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.
SES finds multiple feature subsets with similar predictive power.
Generalizes quantum integrability to all signatures for projectively equivalent metrics.
A new deep learning approach enhances signature transforms for data analysis.
Signature uniquely identifies piecewise linear surfaces up to thin homotopy.
The paper adapts differential signatures to algebraic curves under group actions.
Paper develops approximation and statistical theory for signature-based path regression.
New criteria ensure uniqueness of curve signatures, robust to metric variations.
Two Kähler metrics on a complex manifold are called c-projectively equivalent if their -planar curves coincide. These curves are defined by the property that the acceleration is complex proportional to the velocity. We give an explicit local description of all pairs of c-projectively equivalent Kähler metrics of arb…
Develops a new trading strategy for statistical arbitrage with path-dependent signals.
This note proves that, as K-theory elements, the symbol classes of the de Rham operator and the signature operator on a closed manifold of even dimension are congruent mod 2. An equivariant generalization is given pertaining to the equivariant Euler characteristic and the multi-signature.
Defines and calculates signature invariants for twisted linking forms.
ProbMinHash improves Jaccard similarity hashing for big data applications.
In the algebraic context, we show that null Osserman, spacelike Osserman, and timelike Osserman are equivalent conditions for a model of signature (2,2). We also classify the null Jordan Osserman models of signature (2,2). In the geometric context, we show that a pseudo-Riemannian manifold of signature (2,2) is null Jo…
Paper uses algebraic signatures to identify probabilistic structures in empirical data.
Geodesically equivalent metrics on homogeneous spaces are shown to be affinely equivalent.
The paper develops methods for novelty detection on path space using signature-based statistics.
Let us consider a compact oriented riemannian manifold M without boundary and of dimension n=4k. The signature of M is defined as the signature of a given quadratic form Q. Two different products could be used to define Q and they render equivalent definitions: the exterior product of 2k-forms and the cup product of co…
Proves geometric invariance of signature and cohomology for Riemannian foliations.
Study proves equality of signature classes in codimension two.
The paper generalizes index theory for periodic manifolds and proves equivalence of signatures for tori.
The paper revisits expected signatures in semimartingale models, providing new formulae and simplifying complexity.
New spectral signatures help detect and remove backdoor attacks.
We define a set of "second-order" L^(2)-signature invariants for any algebraically slice knot. These obstruct a knot's being a slice knot and generalize Casson-Gordon invariants, which we consider to be "first-order signatures". As one application we prove: If K is a genus one slice knot then, on any genus one Seifert …
Defines an L2-signature for foliations using spectral triples.
Witt spaces are pseudomanifolds for which the middle-perversity intersection homology with rational coefficients is self-dual. We give a new construction of the symmetric signature for Witt spaces which is similar in spirit to the construction given by Miscenko for manifolds. Our construction has all of the expected pr…
We apply E. Cartan's method of equivalence to classify 7-dimensional, 2-nondegenerate CR manifolds up to local CR equivalence in the case that the cubic form of satisfies a certain symmetry property with respect to the Levi form of . The solution to the equivalence problem is given by a parallelism on a prin…
We use symplectic cobordism, and the localization result of Ginzburg, Guillemin, and Karshon, to find a wall-crossing formula for the signature of regular symplectic quotients of Hamiltonian torus actions. The formula is recursive, depending ultimately on fixed point data. In the case of a circle action, we obtain a fo…
New *K-means method finds cancer signatures without NMF.
We present a novel method for extracting cancer signatures by applying statistical risk models (http://ssrn.com/abstract=2732453) from quantitative finance to cancer genome data. Using 1389 whole genome sequenced samples from 14 cancers, we identify an "overall" mode of somatic mutational noise. We give a prescription …
We provide five examples of conformal geometries which are naturally associated with ordinary differential equations (ODEs). The first example describes a one-to-one correspondence between the Wuenschmann class of 3rd order ODEs considered modulo contact transformations of variables and (local) 3-dimensional conformal …
The study explains why signature methods work in commodity futures term structure classification.
Degree of mobility of a (pseudo-Riemannian) metric is the dimension of the space of metrics geodesically equivalent to it. We describe all possible values of the degree of mobility on a simply connected n-dimensional manifold of lorentz signature. As an application we calculate all possible differences between the dime…
Kernel for Lévy rough paths derived from PDE system.
Study shows space writhe closely correlates with knot signature in polymers.
We prove the Novikov conjecture on oriented Cheeger spaces whose fundamental group satisfies the strong Novikov conjecture. A Cheeger space is a stratified pseudomanifold admitting, through a choice of ideal boundary conditions, an L2-de Rham cohomology theory satisfying Poincare duality. We prove that this cohomology …
New method uses path signatures for efficient likelihood estimation in time-series data.
sig-MMD tests compare path distributions using kernel methods.
Uniformly proves index invariance for signature operators on manifolds.
Estimates path-valued data using signature metrics and local kernels.
While the Lorenzian and Riemanian metrics for which all polynomial scalar curvature invariants vanish (the VSI property) are well-studied, less is known about the four-dimensional neutral signature metrics with the VSI property. Recently it was shown that the neutral signature metrics belong to two distinct subclasses:…
Validates economic scenarios using statistical tests on stochastic processes.
We show that if two 4-dimensional metrics of arbitrary signature on one manifold are geodesically equivalent (i.e., have the same geodesics considered as unparameterized curves) and are solutions of the Einstein field equation with the same stress-energy tensor, then they are affinely equivalent or flat. Under the addi…
This paper provides a new unimodality test with application in hierarchical clustering methods. The proposed method denoted by signature test (Sigtest), transforms the data based on its statistics. The transformed data has much smaller variation compared to the original data and can be evaluated in a simple proposed un…
Optimal timing strategy for mean-reverting price spreads.
This article is about a natural distance function induced by smooth cobordisms between links. We show that the cobordism distance of torus links is determined by the profiles of their signature functions, up to a constant factor.
The equivalence problem for second order ODEs given modulo point transformations is solved in full analogy with the equivalence problem of nondegenerate 3-dimensional CR structures. This approach enables an analog of the Feffereman metrics to be defined. The conformal class of these (split signature) metrics is well de…
Using methods introduced by Scargle in 1978 we derive a cumulative version of the Lomb periodogram that exhibits frequency independent statistics when applied to cumulative noise. We show how this cumulative Lomb periodogram allows us to estimate the significance of log-periodic signatures in the S&P 500 anti-bubble th…
A symmetric matrix invariant is defined for oriented link diagrams.