arXiv research

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

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

A subset of the sphere is said short if it is contained in an open hemisphere. A short closed set which is geodesically convex is called a cap. The following theorem holds: 1. The minimal number of short closed sets covering the $n$-sphere is $n+2$. 2. If $n+2$ short closed sets cover the $n$-sphere then (i) their inte…

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

New examples of Howson groups that are not strongly Howson found.

A new theorem eliminates higher-multiplicity intersections in manifold topology.

The abstract constructs a set of bad 3-orbifolds and shows how any bad 3-orbifold can be transformed into a good one.

In this paper, we give two classes of positive semi-definite metrics on 2-manifolds. The one is called a class of Kossowski metrics and the other is called a class of Whitney metrics: The pull-back metrics of wave fronts which admit only cuspidal edges and swallowtails in $\boldsymbol{R}^3$ are Kossowski metrics, and t…

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

A new algorithm CAP learns optimal policies from observational data with confounding bias and missing observations.

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. …

New degenerate free boundary minimal annuli found in spherical caps, challenging uniqueness.

Study symmetry of cross-cap surfaces with folding maps.

Paper classifies symmetries of cross caps using invariants.

The main result of this paper that a martingale evolution can be chosen for Libor such that all the Libor interest rates have a common market measure; the drift is fixed such that each Libor has the martingale property. Libor is described using a field theory model, and a common measure is seen to be emerge naturally f…

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

Study on VIX options pricing in SABR model, showing infinite prices due to volatility explosion.

Capsule network improves polyp diagnosis accuracy.

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.

We define the notion of a braided link cobordism in $S^3 \times [0,1]$, which generalizes Viro's closed surface braids in $\mathbb{R}^4$. We prove that any properly embedded oriented surface $W \subset S^3 \times [0,1]$ is isotopic to a surface in this special position, and that the isotopy can be taken rel boundary wh…

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.

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.

To study spacelike surfaces of codimension two in the Lorentz-Minkowski space $\Bbb R^{n+1}_1,$ we construct a pair of maps whose values are in $HS_r:=H_+^n(\textbf v,1)\cap \{x_{n+1}=r\},$ called $\textbf n_r^{\pm}$-Gauss maps. It is showed that they are well-defined and useful to study practically flat as well as umb…

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.

A well known result of Drinfeld classifies Poisson Lie groups $(H,Π)$ in terms of Lie algebraic data in the form of Manin triples $(\mathfrak{d},\mathfrak{g},\mathfrak{h})$; he also classified compatible Poisson structures on $H$-homogeneous spaces $H/K$ in terms of Lagrangian subalgebras $\mathfrak{l}\subset\mathfrak{…

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.