Ulam Games, Łukasiewicz Logic, and AF C*-Algebras

1993 ◽  
Vol 18 (2-4) ◽  
pp. 151-161
Author(s):  
Daniele Mundici
Keyword(s):  
Search Space ◽  
Error Correcting Codes ◽  
Strong Unit ◽  
C Algebras ◽  
Finite Dimensional ◽  
Minimum Number ◽  
Boolean Search ◽  
Game Theoretic ◽  
The Relationship ◽  
Mv Algebras

Ulam asked what is the minimum number of yes-no questions necessary to find an unknown number in the search space (1, …, 2n), if up to l of the answers may be erroneous. The solutions to this problem provide optimal adaptive l error correcting codes. Traditional, nonadaptive l error correcting codes correspond to the particular case when all questions are formulated before all answers. We show that answers in Ulam’s game obey the (l+2)-valued logic of Łukasiewicz. Since approximately finite-dimensional (AF) C*-algebras can be interpreted in the infinite-valued sentential calculus, we discuss the relationship between game-theoretic notions and their C*-algebraic counterparts. We describe the correspondence between continuous trace AF C*-algebras, and Ulam games with separable Boolean search space S. whose questions are the clopen subspaces of S. We also show that these games correspond to finite products of countable Post MV algebras, as well as to countable lattice-ordered Specker groups with strong unit.

scholarly journals Nuclear subalgebras of UHF C*-algebras

1986 ◽  
Vol 29 (1) ◽  
pp. 97-100 ◽  
Author(s):  
R. J. Archbold ◽  
Alexander Kumjian
Keyword(s):  
Tensor Product ◽  
Inductive Limit ◽  
Inductive Limits ◽  
C Algebra ◽  
C Algebras ◽  
Finite Dimensional ◽  
The Family ◽  
Algebraic Tensor Product

A C*-algebra A is said to be approximately finite dimensional (AF) if it is the inductive limit of a sequence of finite dimensional C*-algebras(see [2], [5]). It is said to be nuclear if, for each C*-algebra B, there is a unique C*-norm on the *-algebraic tensor product A ⊗B [11]. Since finite dimensional C*-algebras are nuclear, and inductive limits of nuclear C*-algebras are nuclear [16];,every AF C*-algebra is nuclear. The family of nuclear C*-algebras is a large and well-behaved class (see [12]). The AF C*-algebras for a particularly tractable sub-class which has been completely classified in terms of the invariant K0 [7], [5].

scholarly journals Residents' Procedural Experience Does Not Ensure Competence: A Research Synthesis

2017 ◽  
Vol 9 (2) ◽  
pp. 201-208 ◽  
Author(s):  
Jeffrey H. Barsuk ◽  
Elaine R. Cohen ◽  
Joe Feinglass ◽  
William C. McGaghie ◽  
Diane B. Wayne
Keyword(s):  
Venous Catheter ◽  
Research Synthesis ◽  
Medical Procedure ◽  
Clinical Procedures ◽  
Simulated Performance ◽  
Northwestern University ◽  
Minimum Number ◽  
Overall Performance ◽  
Using Data ◽  
The Relationship

ABSTRACT Background Many medical certifying bodies require that a minimum number of clinical procedures be completed during residency training to obtain board eligibility. However, little is known about the relationship between the number of procedures residents perform and their clinical competence. Objective This study evaluated associations between residents' medical procedure skills measured in a simulation laboratory and self-reported procedure experience and year of training. Methods This research synthesis extracted and summarized data from multiple cohorts of internal medicine, emergency medicine, anesthesiology, and neurology resident physicians who performed simulated clinical procedures. The procedures were central venous catheter insertion, lumbar puncture, paracentesis, and thoracentesis. We compared residents' baseline simulated performance to their self-reported procedure experience using data from 7 research reports written by Northwestern University investigators between 2006 and 2016. We also evaluated how performance differed by postgraduate year (PGY). Results A total of 588 simulated procedures were performed during the study period. We found significant associations between passing the skills examinations and higher number of self-reported procedures performed (P = .011) and higher PGY (P < .001). However, performance for all procedures was poor, as only 10% of residents passed the assessments with a mean of 48% of checklist items correct (SD = 24.2). The association between passing the skills examination and year of training was mostly due to differences between PGY-1 and subsequent years of training. Conclusions Despite positive associations between self-reported experience and simulated procedure performance, overall performance was poor. Residents' clinical experience is not a proxy for skill.

scholarly journals Convergence Analysis of Particle Swarm Optimizer and Its Improved Algorithm Based on Velocity Differential Evolution

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Hongtao Ye ◽  
Wenguang Luo ◽  
Zhenqiang Li
Keyword(s):  
Particle Swarm Optimization ◽  
Differential Evolution ◽  
Particle Velocity ◽  
Particle Swarm ◽  
Search Space ◽  
Particle Swarm Optimizer ◽  
Swarm Optimization ◽  
Relationship Of ◽  
The Relationship ◽  
Improved Algorithm

This paper presents an analysis of the relationship of particle velocity and convergence of the particle swarm optimization. Its premature convergence is due to the decrease of particle velocity in search space that leads to a total implosion and ultimately fitness stagnation of the swarm. An improved algorithm which introduces a velocity differential evolution (DE) strategy for the hierarchical particle swarm optimization (H-PSO) is proposed to improve its performance. The DE is employed to regulate the particle velocity rather than the traditional particle position in case that the optimal result has not improved after several iterations. The benchmark functions will be illustrated to demonstrate the effectiveness of the proposed method.

Development of Game Theoretic Protocols for Multilevel Design

2010 ◽  
Author(s):  
Ayan Sinha ◽  
Farrokh Mistree ◽  
Janet K. Allen
Keyword(s):  
Game Theory ◽  
Decision Making ◽  
Geometric Modeling ◽  
Underwater Vehicle ◽  
Design Problems ◽  
Single Level ◽  
Engineering Teams ◽  
Game Theoretic ◽  
Multiple Levels ◽  
The Relationship

The effectiveness of the use of game theory in addressing multi-objective design problems has been illustrated. For the most part, researchers have focused on design problems at single level. In this paper, we illustrate the efficacy of using game theoretic protocols to model the relationship between multidisciplinary engineering teams and facilitate decision making at multiple levels. We will illustrate the protocols in the context of an underwater vehicle with three levels that span material and geometric modeling associated with microstructure mediated design of the material and vehicle.

scholarly journals Characteristic phenomena in combustion

1997 ◽  
Vol 1 (2) ◽  
pp. 147-159
Author(s):  
Dirk Meinköhn
Keyword(s):  
State Space ◽  
Reaction Diffusion ◽  
Stationary Solutions ◽  
The State ◽  
State Variable ◽  
Finite Dimensional ◽  
Dimensional State Space ◽  
Singularity Order ◽  
The Relationship ◽  
Stable Stationary Solutions

For the case of a reaction–diffusion system, the stationary states may be represented by means of a state surface in a finite-dimensional state space. In the simplest example of a single semi-linear model equation given. in terms of a Fredholm operator, and under the assumption of a centre of symmetry, the state space is spanned by a single state variable and a number of independent control parameters, whereby the singularities in the set of stationary solutions are necessarily of the cuspoid type. Certain singularities among them represent critical states in that they form the boundaries of sheets of regular stable stationary solutions. Critical solutions provide ignition and extinction criteria, and thus are of particular physical interest. It is shown how a surface may be derived which is below the state surface at any location in state space. Its contours comprise singularities which correspond to similar singularities in the contours of the state surface, i.e., which are of the same singularity order. The relationship between corresponding singularities is in terms of lower bounds with respect to a certain distinguished control parameter associated with the name of Frank-Kamenetzkii.

Exploring the combinatorial space of complete pathways to chemicals

2018 ◽  
Vol 46 (3) ◽  
pp. 513-522 ◽  
Author(s):  
Lin Wang ◽  
Chiam Yu Ng ◽  
Satyakam Dash ◽  
Costas D. Maranas
Keyword(s):  
De Novo ◽  
Design Procedure ◽  
Search Space ◽  
Performance Criterion ◽  
Mixed Integer ◽  
Design Tools ◽  
Minimum Number ◽  
Comprehensive Search ◽  
Synthetic Routes ◽  
Combinatorial Space

Computational pathway design tools often face the challenges of balancing the stoichiometry of co-metabolites and cofactors, and dealing with reaction rule utilization in a single workflow. To this end, we provide an overview of two complementary stoichiometry-based pathway design tools optStoic and novoStoic developed in our group to tackle these challenges. optStoic is designed to determine the stoichiometry of overall conversion first which optimizes a performance criterion (e.g. high carbon/energy efficiency) and ensures a comprehensive search of co-metabolites and cofactors. The procedure then identifies the minimum number of intervening reactions to connect the source and sink metabolites. We also further the pathway design procedure by expanding the search space to include both known and hypothetical reactions, represented by reaction rules, in a new tool termed novoStoic. Reaction rules are derived based on a mixed-integer linear programming (MILP) compatible reaction operator, which allow us to explore natural promiscuous enzymes, engineer candidate enzymes that are not already promiscuous as well as design de novo enzymes. The identified biochemical reaction rules then guide novoStoic to design routes that expand the currently known biotransformation space using a single MILP modeling procedure. We demonstrate the use of the two computational tools in pathway elucidation by designing novel synthetic routes for isobutanol.

The CCL7-CCL2-CCR2 Axis Regulates Age-Related Alterations in ADSCs 

2021 ◽  
Author(s):  
Keya Li ◽  
Guiying Shi ◽  
Xuepei Lei ◽  
Yiying Huang ◽  
Xinyue Li ◽  
...  
Keyword(s):  
Autologous Transplantation ◽  
Hippo Signaling ◽  
Related Disorder ◽  
Promising Strategy ◽  
Age Related ◽  
Minimum Number ◽  
And Function ◽  
The Relationship ◽  
Harmful Effects

Abstract Background and ObjectivesAdipose-tissue derived stem cells (ADSCs) autologous transplantation have been a promising strategy for aging-related disorder. But the relationship between ADSCs senescence and organismal aging were still no consistent conclusions. Toward this end, we analyzed the senescence properties of ADSCs from different age donors to furthermore understand the differences of cells between young and senile donors and verify the influence of organismal aging on the proliferation and function of ADSCs in vitro, providing the theoretical basis for the clinical application of autologous ADSCs transplantation.Methods and ResultsWe detected the characteristics, function, gene expression, apoptosis, cell cycle, SA-β-gal staining, and transcription features of ADSCs from 1-month mice and 20-month mice. ADSCs from old donors had some senescence-associated changes with less ability to proliferation than ADSCs from 1-month mice. Differentiation ability, cell surface markers, and SA-β-Gal staining did not differ across donor age, while cells exhibit a more remarkable age-related changes through continuous passages. According to the results of transcriptome analysis, the CCL7-CCL2-CCR2 axis and Hippo signaling pathway would be considered as its possible mechanisms. ConclusionsOur study reveals that ADSCs from old donors have some age-related alterations. The CCL7-CCL2-CCR2 which lies behind this change would be a potential target for gene therapy to reduce harmful effects of ADSCs from old donors. To make autologous transplantation work better, we would recommend that ADSCs should be cryopreserved in youth with minimum number of passages.

Moore Cohomology and Central Twisted Crossed Product C*-Algebras

1996 ◽  
Vol 48 (1) ◽  
pp. 159-174 ◽  
Author(s):  
Judith A. Packer
Keyword(s):  
Cohomology Group ◽  
Hausdorff Space ◽  
Countable Group ◽  
Equivalence Classes ◽  
Locally Compact ◽  
C Algebras ◽  
Integer Coefficients ◽  
Direct Sum ◽  
Cech Cohomology ◽  
The Relationship

AbstractLet G be a locally compact second countable group, let X be a locally compact second countable Hausdorff space, and view C(X, T) as a trivial G-module. For G countable discrete abelian, we construct an isomorphism between the Moore cohomology group Hn(G, C(X, T)) and the direct sum Ext(Hn-1(G), Ȟl(βX, Ζ)) ⊕ C(X, Hn(G, T)); here Ȟ1 (βX, Ζ) denotes the first Čech cohomology group of the Stone-Čech compactification of X, βX, with integer coefficients. For more general locally compact second countable groups G, we discuss the relationship between the Moore group H2(G, C(X, T)), the set of exterior equivalence classes of element-wise inner actions of G on the stable continuous trace C*-algebra C0(X) ⊗ 𝒦, and the equivariant Brauer group BrG(X) of Crocker, Kumjian, Raeburn, and Williams. For countable discrete abelian G acting trivially on X, we construct an isomorphism is the group of equivalence classes of principal Ĝ bundles over X first considered by Raeburn and Williams.

C* -Algebras of Real Rank Zero Whose K0's are not Riesz Groups

1996 ◽  
Vol 39 (4) ◽  
pp. 429-437 ◽  
Author(s):  
K. R. Goodearl
Keyword(s):  
Real Rank ◽  
Riesz Decomposition Property ◽  
Real Rank Zero ◽  
Decomposition Property ◽  
Rank Zero ◽  
C Algebras ◽  
Finite Dimensional ◽  
Riesz Decomposition ◽  
Stably Finite ◽  
The Riesz Decomposition Property

AbstractExamples are constructed of stably finite, imitai, separable C* -algebras A of real rank zero such that the partially ordered abelian groups K0(A) do not satisfy the Riesz decomposition property. This contrasts with the result of Zhang that projections in C* -algebras of real rank zero satisfy Riesz decomposition. The construction method also produces a stably finite, unital, separable C* -algebra of real rank zero which has the same K-theory as an approximately finite dimensional C*-algebra, but is not itself approximately finite dimensional.

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