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Chain complex - Wikipedia, the free encyclopedia In mathematics, a chain complex is a construct originally used in the field of algebraic topology. In this case, chain complexes are studied axiomatically as algebraic structures. A weaker notion of equivalence of maps between chain complexes is that of a quasi-isomorphism, which is a chain map in which the induced map on homology is an isomorphism. en.wikipedia.org /wiki/Chain_complex   (827 words)

Complexes of Modules over Basic Algebras The homology of the complex in degree n is the quotient of the kernel of the n^(th) boundary map by the cokernel of the boundary map of degree n - 1. The splice of the complex C with the complex D along the map f from the last term of C to the first term of D. The degree of the last term of the splice is the same as the degree of the last term of the complex D. Extensions Given a complex C of modules over a basic algebra, returns the complex of length one greater that is obtained by adjoining the zero map from the zero module to the term of highest degree in the complex. www.umich.edu /~gpcc/scs/magma/text1013.htm   (1736 words)

Chain Maps A chain map from complex C to complex D is a sequence of homomorphisms between the terms of C and the terms of D such that the maps commute with the boundary homomorphisms on the two complexes. Returns the chain map given by the sequence of maps in Q. Each element in Q is a map from a term of the complex C to a corresponding term of the complex D. The integer n is the degree of the chain map. The long exact sequence on homology for the exact sequence of complexes given by the chain maps f and g as a chain complex with the homology group in degree i for the Cokernel of the complex C appearing in degree 3i. www.umich.edu /~gpcc/scs/magma/text1014.htm   (1337 words)

PlanetMath: homology of a chain complex The chain complex is an exact sequence if and only if all of the homology groups are trivial. The homology groups can therefore be thought of as measuring the extent to which the chain complex fails to be exact. This is version 13 of homology of a chain complex, born on 2002-12-10, modified 2006-11-29. planetmath.org /encyclopedia/HomologyChainComplex.html   (108 words)

Chain (algebraic topology) - Wikipedia, the free encyclopedia The boundary of a chain is the linear combination of boundaries of the simplices in the chain. Boundaries are cycles, so chains form a chain complex, whose homology groups (cycles modulo boundaries) are called simplicial homology groups. In differential geometry, the duality between the boundary operator on chains and the exterior derivative is expressed by the general Stokes' theorem. en.wikipedia.org /wiki/Chain_(algebraic_topology)   (312 words)

United Mitochondrial Disease Foundation - Medical Article List by Subject Issartel ; J.P. ; The ATP synthase (F0-F1) complex in oxidative phosphorylation ; Experientia ; 1992 ; 48(4) ; 351-62 Kretzschmar ; Hans A. ; Pyruvate Dehydrogenase Complex Deficiency as a Cause of Subacute Necrotizing Encephalopathy (Leigh Disease) ; Pediatrics ; 1987 ; 79(3) ; 370-3 Nyhan ; ; 2669 ; Lactic Acidemia--Deficiency of the Pyruvate Dehydrogenase Complex. biochemgen.ucsd.edu /umdf/resp-chain.htm   (12319 words)

DBL: Musings: Simple Gear, Complex Music The guitar, and indeed the guitarist, is needed only to provide a stimulus for the complex processing that occurs in a long chain of pedals or in a digital effects processor. If the player's expressiveness is limited by the signal chain, his playing will conform to the limitations of the chain. When the signal chain radically alters the timbre of the instrument, the player's fretting and picking touch is affected. psg.com /~dlamkins/Articles/simple-gear-complex-music.php?cat=musings   (614 words)

Algebraic Topology: Homology A chain complex (C,d) is a graded Abelian group C with fixed differential d of degree -1. A morphism of chain complexes (a chain map) is a morphism of graded Abelian groups that commutes with the differential. Exercise A simplicial complex K and its barycentric subdivision (that has as vertices the simplices of K, and as m-simplices the chains consisting of i-simplices of K for i=0,...,m, totally ordered by inclusion) are chain equivalent. www.win.tue.nl /~aeb/at/algtop-6.html   (3450 words)

Nuclear genetic defects of oxidative phosphorylation -- Shoubridge 10 (20): 2277 -- Human Molecular Genetics The four respiratory chain complexes and the ATP synthase complex are shown embedded in the inner mitochondrial membrane with the matrix side of the membrane at the bottom. in the assembly of the complex in the absence of this subunit Complex V, the ATP synthase, is composed of 16 subunits. hmg.oxfordjournals.org /cgi/content/full/10/20/2277   (6159 words)

GoldSim - Supply Chain Management Software The objective of supply chain simulation is to understand the dynamics of the system and ultimately to identify and evaluate strategies to minimize inefficiencies in the system. This is critical for supply chain simulation since discrete (usually disruptive) events, such as labor strikes, supplier bankruptcies, equipment failure, and power outages, can play a critical role in the flexibility, robustness, and overall performance of the supply chain. Complex models must be built using simulation software that allows the investigators to construct hierarchical multi-layer models that represent greater detail at lower levels in the model structure. www.goldsim.com /Solutions/WhitepapersHTML/SCM.htm   (3851 words)

InterPro: IPR000804 Clathrin adaptor complex, small chain   (Site not responding. Last check: 2007-10-14) The adaptor complexes are believed to interact with the cytoplasmic tails of membrane proteins, leading to their selection and concentration. In mammals two type of adaptor complexes are known, AP-1 which is associated with the Golgi complex and AP-2 which is associated with the plasma membrane. Both AP-1 and AP-2 are heterotetramers that consist of two large chains, the adaptins, (gamma and beta' in AP-1; alpha and beta in AP-2); a medium chain (AP47 in AP-1; AP50 in AP-2) and a small chain (AP19 in AP-1; AP17 in AP-2). www.ebi.ac.uk /interpro/IEntry?ac=IPR000804   (3291 words)

Supply Chain Management Transformation This new perspective, one that will continue to gain importance, sees all suppliers and customers as part of one complex supply chain network and understands that transforming that supply chain into a synchronized chain is the primary goal. Within the boardroom, improving supply chain management is getting lots of attention because forward-thinking management teams know it is the best strategy to increase and maintain market share while at the same time increasing profits. Good supply chain practitioners know that information should be passed on only to those who need to know it, when they need to know it, and in the form they need to have it in. www.rmdonovan.com /supply_chain_management.htm   (1391 words)

Springer Online Reference Works A cochain complex is defined in a dual manner (as a graded object with a morphism Most frequently, complexes are considered in categories of Abelian groups, modules or sheaves of Abelian groups on a topological space. Thus, a complex of Abelian groups is a graded differential group the differential of which has degree eom.springer.de /c/c024110.htm   (210 words)

Chain Homotopic Two chain maps (which are sort of like functions) are "chain homotopic" if there is an algebraic connection from one to the other. Assume f and g are homotopic chain maps acting on a chain c with subchain a. Since the homotopy equation holds for elements of c, it holds for coset representatives, and hence for cosets of a, so that the modified homomorphism d defines a chain homotopy connecting the chain maps f and g on the two relative chain complexes. www.mathreference.com /mod-hom,topy.html   (566 words)

Electron Transfer Chain that are part of the respiratory chain complex IV are often referred to as cytochromes a and a The structure and roles of complex III are discussed in the section on Axial ligands of the hemes in complex IV are histidine N atoms. www.rpi.edu /dept/bcbp/molbiochem/MBWeb/mb1/part2/redox.htm   (1414 words)

InterPro: IPR001392 Clathrin adaptor complex, medium chain   (Site not responding. Last check: 2007-10-14) The main components of the pits are clathrin, and the clathrin-associated protein complex, AP, (also known as assembly or adaptor proteins) [ 2 ]. Both trans-Golgi adaptor proteins, AP-1, and plasma membrane adaptor proteins, AP-2, are heterotetramers that consist of two large chains (beta' and gamma in AP-1, and alpha and beta in AP-2); a medium chain (AP47 in AP-1, and AP50 in AP-2); and a small chain (AP19 in AP-1, and AP17 in AP-2). The adaptor complexes are believed to couple clathrin lattices with particular membrane proteins by interacting with their cytoplasmic tails, leading to their selection and concentration: the medium chains regulate this process by self-phosphorylation via a mechanism that is still unclear [ 3 ]. www.ebi.ac.uk /interpro/IEntry?ac=IPR001392   (3225 words)

The CHomP Library: chomp/homology/homology.h Source File   (Site not responding. Last check: 2007-10-14) Each entry of the chain contains either a unit (an invertible 00048 // coefficient, whose "delta" function equals 1) or the corresponding 00049 // torsion coefficient. show (sout, "\tf", "x", "y"); 00170 return; 00171 } /* ShowHomology */ 00172 00173 // Show one generator of the homology module of a chain complex; 00174 // the generator is encoded in the given chain (note: numbers of generators 00175 // of the original chain complex are displayed increased by 1). All the boundary cells 00374 // must be present (use the function for pairs with an empty set A 00375 // or "X. addboundaries ()" to add boundaries if necessary), because 00376 // missing cells give rise to missing generators of the corresponding 00377 // chain complex which indicates a relative cubical complex. www.math.gatech.edu /~chomp/libdoc/homology_8h-source.html   (3345 words)

untitled Complex II actually contains the enzyme succinate dehydrogenase which catalyses the reduction of succinate to fumarate (which as we will see later is a reaction of the so called citric acid cycle). The electrons are passed down the chain with each component being reduced as it accepts the electrons and re-oxidised as it passes them on. The reaction takes place via the electron transport chain which allows the energy to be released in a controlled way making it available to do useful work. www.dentistry.leeds.ac.uk /biochem/lecture/etran/etran.htm   (1297 words)

Oxidative Phosphorylation: Chemiosmotic Coupling The respiratory chain is embedded in cristae of the in the half of the complex whose proteins are colored in shades of blue or green. Complex IV (Cytochrome Oxidase): As discussed in the section on the respiratory chain, www.rpi.edu /dept/bcbp/molbiochem/MBWeb/mb1/part2/oxphos.htm   (1538 words)

Chainalytics Asia-Pacific :: The Best Analytical Minds in Supply Chain Management Chainalytics utilizes these technologies to provide our customers with valuable solutions to solve their most complex problems in the areas of supply chain strategy, transportation planning, and inventory planning. This architecture and software technology is packaged as Supply Chain Guru, a highly effective tool for quantifying and mitigating risk throughout supply chains. Optiant is a pioneer in the emerging market of supply chain design and optimisation. www.chainalytics.com /apac/partners/solutionPartners.asp   (490 words)

The Tumor Suppressor cybL, a Component of the Respiratory Chain, Mediates Apoptosis Induction -- Albayrak et al. 14 ... Thirteen hours after starting the transfection, the mitochondria were isolated and complex II activity of the respiratory chain was assessed with succinate, which reduces dichlorophenylindophenol whose concentration was measured photometrically. Mutations in SDHD, a mitochondrial complex II gene, in hereditary paraganglioma. Higuchi, M., Proske, R.J., and Yeh, E.T. Inhibition of mitochondrial respiratory chain complex I by TNF results in cytochrome c release, membrane permeability transition, and apoptosis. www.molbiolcell.org /cgi/content/full/14/8/3082   (6877 words)

The Chain Complex   (Site not responding. Last check: 2007-10-14) Vygotsky (1962) labels this as the "chain complex". A child in this situation who knows that A is a soldier, would also call B and C a soldier. Similar to the Chain Complex, is the Associative Complex (also Vygotsky. bowland-files.lancs.ac.uk /chimp/langac/LECTURE7/7chain.htm   (103 words)

Automated Spectrophotometric Analysis of Mitochondrial Respiratory Chain Complex Enzyme Activities in Cultured Skin ... An evaluation of the measurement of the activities of complexes I-IV in the respiratory chain of human skeletal muscle mitochondria. Diagnosis of complex I deficiency in patients with lactic acidemia using skin fibroblast cultures. Analysis of the mitochondrial encoded subunits of complex I in 20 patients with a complex I deficiency. www.clinchem.org /cgi/content/full/51/11/2110   (3659 words)

Apoptotic Death in Leishmania donovani Promastigotes in Response to Respiratory Chain Inhibition: COMPLEX II INHIBITION ... Inhibition of Respiratory Chain Complexes I, II, and III Induces of respiratory chain complexes I, II, and III that alter the Complex II inhibition in combination with pentamidine treatment leads to increased apoptosis. www.jbc.org /cgi/content/full/279/12/11798   (6791 words)

Maternal smoking is associated with mitochondrial DNA depletion and respiratory chain complex III deficiency in ... Maternal smoking is associated with mitochondrial DNA depletion and respiratory chain complex III deficiency in placenta -- Bouhours-Nouet et al. Complex III activity was determined by measuring the reduction Enzymatic and polarographic measurements of the respiratory chain complexes. ajpendo.physiology.org /cgi/content/full/288/1/E171   (4922 words)

Apoptotic Death in Leishmania donovani Promastigotes in Response to Respiratory Chain Inhibition: COMPLEX II INHIBITION ... Inhibitors of respiratory chain complexes I, II, and concurrent inhibition of respiratory chain complex II with pentamidine complex II inhibition in parallel with pentamidine administration-enhanced www.jbc.org /cgi/content/abstract/279/12/11798   (364 words)

ChainComplex -- the class of all chain complexes The default display for a chain complex shows the modules and the stage at which they appear. Each object of class ChainComplex is called a chain complex. Each chain complex is also a member of class GradedModule. www.msri.org /about/computing/docs/macaulay/2-0.9/0227.html   (266 words)

dd -- differential in a chain complex   (Site not responding. Last check: 2007-10-14) -- a symbol used as a key in a chain complex, under which are stored the differentials. The differentials are stored as the members in a chain complex map of degree ChainComplex -- the class of all chain complexes www.stanford.edu /~mluciano/M2-help/0967.html   (90 words)

Mitochondrial pathways Disorders: Multisystem childhood encephalopathy with Complex I deficiency; Leigh syndrome Supercomplex of I, III, IV Stabilizes structure of Complex I Supercomplex of Complexes I, III, IV Association of Complexes III & IV may be stabilized by cardiolipin www.neuro.wustl.edu /neuromuscular/pathol/diagrams/mito.htm   (451 words)

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