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.
This paper explores ML in power line communications, from modeling to diagnostics.
Paper proposes a new Markov model for efficient PLC system design.
New method uses Ricci curvature for hypergraph clustering, outperforming existing techniques.
On-line portfolio selection has attracted increasing interests in machine learning and AI communities recently. Empirical evidences show that stock's high and low prices are temporary and stock price relatives are likely to follow the mean reversion phenomenon. While the existing mean reversion strategies are shown to …
Estimates cohomology dimensions for Nakano q-semipositive line bundles.
Maximizing the speed and precision of communication while minimizing power dissipation is a fundamental engineering design goal. Also, biological systems achieve remarkable speed, precision and power efficiency using poorly understood physical design principles. Powerful theories like information theory and thermodynam…
This paper tackles energy-efficient machine learning on low-power devices.
Paper introduces reinforcement learning for managing power grids.
The purpose of this paper is first to give an asymptotic formula for the holomorphic analytic torsion forms of a fibration associated with increasing powers of a given line bundle. Secondly, we generalize this formula, thanks to the theory of Toeplitz operators, in the case where the powers of the line bundle is replac…
Identifying a potentially large number of simultaneous line outages in power transmission networks in real time is a computationally hard problem. This is because the number of hypotheses grows exponentially with the network size. A new "Learning-to-Infer" method is developed for efficient inference of every line statu…
Power system studies require the topological structures of real-world power networks; however, such data is confidential due to important security concerns. Thus, power grid synthesis (PGS), i.e., creating realistic power grids that imitate actual power networks, has gained significant attention. In this letter, we cas…
We address the problem of maintaining high voltage power transmission networks in security at all time. This requires that power flowing through all lines remain below a certain nominal thermal limit above which lines might melt, break or cause other damages. Current practices include enforcing the deterministic "N-1" …
Study asymptotics of extension and orthogonal Bergman kernels for high tensor powers of positive line bundles.
New equations reveal how cylinder power in progressive lenses depends on geodesic curvature.
Software and hardware co-design and optimization of HPC systems has become intolerably complex, ad-hoc, time consuming and error prone due to enormous number of available design and optimization choices, complex interactions between all software and hardware components, and multiple strict requirements placed on perfor…
We generalize the results of Montgomery for the Bochner Laplacian on high tensor powers of a line bundle. When specialized to Riemann surfaces, this leads to the Bergman kernel expansion and geometric quantization results for semi-positive line bundles whose curvature vanishes at finite order. The proof exploits the re…
New sparsification technique for SGD reduces communication costs.
The paper proves heat kernel asymptotics for high power line bundles on complex manifolds.
A communication-efficient method controls FDR in network settings.
A new algorithm reduces communication in distributed SVD by factors.
Traditionally, community detection in graphs can be solved using spectral methods or posterior inference under probabilistic graphical models. Focusing on random graph families such as the stochastic block model, recent research has unified both approaches and identified both statistical and computational detection thr…
Paper proposes GPM for simultaneous community detection and group synchronization.
For a symplectic manifold with quantizing line bundle, a choice of almost complex structure determines a Laplacian acting on tensor powers of the bundle. For high tensor powers Guillemin-Uribe showed that there is a well-defined cluster of low-lying eigenvalues, whose distribution is described by a spectral density fun…
We study the asymptotic of the spectrum of the \spin Dirac operator on high tensor powers of a line bundle. As application, we get a simple proof of the main result of Guillemin-Uribe, which was originally proved by using the analysis of Toeplitz operators of Boutet de Monvel and Guillemin.
Analyzes methods for detecting communities in networks.
Study shows Bergman kernel quotient approaches one for punctured surfaces.
The paper studies volumes of direct images for high tensor powers of ample bundles.
Study of torsion forms for positive line bundles.
Derives spectral density function for symplectic manifolds.
The notion of max-plus convex subset of Euclidean space can be naturally extended to other linear spaces. The aim of this paper is to describe the topology of hyperspaces of max-plus convex subsets of Tychonov powers of the real line. We show that the corresponding spaces are AR's if and only if …
We establish the equidistribution of zeros of random holomorphic sections of powers of a semipositive singular Hermitian line bundle, with an estimate of the convergence speed.
Surveying random sections on Kähler manifolds, leading to metrics.
We find the entropy's infinite-size behavior in complex manifold sections.
Simulated Bifurcation outperforms quantum machines in community detection.
Study of Fubini-Study forms on surfaces with punctures.
We obtain a vanishing theorem for the kernel of a Dirac operator on a Clifford module twisted by a sufficiently large power of a line bundle, whose curvature is non-degenerate at any point of the base manifold. In particular, if the base manifold is almost complex, we prove a vanishing theorem for the kernel of a $\spi…
Distributed, controllable energy storage devices offer several benefits to electric power system operation. Three such benefits include reducing peak load, providing standby power, and enhancing power quality. These benefits, however, are only realized during peak load or during an outage, events that are infrequent. T…
Let L be a line bundle over a compact complex manifold X and endow L and TX with Hermitian metrics. Our main result provides a formula for the average distribution of the exponentially small eigenvalues of the corresponding Dolbeault Laplacians associated to high tensor powers of L; which in physics terminology is a me…
Study optimal holomorphic extensions for jets along submanifolds as tensor powers increase.
The paper introduces curvature-based clustering algorithms for graph analysis.
We study the distribution of the common zero sets of -tuples of holomorphic sections of powers of singular Hermitian pseudo-effective line bundles on a compact Kähler manifold. As an application, we obtain sufficient conditions which ensure that the wedge product of the curvature currents of these line bundles c…
An Atlas model is a rank-based system of continuous semimartingales for which the steady-state values of the processes follow a power law, or Pareto distribution. For a power law, the log-log plot of these steady-state values versus rank is a straight line. Zipf's law is a power law for which the slope of this line is …
The growing integration of distributed energy resources (DERs) in urban distribution grids raises various reliability issues due to DER's uncertain and complex behaviors. With a large-scale DER penetration, traditional outage detection methods, which rely on customers making phone calls and smart meters' "last gasp" si…
We study junctions of Wilson lines in refined SU(N) Chern-Simons theory and their local relations. We focus on junctions of Wilson lines in antisymmetric and symmetric powers of the fundamental representation and propose a set of local relations which realize one-parameter deformations of quantum groups $\dot{U}_{q}(\m…
New GNN model detects overlapping communities better than existing methods.
We address the problem of assisting human dispatchers in operating power grids in today's changing context using machine learning, with theaim of increasing security and reducing costs. Power networks are highly regulated systems, which at all times must meet varying demands of electricity with a complex production sys…
New method for spectral and Bergman kernels under local spectral gap condition.
ABCD model generates synthetic graphs for community detection with improved scalability and interpretability.