We compute the volumes of the eigenform loci in the moduli space of genus two Abelian differentials. From this, we obtain asymptotic formulas for counting closed billiards paths in certain L-shaped polygons with barriers.
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16 results for “L-shaped”
Direct proof of one-hook scaling property for Alexander polynomial from Reshetikhin-Turaev formalismmath-ph
Direct proof of Alexander polynomial scaling for L-shaped representations.
problem Proving scaling property of Alexander polynomials for specific representations.
method Direct use of Reshetikhin-Turaev formalism to compute R-matrices.
result Normalized Alexander polynomial for one-hook representations scales with .
Divide knots and links, defined by A'Campo in the singularity theory of complex curves, is a method to present knots or links by real plane curves. The present paper is a continuation of the author's previous result that every knot in the major subfamilies of Berge's lens space surgery (i.e., knots yielding a lens spac…
Study models stock price recovery during COVID-19, distinguishing V and L-shape recoveries.
problem Analyzing stock price recovery during the COVID-19 pandemic.
method Developed a stock price model based on net-fund-flow and financial antifragility.
result Quality stocks with higher financial antifragility show V-shape recovery, while those with lower antifragility show L-shape recovery.
On the Teichmüller geodesic generated by the L-shaped translation surface tiled by three squaresmath.GT
We study the one parameter family of genus 2 Riemann surfaces defined by the orbit of the L-shaped translation surface tiled by three squares under the Teichmüller geodesic flow. These surfaces are real algebraic curves with three real components. We are interested in describing these surfaces by their period matrices.…
The statistical properties of the bid-ask spread of a frequently traded Chinese stock listed on the Shenzhen Stock Exchange are investigated using the limit-order book data. Three different definitions of spread are considered based on the time right before transactions, the time whenever the highest buying price or th…
It is proved that every knot in the major subfamilies of J. Berge's lens space surgery (i.e., knots yielding a lens space by Dehn surgery) is presented by an L-shaped (real) plane curve as a "divide knot" defined by N. A'Campo in the context of singularity theory of complex curves. For each knot given by Berge's parame…
We use high-frequency data of 1364 Chinese A-share stocks traded on the Shanghai Stock Exchange and Shenzhen Stock Exchange to investigate the intraday patterns in the bid-ask spreads. The daily periodicity in the spread time series is confirmed by Lomb analysis and the intraday bid-ask spreads are found to exhibit …
Algorithm constructs algebraic curves from translation surfaces.
problem Creating algebraic curves from translation surfaces.
method Using discrete Riemann surface theory and Riemann theta functions.
result Algorithm approximates Jacobian varieties of translation surfaces.
We prove the existence of Veech groups having a critical exponent strictly greater than any elementary Fuchsian group (i.e. ) but strictly smaller than any lattice (i.e. ). More precisely, every affine covering of a primitive L-shaped Veech surface ramified over the singularity and a non-periodic …
We calculate the Euler characteristics of all of the Teichmuller curves in the moduli space of genus two Riemann surfaces which are generated by holomorphic one-forms with a single double zero. These curves can all be embedded in Hilbert modular surfaces and our main result is that the Euler characteristic of a Teichmu…
GF-Net learns Green's functions for linear reaction-diffusion equations.
problem Learning Green's functions for linear reaction-diffusion equations on arbitrary domains.
method GF-Net, a neural network, learns Green's functions in an unsupervised manner using physics-informed approach and symmetry.
result GF-Net efficiently solves linear reaction-diffusion equations under various boundary conditions and sources.
In this paper we study an experimentally-observed connection between two seemingly unrelated processes, one from computational geometry and the other from differential geometry. The first one (which we call "grid peeling") is the convex-layer decomposition of subsets of the integer grid, previous…
Survival analysis models predict loan write-off risk under IFRS 9.
problem Estimating loan write-off probabilities in credit risk modeling.
method Discrete-time hazard model and conditional inference survival tree compared to cross-sectional logistic regression.
result Discrete-time hazard model outperforms other two-stage LGD-models.
Double descent observed in tree-based models for genomic prediction.
problem Understanding the generalization behavior of tree-based models in machine learning.
method Systematic variation of model complexity in a genomic prediction task using whole-genome sequencing data.
result Double descent emerges only when complexity is scaled jointly across learner capacity and ensemble size.
A new model explains U- and Swoosh-shaped stock price recovery during the COVID-19.
problem Modeling stock price recovery during the COVID-19 with V- and L-shaped recovery.
method Introducing a sentiment variable to quantify investor sentiment and simulate U- and Swoosh-shaped recovery.
result The model explains U- and Swoosh-shaped recovery of sectoral indices with positive sentiment.