arXiv research

Paper categorifies a polynomial related to ribbon graphs.

Proves partial-dual genus polynomial is a knot invariant weight system.

The paper characterizes when the $\partial \overline{\partial}$-lemma holds for twistor spaces.

We study projectively self-dual polygons and curves in the projective plane. Our results provide a partial answer to problem No 1994-17 in the book of Arnold's problems.

Dual-sPLS improves feature selection and prediction in high-dimensional data.

Semi-supervised wrapper methods are concerned with building effective supervised classifiers from partially labeled data. Though previous works have succeeded in some fields, it is still difficult to apply semi-supervised wrapper methods to practice because the assumptions those methods rely on tend to be unrealistic i…

Paper explores how risk-averse individuals' willingness to pay for insurance varies with risk probability.

Paper proposes a method to recover point configurations from noisy distance data.

Improved RL algorithm with linear MDPs for offline learning with partial data coverage.

A complete surface of constant mean curvature 1 (CMC-1) in hyperbolic 3-space with constant curvature -1 has two natural notions of "total curvature"-- one is the total absolute curvature which is the integral over the surface of the absolute value of the Gaussian curvature, and the other is the dual total absolute cur…

Study robust distribution estimation with Wasserstein distance, achieving optimal risk.

We study regularity properties of the dynamic value functions of primal and dual problems of optimal investing for utility functions defined on the whole real line. Relations between decomposition terms of value processes of primal and dual problems and between optimal solutions of basic and conditional utility maximiz…

A unique hyperbolic metric is found for each spherical cone-metric on the boundary of a hyperbolizable 3-manifold.

In approachability with full monitoring there are two types of conditions that are known to be equivalent for convex sets: a primal and a dual condition. The primal one is of the form: a set C is approachable if and only all containing half-spaces are approachable in the one-shot game; while the dual one is of the form…

We prove that the three-dimensional Iwasawa manifold $X$, viewed as a locally holomorphically trivial fibration by elliptic curves over its two-dimensional Albanese torus, is self-dual in the sense that the base torus identifies canonically with its dual torus under a sesquilinear duality, the Jacobian torus of $X$, wh…

The paper tackles partial inference in structured prediction using a convex optimization approach.

New method for classifying disk embeddings in 4-manifolds.

In this paper we study a utility maximization problem with both optimal control and optimal stopping in a finite time horizon. The value function can be characterized by a variational equation that involves a free boundary problem of a fully nonlinear partial differential equation. Using the dual control method, we der…

Oracle-efficient algorithm for offline RL with partial data coverage.

We establish that, over certain ground fields, the set of osculating tangents of Cayley's ruled cubic surface gives rise to a (maximal partial) spread which is also a dual (maximal partial) spread. It is precisely the Betten-Walker spreads that allow for this construction. Every infinite Betten-Walker spread is not an …

Counterexamples to a conjecture on ribbon graph genus changes were found and proven.

Paper tackles distribution matching by partially matching distributions, achieving robust results.

Affine manifolds linked to integrable equations and geometric structures.

Partial connections are (singular) differential systems generalizing classical connections on principal bundles, yielding analogous decompositions for manifolds with nonfree group actions. Connection forms are interpreted as maps determining projections of the tangent bundle onto the partial connection; this approach e…

Study anisotropic flows without global terms and solve dual Orlicz Christoffel-Minkowski problems.

Dual PC algorithm improves structure learning of Bayesian networks.

Dual-space sampling tackles ill-conditioned inverse problems with Bayesian methods.

We study second-order PDEs in 4D for which the conformal structure defined by the characteristic variety of the equation is half-flat (self-dual or anti-self-dual) on every solution. We prove that this requirement implies the Monge-Ampere property. Since half-flatness of the conformal structure is equivalent to the exi…

Coordinate descent methods employ random partial updates of decision variables in order to solve huge-scale convex optimization problems. In this work, we introduce new adaptive rules for the random selection of their updates. By adaptive, we mean that our selection rules are based on the dual residual or the primal-du…

The paper simplifies embedding spaces in manifolds by attaching handles.

We study an optimal control problem related to swing option pricing in a general non-Markovian setting in continuous time. As a main result we show that the value process solves a first-order non-linear backward stochastic partial differential equation. Based on this result we can characterize the set of optimal contro…

Investor optimizes stock investments with noisy future price signals.

This paper is concerned with the construction of special metrics on non-compact 4-manifolds which arise as resolutions of complex orbifold singularities. Our study is close in spirit to the construction of the hyperkaehler gravitational instantons, but we focus on a different class of singularities. We show that any re…

A novel semi-supervised outlier detection model detects anomalies with few labels.

We consider the pricing problem facing a seller of a contingent claim. We assume that this seller has some general level of partial information, and that he is not allowed to sell short in certain assets. This pricing problem, which is our primal problem, is a constrained stochastic optimization problem. We derive a du…

We apply the network Lasso to classify partially labeled data points which are characterized by high-dimensional feature vectors. In order to learn an accurate classifier from limited amounts of labeled data, we borrow statistical strength, via an intrinsic network structure, across the dataset. The resulting logistic …

This paper examines how data affects risk measures in uncertain distributions.

While convergence of the Alternating Direction Method of Multipliers (ADMM) on convex problems is well studied, convergence on nonconvex problems is only partially understood. In this paper, we consider the Gaussian phase retrieval problem, formulated as a linear constrained optimization problem with a biconvex objecti…

The paper proves a logarithmic partial derivative lemma and applies it to several geometric problems.

This paper studies the question of filtering and maximizing terminal wealth from expected utility in a partially information stochastic volatility models. The special features is that the only information available to the investor is the one generated by the asset prices, and the unobservable processes will be modeled …

Paper solves a new Minkowski problem for a specific type of rigidity.

New $T$-dual solutions found for $G_2$-Strominger system.

DCGD improves training of PINNs by adjusting gradients to avoid negative inner products.

This work focuses on the indifference pricing of American call option underlying a non-traded stock, which may be partially hedgeable by another traded stock. Under the exponential forward measure, the indifference price is formulated as a stochastic singular control problem. The value function is characterized as the …

Proposes TgNN-LD to improve neural network effectiveness and efficiency.

We prove a relation between the $\bar\partial_M$ cohomology of a minimal orbit $M$ of a real form $G_0$ of a complex semisimple Lie group $G$ in a flag manifold $G/Q$ and the Dolbeault cohomology of the Matsuki dual open orbit $X$ of the complexification $K$ of a maximal compact subgroup $K_0$ of $G_0$, under the assum…

The paper calculates bounds for risk metrics and entropies under partial information constraints.

FairDTD improves fairness in GNNs by distilling dual teacher knowledge, balancing utility and bias.