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.
New definitions weaken conditions for Alexandrov spaces.
We first define a complex angle between two oriented spacelike planes in 4-dimensional Minkowski space, and then study the constant angle surfaces in that space, i.e. the oriented spacelike surfaces whose tangent planes form a constant complex angle with respect to a fixed spacelike plane. This notion is the natural Lo…
To a knot in 3-space, one can associate a sequence of Laurent polynomials, whose th term is the th colored Jones polynomial. The Volume Conjecture for small angles states that the value of the -th colored Jones polynomial at $e^{\a/n}$ is a sequence of complex numbers that grows subexponentially, for a fixed s…
New quantum algorithm simplifies complex financial derivatives pricing.
Quantum method prices options by evolving a state in imaginary time.
We describe and to some extent characterize a new family of Kähler spin manifolds admitting non-trivial imaginary Kählerian Killing spinors.
In this paper, we extend the study of generalized Killing spinors on Riemannian Spin manifolds started by Moroianu and Herzlich to complex Killing functions. We prove that such spinor fields are always real Spin Killing spinors or imaginary generalized Spin Killing spinors, providing that the dimension of t…
In the quatenions ($\H$, $\H'$, $\H^{C}$) and octonions ($\gC$, $\gC^\prime$, $\gC^C$), we show some results on the conjugacy of two pure imaginary non-zero elements with same norm.
We study upper bounds for the torsion in homology of nonuniform arithmetic lattices. Together with recent results of Calegari-Venkatesh, this can be used to obtain upper bounds on K2 of the ring of integers of totally imaginary fields.
A nonlinear differential equation of Sornette-Ide type with noise, for a complex variable, yields endogenous crashes, preceded by roughly log-periodic oscillations in the real part, and a strong increase in the imaginary part. The latter is interpreted as the trader expectation.
Study large N oscillations in 3D theories related to black hole physics.
We study the geometric structure of Lorentzian spin manifolds, which admit imaginary Killing spinors. The discussion is based on the cone construction and a normal form classification of skew-adjoint operators in signature . Derived geometries include Brinkmann spaces, Lorentzian Einstein-Sasaki spaces and cer…
The paper characterizes spin initial data sets saturating the BPS bound in asymptotically AdS spacetimes.
In the paper [4] is presented a theory which unifies the gravitation theory and the mechanical effects, which is different from the Riemannian theories like GTR. Moreover it is built in the style of the electomagnetic field theory. This paper is a continuation of [4] such that the complex variant of that theory yields …
We prove that the Steinberg module of the special linear group of a quadratic imaginary number ring which is not Euclidean is not generated by integral apartments. Assuming the generalized Riemann hypothesis, this shows that the Steinberg module of a number ring is generated by integral apartments if and only if the ri…
Quantum computer method for pricing lookback options with jumps.
Under some dimension restrictions, we prove that totally umbilical hypersurfaces of Spin manifolds carrying a parallel, real or imaginary Killing spinor are of constant mean curvature. This extends to the Spin case the result of O. Kowalski stating that, every totally umbilical hypersurface of an Einstein manif…
New model-independent compact representations of imaginary-time data are presented in terms of the intermediate representation (IR) of analytical continuation. This is motivated by a recent numerical finding by the authors [J. Otsuki et al., arXiv:1702.03056]. We demonstrate the efficiency of the IR through continuous-…
Classifies manifolds with specific spinors and constructs parallel spinors.
Develops an analytic theory for quantum imaginary time evolution.
In this article it is shown that the study of harmonic diffeomorphisms, with nonvanishing Hopf differential, reduces to the study of the Beltrami equation of a certain type: the imaginary part of the logarithm of the Beltrami function coincides with the imaginary part of the logarithm of the Hopf differential, therefor…
A new approach of solving the ill-conditioned inverse problem for analytical continuation is proposed. The root of the problem lies in the fact that even tiny noise of imaginary-time input data has a serious impact on the inferred real-frequency spectra. By means of a modern regularization technique, we eliminate redun…
New spinor fields reveal local or global geometric properties of manifolds.
In the present paper, we find a system of non-linear ODEs that gives rotationally invariant solutions to the Kapustin-Witten equations in 4-dimensional Euclidean space. We explicitly solve these ODEs in some special cases and find decaying rational solutions, which provide solutions to the Kapustin-Witten equations. Th…
In this paper, we give a new construction of the adapted complex structure on a neighborhood of the zero section in the tangent bundle of a compact, real-analytic Riemannian manifold. Motivated by the "complexifier" approach of T. Thiemann as well as certain formulas of V. Guillemin and M. Stenzel, we obtain the polari…
Suppose that is the -dimensional boundary, with positive (inward) mean curvature , of a connected compact -dimensional Riemannian spin manifold whose scalar curvature , for some $k\textgreater{}0$. If admits an isometric and isospin immersion into the hy…
We study the asymptotic behaviour of tame harmonic bundles. First of all, we prove a local freeness of the prolongation by an increasing order. Then we obtain the polarized mixed twistor structure. As one of the applications, we obtain the norm estimate of holomorphic or flat sections by weight filtrations of the monod…
We propose a novel adaptive kernel based regression method for complex-valued signals: the generalized complex-valued kernel least-mean-square (gCKLMS). We borrow from the new results on widely linear reproducing kernel Hilbert space (WL-RKHS) for nonlinear regression and complex-valued signals, recently proposed by th…
In this paper we investigate relations between solutions to the minimal surface equation in Euclidean -space , the zero mean curvature equation in Lorentz-Minkowski -space and the Born-Infeld equation under Wick rotations. We prove that the existence conditions of real solutions and i…
Let be a local system on a smooth quasi projective variety over $\cnum$. We see that is semisimple if and only if there exists a tame pure imaginary pluri-harmonic metric on . Although it is a rather minor refinement of a result of Jost and Zuo, it is significant for the study of harmonic bundles and pure tw…
On a Lorentzian manifold the existence of a parallel null vector field implies certain constraint conditions on the induced Riemannian geometry of a space-like hypersurface. We will derive these constraint conditions and, conversely, show that every real analytic Riemannian manifold satisfying the constraint conditions…
Study of zero-divisors in sedenions via determinant factorization.
We give a lower bound for the eigenvalues of the Dirac operator on a compact domain of a Riemannian spin manifold under the $\MIT$ bag boundary condition. The limiting case is characterized by the existence of an imaginary Killing spinor.
VAE with noise model learns smoothed densities without seeing noisy data.
Usually, complex-valued RKHS are presented as an straightforward application of the real-valued case. In this paper we prove that this procedure yields a limited solution for regression. We show that another kernel, here denoted as pseudo kernel, is needed to learn any function in complex-valued fields. Accordingly, we…
Defines Kahler angle for a broader context.
Study angle structures on pseudo 3-manifolds, proving existence for some cases.
In this paper we study the right-angled Coxeter groups that acts geometrically on the Salvetti complex of a certain right-angled Artin group, which we refer to as Croke-Kleiner spaces. We prove that any right-angled Coxeter group that acts geometrically on the Croke-Kleiner spaces acts with angles between reflect…
Introduces a new geometry based on difference angles, showing unique properties.
Stiefel-Whitney classes of moment-angle manifolds are trivial.
Many introductory courses in quantum mechanics include Feynman's time-slicing definition of the path integral, with a complete derivation of the propagator in the simplest of cases. However, attempts to generalize this, for instance to non-quadratic potentials, encounter formidable analytic issues in showing the succes…
In this paper, we discuss the Lagrangian angle and the Kähler angle of immersed surfaces in . Firstly, we provide an extension of Lagrangian angle, Maslov form and Maslov class to more general surfaces in than Lagrangian surfaces, and then naturally extend a theorem by J.-M. Morvan to surface…
Uniqueness of quasi-roots explored in right-angled Artin groups.
This paper is dedicated to Oleg Viro on his 60-th birthday. The paper is about Khovanov homology and its relationships with statistical mechanics models such as the Ising model and the Potts model. We give a relatively self-contained introduction to Khovanov homology, and also a reformulation of the Potts model in term…
This note generalizes the visual angle to convex sets in 3D space.
Study proves existence of weak mean curvature flow with contact angle.
Improved volume estimates for right-angled polyhedra in hyperbolic space.
This paper explores historical and philosophical aspects of angles and solid angles, inspired by Euler's work.