arXiv subjects
Publications and source records attributed to Mohammad Mohammadi.
A new generalization of Grassmannians in supergeometry, called $ν-$Grassmannians, are constructed by gluing $ν-$domains. By a $ν-$domain, we mean a superdomain with an odd involution say $ν$ on its structure sheaf, as morphism of modules. Then we show that $ν-$Grassmannians are homogeneous superspaces. In addition, in the last section, a supergroup associated to the odd involution $ν$ is introduced.
Cloud computing recently developed into a viable alternative to on-premises systems for executing high-performance computing (HPC) applications. With the emergence of new vendors and hardware options, there is now a growing need to continuously evaluate the performance of the infrastructure with respect to the most commonly-used simulation workflows. We present an online ecosystem and the corresponding tools aimed at providing a collaborative and repeatable way to assess the performance of the underlying hardware for multiple real-world application-specific benchmark cases. The ecosystem allows for the benchmark results to be stored and shared online in a centrally accessible database in order to facilitate their comparison, traceability, and curation. We include the current up-to-date example results for multiple cloud vendors and explain how to contribute new results and benchmark cases.
In this paper, the single machine scheduling problem with deteriorating jobs and learning effects are considered, which is shown in the previous research that the SDR method no longer provides an optimal solution for the problem. In order to solve the problem, a new exact algorithm is proposed. Various test problems are solved to evaluate the performance of the proposed heuristic algorithm using different measures. The results indicate that the algorithm can solve various test problems with small, medium and large sizes in a few seconds with an error around 1% where solving the test problems with more than 15 jobs is almost impossible by examining all possible permutations in both complexity and time aspects.
Despite multiple successful applications of high-throughput computational materials design from first principles, there is a number of factors that inhibit its future adoption. Of particular importance are limited ability to provide high fidelity in a reliable manner and limited accessibility to non-expert users. We present example applications of a novel approach, where high-fidelity first-principles simulation techniques, Density Functional Theory with Hybrid Screened Exchange (HSE) and GW approximation, are standardized and made available online in an accessible and repeatable setting. We apply this approach to extract electronic band gaps and band structures for a diverse set of 71 materials ranging from pure elements to III-V and II-VI compounds, ternary oxides and alloys. We find that for HSE and G0W0, the average relative error fits within 20%, whereas for conventional Generalized Gradient Approximation the error is 55%. For HSE we find the average calculation time on an up-to-date server centrally available from a public cloud provider to fit within 48 hours. This work provides a cost-effective, accessible and repeatable practical recipe for performing high-fidelity first-principles calculations of electronic materials in a high-throughput manner.
A new generalization of Grassmannians to supergeometry, different from the well known supergrassmannian, is introduced. These are constructed by gluing a finite number of copies of a ν\- domain, i.e. a superdomain with an odd involution, say ν\, on their structure sheaf considered as a sheaf of C^\infty_{R^m}-modules.
A homogeneous space is a manifold on which a Lie group acts transitively. Super generalization of this concept is also studied in [2] and [4]. In this paper we explicitly show that super Lie group GL(m|n) acts transitively on supergrassmannian G_{k|l}(m|n). In this regard, by using functor of point approach, this action is constructed by gluing local actions.
The ever increasing penetration of plug-in hybrid electric vehicles in distribution systems has triggered the need for a more accurate and at the same time fast solution to probabilistic distribution power flow problem. In this paper a novel algorithm is introduced based on finite sample points to determine probabilistic density function of probabilistic distribution power flow results. A modified probabilistic charging behavior of plug-in hybrid electric vehicles at charging stations and their overlap with residential peak load is evaluated in probabilistic distribution power flow problem. The proposed algorithm is faster than Monte Carlo Simulation and at the same time keeps adequate accuracy. It is applied to solve probabilistic distribution power flow for two dimensionally different test systems and is compared with recent probabilistic solutions. Simulation results show the accuracy and efficiency of the proposed algorithm to calculate probability density function of uncertain outputs.
We establish a Gelfand-Naimark-Segal construction which yields a correspondence between cyclic unitary representations and positive definite superfunctions of a general class of $\mathbb Z_2^n$-graded Lie supergroups.
We present a comparative analysis of the maximum performance achieved by the Linpack benchmark on compute intensive hardware publicly available from multiple cloud providers. We study both performance within a single compute node, and speedup for distributed memory calculations with up to 32 nodes or at least 512 computing cores. We distinguish between hyper-threaded and non-hyper-threaded scenarios and estimate the performance per single computing core. We also compare results with a traditional supercomputing system for reference. Our findings provide a way to rank the cloud providers and demonstrate the viability of the cloud for high performance computing applications.
Security-Constrained Unit Commitment (SCUC) is one of the most significant problems in secure and optimal operation of modern electricity markets. New sources of uncertainties such as wind speed volatility and price-sensitive loads impose additional challenges to this large-scale problem. This paper proposes a new Stochastic SCUC using point estimation method to model the power system uncertainties more efficiently. Conventional scenario-based Stochastic SCUC approaches consider the Mont Carlo method; which presents additional computational burdens to this large-scale problem. In this paper we use point estimation instead of scenario generating to detract computational burdens of the problem. The proposed approach is implemented on a six-bus system and on a modified IEEE 118-bus system with 94 uncertain variables. The efficacy of proposed algorithm is confirmed, especially in the last case with notable reduction in computational burden without considerable loss of precision.
Expert systems prove to be suitable replacement for human experts when human experts are unavailable for different reasons. Various expert system has been developed for wide range of application. Although some expert systems in the field of fishery and aquaculture has been developed but a system that aids user in process of selecting a new addition to their aquarium tank never been designed. This paper proposed an expert system that suggests new addition to an aquarium tank based on current environmental condition of aquarium and currently existing fishes in aquarium. The system suggest the best fit for aquarium condition and most compatible to other fishes in aquarium.
Solitary wave and soliton solutions of nonlinear equations are well known for physicists. A soliton is a solitary wave with some outstanding features which make it reasonable to be studied seriously in nonlinear systems. In fact most of the nonlinear systems which have solitary wave solutions, has no soliton solutions. To realize a solitary wave as a soliton, we must prepare some initial conditions to collide two or more solitary wave solutions. In fact it is not possible to prepare such initial conditions for any nonlinear system with solitary wave solutions. In this paper we study the conditions that a system should have, to prepare a combination of its single solitary wave solutions as an initial condition for collision. These systems accept a combination of separated single solitary waves as an initial condition, so we call them separable systems. We see a system with periodic potential that zero is one of its vacuum points is separable. We observed that separable systems have two distinct set of solitons, but in general, if we collide members of different sets, they may not behave like solitons.