243,902 research outputs found
Unmixing the mixed volume computation
Computing mixed volume of convex polytopes is an important problem in
computational algebraic geometry. This paper establishes sufficient conditions
under which the mixed volume of several convex polytopes exactly equals the
normalized volume of the convex hull of their union. Under these conditions the
problem of computing mixed volume of several polytopes can be transformed into
a volume computation problem for a single polytope in the same dimension. We
demonstrate through problems from real world applications that substantial
reduction in computational costs can be achieved via this transformation in
situations where the convex hull of the union of the polytopes has less complex
geometry than the original polytopes. We also discuss the important
implications of this result in the polyhedral homotopy method for solving
polynomial systems
Interval Linear Algebra and Computational Complexity
This work connects two mathematical fields - computational complexity and
interval linear algebra. It introduces the basic topics of interval linear
algebra - regularity and singularity, full column rank, solving a linear
system, deciding solvability of a linear system, computing inverse matrix,
eigenvalues, checking positive (semi)definiteness or stability. We discuss
these problems and relations between them from the view of computational
complexity. Many problems in interval linear algebra are intractable, hence we
emphasize subclasses of these problems that are easily solvable or decidable.
The aim of this work is to provide a basic insight into this field and to
provide materials for further reading and research.Comment: Submitted to Mat Triad 201
Polynomial Homotopies for Dense, Sparse and Determinantal Systems
Numerical homotopy continuation methods for three classes of polynomial
systems are presented. For a generic instance of the class, every path leads to
a solution and the homotopy is optimal. The counting of the roots mirrors the
resolution of a generic system that is used to start up the deformations.
Software and applications are discussed
Chapter 10: Algebraic Algorithms
Our Chapter in the upcoming Volume I: Computer Science and Software
Engineering of Computing Handbook (Third edition), Allen Tucker, Teo Gonzales
and Jorge L. Diaz-Herrera, editors, covers Algebraic Algorithms, both symbolic
and numerical, for matrix computations and root-finding for polynomials and
systems of polynomials equations. We cover part of these large subjects and
include basic bibliography for further study. To meet space limitation we cite
books, surveys, and comprehensive articles with pointers to further references,
rather than including all the original technical papers.Comment: 41.1 page
High order ADER schemes for a unified first order hyperbolic formulation of continuum mechanics: viscous heat-conducting fluids and elastic solids
This paper is concerned with the numerical solution of the unified first
order hyperbolic formulation of continuum mechanics recently proposed by
Peshkov & Romenski, denoted as HPR model. In that framework, the viscous
stresses are computed from the so-called distortion tensor A, which is one of
the primary state variables. A very important key feature of the model is its
ability to describe at the same time the behavior of inviscid and viscous
compressible Newtonian and non-Newtonian fluids with heat conduction, as well
as the behavior of elastic and visco-plastic solids. This is achieved via a
stiff source term that accounts for strain relaxation in the evolution
equations of A. Also heat conduction is included via a first order hyperbolic
evolution equation of the thermal impulse, from which the heat flux is
computed. The governing PDE system is hyperbolic and fully consistent with the
principles of thermodynamics. It is also fundamentally different from first
order Maxwell-Cattaneo-type relaxation models based on extended irreversible
thermodynamics. The connection between the HPR model and the classical
hyperbolic-parabolic Navier-Stokes-Fourier theory is established via a formal
asymptotic analysis in the stiff relaxation limit. From a numerical point of
view, the governing partial differential equations are very challenging, since
they form a large nonlinear hyperbolic PDE system that includes stiff source
terms and non-conservative products. We apply the successful family of one-step
ADER-WENO finite volume and ADER discontinuous Galerkin finite element schemes
in the stiff relaxation limit, and compare the numerical results with exact or
numerical reference solutions obtained for the Euler and Navier-Stokes
equations. To show the universality of the model, the paper is rounded-off with
an application to wave propagation in elastic solids
Predictive biometrics: A review and analysis of predicting personal characteristics from biometric data
Interest in the exploitation of soft biometrics information has continued to develop over the last decade or so. In comparison with traditional biometrics, which focuses principally on person identification, the idea of soft biometrics processing is to study the utilisation of more general information regarding a system user, which is not necessarily unique. There are increasing indications that this type of data will have great value in providing complementary information for user authentication. However, the authors have also seen a growing interest in broadening the predictive capabilities of biometric data, encompassing both easily definable characteristics such as subject age and, most recently, `higher level' characteristics such as emotional or mental states. This study will present a selective review of the predictive capabilities, in the widest sense, of biometric data processing, providing an analysis of the key issues still adequately to be addressed if this concept of predictive biometrics is to be fully exploited in the future
Computational Physics on Graphics Processing Units
The use of graphics processing units for scientific computations is an
emerging strategy that can significantly speed up various different algorithms.
In this review, we discuss advances made in the field of computational physics,
focusing on classical molecular dynamics, and on quantum simulations for
electronic structure calculations using the density functional theory, wave
function techniques, and quantum field theory.Comment: Proceedings of the 11th International Conference, PARA 2012,
Helsinki, Finland, June 10-13, 201
Applications of Soft Computing in Mobile and Wireless Communications
Soft computing is a synergistic combination of artificial intelligence methodologies to model and solve real world problems that are either impossible or too difficult to model mathematically. Furthermore, the use of conventional modeling techniques demands rigor, precision and certainty, which carry computational cost. On the other hand, soft computing utilizes computation, reasoning and inference to reduce computational cost by exploiting tolerance for imprecision, uncertainty, partial truth and approximation. In addition to computational cost savings, soft computing is an excellent platform for autonomic computing, owing to its roots in artificial intelligence. Wireless communication networks are associated with much uncertainty and imprecision due to a number of stochastic processes such as escalating number of access points, constantly changing propagation channels, sudden variations in network load and random mobility of users. This reality has fuelled numerous applications of soft computing techniques in mobile and wireless communications. This paper reviews various applications of the core soft computing methodologies in mobile and wireless communications
Molecular Programming Pseudo-code Representation to Molecular Electronics
This research paper is proposing the idea of pseudo code representation to
molecular programming used in designing molecular electronics devices. Already
the schematic representation of logical gates like AND, OR, NOT etc.from
molecular diodes or resonant tunneling diode are available. This paper is
setting a generic pseudo code model so that various logic gates can be
formulated. These molecular diodes have designed from organic molecules or
Bio-molecules. Our focus is on to give a scenario of molecular computation
through molecular programming. We have restricted our study to molecular
rectifying diode and logic device as AND gate from organic molecules only.Comment: http://www.journalofcomputing.or
Numerically validating the completeness of the real solution set of a system of polynomial equations
Computing the real solutions to a system of polynomial equations is a
challenging problem, particularly verifying that all solutions have been
computed. We describe an approach that combines numerical algebraic geometry
and sums of squares programming to test whether a given set is "complete" with
respect to the real solution set. Specifically, we test whether the Zariski
closure of that given set is indeed equal to the solution set of the real
radical of the ideal generated by the given polynomials. Examples with finitely
and infinitely many real solutions are provided, along with an example having
polynomial inequalities
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