arXiv research

Solves Jang's equation for hyperboloidal data in 4-7 dimensions, proving positive mass theorem.

Study of singular curves in a specific type of hyperbolic distribution.

We study local control of the mechanism with the growth vector (4,7). We study controllability and extremal trajectories on the nilpotent approximation as an example of the control theory on Lie group. We give solutions of the system an show examples of local extremal trajectories.

Study on geodesics in a specific sub-Riemannian structure with two types of behavior.

This is the second of three papers about the Compression Theorem. We give proofs of Gromov's theorem on directed embeddings [M Gromov, Partial differential relations, Springer--Verlag (1986); 2.4.5 C'] and of the Normal Deformation Theorem [The compression theorem I; 4.7], arxiv:math.GT/9712235.

The book can be divided in three parts: the Lagrange geometry of order $k$, presented in the first three chapters, the geometrical theory of the dual manifolds $T^{*k}M$ - chapters 4-7 and the geometry of Hamilton spaces of order $k$ and their subspaces, contained in the last four chapters. They are studied directly an…

We describe the evolution under the mean curvature flow of embedded Lagrangian spherical surfaces in the complex Euclidean plane $\mathbb{C}^2$. In particular, we answer the Question 4.7 addressed in [Ne10b] by A. Neves about finding out a condition on a starting Lagrangian torus in $\mathbb{C}^2$ such that the corresp…

In this paper we prove that a Finsler metrics has constant flag curvature if and only if the curvature of the induced nonlinear connection satisfies an algebraic identity with respect to some arbitrary second rank tensors. Such algebraic identity appears as an obstruction to the formal integrability of some operators i…

Corrected misstatements about invariant rank in ECS manifold papers.

We classify, up to diffeomorphism, all closed smooth manifolds homeomorphic to the complex projective $n$-space $\mathbb{C}\textbf{P}^n$, where $n=3$ and $4$. Let $M^{2n}$ be a closed smooth $2n$-manifold homotopy equivalent to $\mathbb{C}\textbf{P}^n$. We show that, up to diffeomorphism, $M^{6}$ has a unique different…

Integrates ESG data into Black-Litterman for portfolio optimization.

This is the first of two articles in which we give a proof - for a broad class of four-manifolds - of Witten's conjecture that the Donaldson and Seiberg-Witten series coincide, at least through terms of degree less than or equal to c-2, where c is a linear combination of the Euler characteristic and signature of the fo…

We prove that if the lens space $L(n, 1)$ is obtained by a surgery along a knot in the lens space $L(3,1)$ that is distance one from the meridional slope, then $n$ is in $\{-6, \pm 1, \pm 2, 3, 4, 7\}$. This result yields a classification of the coherent and non-coherent band surgeries from the trefoil to $T(2, n)$ tor…

This article is based on a lecture by the first author at the International Georgia Topology Conference 2001 (Athens, Georgia) and the Mathematische Arbeitstagung 2001 (Bonn, Germany). We sketch a proof of Witten's formula relating the Donaldson and Seiberg-Witten series modulo powers of degree c+2, with c = -{1/4}(7 c…

D2P-Fed improves privacy and communication in federated learning.

DARE uses GPT-2 to generate relation examples, improving RE performance.

Study shows Futaki invariant vanishes on most Fano threefolds.

Paper develops MMOT framework for financial applications with neural acceleration.

Machine learning improves learning and memory retention by optimizing study sessions.

In this article we complete the proof---for a broad class of four-manifolds---of Witten's conjecture that the Donaldson and Seiberg-Witten series coincide, at least through terms of degree less than or equal to c-2, where c is a linear combination of the Euler characteristic and signature of the four-manifold. This art…

Study quantizes ropelength and writhe of 12-crossing knots.

In this sequel, employing more commutative algebra than that explored in \cite{CCJ}, we show that an isoparametric hypersurface with four principal curvatures and multiplicities $(3,4)$ in $S^{15}$ is one constructed by Ozeki-Takeuchi \cite[I]{OT} and Ferus-Karcher-Münzner \cite{FKM}, referred to collectively as of OT-…

Trans-dimensional random field language models (TRF LMs) where sentences are modeled as a collection of random fields, have shown close performance with LSTM LMs in speech recognition and are computationally more efficient in inference. However, the training efficiency of neural TRF LMs is not satisfactory, which limit…

Cryo-electron microscopy (cryo-EM) is a powerful technique for determining the structure of proteins and other macromolecular complexes at near-atomic resolution. In single particle cryo-EM, the central problem is to reconstruct the three-dimensional structure of a macromolecule from $10^{4-7}$ noisy and randomly orien…

ELCO enhances graph generation by adding new nodes and edges.

Analyzes NFT market trends, trade networks, and visual features.

Quantum Signal Processing reduces derivative pricing quantum resource requirements.

The paper characterizes Pfaffian embeddings from 2,3,5-manifolds to 7-dimensional isotropic spaces.

Project analyzes drug reviews to predict ratings using machine learning.

Locally Optimal Block Preconditioned Conjugate Gradient (LOBPCG) is demonstrated to efficiently solve eigenvalue problems for graph Laplacians that appear in spectral clustering. For static graph partitioning, 10-20 iterations of LOBPCG without preconditioning result in ~10x error reduction, enough to achieve 100% corr…

New method improves transfer and robustness of supervised contrastive learning.

Ozeki and Takeuchi \cite[I]{OT} introduced the notion of Condition A and Condition B to construct two classes of inhomogeneous isoparametric hypersurfaces with four principal curvatures in spheres, which were later generalized by Ferus, Karcher and Münzner to many more examples via the Clifford representations; we will…

CwA optimizes search performance by jointly learning a balanced database partition and a neural probing function.

Method predicts NAFLD risk with high accuracy and distribution-free coverage guarantees.

AR app visualizes Quranic Surah al-Fil for Islamic education.

It is known that connected translation invariant $n$-dimensional noncommutative differentials $d x^i$ on the algebra $k[x^1,\cdots,x^n]$ of polynomials in $n$-variables over a field $k$ are classified by commutative algebras $V$ on the vector space spanned by the coordinates. This data also applies to construct differe…

DeRegiME forecasts with regime structure, improving probabilistic predictions across various time series.

A novel algorithm predicts customized allergy seasons using multi-variate triple-regression.

Consider an oriented four-dimensional Lorentzian manifold $(\widetilde{M}^{3, 1}, \widetilde{g})$ and an oriented seven-dimensional Riemannian manifold $(M^{7}, g)$. We describe a class of decomposable eleven-dimensional supergravity backgrounds on the product manifold $({\mathcal{M}}^{10, 1}=\widetilde{M}^{3,1} \times…

We consider the problem of governing systemic risk in a banking system model. The banking system model consists in an initial value problem for a system of stochastic differential equations whose dependent variables are the log-monetary reserves of the banks as functions of time. The banking system model considered gen…

In microsurgery, lasers have emerged as precise tools for bone ablation. A challenge is automatic control of laser bone ablation with 4D optical coherence tomography (OCT). OCT as high resolution imaging modality provides volumetric images of tissue and foresees information of bone position and orientation (pose) as we…

Graph neural network optimizes energy-efficient precoding for massive MIMO systems.

Study developed phenotypes for ICU patients' brain dysfunction states.

Defines and classifies Thurston geometries and connects simplicial volume to Kodaira dimension.

Paper relates asymptotic dimension to cofinal dimension using coarse proximities.

We study the Assouad dimension and the Nagata dimension of metric spaces. As a general result, we prove that the Nagata dimension of a metric space is always bounded from above by the Assouad dimension. Most of the paper is devoted to the study of when these metric dimensions of a metric space are locally given by the …

Our goal in this paper is to develop an effective estimator of fractal dimension. We survey existing ideas in dimension estimation, with a focus on the currently popular method of Grassberger and Procaccia for the estimation of correlation dimension. There are two major difficulties in estimation based on this method. …

We establish cohomological and extension dimension versions of the Hurewicz dimension-raising theorem