scholarly journals A finite characterization of perfect equilibria

2021 ◽  
Author(s):  
Ivonne Callejas ◽  
Srihari Govindan ◽  
Lucas Pahl
Keyword(s):  
Algebraic Geometry ◽  
Real Algebraic Geometry ◽  
Recent Developments ◽  
Perfect Equilibria

AbstractGovindan and Klumpp [7] provided a characterization of perfect equilibria using Lexicographic Probability Systems (LPSs). Their characterization was essentially finite in that they showed that there exists a finite bound on the number of levels in the LPS, but they did not compute it explicitly. In this note, we draw on two recent developments in Real Algebraic Geometry to obtain a formula for this bound.

Neurochemistry of L-Glutamate Transport in the CNS: A Review of Thirty Years of Progress

2001 ◽  
Vol 66 (9) ◽  
pp. 1315-1340 ◽  
Author(s):  
Vladimir J. Balcar ◽  
Akiko Takamoto ◽  
Yukio Yoneda
Keyword(s):  
Molecular Biology ◽  
Glutamate Transport ◽  
Mammalian Brain ◽  
Activity Data ◽  
System A ◽  
Recent Developments ◽  
The Central Nervous System ◽  
Health And Disease ◽  
Disease Analysis

The review highlights the landmark studies leading from the discovery and initial characterization of the Na+-dependent "high affinity" uptake in the mammalian brain to the cloning of individual transporters and the subsequent expansion of the field into the realm of molecular biology. When the data and hypotheses from 1970's are confronted with the recent developments in the field, we can conclude that the suggestions made nearly thirty years ago were essentially correct: the uptake, mediated by an active transport into neurons and glial cells, serves to control the extracellular concentrations of L-glutamate and prevents the neurotoxicity. The modern techniques of molecular biology may have provided additional data on the nature and location of the transporters but the classical neurochemical approach, using structural analogues of glutamate designed as specific inhibitors or substrates for glutamate transport, has been crucial for the investigations of particular roles that glutamate transport might play in health and disease. Analysis of recent structure/activity data presented in this review has yielded a novel insight into the pharmacological characteristics of L-glutamate transport, suggesting existence of additional heterogeneity in the system, beyond that so far discovered by molecular genetics. More compounds that specifically interact with individual glutamate transporters are urgently needed for more detailed investigations of neurochemical characteristics of glutamatergic transport and its integration into the glutamatergic synapses in the central nervous system. A review with 162 references.

scholarly journals Molecular Modeling of Histamine Receptors—Recent Advances in Drug Discovery

Molecules ◽  
2021 ◽  
Vol 26 (6) ◽  
pp. 1778
Author(s):  
Pakhuri Mehta ◽  
Przemysław Miszta ◽  
Sławomir Filipek
Keyword(s):  
Central Nervous System ◽  
Nervous System ◽  
Molecular Modeling ◽  
Molecular Targets ◽  
Histamine Receptors ◽  
Experimental Characterization ◽  
Complex Disorders ◽  
Theoretical Investigations ◽  
Recent Developments

The recent developments of fast reliable docking, virtual screening and other algorithms gave rise to discovery of many novel ligands of histamine receptors that could be used for treatment of allergic inflammatory disorders, central nervous system pathologies, pain, cancer and obesity. Furthermore, the pharmacological profiles of ligands clearly indicate that these receptors may be considered as targets not only for selective but also for multi-target drugs that could be used for treatment of complex disorders such as Alzheimer’s disease. Therefore, analysis of protein-ligand recognition in the binding site of histamine receptors and also other molecular targets has become a valuable tool in drug design toolkit. This review covers the period 2014–2020 in the field of theoretical investigations of histamine receptors mostly based on molecular modeling as well as the experimental characterization of novel ligands of these receptors.

scholarly journals TOPOLOGICAL CELL DECOMPOSITION AND DIMENSION THEORY IN P-MINIMAL FIELDS

2017 ◽  
Vol 82 (1) ◽  
pp. 347-358 ◽  
Author(s):  
PABLO CUBIDES KOVACSICS ◽  
LUCK DARNIÈRE ◽  
EVA LEENKNEGT
Keyword(s):  
Algebraic Geometry ◽  
Open Subset ◽  
Cell Decomposition ◽  
Real Algebraic Geometry ◽  
Dimension Theory ◽  
Definable Set ◽  
Image Position ◽  
Definable Function

AbstractThis paper addresses some questions about dimension theory for P-minimal structures. We show that, for any definable set A, the dimension of $\bar A\backslash A$ is strictly smaller than the dimension of A itself, and that A has a decomposition into definable, pure-dimensional components. This is then used to show that the intersection of finitely many definable dense subsets of A is still dense in A. As an application, we obtain that any definable function $f:D \subseteq {K^m} \to {K^n}$ is continuous on a dense, relatively open subset of its domain D, thereby answering a question that was originally posed by Haskell and Macpherson.In order to obtain these results, we show that P-minimal structures admit a type of cell decomposition, using a topological notion of cells inspired by real algebraic geometry.

scholarly journals A Representation Theorem for Archimedean Quadratic Modules on ∗-Rings

2009 ◽  
Vol 52 (1) ◽  
pp. 39-52 ◽  
Author(s):  
Jakob Cimprič
Keyword(s):  
Algebraic Geometry ◽  
Representation Theory ◽  
Representation Theorem ◽  
Commutative Rings ◽  
Real Algebraic Geometry ◽  
New Approach ◽  
Noncommutative Version ◽  
Quadratic Modules ◽  
Rings With Involution ◽  
Associative Rings

AbstractWe present a new approach to noncommutative real algebraic geometry based on the representation theory of C*-algebras. An important result in commutative real algebraic geometry is Jacobi's representation theorem for archimedean quadratic modules on commutative rings. We show that this theorem is a consequence of the Gelfand–Naimark representation theorem for commutative C*-algebras. A noncommutative version of Gelfand–Naimark theory was studied by I. Fujimoto. We use his results to generalize Jacobi's theorem to associative rings with involution.

Characterization of tissue engineered cartilage products: Recent developments in advanced therapy

2016 ◽  
Vol 113 ◽  
pp. 823-832 ◽  
Author(s):  
Justinas Mačiulaitis ◽  
Sima Rekštytė ◽  
Arvydas Ūsas ◽  
Virginija Jankauskaitė ◽  
Rimtautas Gudas ◽  
...  
Keyword(s):  
Advanced Therapy ◽  
Recent Developments ◽  
Engineered Cartilage

Hilbert’s 17th Problem. Quadratic Forms in Real Algebraic Geometry

1998 ◽  
pp. 103-131
Author(s):  
Jacek Bochnak ◽  
Michel Coste ◽  
Marie-Françoise Roy
Keyword(s):  
Algebraic Geometry ◽  
Quadratic Forms ◽  
Real Algebraic Geometry ◽  
17Th Problem
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