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.
We prove that the curvature flow of an embedded planar network of three curves connected through a triple junction, with fixed endpoints on the boundary of a given strictly convex domain, exists smooth until the lengths of the three curves stay far from zero. If this is the case for all times, then the evolution exists…
We consider a regular embedded network composed by two curves, one of them closed, in a convex domain Ω. The two curves meet only in one point, forming angle of 120 degrees. The non-closed curve has a fixed end point on ∂Ω. We study the evolution by curvature of this network. We show that the maximal exist…
Health care is one of the most exciting frontiers in data mining and machine learning. Successful adoption of electronic health records (EHRs) created an explosion in digital clinical data available for analysis, but progress in machine learning for healthcare research has been difficult to measure because of the absen…
We analyse the structure of the distribution of eigenvalues of the stock market correlation matrix with increasing length of the time series representing the price changes. We use 100 highly-capitalized stocks from the American market and relate result to the corresponding ensemble of Wishart random matrices. It turns …
Markov's theorem classifies the worst irrational numbers with respect to rational approximation and the indefinite binary quadratic forms whose values for integer arguments stay farthest away from zero. The main purpose of this paper is to present a new proof of Markov's theorem using hyperbolic geometry. The main ingr…
We consider the limit set in Thurston's compactification PMF of Teichmueller space of some Teichmueller geodesics defined by quadratic differentials with minimal but not uniquely ergodic vertical foliations. We show that a) there are quadratic differentials so that the limit set of the geodesic is a unique point, b) th…
A geodesic g is Morse, for every L≥1,A≥0 there exists a C=Cg(L,A) such that any (L,A)-quasi-geodesic connecting two points on g stays C-close to g. The Morse lemma implies that in a hyperbolic space every geodesic is Morse. Here we prove the converse: If a homogeneous proper geodesic space is …
We show that simple random walks on (non-trivial) relatively hyperbolic groups stay O(log(n))-close to geodesics, where n is the number of steps of the walk. Using similar techniques we show that simple random walks in mapping class groups stay O(nlog(n))-close to geodesics and hierarchy paths. Along the…
In our empirical study, we examine the price of liquid stocks after experiencing a large intraday price change using data from the NYSE and the NASDAQ. We find significant reversal for both intraday price decreases and increases. The results are stable against varying parameters. While on the NYSE the large widening of…
Machine learning models trained on hospital data degrade over time due to changing practices.
problem Machine learning models trained on hospital data degrade over time due to changing practices.
method We augmented MIMIC with the year of care and showed that a model trained using standard feature representations will significantly degrade in quality over time.
result Clinically-oriented aggregates of raw features significantly mitigate future deterioration.
We prove existence and uniqueness of entire spacelike hypersurfaces in the Minkowski space with prescribed negative scalar curvature, and with given values at infinity which stay at a bounded distance of a lightcone.
Public benchmark for machine learning models in critical care.
problem Lack of public benchmarks for machine learning in critical care.
method Defined four tasks (mortality prediction, length of stay, phenotyping, decompensation risk) and compared clinical and deep learning models on eICU dataset.
result First public benchmark on multi-centre critical care dataset, comparing clinical models with predictive models.
We show that any number of disjointly embedded 2-spheres in 4-space can be pulled apart by a link homotopy, ie, by a motion in which the 2-spheres stay disjoint but are allowed to self-intersect.
We study the properties of Modified Riemann extensions evolving under Ricci flow. We obtain the necessary and sufficient condition for modified Riemann extension under Ricci flow to stay as modified Riemann extension. We also discuss the properties of the curvature tensors under Ricci flow.