arXiv research

Mathematical framework for brane quantization using SYZ mirror symmetry.

This paper connects symplectic and Kähler manifolds via brane quantization.

Let $\OO$ be an orbit of the group of Hamiltonian symplectomorphisms acting on the space of Lagrangian submanifolds of a symplectic manifold $(X,ω).$ We define a functional $\CC:\OO \to \R$ for each differential form $β$ of middle degree satisfying $β\wedge ω= 0$ and an exactness condition. If the exactness condition d…

Constructing brane quantization for $A_n$-resolutions using SYZ mirror symmetry.

The main results of the paper are: \begin{Prop}\label{GenSvarc-Milnor} A group $G$ acting coarsely on a coarse space $(X,\CC)$ induces a coarse equivalence $g\to g\cdot x_0$ from $G$ to $X$ for any $x_0\in X$. \end{Prop} Theorem: \label{GenGromovThm} Two coarse structures $\CC_1$ and $\CC_2$ on the same set $X$ are equ…

An axiomatic characterization of buildings of type $\CC_3$ due to Tits is used to prove that any cohomogeneity two polar action of type $\CC_3$ on a positively curved simply connected manifold is equivariantly diffeomorphic to a polar action on a rank one symmetric space. This includes two actions on the Cayley plane w…

We construct embeddings $\mathcal{Y}_{n,τ} \to {Hilb}^n (Σ_τ)$ for each of the classical Lie algebras $\ger{sp}_{2m}(\Cc)$, $\ger{so}_{2m}(\Cc)$, and $\ger{so}_{2m+1}(\Cc)$. The space $\mathcal{Y}_{n,τ}$ is the fiber over a point $τ\in \ger h / W$ of the restriction of the adjoint quotient map $χ: \ger g \to \ger h /W$…

We present examples of hyperbolizable 3-manifolds $M$ with the following property. Let $CC(π_1(M))$ denote the space of convex co-compact representations of $π_1(M)$. We show that for every $K\geq 1$ there exists a representation $ρ$ in $\bar {CC(π_1(M))}$ so that every $K$-quasiconformal deformation of $ρ$ lies in the…

The aim of this paper is to investigate uniqueness of conic constant scalar curvature Kaehler (cscK) metrics, when the cone angle is less than $π$. We introduce a new Hölder space called $\cC^{4,\a,\b}$ to study the regularities of this fourth order elliptic equation, and prove that any $\cC^{2,\a,\b}$ conic cscK metri…

We obtain the semi-classical expansion of the kernels and traces of Toeplitz operators with $\cC^k$--\,symbol on a symplectic manifold. We also give a semi-classical estimate of the distance of a Toeplitz operator to the space of self-adjoint and multiplication operators.

Geometric quantization on hyperKähler manifolds via brane quantization.

In this paper we study the main geometric properties of the Carnot-Carathéodory (abbreviated CC) distance $\dc$ in the setting of $k$-step sub-Riemannian Carnot groups from many different points of view. An extensive study of the so-called normal CC-geodesics is given. We state and prove some related variational formul…

Sharp bounds derived for eigenvalues on specific geometric spaces.

Channel charting (CC) has been proposed recently to enable logical positioning of user equipments (UEs) in the neighborhood of a multi-antenna base-station solely from channel-state information (CSI). CC relies on dimensionality reduction of high-dimensional CSI features in order to construct a channel chart that captu…

Unified framework identifies nonlinear systems using characteristic curves and neural networks.

Given a group $G$ and a class of manifolds $\CC$ (e.g. symplectic, contact, Kähler etc), it is an old problem to find a manifold $M_G \in \CC$ whose fundamental group is $G$. This article refines it: for a group $G$ and a positive integer $r$ find $M_G \in \CC$ such that $π_1(M_G)=G$ and $π_i(M_G)=0$ for $1<i<r$. We th…

The study identifies core and satellite segments in the cryptocurrency market.

New scalars measure failure of CC metrics to solve singular Yamabe problem.

Investing in cryptocurrencies can improve portfolio risk-return profile, especially with diversification strategies.

The paper analyzes the risk of investing in a basket of 27 cryptocurrencies using statistical distributions.

GP CC-OPF solves uncertain power grid optimization with Gaussian Process.

Compressed Counting (CC) [22] was recently proposed for estimating the ath frequency moments of data streams, where 0 < a <= 2. CC can be used for estimating Shannon entropy, which can be approximated by certain functions of the ath frequency moments as a -> 1. Monitoring Shannon entropy for anomaly detection (e.g., DD…

Proposes Contrastive Clustering for improved clustering performance.

Paper explores robustness of CCS model for matrix completion.

We propose channel charting (CC), a novel framework in which a multi-antenna network element learns a chart of the radio geometry in its surrounding area. The channel chart captures the local spatial geometry of the area so that points that are close in space will also be close in the channel chart and vice versa. CC w…

Let X be a topological space, and let C(X) be the complex of singular cochains on X with real coefficients. We denote by Cc(X) the subcomplex given by continuous cochains, i.e. by such cochains whose restriction to the space of simplices (endowed with the compact-open topology) defines a continuous real function. We pr…

Introduces t-CCS for flexible tensor sampling.

This work is an investigation of perimeter measures in the metric measure space given by the Heisenberg group with Haar measure and a Carnot-Carathéodory metric, which is in general a sub-Finsler metric. Included is a reduction of Minkowski content in any CC-metric to an integral formula in terms of Lebesgue surface ar…

Inspired by recent works of Zang Liu, Alan Weinstein and Ping Xu, we introduce the notions of CC algebroids and non asymmetric Courant algebroids and study these structures. It is shown that CC algebroids of rank greater than 3 are the same as Courant algebroids up to a constant factor, though the definition of CC alge…

In construction projects, estimation of the settlement of fine-grained soils is of critical importance, and yet is a challenging task. The coefficient of consolidation for the compression index (Cc) is a key parameter in modeling the settlement of fine-grained soil layers. However, the estimation of this parameter is c…

We present two families of exterior differential systems (EDS) for non-isometric embeddings of orthonormal frame bundles over Riemannian spaces of dimension q = 2, 3, 4, 5.... into orthonormal frame bundles over flat spaces of sufficiently higher dimension. We have calculated Cartan characters showing that these EDS sa…

New attack strategy circumvents CC framework's defences in federated learning.

ETF on CRIX reduces crypto risk and diversifies growth.

Quantization and reduction for coisotropic A-branes on Hamiltonian manifolds.

Develops a machine learning approach for solving AC-OPF problems.

Proposes continuous convolution layers for flexible feature map resizing.

From a spray space $S$ on a manifold $M$ we construct a new geometric space $P$ of larger dimension with the following properties: 1. Geodesics in $P$ are in one-to-one correspondence with parallel Jacobi fields of $M$. 2. $P$ is complete if and only if $S$ is complete. 3. If two geodesics in $P$ meet at one point, the…

Recent networking research has identified that data-driven congestion control (CC) can be more efficient than traditional CC in TCP. Deep reinforcement learning (RL), in particular, has the potential to learn optimal network policies. However, RL suffers from instability and over-fitting, deficiencies which so far rend…

Establishes a condition for multiclass classification-calibration of Gamma-Phi losses.

CCs learn high-dimensional distributions from heterogeneous data.

Despite the success of ensemble classification methods in multi-class classification problems, ensemble methods based on approaches other than bagging have not been widely explored for multi-label classification problems. The Kalman Filter-based Heuristic Ensemble (KFHE) is an ensemble method that exploits the sensor f…

We study the geometry associated to the Grusin operator G=Δ_{x}+|x|^{2}\partial_{u}^{2} on \mathbb{R}_{x}^{n}\times\mathbb{R}_{u}, to obtain heat kernel estimates for this operator. The main work is to find the shortest geodesics connecting two given points in $\mathbb{R}^{n+1}$. This gives the Carnot-Caratheodory dist…

Classifier chain (CC) is a multi-label learning approach that constructs a sequence of binary classifiers according to a label order. Each classifier in the sequence is responsible for predicting the relevance of one label. When training the classifier for a label, proceeding labels will be taken as extended features. …

The paper develops techniques to study dynamical systems with Carnot metrics.

In this paper, we determine the maximally stable, rotationally invariant domains on the catenoids $\cC_a$ (minimal surfaces invariant by rotations) in the Heisenberg group with a left-invariant metric. We show that these catenoids have Morse index at least 3 and we bound the index from above in terms of the parameter $…

Large speech dataset for commercial use with 9.98% word error rate.

Neural networks have been proposed recently for positioning and channel charting of user equipments (UEs) in wireless systems. Both of these approaches process channel state information (CSI) that is acquired at a multi-antenna base-station in order to learn a function that maps CSI to location information. CSI-based p…

Cobordism and signatures of manifolds with similar fundamental groups.