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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.

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13 results for FOCI

Confocal conics form an orthogonal net. Supplementing this net with one of the following: 1) the net of Cartesian coordinate lines aligned along the principal axes of conics, 2) the net of Apollonian pencils of circles whose foci coincide with the foci of conics, 3) the net of tangents to a conic of the confocal family…

2019-12-04abs ↗pdf ↗

New method uncovers small but significant local activities in time-series data.

problem Reconstructing small but important local activities in time-series data.
method Neural state-space models with latent causal-effect disentanglement.
result Demonstrated proof-of-concept on reconstructing ectopic foci in cardiac electrical propagation.

This technical note considers the problems of blind sparse learning and inference of electrogram (EGM) signals under atrial fibrillation (AF) conditions. First of all we introduce a mathematical model for the observed signals that takes into account the multiple foci typically appearing inside the heart during AF. Then…

2012-12-31abs ↗pdf ↗

Study global geometry of dynamical systems with entire vector fields.

problem Understanding the global structure of equilibria and their basins.
method Step-by-step analysis of basins of centers, nodes, and foci; introduction of global elliptic sectors.
result Characterization of heteroclinic regions connecting equilibria.

We describe and study the loci equidistant from finitely many points in the so-called complex hyperbolic geometry, i.e., in the geometry of a holomorphic 22-ball B\Bbb B. In particular, we show that the bisectors (= the loci equidistant from 22 points) containing the (smooth real algebraic) curve equidistant from gi…

2014-06-23abs ↗pdf ↗

This study classifies quadric surfaces in 3-sphere as Weingarten surfaces.

problem Extension of quadric surfaces of revolution to 3-sphere.
method Rigorous classification and characterization using spherical angular momentum.
result Spherical ellipsoids, hyperboloids, and paraboloids are Weingarten surfaces with a specific cubic relation between principal curvatures.