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 mass inequalities and proofs for causal variational principles.
Proves critical points of ADM mass correspond to specific initial data sets.
Investigates convexity of minimizers under mass constraint using nonlocal perimeter and potential.
New bounds on Bartnik mass for surfaces with non-negative first eigenvalue.
We derive the Riemannian Positive Mass theorem in arbitrary dimensions, without any topological constraints. The main new tools are skin structures and surgeries on minimal hypersurfaces.
We derive the Space-Time Positive Mass theorem in arbitrary dimensions, without topological constraints. The main new tools are skin structures and surgeries on minimal and marginally outer trapped hypersurfaces.
One-dimensional crystals have convex shapes under certain conditions.
This work removes logarithmic singularities from hyperboloidal initial data without creating new ones.
Topological constraints improve neural network generalization.
We construct solutions with prescribed asymptotics to the Einstein constraint equations using a cut-off technique. Moreover, we give various examples of vacuum asymptotically flat manifolds whose center of mass and angular momentum are ill-defined.
The Besse's conjecture was posted on the well-known book Einstein manifolds by Arthur L. Besse, which describes the critical point of Hilbert-Einstein functional with constraint of unit volume and constant scalar curvature. In this article, we show that there is an interesting connection between Besse's conjecture and …
Solves probabilistic Lambert problem connecting astrodynamics with optimal mass transport.
Study on fractional mass for codimension-two currents, proving equi-coercivity and Γ-convergence.
The goal of this paper is to establish the existence of a foliation of the asymptotic region of an asymptotically flat manifold with nonzero mass by surfaces which are critical points of the Willmore functional subject to an area constraint. Equivalently these surfaces are critical points of the Geroch-Hawking mass. Th…
We survey some results on scalar curvature and properties of solutions to the Einstein constraint equations. Topics include an extended discussion of asymptotically flat solutions to the constraint equations, including recent results on the geometry of the center of mass of such solutions. We also review methods to con…
The paper connects mass, harmonic functions, and capacity in asymptotically flat 3-manifolds.
A new GP method enforces physical constraints in probabilistic terms.
Optimal transport with path constraints for distributions of different masses.
In this paper, we proved the mass angular momentum inequality\cite{D1}\cite{ChrusLiWe}\cite{SZ} for axisymmetric, asymptotically flat, vacuum constraint data sets with small trace. Given an initial data set with small trace, we construct a boost evolution spacetime of the Einstein vacuum equations as \cite{ChOM}. Then …
We show that it is possible to perturb arbitrary vacuum asymptotically flat spacetimes to new ones having exactly the same energy and linear momentum, but with center of mass and angular momentum equal to any preassigned values measured with respect to a fixed affine frame at infinity. This is in contrast to the axisym…
There are different problems for resolution of complex LC-MS or GC-MS data, such as the existence of embedded chromatographic peaks, continuum background and overlapping in mass channels for different components. These problems cause rotational ambiguity in recovered profiles calculated using multivariate curve resolut…
In this paper, we are concerned with obtaining distribution-free concentration inequalities for mixture of independent Bernoulli variables that incorporate a notion of variance. Missing mass is the total probability mass associated to the outcomes that have not been seen in a given sample which is an important quantity…
We explain how to derive largeness constraints in scalar curvature geometry using some basic splitting results and the potential theory on singular area minimizing hypersurfaces. This includes a variety of results like the non-existence of positive scalar curvature metrics on enlargeable manifolds or simplified proofs …
Neural networks are increasingly used in complex (data-driven) simulations as surrogates or for accelerating the computation of classical surrogates. In many applications physical constraints, such as mass or energy conservation, must be satisfied to obtain reliable results. However, standard machine learning algorithm…
The paper proves stability of manifolds with boundary under volume and distance constraints.
CANs improve GANs by enforcing structured constraints during training.
In the first half of this article, we survey the new quasi-local and total angular momentum and center of mass defined in [9] and summarize the important properties of these definitions. To compute these conserved quantities involves solving a nonlinear PDE system (the optimal isometric embedding equation), which is ra…
New method calibrates classifier probabilities with guaranteed coverage.
Study on capillarity minimizers with nonlocal repulsion and gravity, proving existence and nonexistence.
AMORE uses neural operators to efficiently predict multiple thermochemical states in stiff chemical kinetics.
Researchers simplify Einstein-scalar field equations on specific manifolds.
Automates building structural design with reduced mass and carbon footprint.
A framework to quantify deployment risk in ML systems, especially for rare states.
MESMOC optimizes constrained multi-objective problems efficiently.
The paper explores infinite-dimensional nonholonomic and vakonomic systems.
NN-EVCLUS uses neural networks to cluster data with uncertainty.
In his book on Convex Polyhedra (section 7.2), A.D. Aleksandrov raised a general question of finding variational statements and proofs of existence of polytopes with given geometric data. The first goal of this paper is to give a variational solution to the problem of existence and uniqueness of a closed convex hypersu…
The paper improves GP regression for sparse sensor data in structural mode shape reconstruction.
Maximizes capacity of extensions with fixed boundary data.
In this dissertation, we prove a number of results regarding the conformal method of finding solutions to the Einstein constraint equations. These results include necessary and sufficient conditions for the Lichnerowicz equation to have solutions, global supersolutions which guarantee solutions to the conformal constra…
The paper proves positive energy-momentum theorems for charged AdS initial data sets.
The X-ADM mass is shown to be equivalent to the ADM mass, proving the X-positive mass theorem in all dimensions.
We construct embedded Willmore tori with small area constraint in Riemannian three-manifolds under some curvature condition used to prevent Möbius degeneration. The construction relies on a Lyapunov-Schmidt reduction; to this aim we establish new geometric expansions of exponentiated small symmetric Clifford tori and a…
In general relativity, spatial light rays of static spherically symmetric spacetimes are geodesics of surfaces in Riemannian optical geometry. In this paper, we apply results on the isoperimetric problem to show that length-minimizing curves subject to an area constraint are circles, and discuss implications for the ph…
We report on results concerning a partially aggregated Stock Flow Consistent (SFC) macroeconomic model in the stationary state where the sectors of banks and firms are aggregated, the sector of households is dis-aggregated, and the probability density function (pdf) of the wealth of households is exogenous, constrained…
The paper studies nonlinear mass concepts in 3-manifolds with nonnegative scalar curvature.
Optimizes angular velocity transfers for rigid bodies under deadline constraints.
We perform an optimal localization of asymptotically flat initial data sets and construct data that have positive ADM mass but are exactly trivial outside a cone of arbitrarily small aperture. The gluing scheme that we develop allows to produce a new class of -body solutions for the Einstein equation, which patently…