arXiv research

The paper uses LSMC to price capped American options with time-dependent caps.

Method finds all cross caps formally isometric to a given one.

It is classically known that generic smooth maps of R^2 into R^3 admit only cross cap singularities. This suggests that the class of cross caps might be an important object in differential geometry. We show that the standard cross cap (u,uv,v^2) has non-trivial isometric deformations with infinite dimensional freedom. …

Study symmetry of cross-cap surfaces with folding maps.

Paper classifies symmetries of cross caps using invariants.

The paper analyzes American options with time-varying caps, finding complex exercise regions and deriving option pricing formulas.

This paper proves geodesic curvature measures are bounded for curves near cross cap singularities.

Contact surgeries transform manifolds, and all admit symplectic caps.

This study improves mid-cap equity performance with a data-driven, market-neutral approach.

We give a variational proof of the existence and uniqueness of a convex cap with the given upper boundary. The proof uses the concavity of the total scalar curvature functional on the space of generalized convex caps. As a byproduct, we prove that generalized convex caps with the fixed boundary are globally rigid, that…

3D spherical caps are rigid under certain perturbations.

Improved LDA with capped l_{2,1}-norm reduces outlier sensitivity.

Study analyzes order transitions in high, medium, and low market cap stocks using Markov chains.

In the paper we consider the following conjecture: if a finite group $G$ possesses a solvable $π$-Hall subgroup $H$, then there exist elements $x,y,z,t\in G$ such that the identity $H\cap H^x\cap H^y\cap H^z\cap H^t=O_π(G)$ holds. The minimal counter example is shown to be an almost simple group of Lie type.

Study of free boundary minimal Möbius bands in spherical caps.

Proposes a diagnostic method to evaluate factor models using cap-axis integrals.

Proposes a diagnostic method to evaluate factor models using cap-axis integrals.

Proves rigidity for spherical cap eigenvalue problem.

We show that there is a well-defined cap-product structure on the Fintushel-Stern spectral sequence. Hence we obtain the induced cap-product structure on the ${\BZ}_8$-graded instanton Floer homology. The cap-product structure provides an essentially new property of the instanton Floer homology, from a topological poin…

Let $M$ be a smooth closed $4k$-manifold whose Yamabe invariant $Y(M)$ is nonpositive. We show that $Y(M\sharp l \Bbb HP^k\sharp m \bar{\Bbb HP^k})=Y(M),$ where $l,m$ are nonnegative integers, and $\Bbb HP^k$ is the quaternionic projective space. When $k=4$, we also have $$Y(M\sharp l CaP^2\sharp m \bar{CaP^2})=Y(M),…

The paper uses Floer homology to study twist coefficients and their behavior after capping off.

Minimal number of caps covering an n-sphere is n+2.

We construct cup and cap products in intersection (co)homology with field coefficients. The existence of the cap product allows us to give a new proof of Poincare duality in intersection (co)homology which is similar in spirit to the usual proof for ordinary (co)homology of manifolds.

CAP adapts optimization to class attributes for better fairness.

Investors face constraints in Heston's model; optimal allocation differs from naive capped strategy.

The paper studies parallel surfaces of cuspidal cross caps and their degeneracy.

Study on cuspidal edges and cross-caps in 3D geometry.

New method distinguishes 4-manifold types using trisections.

We prove relative versions of the symplectic capping theorem and sufficiency of Giroux's criterion for Stein fillability and use these to study the 4-genus of knots.

FSD-CAP improves graph feature imputation under high missing rates.

The study finds the optimal metrics for free boundary minimal surfaces in spherical caps.

Let $(G,h)$ be a nilpotent Lie group endowed with a left invariant Riemannian metric, $\mathfrak{g}$ its Euclidean Lie algebra and $Z(\mathfrak{g})$ the center of $\mathfrak{g}$. By using an orthonormal basis adapted to the splitting $\mathfrak{g}=(Z(\mathfrak{g})\cap[\mathfrak{g},\mathfrak{g}])\oplus O^+\oplus (Z(\mat…

CAP algorithm controls FCR in online selective prediction.

We study PCA as a stochastic optimization problem and propose a novel stochastic approximation algorithm which we refer to as "Matrix Stochastic Gradient" (MSG), as well as a practical variant, Capped MSG. We study the method both theoretically and empirically.

Study a flow in a ball that preserves volume and converges to spherical caps.

Geometric Brownian motion simulates stock prices for Brazilian small caps index.

Paper calculates perpetual put option pricing with drawdown cap.

It is well-known:Suppose there are three 1-dimensional links $K_+$, $K_-$, $K_0$ such that $K_+$, $K_-$, and $K_0$ coincide out of a 3-ball $B$ trivially embedded in $S^3$ and that $K_+\cap B$, $K_-\cap B$, and $K_0\cap B$ are drawn as follows. Then $Δ_{K_+}-Δ_{K_+}=(t-1)\cdotΔ_{K_0}$, where $Δ_{K}$ is the Alexander po…

An important class of contact 3--manifolds are those that arise as links of rational surface singularities with reduced fundamental cycle. We explicitly describe symplectic caps (concave fillings) of such contact 3--manifolds. As an application, we present a new obstruction for such singularities to admit rational homo…

New flow for capillary surfaces converges to spherical caps.

Proves existence of a rank-preserving map for subgroup joins in free groups.

Study proves a new formula for capillary hypersurfaces and shows a flow converging to a special shape.

New symplectic caps and embeddings found in complex projective plane.

The study examines critical Hölder spaces for isometric embeddings of polar caps.

The study proves rigidity and non-rigidity of spherical caps in mean curvature.

This paper works out fair values of stock loan model with automatic termination clause, cap and margin. This stock loan is treated as a generalized perpetual American option with possibly negative interest rate and some constraints. Since it helps a bank to control the risk, the banks charge less service fees compared …

Mathematical properties of the historical GDP/cap distributions are discussed and explained. These distributions are frequently incorrectly interpreted and the Unified Growth Theory is an outstanding example of such common misconceptions. It is shown here that the fundamental postulates of this theory are contradicted …

Study investigates minimal surfaces in spherical caps, extending previous findings.