arXiv research

Utilizing a weight matrix we study surfaces of prescribed weighted mean curvature which yield a natural generalisation to critical points of anisotropic surface energies. We first derive a differential equation for the normal of immersions with prescribed weighted mean curvature, generalising a result of Clarenz and vo…

The study examines constant weighted mean curvature hypersurfaces in shrinking Ricci solitons.

Derives integral formulae on weighted manifolds.

In this paper, we prove that a noncompact complete hypersurface with finite weighted volume, weighted mean curvature vector bounded in norm, and isometrically immersed in a complete weighted manifold is proper. In addition, we obtain an estimate for $f$-stability index of a constant weighted mean curvature hypersurface…

In this paper, we prove a classification for complete embedded constant weighted mean curvature hypersurfaces $Σ\subset\mathbb{R}^{n+1}$. We characterize the hyperplanes and generalized round cylinders by using an intrinsic property on the norm of the second fundamental form. Furthermore, we prove an equivalence of pro…

Let $Σ$ be a compact immersed surface with constant weighted mean curvature $H_f$ in a weighted manifold $(M^3,g,f)$. In this paper we obtain upper bounds for the first eigenvalue of the weighted Jacobi operator on $Σ$ in terms of $H_f$ and the curvature of the ambient. As consequence we obtain that there is no stable …

Optimal fuzzy classification aggregation functions are weighted means.

The paper explores rigidity of hypersurfaces with constant shifted curvature functions in hyperbolic space.

The paper studies hypersurfaces with constant weighted mean curvature in Gaussian space.

New method constructs synthetic treatment groups without mean exchangeability assumption.

Optimizes sparse mean-reverting portfolios for higher returns.

A new neural network model using weighted Lehmer means and multiplets.

It is well known that the out-of-sample performance of Markowitz's mean-variance portfolio criterion can be negatively affected by estimation errors in the mean and covariance. In this paper we address the problem by regularizing the mean-variance objective function with a weighted elastic net penalty. We show that the…

This letter presents an improved version of diffusion least mean ppower (LMP) algorithm for distributed estimation. Instead of sum of mean square errors, a weighted sum of mean square error is defined as the cost function for global and local cost functions of a network of sensors. The weight coefficients are updated b…

The classical $k$-means algorithm for partitioning $n$ points in $\mathbb{R}^d$ into $k$ clusters is one of the most popular and widely spread clustering methods. The need to respect prescribed lower bounds on the cluster sizes has been observed in many scientific and business applications. In this paper, we present an…

The paper proposes a method to improve forecast combination accuracy using portfolio theory.

Much of the focus in machine learning research is placed in creating new architectures and optimization methods, but the overall loss function is seldom questioned. This paper interprets machine learning from a multi-objective optimization perspective, showing the limitations of the default linear combination of loss f…

This paper extends liquidity returns in geometric mean markets to time-varying weights.

Investigates portfolio optimization with and without gearing constraints.

Clustering is a separation of data into groups of similar objects. Every group called cluster consists of objects that are similar to one another and dissimilar to objects of other groups. In this paper, the K-Means algorithm is implemented by three distance functions and to identify the optimal distance function for c…

The paper proves inequalities for star-shaped and $F$-mean convex hypersurfaces in $\mathbb{R}^{n+1}$.

Estimates multiple means in high dimensions using convex combinations.

Study of metrics on positive-definite matrices from power potential, linking to power means.

Combines VaR and ES forecasts from a large pool of methods.

Study introduces a new investment strategy model using lazy factor and probability weights.

The paper studies topological properties of Ricci shrinkers using weighted $L^2$ cohomology.

We challenge the longstanding assumption that the mean-field approximation for variational inference in Bayesian neural networks is severely restrictive, and show this is not the case in deep networks. We prove several results indicating that deep mean-field variational weight posteriors can induce similar distribution…

This paper presents a new fuzzy k-means algorithm for the clustering of high-dimensional data in various subspaces. Since high-dimensional data, some features might be irrelevant and relevant but may have different significance in the clustering process. For better clustering, it is crucial to incorporate the contribut…

Many leading classification algorithms output a classifier that is a weighted average of kernel evaluations. Optimizing these weights is a nontrivial problem that still attracts much research effort. Furthermore, explaining these methods to the uninitiated is a difficult task. Letting all the weights be equal leads to …

We propose the Lasso Weighted $k$-means ($LW$-$k$-means) algorithm as a simple yet efficient sparse clustering procedure for high-dimensional data where the number of features ($p$) can be much larger compared to the number of observations ($n$). In the $LW$-$k$-means algorithm, we introduce a lasso-based penalty term,…

The study proves topological rigidity for certain geometric shapes using Poincaré inequalities.

In this article, we study properly immersed complete noncompact submanifolds in a complete shrinking gradient Ricci soliton with weighted mean curvature vector bounded in norm. We prove that such a submanifold must have polynomial volume growth under some mild assumption on the potential function. On the other hand, if…

This paper describes a method for clustering data that are spread out over large regions and which dimensions are on different scales of measurement. Such an algorithm was developed to implement a robotics application consisting in sorting and storing objects in an unsupervised way. The toy dataset used to validate suc…

The paper proves a Harnack inequality for heat equations on Finsler metric measure manifolds.

Solves constant mean curvature Dirichlet problem on catenoids with improved estimates.

A feature-weighted mean shift algorithm improves clustering in high-dimensional data.

The current trend of pushing CNNs deeper with convolutions has created a pressing demand to achieve higher compression gains on CNNs where convolutions dominate the computation and parameter amount (e.g., GoogLeNet, ResNet and Wide ResNet). Further, the high energy consumption of convolutions limits its deployment on m…

The mean field algorithm is a widely used approximate inference algorithm for graphical models whose exact inference is intractable. In each iteration of mean field, the approximate marginals for each variable are updated by getting information from the neighbors. This process can be equivalently converted into a feedf…

Paper improves MIRACLE for faster, more robust neural network compression.

Decentralized optimization on dynamic manifolds with improved regret bound.

We prove two weighted geometric inequalities that hold for strictly mean convex and star-shaped hypersurfaces in Euclidean space. The first one involves the weighted area and the area of the hypersurface and also the volume of the region enclosed by the hypersurface. The second one involves the total weighted mean curv…

In this paper, we introduce a definition of $λ$-hypersurfaces of weighted volume-preserving mean curvature flow in Euclidean space. We prove that $λ$-hypersurfaces are critical points of the weighted area functional for the weighted volume-preserving variations. Furthermore, we classify complete $λ$-hypersurfaces with …

The study characterizes hypersurfaces in weighted cylinders and generalizes confinement properties.

As first noted in Korevaar, Kusner and Solomon ("KKS"), constant mean curvature implies a homological conservation law for hypersurfaces in ambient spaces with Killing fields.In Theorem 3.5 here, we generalize that law by relaxing the topological restrictions assumed in [KKS] and by allowing a weighted mean curvature f…

The paper proves rigidity results for self-shrinkers and surfaces with parallel weighted mean curvature.

We study in this paper the consequences of using the Mean Absolute Percentage Error (MAPE) as a measure of quality for regression models. We prove the existence of an optimal MAPE model and we show the universal consistency of Empirical Risk Minimization based on the MAPE. We also show that finding the best model under…

In this paper we prove general inequalities involving the weighted mean curvature of compact submanifolds immersed in weighted manifolds. As a consequence we obtain a relative linear isoperimetric inequality for such submanifolds. We also prove an extrinsic upper bound to the first non zero eigenvalue of the drift Lapl…

We obtain upper estimates for the bottom (that is, greatest lower bound) of the essential spectrum of weighted Laplacian operator of a weighted manifold under assumptions of the volume growth of their geodesic balls and spheres. Furthermore, we find examples where the equality occurs in the estimates obtained. As a con…