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.
Proves rigidity for specific initial data sets under the dominant energy condition.
We find necessary and sufficient conditions ensuring that the vacuum development of an initial data set of the Einstein's field equations admits a conformal Killing vector. We refer to these conditions as conformal Killing initial data (CKID) and they extend the well-known Killing initial data (KID) that have been know…
Initial data for -wave spacetimes constructed in 4D.
The dominant energy condition imposes a restriction on initial value pairs found on a spacelike hypersurface of a Lorentzian manifold. In this article, we study the space of initial values that satisfy this condition strictly. To this aim, we introduce an index difference for initial value pairs and compare it to its c…
Genus one singularity appears in mean curvature flow for certain initial conditions.
Smooth dec initial data sets may not extend to smooth spacetimes.
New method solves PDEs for any initial condition without retraining.
Proves density and mass theorems for specific initial data sets.
Solves initial boundary value problem for vacuum Einstein equations and proves geometric uniqueness.
In this paper, we show existence and uniqueness of Ricci flow whose initial condition is a compact Alexandrov surface with curvature bounded from below. This requires a weakening of the notion of initial condition which is able to deal with a priori non-Riemannian metric spaces. As a by-product, we obtain that the Ricc…
Develops path integral for spiked tensor model dynamics.
FCNv2 robustness tested under noise and random initial conditions.
New findings show cosmological constant as initial condition for non-isotropic spacetimes.
This paper studies the problem of learning the conditional distribution of a high-dimensional output given an input, where the output and input may belong to two different domains, e.g., the output is a photo image and the input is a sketch image. We solve this problem by cooperative training of a fast thinking initial…
New boundary conditions improve Hamiltonian analysis in GR.
Recent developments in system identification have brought attention to regularized kernel-based methods, where, adopting the recently introduced stable spline kernel, prior information on the unknown process is enforced. This reduces the variance of the estimates and thus makes kernel-based methods particularly attract…
Despite the widespread practical success of deep learning methods, our theoretical understanding of the dynamics of learning in deep neural networks remains quite sparse. We attempt to bridge the gap between the theory and practice of deep learning by systematically analyzing learning dynamics for the restricted case o…
We present a local gluing construction for general relativistic initial data sets. The method applies to generic initial data, in a sense which is made precise. In particular the trace of the extrinsic curvature is not assumed to be constant near the gluing points, which was the case for previous such constructions. No…
The paper proves rigidity results for compact initial data sets.
During the development of autonomous systems such as driverless cars, it is important to characterize the scenarios that are most likely to result in failure. Adaptive Stress Testing (AST) provides a way to search for the most-likely failure scenario as a Markov decision process (MDP). Our previous work used a deep rei…
The Degasperis-Procesi equation's solutions define pseudospherical metrics and can lead to surface collapse.
Article strengthens initial data rigidity theorem to show unique spacetime extension.
Proof of local well-posedness for a specific boundary condition in general relativity.
The principle of convergence stability for geometric flows is the combination of the continuous dependence of the flow on initial conditions, with the stability of fixed points. It implies that if the flow from an initial state exists for all time and converges to a stable fixed point, then the flows of solutions…
The paper proves uniqueness of evolving graphs by mean curvature flow under specific conditions.
Proves initial data on big bang singularities for Einstein-nonlinear scalar field equations lead to unique solutions.
Ricci flow solves curvature-bound initial spaces to smooth manifolds.
Optimizes deep neural network initialization variance for better performance.
The paper studies Ricci flow on manifolds with boundary, proving existence, uniqueness, and boundary conditions preservation.
We consider the Einstein-Maxwell-fluid constraint equations, and make use of the conformal method to construct and parametrize constant-mean-curvature hyperboloidal initial data sets that satisfy the shear-free condition. This condition is known to be necessary in order that a spacetime development admit a regular conf…
This work provides an additional step in the theoretical understanding of neural networks. We consider neural networks with one hidden layer and show that when learning symmetric functions, one can choose initial conditions so that standard SGD training efficiently produces generalization guarantees. We empirically ver…
Global properties of maximal future Cauchy developments of stationary, m-dimensional asymptotically flat initial data with an outer trapped boundary are analyzed. We prove that, whenever the matter model is well posed and satisfies the null energy condition, the future Cauchy development of the data is a black hole spa…
The Positive Mass Theorem for special singular initial data.
Geometrically interpolates rigid body motions with initial and terminal twists.
Paper proves rigidity for spin bands with specific conditions.
We consider the area preserving curve shortening flow with Neumann free boundary conditions outside of a convex domain or at a straight line. We give a criterion on initial curves that guarantees the appearance of a singularity in finite time. We prove that the singularity is of type II. Furthermore, if these initial c…
New PDE systems generalize Hawking mass monotonicity.
In this paper we test for the sensitive dependence on initial conditions (the so called "butterfly effect") of energy futures time series (heating oil, natural gas), and thus the determinism of those series. This paper is distinguished from previous studies in the following points: first, we reread existent works in th…
Sharp conditions found for solving heat equation on Riemannian manifolds.
The paper proves a spacetime positive mass theorem for singular initial data sets.
Curve shortening flow's regularity depends on initial conditions after a certain time.
Study well-posedness of SPDE on Riemannian manifolds with rough initial conditions.
Rigidity results for initial data sets related to the positive mass theorem.
In [8] Gerhardt proves longtime existence for the inverse mean curvature flow in globally hyperbolic Lorentzian manifolds with compact Cauchy hypersurface, which satisfy three main structural assumptions: a strong volume decay condition, a mean curvature barrier condition and the timelike convergence condition. Further…
New method learns good initialization for gradient descent from past solutions.
The techniques developed by Butscher in arXiv:math/0703469 for constructing constant mean curvature (CMC) hypersurfaces in the (n+1)-sphere by gluing together spherical building blocks are generalized to handle less symmetric initial configurations. The outcome is that the approximately CMC hypersurface obtained by glu…
Scale-free distributions and correlation functions found in financial data are reminiscent of the scale invariance of physical observables in the vicinity of a critical point. Here, we present empirical evidence for a transition phenomenon, accompanied by a symmetry breaking, in the investors' demand for stocks. We stu…
When working with asymptotically hyperbolic initial data sets for general relativity it is convenient to assume certain simplifying properties. We prove that the subset of initial data sets with such properties is dense in the set of physically reasonable asymptotically hyperbolic initial data sets. More specifically, …