dablink This article is about the specific problem of determining whether a Hamiltonianpath or cycle exists in a given graph. For the general graph theory concepts, see Hamiltonianpath . In the mathematics mathematical field of graph theory the Hamiltonianpathproblem and the Hamiltonian cycle problem are problems of determining whether a Hamiltonianpath or a Hamiltonian cycle exists in a given ... are NP complete . The problem of finding a Hamiltonian cycle or path is in FNP complexity FNP . There is a simple relation between the two problems. The Hamiltonianpathproblem for graph G is equivalent to the Hamiltonian cycle problem in a graph H obtained from G by adding a new vertex and connecting it to all vertices of G . The Hamiltonian cycle problem is a special case of the travelling salesman problem , obtained by setting the distance between two cities to a finite constant if they are adjacent and infinity otherwise. The directed and undirected Hamiltonian cycle problems were two ... his work on solving a 7 vertex instance of the HamiltonianPathProblem using a DNA computing DNA ... pathproblem using three locations . ref name Guard http www.jbioleng.org content 3 1 11 ref Hamiltonian ... 1045 5 A1.3 GT37&ndash 39, pp. 199&ndash 200. Refend DEFAULTSORT HamiltonianPathProblem Category ... Hamiltonian cycle problem remains NP complete for planar graph s and the undirected Hamiltonian cycle problem remains NP complete for cubic graph cubic planar graphs. Algorithms A trivial heuristic algorithm for locating Hamiltonian paths is to construct a path abc... and extend it until no longer possible when the path abc...xyz cannot be extended any longer because all neighbours of z already ... neighbour of y if no choice produces a Hamiltonianpath, then one takes a further step back, removing ... will certainly find an Hamiltonianpath if any but it runs in exponential time. Some algorithms ... path will eventually be found. Solving the problem Due to the complexity of the problem computers ... more details
in the knight s graph Hamiltonianpathproblem , the computational problem of finding Hamiltonian ...dablink This article is about the overall graph theory concept of a Hamiltonianpath. For the specific problem of determining whether a Hamiltonianpath or cycle exists in a given graph, see Hamiltonianpathproblem . Image Hamiltonian path.svg right thumb A Hamiltonian cycle in a dodecahedron . Like all platonic solid s, the dodecahedron is Hamiltonian. Image Herschel graph.svg thumb The Herschel graph is the smallest possible polyhedral graph that does not have a Hamiltonian cycle. In the mathematics mathematical field of graph theory , a Hamiltonianpath or traceable path is a path graph theory path in an undirected graph that visits each vertex graph theory vertex exactly once. A Hamiltonian cycle or Hamiltonian circuit is a Hamiltonianpath that is a cycle graph theory cycle . Determining whether such paths and cycles exist in graphs is the Hamiltonianpathproblem , which is NP complete problem NP complete . Hamiltonian paths and cycles are named after William Rowan Hamilton who invented the Icosian game , now also known as Hamilton s puzzle , which involves finding a Hamiltonian ... volume 13 year 1981 . ref Definitions A Hamiltonianpath or traceable path is a path graph theory path that visits each vertex exactly once. A graph that contains a Hamiltonianpath is called ... path between the two vertices. A Hamiltonian cycle , Hamiltonian circuit , vertex tour or graph ... September 2011 Properties Any Hamiltonian cycle can be converted to a Hamiltonianpath by removing one of its edges, but a Hamiltonianpath can be extended to Hamiltonian cycle only if its endpoints ... is Hamiltonian if and only if it is Strongly connected component strongly connected . The problem ... a Hamiltonianpath in a permutohedron Tait s conjecture now known false that 3 regular polyhedral graph s are Hamiltonian Travelling salesman problem refend Notes reflist References Citation last1 ... more details
all the vertices of the graph without repetition, and this is a Hamiltonianpath by definition. Since the Hamiltonianpathproblem is NP complete, this reduction shows that this problem is NP hard ... pathproblem is the problem of finding a simple path of maximum length in a given graph. A path is called simple if it does not have any repeated vertices. Unlike the shortest pathproblem , which asks for the shortest path between two vertices and can be solved in polynomial time in graphs without negative weight cycles, the decision version of this problem is NP complete , which means that the optimal ... version of this problem asks whether the graph contains a simple path of length greater than or equal to k , where the length of a path is defined to be the number of Edge geometry edges along the path. NP completeness The NP completeness of the decision problem can be shown using a reduction from the Hamiltonianpathproblem . Clearly, if a certain general graph has a Hamiltonianpath, this Hamiltonianpath is the longest path possible, as it traverses all possible vertices. To solve the Hamiltonianpathproblem using an algorithm for the longest pathproblem, we use the algorithm for the longest pathproblem on the same input graph and set k V 1, where V is the number of vertices in the graph. If there is a Hamiltonianpath in the graph, then the algorithm will return yes , since the Hamiltonian ... k . Relation to the shortest pathproblem The longest pathproblem can be reduced to the shortest pathproblem although the graph may have negative weight cycles , by exploiting the duality of optimizations ... graph to the longest pathproblem is G , the shortest simple path on the graph H , which is exactly ... on H to solve the original problem in polynomial time. Thus the longest pathproblem is easy on acyclic graphs. Algorithms for acyclic graphs As mentioned above, the longest pathproblem on acyclic ... vertex 6 marked If G is a directed acyclic graph , the longest pathproblem on G can be solved in linear ... more details
theory , the shortest pathproblem is the problem of finding a path graph theory path between ... mathematics Mixed graph mixed . For undirected graphs, the shortest pathproblem can be formally ... connecting v to v . The problem is also sometimes called the single pair shortest pathproblem , to distinguish it from the following variations The single source shortest pathproblem , in which ... destination shortest pathproblem , in which we have to find shortest paths from all vertices in the directed ... pathproblem by reversing the arcs in the directed graph. The all pairs shortest pathproblem , in which ... problem is sometimes called the min delay pathproblem and usually tied with a widest pathproblem ... problems in computational geometry , see Euclidean shortest path . The traveling salesman problem travelling salesman problem is the problem of finding the shortest path that goes through every vertex exactly once, and returns to the start. Unlike the shortest pathproblem, which can be solved in polynomial ... . The problem of Longest pathproblem finding the longest path in a graph is also NP complete. The Canadian traveller problem and the stochastic shortest pathproblem are generalizations where either ..., 2006, pp. 68 75. Verify source date June 2009 ref The widest pathproblem seeks a path so that the minimum ... linear programming formulation for the shortest pathproblem, given below. It is very trivial compared ... shortest pathproblem author D. Frigioni coauthors A. Marchetti Spaccamela and U. Nanni year 1998 booktitle ... path lt Trumpiausio kelio problema ja pl Problem najkr tszej cie ki pt Problema do caminho ... number real valued weight function f E R , and elements v and v of V , find a path ... pair shortest path algorithm on all relevant pairs of vertices. Algorithms The most important algorithms for solving this problem are Dijkstra s algorithm solves the single source shortest path problems. Bellman Ford algorithm solves the single source problem if edge weights may be negative. A search ... more details
s, the widest pathproblem , also known as the bottleneck shortest pathproblem or the maximum capacity pathproblem , is the problem of finding a path graph theory path between two designated vertex ... between two routers, the widest pathproblem is the problem of finding an end to end path between ... ref The weight of the minimum weight edge is known as the capacity or bandwidth of the path. As well as its applications in network routing, the widest pathproblem is also an important .... A closely related problem, the minimax pathproblem , asks for the path that minimizes the maximum ... pathproblem can be transformed into an algorithm for the minimax pathproblem, or vice versa, by reversing ... punnen citation title A linear time algorithm for the maximum capacity pathproblem first Abraham ... shortest pathproblem first1 Volker last1 Kaibel first2 Matthias A. F. last2 Peinhardt series ZIB ... be found simultaneously. All pairs The all pairs widest pathproblem has applications in the Schulze ... of the edge with position mvar i in the sorted order. This method allows the widest pathproblem ... flow problem . Repeatedly augmenting a flow along a maximum capacity path in the residual network ... Science FOCS 2002 year 2002 . ref Euclidean point sets A variant of the minimax pathproblem ...File CPT Graphs undirected weighted.svg thumb 240px In this graph, the widest path from Maldon to Feering ... in the path. For instance, if the graph represents connections between Router computing router s in the internet ... flow s. ref name amo It is possible to adapt most shortest path algorithms to compute widest paths, by modifying them to use the bottleneck distance instead of path length. ref citation title The maximum ... issue 2 journal Transportation Science pages 115 122 title Optimal Minimax Path of a Single Service ... every edge weight by its negation. Undirected graphs In an undirected graph , a widest path may be found as the path between the two vertices in the minimum spanning tree maximum spanning tree of the graph ... more details
Hamiltonian may refer to In mathematics after William Rowan Hamilton the term Hamiltonian refers to any energy function defined by a Hamiltonian vector field , a particular vector field on a symplectic manifold more specifically, as an adjective it is used in the phrases Hamiltonian system Hamiltonianpath , in graph theory Hamiltonian cycle, a special case of a HamiltonianpathHamiltonian group , in group theory Hamiltonian control theory Hamiltonian matrix Hamiltonian flow Hamiltonian vector field Quaternions Hamiltonian numbers or quaternions In physics after William Rowan Hamilton Hamiltonian system Hamiltonian mechanics in classical mechanics Hamilton s principle Hamilton Jacobi equation Hamilton Jacobi Bellman equation Hamiltonian quantum mechanics Molecular HamiltonianHamiltonian constraint Hamiltonian fluid mechanics Hamiltonian lattice gauge theory Hamiltonian vector field In Chemistry Molecular Hamiltonian Dyall Hamiltonian In Language Hamiltonian method http www.theamericanscholar.org the new old way of learning languages Other uses Hamiltonian economic program as put forward by the eighteenth century American politician Alexander Hamilton a demonym for a person from any of several places named Hamilton . See also William Rowan Hamilton disambig Category Mathematical disambiguation ar de Hamiltonian es Hamiltoniano fr Hamiltonien gl Hamiltoniano it Hamiltoniano lt Hamiltonianas ... more details
The Hamiltonian completion problem is to find the minimal number of edges to add to a graph mathematics graph to make it Hamiltonian graph Hamiltonian . The problem is clearly NP hard in general case since its solution gives an answer to the NP complete problem of determining whether a given graph has a Hamiltonian cycle . The associated decision problem of determining whether K edges can be added to a given graph to produce a Hamiltonian graph is NP complete. Moreover, Hamiltonian completion belongs to the APX complexity class , i.e., it is unlikely that efficient constant ratio approximation algorithms exist for this problem. ref Q. S. Wu, C. L. Lu, R. C. T. Lee, http www.springerlink.com content 103cnuhn3aknv262 An Approximate Algorithm for the Weighted HamiltonianPath Completion Problem on a Tree , Lecture Notes in Computer Science , Vol. 1969 2000 Pages 156 167 ref The problem may be solved in polynomial time for certain classes of graphs, including series parallel graph s ref K. Takamizawa, T. Nishizeki, and N. Saito, Linear Time Computability of Combinatorial Problems on Series Parallel Graphs, J. ACM 29 1982 623 641 ref and their generalizations ref N. M. Korneyenko, Combinatorial algorithms on a class of graphs, Discrete Applied Mathematics , v.54 n.2 3, p.215 217, 1994 ref , which include outerplanar graph s, as well as for a line graph of a tree ref Arundhati Raychaudhuri ... The total interval number of a tree and the Hamiltonian completion number of its line graph , Information .... Meloni, D. Pacciarelli, http portal.acm.org citation.cfm?id 381021 A linear algorithm for the Hamiltonian ... citation.cfm?id 975923&dl GUIDE&coll GUIDE&CFID 13226110&CFTOKEN 18722093 A linear algorithm for the Hamiltonian ... 136 , Issue 2 3 February 2004 197 215 ref Gamarnik et al. use a linear time algorithm for solving the problem ... s to make them Hamiltonian. ref David Gamarnik, Maxim Sviridenko, http www.mit.edu gamarnik Papers HamCompletionPublished.pdf Hamiltonian completions of sparse random graphs , Discrete Applied Mathematics ... more details
Introduction to Hamiltonian dynamical systems and the math N body problem publisher Springer Science ...In mathematics , a Hamiltonian matrix math A is any real math 2 n 2 n matrix mathematics matrix math A that satisfies the condition that math KA is symmetric matrix symmetric , where math K is the skew symmetric matrix math K begin bmatrix 0 & I n I n & 0 end bmatrix math and math I sub n sub is the math n n identity matrix . In other words, math A is Hamiltonian if and only if math KA A T K T KA A T K 0. , math In the vector space of all math 2 n 2 n matrices, Hamiltonian matrices form a subspace of dimension math 2 n sup 2 sup n . Properties Let math M be a math 2 n 2 n block matrix given by math ... n n matrices. Then math M is a Hamiltonian matrix provided that the matrices math B and math C are symmetric, and that math 1 A D sup T sup 0 . The matrix transpose transpose of a Hamiltonian matrix is Hamiltonian. The trace linear algebra trace of a Hamiltonian matrix is zero. The commutator of two Hamiltonian matrices is Hamiltonian. The eigenvalues of any Hamiltonian matrix are symmetric about the imaginary axis. The space of all Hamiltonian matrices is a Lie algebra math mathfrak Sp 2n math ... 1 pages 291 307 . ref Hamiltonian operators Let math V be a vector space, equipped with a symplectic form math . A linear map math A V mapsto V math is called a Hamiltonian operator with respect to math ... , such that math is written as math sum i e i wedge e n i math . A linear operator is Hamiltonian with respect to math if and only if its matrix in this basis is Hamiltonian. ref citation first William ... of alternating Hamiltonian matrices journal Linear Algebra and its Applications volume 396 ... of a Hamiltonian matrix is skew Hamiltonian matrix skew Hamiltonian . An exponential of a Hamiltonian matrix is symplectic matrix symplectic , and a logarithm of a symplectic matrix is Hamiltonian. See ... September 2010 DEFAULTSORT Hamiltonian Matrix Category Matrices fr Matrice hamiltonienne it Matrice ... more details
Unreferenced stub auto yes date December 2009 About the classical theory Hamiltonian disambiguation Hamiltonian In physics and classical mechanics , a Hamiltonian system is a physical system in which force s are momentum Invariant physics invariant . Hamiltonian systems are studied in Hamiltonian mechanics . In mathematics , a Hamiltonian system is a system of differential equation s which can be written in the form of Hamilton s equations . Hamiltonian systems are usually formulated in terms of Hamiltonian vector field s on a symplectic manifold or Poisson manifold . Hamiltonian systems are a special case of dynamical system s. Examples Dynamical billiards Planetary system s Canonical general relativity See also Action angle coordinates Liouville s theorem Hamiltonian Liouville s theorem Integrable system Further Reading Treschev, D., & Zubelevich, O. 2010 . Introduction to the perturbation theory of Hamiltonian systems. Heidelberg Springer Audin, M., & Babbitt, D. G. 2008 . Hamiltonian systems and their integrability. Providence, R.I American Mathematical Society. Zaslavsky, G. M. 2007 . The physics of chaos in Hamiltonian systems. London Imperial College Press. Dickey, L. A. 2003 . Soliton equations and Hamiltonian systems. Advanced series in mathematical physics, v. 26. River Edge, NJ World Scientific. Almeida, A. M. 1992 . Hamiltonian systems Chaos and quantization. Cambridge monographs on mathematical physics. Cambridge u.a. Cambridge Univ. Press. DEFAULTSORT Hamiltonian System Category Hamiltonian mechanics Classicalmechanics stub ru zh ... more details
Classical mechanics cTopic Formulations Hamiltonian mechanics is a reformulation of classical mechanics ... spaces see Mathematical formalism Mathematical formalism , below . The Hamiltonian method differs ... Citation last1 LaValle first1 Steven M. chapter 13.4.4 Hamiltonian mechanics chapter url http planning.cs.uiuc.edu ... provide a convenient way of solving a particular problem in classical mechanics. Also ... to quantum mechanics as understood through Hamiltonian mechanics, as well as its connection to other areas of science. Simplified overview of uses The value of the Hamiltonian is the total energy ... section03.html chapter 16.3 The Hamiltonian title MIT OpenCourseWare website 18.013A accessdate February ... mathbf q , mathbf p ,t math is the scalar valued Hamiltonian function , and specify the domain of values ... the solutions cannot be found exactly the many body problem . It is still possible to obtain qualitative ... system consisting of one particle of mass m under time independent boundary conditions The Hamiltonian ... by inverting the expressions in the previous step. The Hamiltonian is calculated using the usual ... partial mathcal L partial t mathrm d t ,. math The term on the left hand side is just the Hamiltonian ... variables understood to represent all N variables of that type. Hamiltonian mechanics ... symplectic manifold . The Hamiltonian is the Legendre transformation Legendre transform of the Lagrangian ... of motion of Hamiltonian mechanics, known as the canonical equations of Hamilton math frac partial mathcal ... does not occur in the Hamiltonian, the corresponding momentum is conserved, and that coordinate can be ignored in the other equations of the set. Effectively, this reduces the problem ... isbn 0201657023 ref The Lagrangian and Hamiltonian approaches provide the groundwork for deeper results in the theory of classical mechanics, and for formulations of quantum mechanics. Geometry of Hamiltonian systems A Hamiltonian system may be understood as a fiber bundle E over time R , with the Level ... more details
math . A different approach to solving this problem consists in defining a Hamiltonian taking a Legendre ... A mathbf p cdot d mathbf s 0 math Image Hamiltonian Optics Optical Path Length.png 200px thumb right ... Netherlands, 2011 ISBN 978 0792375821 ref and Hamiltonian optics ref name IntroductionHO H. A. Buchdahl, An Introduction to Hamiltonian Optics , Dover Publications, 1993 ISBN 978 0486675978 ref are two ... mechanics and Hamiltonian mechanics . Hamilton s principle main Hamilton s principle In physics ... a new set of differential equations Hamiltonian mechanics Deriving Hamilton s equations can be derived ... as in Hamiltonian mechanics, only with time t now replaced by a general parameter &sigma ... s, while Euler Lagrange s equations are second order. Lagrangian and Hamiltonian optics The general ... that the optical length of the path followed by light between two fixed points, A and B , is an extremum ... now that light travels along the x sub 3 sub axis, the path of a light ray may be parametrized ... x 2 2 math is the optical Lagrangian and math dot x k dx k dx 3 math . The optical path length OPL ... refractive index as a function of position along the path between points A and B . The Euler ... 2 n frac dx k ds math Image Hamiltonian Optics Optical Momentum.png 200px thumb right Optical momentum ... index optic the path of the light ray is curved and vector p is tangent to the light ray. The expression for the optical path length can also be written as a function of the optical momentum. Having ... math and the expression for the optical path length is math S int L , dx 3 int mathbf p cdot d mathbf s math Hamilton s equations Similarly to what happens in Hamiltonian mechanics , also in optics the Hamiltonian ..., only p sub 3 sub changes from p sub 3 A sub to p sub 3 B sub . Image Hamiltonian Optics Refraction.png ... mathbf i cdot mathbf n right mathbf n math Rays and wavefronts From the definition of optical path length ... int frac dp k dx 3 , dx 3 p k math Image Hamiltonian Optics Rays and Wavefronts.png 200px thumb left ... more details
of the Coulomb Hamiltonian first devised by Born Oppenheimer approximation Born and Oppenheimer . The nuclear kinetic energy terms are omitted from the Coulomb Hamiltonian and one considers the remaining Hamiltonian as a Hamiltonian of electrons only. The stationary nuclei enter the problem ... wavefunctions the electronic problem is solved with the clamped nucleus Hamiltonian arising in the first ...In atomic, molecular, and optical physics and quantum chemistry , the molecular Hamiltonian is the Hamiltonian quantum mechanics Hamiltonian operator representing the energy of the electron s and Atomic ... Hamiltonian is a sum of several terms its major terms are the kinetic energy kinetic energies of the electrons ... particles. The Hamiltonian that contains only the kinetic energies of electrons and nuclei, and the Coulomb interactions between them, is known as the Coulomb Hamiltonian . From it are missing a number ... Hamiltonian will predict most properties of the molecule, including its shape three dimensional structure , calculations based on the full Coulomb Hamiltonian are very rare. The main reason ... way. Within this framework the molecular Hamiltonian has been simplified to the so called clamped nucleus Hamiltonian , also called electronic Hamiltonian , that acts only on functions of the electronic coordinates. Once the Schr dinger equation of the clamped nucleus Hamiltonian has been solved ... Coulomb Hamiltonian that depends on the electrons is replaced by the potential energy surface. This converts the total molecular Hamiltonian into another Hamiltonian that acts only on the nuclear ... the internal atomic vibration s enter the problem. Further, for molecules larger than triatomic ... motion Hamiltonian . Making the harmonic approximation, we can convert the Hamiltonian into a sum ... fixed frame the Hamiltonian accounts for rotation , translation and vibration of the nuclei. Since Watson introduced in 1968 an important simplification to this Hamiltonian, it is often referred ... more details
No footnotes date April 2009 In loop quantum gravity , dynamics such as time evolutions of fields are controlled by the Hamiltonian constraint . The identity of the Hamiltonian constraint is a major open question in quantum gravity , as is extracting of physical observables from any such specific constraint. The Thomas Thiemann Thiemann Operator physics operator has been proposed as such a constraint. Although this operator defines a complete and consistent quantum theory, doubts have been raised as to the physical reality of this theory due to inconsistencies with classical general relativity the quantum constraint algebra closes, but it is not isomorphic to the classical constraint algebra of GR, which is seen as circumstantial evidence of inconsistencies definitely not a proof of inconsistencies , and so variants have been proposed. External links http relativity.livingreviews.org open?pubNo lrr 1998 1&page node27.html Overview by Carlo Rovelli http arxiv.org abs gr qc 9606088 Thiemann s paper in Physics Letters http arxiv.org pdf gr qc 9710008 Good information on LQG Category Loop quantum gravity quantum stub ... more details
unreferenced date January 2010 Unreferenced stub auto yes date December 2009 Orphan date December 2009 In quantum chemistry , the Dyall Hamiltonian is a modified Hamiltonian quantum mechanics Hamiltonian with two electron nature. It can be written as follows math hat mathcal H D hat mathcal H D i hat mathcal H D v C math math hat mathcal H D i sum i rm core epsilon i E ii sum r rm virt epsilon r E rr math math hat mathcal H D v sum ab rm act h ab rm eff E ab frac 1 2 sum abcd rm act left langle ab left. right cd right rangle left E ac E bd delta bc E ad right math math C 2 sum i rm core h ii sum ij rm core left 2 left langle ij left. right ij right rangle left langle ij left. right ji right rangle right 2 sum i rm core epsilon i math math h ab rm eff h ab sum j left 2 left langle aj left. right bj right rangle left langle aj left. right jb right rangle right math where labels math i,j, ldots math , math a,b, ldots math , math r,s, ldots math denote core, active and virtual orbitals see Complete active space respectively, math epsilon i math and math epsilon r math are the orbital energies of the involved orbitals, and math E mn math operators are the spin traced operators math a dagger m alpha a n alpha a dagger m beta a n beta math . These operators commute with math S 2 math and math S z math , therefore the application of these operators on a spin pure function produces again a spin pure function. The Dyall Hamiltonian behaves like the true Hamiltonian inside the CAS space, having the same eigenvalues and eigenvectors of the true Hamiltonian projected onto the CAS space. Category Quantum chemistry Chem stub it Hamiltoniano di Dyall ... more details
indicates Hamiltonian elements as well. Infanticide is a biologically spiteful action in that it costs ... DEFAULTSORT Hamiltonian Spite Category Evolution Category Selection Category Human behavior Category ... more details
About uses of path and pathway the acronym PATHPATH disambiguation PATH wiktionarypar path pathway TOC right Path , pathway or PATH may refer to Path Course navigation , the intended path of a vehicle over the surface of the Earth Trail , hiking trail , footpath , or bridle path See also Track disambiguation Footpath disambiguation Shining Path , Maoist guerrilla insurgent organization in Peru Sidewalk running along the edge of a road, in some varieties of English Bicycle path or bikeway way Golden Path Dune , a metaphysical theme from Frank Herbert s Dune novels Path Vol.2 is a 2000 single by Apocalyptica from their album Cult Mathematics Path graph theory , a sequence of vertices of a graph Path topology , a continuous function Computing Path computing , in computer file systems, the human readable address of a resource PATH variable , an environment variable specifying a list of directories where executable programs are located Path social network , a social networking enabled photo sharing and messaging service Clipping path , a computer image outlining option to remove background and create transparency Control flow path, a possible execution sequence in a program often depicted as a sequence of edges in a control flow graph The st connectivity problem is sometimes known as the pathproblem. Pathway Biology Genetic pathway , a group of genes interacting to form an aggregate biological function Metabolic pathway , a series of chemical reactions within a cell Signal transduction Signalling pathway , a series of interactions eg from cell receptors to affect gene expression. Neural pathway , a neural tract connecting one part of the nervous system with another Dopaminergic ... Path , various businesses founded and originally run by the Path Brothers of France PATH disambiguation , disambiguation page for the acronym PATH The Path disambiguation disambiguation cs Path da Sti de PATH fr Path ko nl Pad pt Caminho simple Path ... more details
The Path may refer to The Path album The Path album , a 2003 studio album by Show Of Hands The Path book The Path book , collection of short essayes by Konosuke Matsushita The Path comics The Path comics , an American comic book series by CrossGen Entertainment The Path video game The Path video game , a psychological horror art PC game See also Path disambiguation disambig fr The Path it The Path ... more details
About the acronym PATH other uses of pathPath disambiguation PathPATH may refer to Port Authority Trans Hudson , a subway system linking Manhattan, New York with locations in northern New Jersey PATH Atlanta , trail building organization Georgia, USA PATH Toronto , a network of underground pedestrian tunnels in Toronto, Ontario, Canada Partners for Advanced Transit and Highways , a research organization operated by the University of California The Performance Assessment Tool For Quality Improvement In Hospitals , a performance assessment system designed by the World Health Organization to support hospitals in defining quality improvement strategies, questioning their own results and translating them into actions for improvement. Positive Alternatives to Homosexuality , a coalition of ex gay organizations Program for Appropriate Technology in Health , an international, nonprofit organization based in Seattle, Washington, USA Projects for Assistance in Transition from Homelessness , to support service delivery to individuals with serious mental illnesses who are homeless or at risk of becoming homeless Potomac Appalachian Transmission Highline , proposed electrical line PATH variable , a computer operating system environment variable specifying a list of directories where executable programs are located disambig ... more details
Infobox film name On the Path image On the Path.jpg image size caption director Jasmila bani producer Damir Ibrahimovic writer Jasmila bani starring Mirjana Karanovi music cinematography Christine A. Maier editing distributor released Film date 2010 2 18 60th Berlin International Film Festival Berlinale 2010 2 20 Bosnia and Herzegovina runtime country Bosnia and Herzegovina language Bosnian budget On the Path lang bs Na putu is a 2010 Bosnian and Herzegovinan drama film directed by Jasmila bani . Plot Luna and Amar are a young Bosniaks Bosnian couple living in Sarajevo. Both have traumatic memories from the Bosnian War of the 1990 s. Luna had seen her parents killed by an anti Muslim militia in Bijeljina , and had come to Sarajevo with her grandparents as a child refugee. Amar had served as a soldier in the war and lost his brother. At present, however, they have apparently built up a successful life she as an air hostess with B&H Airlines , he as an air traffic controller at the Sarajevo International Airport . When she comes back from a flight they make love passionately and go to have a good time at a local nightclub. Though identifying as Islam in Bosnia and Herzegovina Muslim s in the context of Bosnia s ethnic set up, religion plays no part in their life. In fact, Amar drinks alcoholic drinks a bit too much which is forbidden by Islam and it is this which begins to put their relationship under strain. First of all, Amar loses his job for being drunk at work. Luna is very worried and has little hope of realizing her fragile dream of having a child with Amar. But her fears for their future increase when Amar takes on a well paid job in a Muslim community hours away from where they live. Only after quite some time has elapsed during which they have had no contact ... and Amar together on the path to a lifetime of happiness. Cast Zrinka Cvite i Leon Lu ev Mirjana ... accessdate 2011 01 01 ref References reflist External links imdb title 1156531 DEFAULTSORT On The Path ... more details
No Problem may refer to No Problem Sonny Rollins album No Problem Sonny Rollins album , a 1981 album No Problem Fann Wong album No Problem Fann Wong album , a 2000 album No Problem TV series No Problem TV series , a British television series No Problem film No Problem film , a 2010 Bollywood film disambig it No problem ... more details
other uses A problem is an obstacle, impediment, difficulty or challenge, or any situation that invites ... or goal. A problem implies a desired outcome coupled with an apparent deficiency, doubt or inconsistency that prevents the outcome from taking place. Problem solving main Problem solving Every theoretical problem asks for an answer or solution. Trying to find a solution to a problem is known as problem solving . There are many standard techniques for problem solving, such as Proof by Contradiction ... Problem posed by Leonhard Euler . A problem is a gap between an actual and desired situation. The time it takes to solve a problem is a way of measuring complexity . ref cite book last first authorlink ... solution and are therefore classified as an open problem . See also List of unsolved problems ... to solve problems. Examples Mathematical problem is a question about mathematical objects and structures ... Word problem mathematics education word problems at school level or deeper problems such as Four color theorem shading a map with only four colours . In society , a problem can refer to particular ..., and conversely diminished hostility and disruption. See also Wicked problem In business and engineering , a problem is a difference between actual conditions and those that are required or desired. Often, the causes of a problem are not known, in which case root cause analysis is employed to find the causes and identify corrective actions. In Chess problem chess , a problem is a puzzle set ... from determining the solution. In theology , there is what is referred to as the Synoptic Problem , regarding the Gospels relationship to each other. In academic discourse a problem is a challenge ... or idea. An optimization problem is finding the best solution from all feasible solutions. A good example of this type of problem is the travelling salesperson problem which is based on calculating the most efficient route between many places In computability theory a decision problem requires ... more details
Hamiltonian completions and path covers for trees, and a reduction to maximum flow journal ANZIAM ...Given a directed graph G V , E , a path cover is a set of directed path s such that every vertex v V belongs to at least one path. Note that a path cover may include paths of length 0 a single vertex . ref harvtxt Diestel 2005 , Section 2.5. ref A path cover may also refer to a vertex disjoint path cover , i.e., a set of paths such that every vertex v V belongs to exactly one path. ref harvtxt Franzblau Raychaudhuri 2002 . ref Properties A theorem by Gallai and Milgram shows that the number of paths in a smallest path cover cannot be larger than the number of vertices in the largest Independent set graph theory independent set . ref harvtxt Diestel 2005 , Theorem 2.5.1. ref In particular, for any graph G , there is a path cover P and an independent set I such that I contains exactly one vertex from each path in P . Dilworth s theorem follows as a corollary of this result. Computational complexity Given a directed graph G , the minimum path cover problem consists of finding a path cover for G having the least number of paths. A minimum path cover consists of one path if and only if there is a Hamiltonianpath in G . The Hamiltonianpathproblem is NP complete , and hence the minimum path cover problem is NP hard . Applications The applications of minimum path covers include software testing. ref harvtxt Ntafos Hakimi 1979 ref For example, if the graph G represents all possible execution sequences of a computer program, then a path cover is a set of test runs that covers each program statement at least once. See also Covering graph theory Notes Reflist 2 References citation last1 Bang Jensen first1 J rgen last2 Gutin first2 Gregory title .... title On path cover problems in digraphs and applications to program testing journal IEEE Transactions ... xpls abs all.jsp?arnumber 1702662 . DEFAULTSORT Path Cover Category Graph theory objects Compsci stub ... more details
The Hamiltonian of Optimal control optimal control theory was developed by Lev Semyonovich Pontryagin L. S. Pontryagin as part of his Pontryagin s minimum principle minimum principle . It was inspired by, but is distinct from, the Hamiltonian mechanics Hamiltonian of classical mechanics. Pontryagin proved that a necessary condition for solving the optimal control problem is that the control should be chosen so as to minimize the Hamiltonian. For details see Pontryagin s minimum principle . Notation and Problem statement A control math u t math is to be chosen so as to minimize the objective function math J u Psi x T int T 0 L x,u,t dt math The system state math x t math evolves according to the state equations math dot x f x,u,t qquad x 0 x 0 quad t in 0,T math the control must satisfy the constraints math a le u t le b quad t in 0,T math Definition of the Hamiltonian math H x, lambda,u,t lambda T t f x,u,t L x,u,t , math where math lambda t math is a vector of Costate equations costate variables of the same dimension as the state variables math x t math . For information on the properties of the Hamiltonian, see Pontryagin s minimum principle . The Hamiltonian in discrete time When the problem is formulated in discrete time, the Hamiltonian is defined as math H x, lambda,u,t lambda T t 1 f x,u,t L x,u,t , math and the costate equations are math lambda t frac partial H partial x math Note that the discrete time Hamiltonian at time math t math involves the costate variable at time ... equation which is not a backwards difference equation . The Hamiltonian of control compared to the Hamiltonian of mechanics William Rowan Hamilton defined the Hamiltonian mechanics Hamiltonian as a function ... d dt q t frac partial partial p mathcal H math In contrast the Hamiltonian of control theory as defined ..., nevertheless a specific problem, such as the Brachystochrone problem, can be solved by either ... varaiya papers ps.dir NOO.pdf reflist DEFAULTSORT Hamiltonian Control Theory Category ... more details
saved book title Hamiltonian Mechanics and Mathematics subtitle cover image cover color Hamiltonian Mechanics and Mathematics Basic Concepts Classical mechanics Dynamical system definition Dynamical system Equations of motion Canonical transformation Canonical transformations Generalized coordinates Phase space Hamiltonian mechanics William Rowan Hamilton Hamilton s principle Hamiltonian mechanics Hamiltonian vector field Hamilton Jacobi equation Hamilton Jacobi equations Lie bracket of vector fields Euler Lagrange equation Euler Lagrange equations Lagrangian mechanics Legendre transformation Legendre transformations Convex conjugate Legendre Fenchel transformations Poisson bracket Poisson algebra Poisson manifold Vector space Differential Geometry and Molecular Mechanics Differential geometry Symplectic vector space Symplectic manifold Symplectic group Almost complex manifold Symplectic matrix Symplectic representation Symplectic sum Symplectic geometry Symplectomorphism Symplectomorphisms Algebraic geometry Category theory Molecular Dynamics and Integrators Dynamical system Symplectic integrator Molecular dynamics Molecular modelling Relativity Theory Einstein Hilbert action General relativity Einstein field equations Solutions of the Einstein field equations Spherical coordinate system Maxwell s equations in curved spacetime Riemannian manifold Riemannian manifolds Pseudo Riemannian manifold Pseudo Riemannian manifolds Quantum Theory in Feynman s Formulation and Hamiltonian formalism inadequacies Quantum mechanics Commutator Commutators Canonical quantization Moyal bracket Path integral formulation Dirac bracket Quantum field theory Jacobi identity Lie algebra Lie group Lie groups Lie theory Lie groupoid Lie groupoids Lie algebroid Lie algebroids R algebroid Algebraic topology Double groupoid Double groupoids Higher dimensional algebra Poisson superalgebra Quantum Symmetry and TQFT Symmetry Chiral symmetry Loop quantum cosmology Quantum cohomology Topological quantum ... more details
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