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…
On-device research index
arXiv research
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.
169,341 papers · 148 categories
Trend · papers per month
48 results for “imaginary generators”
New invariant for braids found by adding imaginary generators.
problem Finding new invariants for classical braids.
method Constructing a monomorphism from pure braid group into a larger group by adding imaginary generators.
result Examples of minimal words in are shown using the new invariant.
Non-Euclidean number rings have non-integral Steinberg modules.
problem Characterizing when Steinberg modules are generated by integral elements.
method Analyzing special linear groups over non-Euclidean imaginary number rings.
result Steinberg modules are not generated by integral elements in non-Euclidean rings.
Quantum method prices options by evolving a state in imaginary time.
problem Pricing options in a quantum setting.
method Prepares an initial state, evolves it using imaginary time algorithms, and maps to quantum state.
result Numerical verification for European options; extension to path-dependent options.
We describe and to some extent characterize a new family of Kähler spin manifolds admitting non-trivial imaginary Kählerian Killing spinors.
The paper characterizes spin initial data sets saturating the BPS bound in asymptotically AdS spacetimes.
problem Characterizing spin initial data sets saturating the BPS bound in asymptotically AdS spacetimes.
method The paper introduces a theorem for replacing imaginary Killing spinors with strictly timelike or null ones and uses spinors to construct a codimension-2 slicing.
result The paper establishes a sharp dimension threshold for saturating the BPS bound in gravitational waves and rotating black holes in higher dimensions.
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.
New definitions weaken conditions for Alexandrov spaces.
problem Weak conditions for Alexandrov spaces with curvature bounds.
method Introducing imaginary comparison and angles, and right/left bounded second derivative.
result New proofs for Doubling and Globalization Theorems.
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.
Sornette-Ide model for markets: Trader expectations as imaginary partcond-mat.stat-mech
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.
Classifies manifolds with specific spinors and constructs parallel spinors.
problem Classifying manifolds with generalized Killing spinors.
method Explicitly constructs parallel spinors and considers modified Dirac currents.
result Classifies Riemannian spin^c manifolds with type I and II imaginary generalized Killing spinors.
Study large N oscillations in 3D theories related to black hole physics.
problem Understanding large N sign oscillations in 3D theories via holography.
method Holographic computation of on-shell actions for Euclidean supergravity solutions, Wick rotation of magnetically charged AdS4 black holes.
result Proposed a non-trivial mathematical conjecture regarding phase factors of twisted Reidemeister-Ray-Singer torsion.
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…
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 …
Develops an analytic theory for quantum imaginary time evolution.
problem Lack of a first-principle understanding of quantum imaginary time evolution.
method Interprets QITE as a form of VQA trained with QNGD and connects it to the geometric geodesic distance in the quantum Fisher information metric.
result QITE converges faster than vanilla gradient descent-based VQAs, though the advantage is suppressed by Hilbert space dimensionality.
New spinor fields reveal local or global geometric properties of manifolds.
problem Characterizing spinor fields on manifolds.
method Analyzing generalized imaginary Spin^c-Killing spinors and their associated vector fields.
result Local or global geometric descriptions of manifolds based on spinor fields.
Sparse modeling approach to analytical continuation of imaginary-time quantum Monte Carlo datacond-mat.str-el
New method stabilizes quantum Monte Carlo data analysis.
problem Noise in imaginary-time data impacts real-frequency spectra.
method Sparse modeling and regularization technique.
result Stable analytical continuation achieved with minimal bases.
The paper finds solutions to Kapustin-Witten equations with singular imaginary parts.
problem Finding solutions to Kapustin-Witten equations with specific properties.
method Solving a system of non-linear ODEs to find rotationally invariant solutions.
result Explicit solutions found, including decaying rational solutions and singular imaginary parts.
Quantum computer method for pricing lookback options with jumps.
problem Pricing lookback options with discrete monitoring and jump conditions.
method Variational Quantum Imaginary Time Evolution (VarQITE) method to solve non-Hermitian Schrodinger equation.
result Quantum algorithm can handle jump conditions in lookback options pricing.
Compressing Green's function using intermediate representation between imaginary-time and real-frequency domainscond-mat.str-el
New method compresses Green's function data efficiently.
problem Efficiently representing complex correlation functions.
method Intermediate representation (IR) of analytical continuation.
result IR yields significantly compact form of correlation functions.
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…
A new method for complex-valued signals improves convergence and performance.
problem Nonlinear channel equalization and complex-valued signals with different properties.
method Generalized complex kernel least-mean-square (gCKLMS) algorithm.
result The gCKLMS algorithm converges faster and performs better than previous methods.
Study on Killing vector fields with constant length on Riemannian manifolds.
problem Properties of Killing vector fields of constant length on Riemannian manifolds.
method Analysis of the linear operator ad(X) and its spectrum.
result The linear operator ad(X) has a pure imaginary spectrum.
Totally umbilical hypersurfaces in Spin^c manifolds with special spinors have constant mean curvature.
problem Characterizing totally umbilical hypersurfaces in Spin^c manifolds with specific spinor fields.
method Proving constant mean curvature for hypersurfaces carrying parallel, real or imaginary Killing spinors.
result Results extend to Spin^c case, generalizing O. Kowalski's theorem.
Paper proposes MS-k-NN for improved convergence rate in k-NN classification.
problem Improving convergence rate of k-NN classification methods.
method Proposes MS-k-NN that extrapolates unweighted k-NN estimators to k=0.
result MS-k-NN achieves improved convergence rate under certain conditions.
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…
The goal of this article is to show that five explicitly given transformations, a rotation, two screw Heisenberg rotations, a vertical translation and an involution generate the Euclidean Picard modular groups with coefficient in the Euclidean ring of integers of a quadratic imaginary number field. We also obtain the r…
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…
The study of harmonic diffeomorphisms reduces to solving a specific Beltrami equation.
problem Classifying harmonic diffeomorphisms between surfaces.
method Reduction to solving a Beltrami equation and an elliptic sinh-Gordon equation.
result Solutions to the sinh-Gordon equation classify harmonic maps.
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…
We generalize the Moishezon Teicher algorithm that was suggested for the computation of the braid monodromy of an almost real curve. The new algorithm suits a larger family of curves, and enables the computation of braid monodromy not only of caspidal curves, but of general algebraic curves, with some non simple singul…
Study of zero-divisors in sedenions via determinant factorization.
problem Characterizing zero-divisors in the sedenion algebra.
method Factorization of determinant of left multiplication, reduction to quaternionic normal form, block computation.
result Quartic polynomial factorization of determinant, geometric model of zero-divisor locus.
New method identifies latent causal graphs without parametric assumptions.
problem Identifying latent causal graphs without parametric assumptions.
method Constructive proofs with new graphical concepts.
result Conditions for nonparametric identification of latent causal graphs.
We generalize Conway's approach to integral binary quadratic forms on Q to study integral binary hermitian forms on quadratic imaginary extensions of Q. In Conway's case, an indefinite form that doesn't represent 0 determines a line ("river") in the spine T associated with SL(2,Z) in the hyperbolic plane. In our genera…
New proof of stability for manifolds with imaginary Killing spinors.
problem Stability of Riemannian manifolds with Killing spinors.
method Using a Bochner type formula from \cite{DWW05} and \cite{Wan91}.
result Proves instability of certain Sasaki-Einstein manifolds.
VAE with noise model learns smoothed densities without seeing noisy data.
problem Learning smoothed densities with noisy data.
method Imaginary noise model in variational autoencoders (σ-VAE).
result All σ-VAEs are equivalent via β-VAE expansion.
For certain problems involving vector fields, it is possible to find an associated imaginary field that, in conjunction with the first, forms a complex field for which the equation can be solved. This result is generalized to arbitrary Clifford algebras, followed by quaternionic vectors as a special case. All results a…
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.
Completes proof of index theorem using rigorous path integrals for supersymmetric quantum mechanics.
problem Analytic difficulties in generalizing Feynman's path integral to non-quadratic potentials.
method Develops rigorous path integrals for a class of Lagrangians including spinors on Riemannian manifolds.
result Steepest-descent approximation to path integral for twisted supersymmetric quantum mechanics is provably correct.
A method of constructing a class of bihamiltonian structures is presented. Elements of this class are generalizations of the so-called bihamiltonian structures of general position on odd-dimensional manifolds. The method consists in a simultaneous reduction of both the real and imaginary parts of a complex symplectic f…
The paper explores connections between three equations via Wick rotations and symmetries.
problem Investigating relations between solutions to specific equations under Wick rotations.
method Analyzing symmetries and transformations of solutions to the minimal surface, zero mean curvature, and Born-Infeld equations.
result Existence conditions and transformations of real and imaginary solutions under Wick rotations.
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…
Paper introduces new complex-valued kernel for improved regression.
problem Limited solution for complex-valued regression using real-valued kernels.
method Derives widely RKHS (WRKHS) and pseudo-kernel to address limitations.
result WRKHS yields better performance in complex-valued regression.
Mackey showed that for a compact Lie group , the pair has a unique non-trivial irreducible covariant pair of representations. We study the relevance of this result to the unitary equivalence of quantizations for an infinite-dimensional family of invariant polarizations on . The …
This work generates training-time adversarial data using auto-encoders to manipulate classifiers.
problem Manipulating the behavior of trained classifiers during test time with bounded perturbation.
method An auto-encoder-like network generates perturbations, learning to update weights to produce harmful noise.
result The method can manipulate classifiers effectively, showing good transferability.
Measures on Banach Manifolds, Random Surfaces, and Nonperturbative String Field Theory with Cut-offsmath-ph
We construct a cut-off version of nonpertubative closed Bosonic string field theory in the light-cone gauge with imaginary string coupling constant. We show that the partition function is a continuous function of the string coupling constant, and conjecture a relation between the formal power series expansion of this p…
We present an alternate definition of the mod {\bf Z} component of the Atiyah-Patodi-Singer invariant associated to (not necessary unitary) flat vector bundles, which identifies explicitly its real and imaginary parts. This is done by combining a deformation of flat connections introduced in a previous paper with t…