相关论文: A bridge connecting convex analysis and complex an…
This is a survey article about $L^2$ estimates for the $\bar \partial$ operator. After a review of the basic approach that has come to be called the "Bochner-Kodaira Technique", the focus is on twisted techniques and their applications to…
We demonstrate how analysis of co-clustering in bipartite networks may be used as a bridge to connect, compare and complement clustering results about community structure in two different spaces: single-mode bipartite network projections.…
Convexification techniques have gained increasing interest over the past decades. In this work, we apply a recently developed convexification technique for fractional programs by He, Liu and Tawarmalani (2024) to the problem of determining…
Convexity is an important notion in non linear optimization theory as well as in infinite dimensional functional analysis. As will be seen below, very simple and powerful tools will be derived from elementary duality arguments (which are…
We treat the classical notion of convexity in the context of hard real analysis. Definitions of the concept are given in terms of defining functions and quadratic forms, and characterizations are provided of different concrete notions of…
In this paper, we present a converse to a version of Skoda's $L^2$ division theorem by investigating the solvability of $\bar{\partial}$ equations of a specific type.
In this paper, we extend the uniform $L^2$-estimate of $\bar{\partial}$-equations for flat nontrivial line bundles, proved for compact K\"ahler manifolds in the previous work, to compact complex manifolds. In the proof, by tracing the…
Testing a graph on 2-vertex- and 2-edge-connectivity are two fundamental algorithmic graph problems. For both problems, different linear-time algorithms with simple implementations are known. Here, an even simpler linear-time algorithm is…
It is well known that high energy data alone do not discriminate between asymptotic $\ln s$ and $\ln^2s$ behavior of $pp$ and $\bar pp$ cross sections. By exploiting high quality low energy data, analyticity resolves this ambiguity in favor…
The topics of Convexity and Concavity and Envelopes are central in Complex Analysis and extensively investigated. The aim of this paper is to find a possible counterpart in Algebraic Geometry. The article presents preliminary results on…
In the first part of this note, we review results concerning analytic characterization of convexity for planar sets. The second part is devoted to results valid for arbitrary $m \ge 2$.
The bridge regression estimator generalizes both ridge regression and LASSO estimators. Since it minimizes the sum of squared residuals with a $L_{\gamma }$ penalty, this estimator is typically not robust against outliers in the data. There…
Pattern classification with compact representation is an important component in machine intelligence. In this work, an analytic bridge solution is proposed for compressive classification. The proposal has been based upon solving a penalized…
This article is concerned with the Bridge Regression, which is a special family in penalized regression with penalty function $\sum_{j=1}^{p}|\beta_j|^q$ with $q>0$, in a linear model with linear restrictions. The proposed restricted bridge…
It is an old idea to replace averages of observables with respect to a complex weight by expectation values with respect to a genuine probability measure on complexified space. This is precisely what one would like to get from complex…
While sparse inverse covariance matrices are very popular for modeling network connectivity, the value of the dense solution is often overlooked. In fact the L2-regularized solution has deep connections to a number of important applications…
The importance of exploring a potential integration among surveys has been acknowledged in order to enhance effectiveness and minimize expenses. In this work, we employ the alignment method to combine information from two different surveys…
In this paper, we define a Dolbeault complex with weights according to normal crossings, which is a useful tool for studying the d-bar-equation on singular complex spaces by resolution of singularities (where normal crossings appear…
In the mixture of experts model, a common assumption is the linearity between a response variable and covariates. While this assumption has theoretical and computational benefits, it may lead to suboptimal estimates by overlooking potential…
We introduce a trick of dealing with $L^2$ estimates of $\bar{\partial}$ with singular weights on complete K\"ahler domains.