Search results for "monotonicity"
showing 10 items of 10 documents
Overview of Prognostic Systems for Hepatocellular Carcinoma and ITA.LI.CA External Validation of MESH and CNLC Classifications
2021
Simple Summary This review proposes a comprehensive overview of the main prognostic systems for HCC classified as prognostic scores, staging systems, or combined systems. Prognostic systems for HCC are usually compared in terms of homogeneity, monotonicity of gradients, and discrimination ability. However, despite the great number of published studies comparing HCC prognostic systems, it is rather difficult to identify a system that could be universally accepted as the best prognostic scheme for all HCC patients encountered in clinical practice. In order to give a contribute in this topic, we conducted a study aimed at externally validate the MESH score and the CNLC classification using the…
An Adaptive Alternating Direction Method of Multipliers
2021
AbstractThe alternating direction method of multipliers (ADMM) is a powerful splitting algorithm for linearly constrained convex optimization problems. In view of its popularity and applicability, a growing attention is drawn toward the ADMM in nonconvex settings. Recent studies of minimization problems for nonconvex functions include various combinations of assumptions on the objective function including, in particular, a Lipschitz gradient assumption. We consider the case where the objective is the sum of a strongly convex function and a weakly convex function. To this end, we present and study an adaptive version of the ADMM which incorporates generalized notions of convexity and penalty…
Monotonicity and enclosure methods for the p-Laplace equation
2018
We show that the convex hull of a monotone perturbation of a homogeneous background conductivity in the $p$-conductivity equation is determined by knowledge of the nonlinear Dirichlet-Neumann operator. We give two independent proofs, one of which is based on the monotonicity method and the other on the enclosure method. Our results are constructive and require no jump or smoothness properties on the conductivity perturbation or its support.
Stochastic monotonicity in intergenerational mobility tables
2010
SUMMARY The aim of this paper is to test for stochastic monotonicity in intergenerational socio-economic mobility tables. In other words, we question whether having a parent from a high socio-economic status is never worse than having one with a lower status. Using existing inferential procedures for testing unconditional stochastic monotonicity, we first test a set of 149 intergenerational mobility tables in 35 different countries and find that monotonicity cannot be rejected in hardly any table. In addition, we propose new testing procedures for testing conditional stochastic monotonicity and investigate whether monotonicity still holds after conditioning on a number of covariates such as…
Monotonicity and local uniqueness for the Helmholtz equation
2017
This work extends monotonicity-based methods in inverse problems to the case of the Helmholtz (or stationary Schr\"odinger) equation $(\Delta + k^2 q) u = 0$ in a bounded domain for fixed non-resonance frequency $k>0$ and real-valued scattering coefficient function $q$. We show a monotonicity relation between the scattering coefficient $q$ and the local Neumann-Dirichlet operator that holds up to finitely many eigenvalues. Combining this with the method of localized potentials, or Runge approximation, adapted to the case where finitely many constraints are present, we derive a constructive monotonicity-based characterization of scatterers from partial boundary data. We also obtain the local…
Least Energy Solutions with Sign Information for Parametric Double Phase Problems
2022
We consider a parametric double phase Dirichlet problem. In the reaction there is a superlinear perturbation term which satisfies a weak Nehari-type monotonicity condition. Using the Nehari manifold method, we show that for all parameters below a critical value, the problem has at least three nontrivial solutions all with sign information. The critical parameter value is precisely identified in terms of the spectrum of the lower exponent part of the differential operator.
Nonlinear scalar field equations with general nonlinearity
2018
Consider the nonlinear scalar field equation \begin{equation} \label{a1} -\Delta{u}= f(u)\quad\text{in}~\mathbb{R}^N,\qquad u\in H^1(\mathbb{R}^N), \end{equation} where $N\geq3$ and $f$ satisfies the general Berestycki-Lions conditions. We are interested in the existence of positive ground states, of nonradial solutions and in the multiplicity of radial and nonradial solutions. Very recently Mederski [30] made a major advance in that direction through the development, in an abstract setting, of a new critical point theory for constrained functionals. In this paper we propose an alternative, more elementary approach, which permits to recover Mederski's results on the scalar field equation. T…
Monotonicity Formulas for Harmonic Functions in RCD(0,N) Spaces
2023
We generalize to the RCD(0,N) setting a family of monotonicity formulas by Colding and Minicozzi for positive harmonic functions in Riemannian manifolds with nonnegative Ricci curvature. Rigidity and almost rigidity statements are also proven, the second appearing to be new even in the smooth setting. Motivated by the recent work in Agostiniani et al. (Invent. Math. 222(3):1033–1101, 2020), we also introduce the notion of electrostatic potential in RCD spaces, which also satisfies our monotonicity formulas. Our arguments are mainly based on new estimates for harmonic functions in RCD(K,N) spaces and on a new functional version of the ‘(almost) outer volume cone implies (almost) outer metric…
Multidimensional Health Modelling: Association between Socioeconomic Factors and Health in Latvia
2012
This paper proposes new approach for modelling self-assessed health. We find that the concept of health is too complicated to measure effects of health determinants using a one-dimensional econometric model. We apply two-dimensional stereotype logistic model that allows capturing nonmonotonicity in effects of factors and revealing significant effects that remain unrevealed if single dimension models, such as ordered logit or ordered probit, are used. Modelling self-assessed health using multi-dimensional stereotype logit provides higher model goodness of fit and quality measures in comparison to ordered probit model. Multi-dimensional stereotype logit is applied to estimate association betw…
Multidimensional health modeling: Association between socioeconomic and psychosocial factors and health in Latvia
2009
This research aims at estimating association between socioeconomic and psychosocial factors on the one hand and health in Latvia on the other hand. While information on association between socioeconomic determinants of population health in Latvia is scarce, effect of psychosocial resources on individual health in this country hasn’t been estimated before. We find empirical support for the association between different psychosocial factors and physical health in Latvia. This paper proposes new approach for modelling self-assessed health. We find that the concept of health is too complicated to measure effects of health determinants using a one-dimensional econometric model. We apply two-dime…