arXiv research

The paper studies volume and area comparisons in non-compact 3-manifolds with non-negative scalar curvature.

We analyze the level sets of the norm of the Witten spinor in an asymptotically flat Riemannian spin manifold of positive scalar curvature. Level sets of small area are constructed. We prove curvature estimates which quantify that, if the total mass becomes small, the manifold becomes flat with the exception of a set o…

Study minimal annuli in a slab, estimating their area.

In this paper we study the stochastic area swept by a regular time-homogeneous diffusion till a stopping time. This unifies some recent literature in this area. Through stochastic time change we establish a link between the stochastic area and the stopping time of another associated time-homogeneous diffusion. Then we …

Study on spin random fields using chaos decomposition for cosmic microwave background modeling.

We present an approach to estimate the severity of traffic related accidents in aggregated (area-level) and disaggregated (point level) data. Exploring spatial features, we measure complexity of road networks using several area level variables. Also using temporal and other situational features from open data for New Y…

Scharlemann and Thompson define a numerical complexity for a 3-manifold using handle decompositions of the manifold. We show that for compact hyperbolic 3-manifolds this is linearly related to a definition of metric complexity in terms of the areas of level sets of Morse functions.

Existing attention mechanisms are trained to attend to individual items in a collection (the memory) with a predefined, fixed granularity, e.g., a word token or an image grid. We propose area attention: a way to attend to areas in the memory, where each area contains a group of items that are structurally adjacent, e.g…

Study finds environmental liability insurance reduces industrial carbon emissions.

Study area and coarea formulas for graphs and submanifolds in Carnot groups.

We study the asymptotic behaviour of 1-parameter subgroups with respect to Hofer's metric when the underlying symplectic manifold is an open surface of infinite area. We prove that, depending on the topology of the level sets of the Hamiltonian H, the distance either is bounded or behaves asymptotically linear. Moreove…

We introduce novel equations, in the spirit of rough path theory, that parametrize level sets of intrinsically regular maps on the Heisenberg group with values in $\mathbb{R}^2$. These equations can be seen as a sub-Riemannian counterpart to classical ODEs arising from the implicit function theorem. We show that they e…

We applied Generative Adversarial Networks (GANs) to learn a model of DOOM levels from human-designed content. Initially, we analysed the levels and extracted several topological features. Then, for each level, we extracted a set of images identifying the occupied area, the height map, the walls, and the position of ga…

Paper proposes model to assess financial risk of grid-ignited wildfires.

The paper analyzes tech specialization and diversification at various scales.

The paper calculates area Siegel--Veech constants for specific submanifolds of REL zero.

A deep learning model is applied for predicting block-level parking occupancy in real time. The model leverages Graph-Convolutional Neural Networks (GCNN) to extract the spatial relations of traffic flow in large-scale networks, and utilizes Recurrent Neural Networks (RNN) with Long-Short Term Memory (LSTM) to capture …

In this note we prove that the level-set flow of the topologist's sine curve is a smooth closed curve. In previous work it was shown by the second author that under level-set flow, a locally-connected set in the plane evolves to be smooth, either as a curve or as a positive area region bounded by smooth curves. Here we…

Random forests and LASSO methods improve small area estimation using auxiliary data.

Topology-GS improves 3D GS for better structural and feature integrity.

The paper proves prevalent existence and partially determines moduli space of area-minimizing surfaces with fractal singular sets.

This research tackles uncertainty estimation in autoregressive structured prediction tasks.

Distributed securities exchanges may become de facto fragmented if they span geographical regions with asymmetric computer infrastructure. First, we build an economic model of a decentralized exchange with two miner clusters, standing in for compact areas of economic activity (e.g., cities). "Local" miners in the area …

This paper investigates two mechanisms of financial contagion that are, firstly, the correlated exposure of banks to the same source of risk, and secondly the direct exposure of banks in the interbank market. It will consider a random network of banks which are connected through the inter-bank market and will discuss t…

Examines insurance market development and similarity post-2004 EU enlargement.

Characterizations of entire subsolutions for the 1-harmonic equation of a constant 1$-tension field are given with applications in geometry via transformation group theory. In particular, we prove that every level hypersurface of such a subsolution is calibrated and hence is area-minimizing over$\mathbb{R}$; and every…

New pseudometrics defined on knot spaces based on curve thickness and length.

Researchers solved a model of an exhaustible resource with stochastic discoveries.

Graph neural networks improve predictions on graph data.

Horseshoe priors improve small area estimation by borrowing strength globally but locally.

Scharlemann and Thompson define the width of a 3-manifold M as a notion of complexity based on the topology of M. Their original definition had the property that the adjacency relation on handles gave a linear order on handles, but here we consider a more general definition due to Saito, Scharlemann and Schultens, in w…

Machine learning has been applied to several problems in particle physics research, beginning with applications to high-level physics analysis in the 1990s and 2000s, followed by an explosion of applications in particle and event identification and reconstruction in the 2010s. In this document we discuss promising futu…

The objective of this paper is to fill a gap in the literature on internationalization, in relation to the absence of objective and measurable performance indicators on the process of how firms sequentially enter external markets. To that end, this research develops a quantitative tool that can be used as a performance…

Estimating temporal patterns in travel times along road segments in urban settings is of central importance to traffic engineers and city planners. In this work, we propose a methodology to leverage coarse-grained and aggregated travel time data to estimate the street-level travel times of a given metropolitan area. Ou…

In the present work we propose an original analytical model of coopetitive game. We try to apply this analytical model of coopetition - based on game theory and conceived at a macro level - to the Greek crisis, suggesting feasible solutions in a cooperative perspective for the divergent interests which drive the econom…

We study global variational properties of the space of solutions to $-\varepsilon^2Δu + W'(u)=0$ on any closed Riemannian manifold $M$. Our techniques are inspired by recent advances in the variational theory of minimal hypersurfaces and extend a well-known analogy with the theory of phase transitions. First, we show t…

Predicting panic is of critical importance in many areas of human and animal behavior, notably in the context of economics. The recent financial crisis is a case in point. Panic may be due to a specific external threat, or self-generated nervousness. Here we show that the recent economic crisis and earlier large single…

We developed an automated deep learning system to detect hip fractures from frontal pelvic x-rays, an important and common radiological task. Our system was trained on a decade of clinical x-rays (~53,000 studies) and can be applied to clinical data, automatically excluding inappropriate and technically unsatisfactory …

Traditional load analysis is facing challenges with the new electricity usage patterns due to demand response as well as increasing deployment of distributed generations, including photovoltaics (PV), electric vehicles (EV), and energy storage systems (ESS). At the transmission system, despite of irregular load behavio…

RandNLA uses randomness for matrix problems in machine learning.

Improved mass-capacity bounds for specific 3D manifolds.

PACE explains ViTs by modeling patch-level concept distributions, surpassing existing methods.

Predictive policing models can be biased by differential crime reporting rates.

With the breakthrough of computational power and deep neural networks, many areas that we haven't explore with various techniques that was researched rigorously in past is feasible. In this paper, we will walk through possible concepts to achieve robo-like trading or advising. In order to accomplish similar level of pe…

The increasing penetration level of energy generation from renewable sources is demanding for more accurate and reliable forecasting tools to support classic power grid operations (e.g., unit commitment, electricity market clearing or maintenance planning). For this purpose, many physical models have been employed, and…

Existing supervised approaches didn't make use of the low-level features which are actually effective to this task. And another deficiency is that they didn't consider the relation between pixels, which means effective features are not extracted. In this paper, we proposed a novel convolutional neural network which mak…

The present research aims to highlight the main factors influencing the development of entrepreneurial innovation in a rural environment and to perform an empirical study with the purpose of assessing the main problems in rural development. The research performed is mostly of a quantitative nature, being based on the u…

FIGARO generates symbolic music with fine-grained control.