相关论文: Integrating Amdahl-like Laws and Divisible Load Th…
The paper explains why Amdahl's Law shall be interpreted specifically for distributed parallel systems and why it generated so many debates, discussions, and abuses. We set up a general model and list many of the terms affecting parallel…
On the base of Lie algebraic and differential geometry methods, a wide class of multidimensional nonlinear integrable systems is obtained, and the integration scheme for such equations is proposed.
This paper reinterprets Amdahl's law in terms of execution time and applies this simple model to supercomputing. The systematic discussion results in practical formulas enabling to calculate expected running time using large number of…
The author's research of topologies of parallel computing systems and the tasks solved with them, including the corresponding tools of their modeling, is summarized in the present paper. The original topological model of such systems is…
In this work I present a generalization of Amdahl's law on the limits of a parallel implementation with many processors. In particular I establish some mathematical relations involving the number of processors and the dimension of the…
We present a theory of compatible differential constraints of a hydrodynamic hierarchy of infinite-dimensional systems. It provides a convenient point of view for studying and formulating integrability properties and it reveals some hidden…
An approach to infinite dimensional integration which unifies the case of oscillatory integrals and the case of probabilistic type integrals is presented. It provides a truly infinite dimensional construction of integrals as linear…
On the base of Lie algebraic and differential geometry methods, a wide class of multidimensional nonlinear systems is obtained, and the integration scheme for such equations is proposed.
This paper presents the current possible applications of Dynamical Systems in Engineering. The applications of chaos, fractals have proven to be an exciting and fruitful endeavor. These applications are highly diverse ranging over such…
Thermodynamic systems involving reversible and non-reversible heat transfer are used to derive integral inequalities expected from the Second of Law of Thermodynamics. Then, the inequalities are proved and generalized to higher dimensions…
During modeling of dynamical systems, often two or more model architectures are combined to obtain a more powerful or efficient model regarding a specific application area. This covers the combination of multiple machine learning…
We introduce the concept of linked systems of symmetric group divisible designs. The connection with association schemes is established, and as a consequence we obtain an upper bound on the number of symmetric group divisible designs which…
Classical Amdahl's Law conceptualized the limit of speedup for an era of fixed serial-parallel decomposition and homogeneous replication. Modern heterogeneous systems need a different conceptual framework: constrained resources must be…
The paper deals with the problem of integration of equations of motion in nonholonomic systems. By means of well-known theory of the differential equations with an invariant measure the new integrable systems are discovered. Among them…
The problem of learning parallel computer performance is investigated in the context of multicore processors. Given a fixed workload, the effect of varying system configuration on performance is sought. Conventionally, the performance…
In this paper we construct nonlinear partial differential equations in more than 3 independent variables, possessing a manifold of analytic solutions with high, but not full, dimensionality. For this reason we call them ``partially…
The role of geometrically infinitely divisible laws in renewal equations and superposition of renewal processes are explored here. Some examples are also discussed.
This note argues for more use of simple models beyond Amdahl's Law: Bottleneck Analysis, Little's Law, and a M/M/1 Queue.
The concept of integrable boundary conditions is applied to hydrodynamic type systems. Examples of such boundary conditions for dispersionless Toda systems are obtained. The close relation of integrable boundary conditions with integrable…
Motivated by the theory of self-duality which provides a variational formulation and resolution for non self-adjoint partial differential equations \cite{G1, G2}, we propose new templates for solving large non-symmetric linear systems. The…