arXiv research

Proposes a new deep ordinal classification model enforcing label uni-modality.

Analyzing available FAO data from 176 countries over 21 years, we observe an increase of complexity in the international trade of maize, rice, soy, and wheat. A larger number of countries play a role as producers or intermediaries, either for trade or food processing. In consequence, we find that the trade networks bec…

Minimal hypersurfaces in real projective spaces have at least n+2 Morse index.

Paper introduces Lie algebroid index theory and a generalized Riemann-Roch theorem.

For an immersed minimal surface in $\mathbb{R}^3$, we show that there exists a lower bound on its Morse index that depends on the genus and number of ends, counting multiplicity. This improves, in several ways, an estimate we previously obtained bounding the genus and number of ends by the index. Our new estimate resol…

We show that for an immersed two-sided minimal surface in $R^3$, there is a lower bound on the index depending on the genus and number of ends. Using this, we show the nonexistence of an embedded minimal surface in $R^3$ of index $2$, as conjectured by Choe. Moreover, we show that the index of a immersed two-sided mini…

Paper proves index theorem for self-adjoint elliptic boundary problems.

The stability and the index of complete one-sided minimal surfaces of certain three-dimensional Riemannian manifolds with positive scalar curvature are studied.

New spectral estimates for minimal surfaces with boundary conditions.

The combined work of Guaraco, Hutchinson, Tonegawa and Wickramasekera has recently produced a new proof of the classical theorem that any closed Riemannian manifold of dimension $n + 1 \geq 3$ contains a minimal hypersurface with a singular set of Hausdorff dimension at most $n-7$. This proof avoids the Almgren--Pitts …

Study on minimal surfaces with Y-singularities, proving rigidity for Morse index one.

Found a minimal surface in curved space.

The comparison theory for the Riccati equation satisfied by the shape operator of parallel hypersurfaces is generalized to semi-Riemannian manifolds of arbitrary index, using one-sided bounds on the Riemann tensor which in the Riemannian case correspond to one-sided bounds on the sectional curvatures. Starting from 2-d…

We revisit the cohomological index theorem for elliptic elements in the universal enveloping algebra of a Lie groupoid previously proved by the authors. We prove a Thom isomorphism for Lie algebroids which enables us to rewrite the "topological side" of the index theorem. This results in index formulae for Lie groupoid…

Left orderability proven for certain 3-manifolds with specific foliations.

New minimal surfaces can have huge area and index.

The use of bundle gerbes and bundle gerbe modules is considered as a replacement for the usual theory of Clifford modules on manifolds that fail to be spin. It is shown that both sides of the Atiyah-Singer index formula for coupled Dirac operators can be given natural interpretations using this language and that the re…

Study of bandit problem with Poisson decision times and Lévy processes.

In this paper, we establish a fluid limit for a two--sided Markov order book model. Our main result states that in a certain asymptotic regime, a pair of measure-valued processes representing the "sell-side shape" and "buy-side shape" of an order book converges to a pair of deterministic measure-valued processes in a c…

Defines and computes geometric pairings for discrete groups using Baum-Connes assembly map.

The Allen-Cahn equation is a semilinear PDE which is deeply linked to the theory of minimal hypersurfaces via a singular limit. We prove curvature estimates and strong sheet separation estimates for stable solutions (building on recent work of Wang-Wei) of the Allen-Cahn equation on a 3-manifold. Using these, we are ab…

This paper explores topological aspects of index theory for infinite-dimensional manifolds.

In this paper, we consider immersed two-sided minimal hypersurfaces in $\mathbb{R}^n$ with finite total curvature. We prove that the sum of the Morse index and the nullity of the Jacobi operator is bounded from below by a linear function of the number of ends and the first Betti number of the hypersurface. When $n=4$, …

Machine learning improves measuring climate adaptation impacts.

Paper introduces IC-index to evaluate interaction prediction methods.

Study proves rigidity of capillary surfaces in curved 3D spaces.

Near a birth-death critical point in a one-parameter family of gradient flows, there are precisely two Morse critical points of index difference one on the birth side. This paper gives a self-contained proof of the folklore theorem that these two critical points are joined by a unique gradient trajectory up to time-shi…

Tensor completion requires fewer samples with weak side information.

We propose a model for price formation in financial markets based on clearing of a standard call auction with random orders, and verify its validity for prediction of the daily closing price distribution statistically. The model considers random buy and sell orders, placed following demand- and supply-side valuation di…

We prove that for generic metrics on a 3-sphere, the minimal surface obtained from the min-max procedure of Simon-Smith has index 1. We prove an analogous result for minimal surfaces arising from strongly irreducible Heegaard sweepouts in 3-manifolds. We also confirm a conjecture of Pitts-Rubinstein that a strongly irr…

A new framework for SPX and VIX hedging that combines AI and market dynamics.

The realized GARCH framework is extended to incorporate the two-sided Weibull distribution, for the purpose of volatility and tail risk forecasting in a financial time series. Further, the realized range, as a competitor for realized variance or daily returns, is employed in the realized GARCH framework. Further, sub-s…

The recent adoption of recurrent neural networks (RNNs) for session modeling has yielded substantial performance gains compared to previous approaches. In terms of context-aware session modeling, however, the existing RNN-based models are limited in that they are not designed to explicitly model rich static user-side c…

Proof that stable minimal surfaces in 3D are flat.

This study compares Bitcoin and S&P 500 returns using a new GTS distribution method.

Extends a theorem for first-order elliptic operators on manifolds.

Given a compact Riemannian manifold with boundary, we prove that the limit of a sequence of embedded, almost properly embedded free boundary minimal hypersurfaces, with uniform area and Morse index upper bound, always inherits a non-trivial Jacobi field. To approach this, we prove a one-sided Harnack inequality for min…

We consider a continuous curve of linear elliptic formally self-adjoint differential operators of first order with smooth coefficients over a compact Riemannian manifold with boundary together with a continuous curve of global elliptic boundary value problems. We express the spectral flow of the resulting continuous fa…

Proves properties of CMC hypersurfaces in specific spaces.

DINOSAUR improves retrieval by accounting for embedding uncertainty in recommender systems.

Over the last decade, dividends have become a standalone asset class instead of a mere side product of an equity investment. We introduce a framework based on polynomial jump-diffusions to jointly price the term structures of dividends and interest rates. Prices for dividend futures, bonds, and the dividend paying stoc…

The common wisdom argues that, in general, large trades cause large price changes, while small trades cause small price changes. However, for extremely large price changes, the trade size and news play a minor role, while the liquidity (especially price gaps on the limit order book) is a more influencing factor. Hence,…

A new algorithm for competing agents in a two-sided market setting.

In this paper, we prove a Morse index theorem for the index form of even order linear Hamiltonian systems on the closed interval with reasonable self-adjoint boundary conditions. The highest order term is assumed to be nondegenerate.

A new index rebalancing strategy reduces large constituent weights without undesirable effects.

Study identifies Kähler-Einstein, Kähler-Ricci soliton, and Sasaki-Einstein metrics on log del Pezzo surfaces.

We establish multiplicity results for geometrically distinct contractible closed Reeb orbits of non-degenerate contact forms on a broad class of prequantization bundles. The results hold under certain index requirements on the contact form and are sharp for unit cotangent bundles of CROSS's. In particular, we generaliz…

Paper studies involutions generating the twist subgroup of nonorientable surfaces.