions. This forms a {\it pairing}. To relate two pairings, we define an operator called a cut-and-glue operation. We show that this operation does not change an invariant of pairings know…
The splitting number of a link is the minimal number of crossing changes between different components required to convert it into a split link. We obtain a lower bound on the splitting number in terms of the (multivariable) signature and nullity. Although very elementary and easy to compute, this bound turns out to be …
Scalable GPLVM reduces complexity in scRNA-seq data, accounting for technical and biological confounders.
We report on some advances made in the problem of singularities in general relativity. First is introduced the singular semi-Riemannian geometry for metrics which can change their signature (in particular be degenerate). The standard operations like covariant contraction, covariant derivative, and constructions like th…
The paper revisits expected signatures in semimartingale models, providing new formulae and simplifying complexity.
In this paper we discuss the refined analytic torsion on an odd dimensional compact oriented Riemannian manifold with boundary under some assumption. For this purpose we introduce two boundary conditions which are complementary to each other and well-posed for the odd signature operator in the sense of Se…
Defines knot signature invariant using G-signature theorem.
Deep signature/log-signature FBSDE algorithm improves accuracy and training time.
A well-known property of the signature of closed oriented 4n-dimensional manifolds is Novikov additivity, which states that if a manifold is split into two manifolds with boundary along an oriented smooth hypersurface, then the signature of the original manifold equals the sum of the signatures of the resulting manifol…
Transformer models show distinct spectral fingerprints under voice changes.
Maximum Levine-Tristram signature of torus knots follows a reduction formula.
New findings on mesh group-planes validate Signature-inverse Theorem under specific conditions.
Introduces flat discrete signatures for financial data analysis.
This is a sequel to the paper "The signature package on Witt spaces, I. Index classes" by the same authors. In the first part we investigated, via a parametrix construction, the regularity properties of the signature operator on a stratified Witt pseudomanifold, proving, in particular, that one can define a K-homology …
We define the Analytical signature, the Hodge signature and the de Rham signature for a foliated manifold with boundary with foliation transverse to the boundary. We show that all these signatures coincide and a Hirzebruch formula is valid.
New methods price American options in rough volatility models.
The paper examines the consistency of Lasso regression applied to signature analysis of time series data.
Study signatures of torus links and their cores using Neumann's equivariant signatures and Hirzebruch's formula.
This paper extends the C*-signature to non-Witt spaces using noncommutative geometric methods.