HIV-1 dynamics revisited: biphasic decay by cytotoxic T lymphocyte killing?

International Journal of Computational Engineering ScienceVol. 03, No. 02, pp. 103-116 (2002) No AccessAN OPTIMAL ALGORITHM FOR SOLVING ALL-PAIRS SHORTEST PATHS ON TRAPEZOID GRAPHSSUKUMAR MONDAL, MADHUMANGAL PAL, and TAPAN K. PALSUKUMAR MONDALDepartment of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore - 721 102, West Bengal, India Search for more papers by this author , MADHUMANGAL PALDepartment of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore - 721 102, West Bengal, India Search for more papers by this author , and TAPAN K. PALDepartment of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore - 721 102, West Bengal, India Search for more papers by this author https://doi.org/10.1142/S1465876302000575Cited by:14 Next AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend to Library ShareShare onFacebookTwitterLinked InRedditEmail AbstractThe shortest-paths problem is an important problem in graph theory and finds diverse applications in various fields. This is why shortest path algorithms have been designed more thoroughly than any other algorithm in graph theory. A large number of optimization problems are mathematically equivalent to the problem of finding shortest paths in a graph. The Shortest-path between a pair of vertices is defined as the path with shortest length between the pair of vertices. The shortest path from one node to another often gives the best way to route message between the nodes. This paper presents an O(n2) time algorithm for solving all pairs shortest path problems on trapezoid graphs which are extensions of interval graphs and permutation graphs. The space complexity of this algorithm is of O(n2). This problem has been solved by constructing n breadth-first search (BFS) trees with each of the n vertices as root. As the lower bound of time complexity for computing the all pairs shortest paths is known to be of O(n2), this proposed algorithm is optimal.Keywords:Design of algorithmsanalysis of algorithmsbreadth-first searchshortest-pathstrapezoid graph FiguresReferencesRelatedDetailsCited By 14Computation of diameter, radius and center of permutation graphsShaoli Nandi, Sukumar Mondal, and Sambhu Charan Barman6 December 2021 | Discrete Mathematics, Algorithms and Applications, Vol. 14, No. 08An optimal algorithm to find minimum k-hop connected dominating set of permutation graphsAmita Samanta Adhya, Sukumar Mondal, and Sambhu Charan Barman25 March 2020 | Asian-European Journal of Mathematics, Vol. 14, No. 04An Introduction to Intersection GraphsMadhumangal Pal1 Jan 2020Computation of Inverse 1-Center Location Problem on the Weighted Trapezoid GraphsBiswanath Jana, Sukumar Mondal and Madhumangal Pal1 May 2019 | Missouri Journal of Mathematical Sciences, Vol. 31, No. 1An optimal algorithm to find minimum k-hop dominating set of interval graphsSambhu Charan Barman, Madhumangal Pal, and Sukumar Mondal24 April 2019 | Discrete Mathematics, Algorithms and Applications, Vol. 11, No. 02Surjective L (2, 1)-labeling of cycles and circular-arc graphsSk. Amanathulla and Madhumangal Pal27 Jul 2018 | Journal of Intelligent & Fuzzy Systems, Vol. 35, No. 1L(0, 1)-Labelling of Trapezoid GraphsSatyabrata Paul, Madhumangal Pal and Anita Pal8 June 2017 | International Journal of Applied and Computational Mathematics, Vol. 3, No. S1Scheduling Algorithm to Select Optimal Programme Slots in Television Channels: A Graph Theoretic ApproachMadhumangal Pal and Anita Pal20 July 2016 | International Journal of Applied and Computational Mathematics, Vol. 3, No. 3Unrestricted and complete Breadth-First Search of trapezoid graphs in timeChristophe Crespelle and Philippe Gambette1 Jun 2010 | Information Processing Letters, Vol. 110, No. 12-13A linear time algorithm to construct a tree 4-spanner on trapezoid graphsSambhu Charan Barman, Sukumar Mondal and Madhumangal Pal1 Mar 2010 | International Journal of Computer Mathematics, Vol. 87, No. 4Counting the number of vertex covers in a trapezoid graphMin-Sheng Lin and Yung-Jui Chen1 Oct 2009 | Information Processing Letters, Vol. 109, No. 21-22An efficient algorithm to find next-to-shortest path on permutation graphsSambhu Charan Barman, Sukumar Mondal and Madhumangal Pal11 December 2008 | Journal of Applied Mathematics and Computing, Vol. 31, No. 1-2Efficient algorithms for the minimum connected domination on trapezoid graphsYin-Te Tsai, Yaw-Ling Lin and F.R. Hsu1 Jun 2007 | Information Sciences, Vol. 177, No. 12An optimal parallel algorithm for solving all-pairs shortest paths problem on circular-arc graphsAnita Saha, Madhumangal Pal and Tapan K. Pal1 Mar 2005 | Journal of Applied Mathematics and Computing, Vol. 17, No. 1-2 Recommended Vol. 03, No. 02 Metrics History KeywordsDesign of algorithmsanalysis of algorithmsbreadth-first searchshortest-pathstrapezoid graphPDF download

We formulate and study a one–dimensional single–species diffusive–delay population model. The time delay is the time taken from birth to maturity. Without diffusion, the delay differential model extends the well–known logistic differential equation by allowing delayed constant birth processes and instantaneous quadratically regulated death processes. This delayed model is known to have simple global dynamics similar to that of the logistic equation. Through the use of a sub/supersolution pair method, we show that the diffusive delay model continues to generate simple global dynamics. This has the important biological implication that quadratically regulated death processes dramatically simplify the growth dynamics. We also consider the possibility of travelling wavefront solutions of the scalar equation for the mature population, connecting the zero solution of that equation with the positive steady state. Our main finding here is that our fronts appear to be all monotone, regardless of the size of the delay. This is in sharp contrast to the frequently reported findings that delay causes a loss of monotonicity, with the front developing a prominent hump in some other delay models.

Existence and uniqueness of classical solutions for the multidimensional expanding Hele{Shaw problem are proved.

On the Construction and Comparison of Difference Schemes

The global Riemann problem for a nonstrictly hyperbolic system of conservation laws modeling polymer flooding is solved. In particular, the system contains a term that models adsorption effects.

The Numerical Solution of Integral Equations on the Half-Line

In this paper, trapped modes are shown to exist for a pair of bodies that are submerged in deep water. An inverse procedure is used whereby a flow that represents a local oscillation is constructed and closed streamlines that surround the singularities of the flow are interpreted as body boundaries. The velocity potential for the flow is constructed from a symmetric combination of horizontal and vertical dipoles. This combination of singular solutions of Laplace's equation satisfies the free-surface boundary condition, and the spacing and relative amplitudes of the singularities are related in such a way that there is no radiation of waves to infinity. The existence of closed streamlines that surround the singularities is demonstrated by investigating how the structure of the streamlines varies as the parameters of the flow change.

Dynamics of fractional order HIV infection model with antibody and cytotoxic T-lymphocyte immune responses

In this paper, a linear theory of elastic boundary reinforcement of an elastic solid is developed for plane–strain deformations. The reinforcement consists of a thin elastic coating bonded to part of the boundary of the solid. The elastic properties of the coating incorporate both extensibility and bending rigidity. Interior and exterior mixed–boundary problems are formulated and solved using integral equation methods. The boundary value problems are reduced to systems of singular integro–differential equations to which Noether–type theorems are shown to apply. The case corresponding to a coating which has only extensibility properties and no bending rigidity is particularly interesting from a mathematical point of view and is given special attention. Finally, existence and uniqueness results are presented for both interior and exterior reinforcement problems of plane–strain.

We consider the general system of n first order linear ordinary differential equations y'(t)=A(t)y(t)+g(t), a<t< b, subject to "boundary" conditions, or rather linear constraints, of the form Σ^(N)_(ν=1) B_(ν)y(τ_ν)=β Here y(t), g(t) and II are n-vectors and A(t), Bx,..., BN are n × n matrices. The N distinct points {τ_ν} lie in [a,b] and we only require N ≧ 1. Thus as special cases initial value problems, N=1, are included as well as the general 2-point boundary value problem, N=2, with τ_1=a, τ_2=b. (More general linear constraints are also studied, see (5.1) and (5.17).)

This paper deals with an optimal control problem for an HIV infection model with logistic growth, cytotoxic T-lymphocytes (CTL) immune response, and infected cells in eclipse phase. The model under consideration describes the interaction between the uninfected cells, the latently infected cells, the productively infected cells, the free viruses, and the CTL cells. The two treatments represent the efficiency of drug treatment in inhibiting viral production and preventing new infections. Existence of the optimal control pair is established and the Pontryagin’s minimum principle is used to characterize these two optimal controls. The optimality system is derived and solved numerically using the forward and backward difference approximation. Finally, numerical simulations are performed in order to show the role of optimal therapy in controlling the infection severity.

A Limit Theorem for the Solutions of Differential Equations with Random Right-Hand Sides

Plane Pursuit with Curvature Constraints

This paper discusses some normlike properties of the logarithmic norm and related efficiency questions. Some computational questions are raised and some examples of use are indicated.

Axisymmetric Slipless Indentation of an Infinite, Elastic Cylinder