Coderivatives and the Solution Map of a Linear Constraint System

2016 ◽  
Vol 26 (2) ◽  
pp. 986-1007 ◽  
Author(s):  
Duong Thi Kim Huyen ◽  
Nguyen Dong Yen
Keyword(s):  
Linear Constraint ◽  
Solution Map ◽  
Constraint System

scholarly journals Synchronous linear constraint system games

2021 ◽  
Vol 62 (3) ◽  
pp. 032201
Author(s):  
Adina Goldberg
Keyword(s):  
Linear Constraint ◽  
Constraint System

scholarly journals ATLAS: Automated Amortised Complexity Analysis of Self-adjusting Data Structures

2021 ◽  
pp. 99-122
Author(s):  
Lorenz Leutgeb ◽  
Georg Moser ◽  
Florian Zuleger
Keyword(s):  
Potential Function ◽  
Data Structures ◽  
Recent Progress ◽  
Complexity Analysis ◽  
Target Function ◽  
Linear Constraint ◽  
Potential Functions ◽  
Resource Analysis ◽  
Constraint System ◽  
Scalable Analysis

AbstractBeing able to argue about the performance of self-adjusting data structures such as splay trees has been a main objective, when Sleator and Tarjan introduced the notion of amortised complexity.Analysing these data structures requires sophisticated potential functions, which typically contain logarithmic expressions. Possibly for these reasons, and despite the recent progress in automated resource analysis, they have so far eluded automation. In this paper, we report on the first fully-automated amortised complexity analysis of self-adjusting data structures. Following earlier work, our analysis is based on potential function templates with unknown coefficients.We make the following contributions: 1) We encode the search for concrete potential function coefficients as an optimisation problem over a suitable constraint system. Our target function steers the search towards coefficients that minimise the inferred amortised complexity. 2) Automation is achieved by using a linear constraint system in conjunction with suitable lemmata schemes that encapsulate the required non-linear facts about the logarithm. We discuss our choices that achieve a scalable analysis. 3) We present our tool $$\mathsf {ATLAS}$$ ATLAS and report on experimental results for splay trees, splay heaps and pairing heaps. We completely automatically infer complexity estimates that match previous results (obtained by sophisticated pen-and-paper proofs), and in some cases even infer better complexity estimates than previously published.

scholarly journals A singular eigenvalue problem for the Dirichlet (p, q)-Laplacian

2021 ◽  
Author(s):  
Yunru Bai ◽  
Nikolaos S. Papageorgiou ◽  
Shengda Zeng
Keyword(s):  
Dirichlet Problem ◽  
Eigenvalue Problem ◽  
Positive Solution ◽  
Positive Solutions ◽  
Singular Term ◽  
Type Theorem ◽  
Solution Map ◽  
Continuity Properties ◽  
Variational Tools ◽  
Superlinear Reaction

AbstractWe consider a parametric nonlinear, nonhomogeneous Dirichlet problem driven by the (p, q)-Laplacian with a reaction involving a singular term plus a superlinear reaction which does not satisfy the Ambrosetti–Rabinowitz condition. The main goal of the paper is to look for positive solutions and our approach is based on the use of variational tools combined with suitable truncations and comparison techniques. We prove a bifurcation-type theorem describing in a precise way the dependence of the set of positive solutions on the parameter $$\lambda $$ λ . Moreover, we produce minimal positive solutions and determine the monotonicity and continuity properties of the minimal positive solution map.

scholarly journals On the linear ranking problem for integer linear-constraint loops

2013 ◽  
Vol 48 (1) ◽  
pp. 51-62 ◽  
Author(s):  
Amir M. Ben-Amram ◽  
Samir Genaim
Keyword(s):  
Linear Constraint ◽  
Ranking Problem

scholarly journals Modeling and Simulation of Thermo-Fluid-Electrochemical Ion Flow in Biological Channels

2015 ◽  
Vol 3 (1) ◽  
Author(s):  
Riccardo Sacco ◽  
Fabio Manganini ◽  
Joseph W. Jerome
Keyword(s):  
Driving Forces ◽  
The Novel ◽  
Thermodynamical Equilibrium ◽  
Finite Element Scheme ◽  
Equilibrium Conditions ◽  
Solution Map ◽  
Ion Flow ◽  
Stabilized Finite Element ◽  
A Cell ◽  
Biological Channels

AbstractIn this articlewe address the study of ion charge transport in the biological channels separating the intra and extracellular regions of a cell. The focus of the investigation is devoted to including thermal driving forces in the well-known velocity-extended Poisson-Nernst-Planck (vPNP) electrodiffusion model. Two extensions of the vPNP system are proposed: the velocity-extended Thermo-Hydrodynamic model (vTHD) and the velocity-extended Electro-Thermal model (vET). Both formulations are based on the principles of conservation of mass, momentum and energy, and collapse into the vPNP model under thermodynamical equilibrium conditions. Upon introducing a suitable one-dimensional geometrical representation of the channel,we discuss appropriate boundary conditions that depend only on effectively accessible measurable quantities. Then, we describe the novel models, the solution map used to iteratively solve them, and the mixed-hybrid flux-conservative stabilized finite element scheme used to discretize the linearized equations. Finally,we successfully apply our computational algorithms to the simulation of two different realistic biological channels: 1) the Gramicidin-A channel considered in [12]; and 2) the bipolar nanofluidic diode considered in [45].

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