Institute of Applied Mathematics

Heidelberg, Germany

Institute of Applied Mathematics

Heidelberg, Germany
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News Article | September 21, 2017

The scientists from the Center for Applied Probabilistic Analysis of the Institute of Applied Mathematics and Telecommunications of the RUDN University have used a new mathematical model to find out why telecommunication systems and electronic equipment that handles numerous client requests break down. The results of the study were published in the Applied Mathematics and Computation journal. What does a central processor, an Internet provider, a supermarket cash desk and a call center have in common? Their common feature is that these systems handle numerous user requests. Such systems are called queuing systems (QS). They are often used in electronic engineering and telecommunications. Any QS includes the following elements: incoming client requests, servers, and data storage (buffer). The buffer is needed in order not to lose requests that cannot be processed immediately when all servers are busy. The contents of the buffer form a waiting queue. Scientists use the methods of queuing theory which is a part of the theory of stochastic processes to describe and model queuing systems. This is because the processes going on in the QS are random. For example, customer requests do not enter the system on a strict schedule, but at some random time. Servers can break, which significantly affects the performance of QSs. If one of the cell towers fails, the phone carrier will not be able to satisfy the user's requests for a phone call in the area. The model created by the authors of the paper takes the unreliability of the servicing devices into account and predicts the impact of breakdowns on the efficiency of the system. Scientists have described the processes of requests coming and server failures using the mathematical model of a Markovian Arrival Process. The Markovian Arrival Process is a random process of events occurring randomly in time. "In this paper we studied a queuing system with a finite number of parallel independent identical servers and an infinite buffer. The system handles the Batch Markovian Arrival Process (BMAP) of requests. Servers are subject to breakdowns at some moments defined by the Markovian Arrival Process. After the breakdown the device immediately starts to recover. The periods of time for maintenance and restoration have phase-type distribution," explained one of the authors of the paper Valentina Klimenok, doctor of physics and mathematics, chief researcher of the Center for Applied Probabilistic Analysis of the RUDN University. Earlier QS processes models, although they are rather simple, give large errors in the system performance evaluation. To avoid such errors, scientists use more complex models of the requests and breakdowns occurrence (namely, Markovian arrival process). The paper includes the following performance indicators: the average number of requests; the distribution and the average number of busy devices; the distribution and the average number of devices under repair; the probability of the incoming request to be immediately processed (rather than getting into the waiting queue). "The results of this study can be used to analyze and optimize real stochastic systems in which servers are subject to breakdowns and recovery. These systems include any computer network, "- Valentina Klimenok concluded. The study was conducted in cooperation with scientists from the Belarusian State University and the University of Sanji (Republic of Korea).

Smailov Y.S.,Institute of Applied Mathematics
AIP Conference Proceedings | Year: 2016

The theorems for the Fourier-Haar series on coefficient conditions that the function belongs to Lebesgue space Lq(0, 1), 1 < q < +∞ are relevant due to wide using of the Fourier-Haar series theory in the theoretical and applied issues of function theory, approximation theory, embedding of the function spaces. In this paper, there were established the coefficient necessary and sufficient conditions that the function belongs to the Besov spaces with the Haar basis. Such result for the Besov spaces with the trigonometric basis and for the Besov spaces with the Price basis was obtained. © 2016 Author(s).

Weber G.-W.,Institute of Applied Mathematics
Communications in Computer and Information Science | Year: 2015

Desirability functions (DFs) play an increasing role for solving the optimization of process or product quality problems having various quality characteristics to obtain a good compromise between these characteristics. There are many alternative formulations to these functions and solution strategies suggested for handling their weaknesses and improving their strength. Although the DFs of Derringer and Suich are the most popular ones in multiple-response optimization literature, there is a limited number of solution strategies to their optimization which need to be updated with new research results obtained in the area of nonlinear optimization. © Springer International Publishing Switzerland 2015.

Arous G.B.,New York University | Kirkpatrick K.,University of Illinois at Urbana - Champaign | Schlein B.,Institute of Applied Mathematics
Communications in Mathematical Physics | Year: 2013

We study the many body quantum evolution of bosonic systems in the mean field limit. The dynamics is known to be well approximated by the Hartree equation. So far, the available results have the form of a law of large numbers. In this paper we go one step further and we show that the fluctuations around the Hartree evolution satisfy a central limit theorem. Interestingly, the variance of the limiting Gaussian distribution is determined by a time-dependent Bogoliubov transformation describing the dynamics of initial coherent states in a Fock space representation of the system. © 2013 Springer-Verlag Berlin Heidelberg.

Mercker M.,BioQuant | Richter T.,Institute of Applied Mathematics | Hartmann D.,BioQuant | Hartmann D.,Siemens AG
Journal of Physical Chemistry B | Year: 2011

A continuous model of two coupled monolayers constituting a fluid bilayer membrane is presented. The model is based on the minimization of a membrane free energy considering in both monolayer leaflets two different molecule types, undergoing lateral phase separation. Differences in the mechanical properties of the molecules, such as shape, stiffness, and length are accounted explicitly by the model. In the presented model, coupling between monolayers is realized via an energy-based model depending on the local distance between the two monolayers as well as the lengths of molecules constituting the local monolayer region. We numerically study different passive mechanisms for molecule sorting and correlation across the bilayer induced by first-order mechanical constraints. Here, we focus on three aspects: First, we find that stretching of the two monolayers in the normal direction yields a sorting of molecules according to their length. Furthermore, we show that the length of molecules can be used to synchronize phases across the bilayer membrane. Moreover, we find that generating curvature in one layer (induced by different curvature creating mechanisms) sorts molecules of the other layer according to their shape and stiffness. Many recent experimental data indicate the importance of specific lipid-protein interactions and the role of the bilayer thickness in membrane protein function and sorting. The presented model proposes different mechanisms leading to a colocalization of different components in different monolayers at the same place at the same time. © 2011 American Chemical Society.

Kavun E.B.,Institute of Applied Mathematics | Yalcin T.,Institute of Applied Mathematics
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) | Year: 2010

In this paper, we present a lightweight implementation of the permutation Keccak-f[200] and Keccak-f[400] of the SHA-3 candidate hash function Keccak. Our design is well suited for radio-frequency identification (RFID) applications that have limited resources and demand lightweight cryptographic hardware. Besides its low-area and low-power, our design gives a decent throughput. To the best of our knowledge, it is also the first lightweight implementation of a sponge function, which differentiates it from the previous works. By implementing the new hash algorithm Keccak, we have utilized unique advantages of the sponge construction. Although the implementation is targeted for Application Specific Integrated Circuit (ASIC) platforms, it is also suitable for Field Programmable Gate Arrays (FPGA). To obtain a compact design, serialized data processing principles are exploited together with algorithm-specific optimizations. The design requires only 2.52K gates with a throughput of 8 Kbps at 100 KHz system clock based on 0.13-μm CMOS standard cell library. © 2010 Springer-Verlag.

Sospedra-Alfonso R.,Institute of Applied Mathematics | Shizgal B.D.,Institute of Applied Mathematics
Transport Theory and Statistical Physics | Year: 2012

We study the relaxation of Li + ions dilutely dispersed in He at equilibrium. We employ the Henyey-Greenstein phase function to model the angular dependence of the differential scattering cross section for Li +-He collisions. We solve the spatially homogeneous linear Boltzmann equation for this model cross section with the collision operator explicitly given in terms of the scattering kernel. With the Quadrature Discretization Method based on the speed polynomials, the Boltzmann equation is reduced to a set of ordinary differential equations. This numerical method provides a rapid convergence for the Li + distribution function. We study the relaxation of the shape of the Li + distribution function in terms of the Kullback-Leibler information relative to the steady state and local in time Maxwellians. A comparison of the relaxation times of these two functionals show that there is no formation of a local Maxwellian during the relaxation process. This was verified for several values of the g-parameter in the Henyey-Greenstein phase function model and the initial average energies investigated. © 2012 Copyright Taylor and Francis Group, LLC.

McLeod J.B.,University of Oxford | Niethammer B.,University of Oxford | Velazquez J.J.L.,Institute of Applied Mathematics
Journal of Statistical Physics | Year: 2011

We consider mass-conserving self-similar solutions for Smoluchowski's coagulation equation with kernel K(ξ, η) = (ξη) λ with λ ∈ (0, 1/2). It is known that such self-similar solutions g(x) satisfy that x -1+2λg(x) is bounded above and below as x → 0. In this paper we describe in detail via formal asymptotics the qualitative behavior of a suitably rescaled function h(x) = h λx -1+2λg(x) in the limit λ → 0. It turns out that, as x → 0. As x becomes larger h develops peaks of height 1/λ that are separated by large regions where h is small. Finally, h converges to zero exponentially fast as x → ∞. Our analysis is based on different approximations of a nonlocal operator, that reduces the original equation in certain regimes to a system of ODE. © 2011 Springer Science+Business Media, LLC.

Daya B.,Lebanese University | Akoum A.P.,Institute of Applied Mathematics | Chauvet H.,Institute of Applied Mathematics
Proceedings - 2010 International Conference on Computational Intelligence and Communication Networks, CICN 2010 | Year: 2010

This paper represents a framework for multiclass vehicle type identification based on several geometrical parameters. The system of identification of object must thus have a very great adaptability. We represent a system of identification of the type (model) of vehicles per vision. Several geometrical parameters (distance, surface, ratio ...) of decision, on bases of images taken in real conditions, were tested and analyzed. The details of preprocessing as well as the features represented above are described in this paper. According to these parameters, the rate of identification can reach 95% on a basis of images made up of 9 classes of the type of vehicles. Then artificial neural network (ANNE) was used to verify and to classify the different types of the vehicles, and a ratio of identification of about 97% was obtained. The details of the implementation and results of the simulation are discussed in this paper. © 2010 IEEE.

Sospedra-Alfonso R.,Institute of Applied Mathematics | Shizgal B.D.,Institute of Applied Mathematics
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics | Year: 2011

We study the thermalization of energetic electrons dilutely dispersed in inert gas atomic moderators, with and without the presence of an external electric field. We investigate the shape relaxation of the electron distribution function relative to the steady-state distribution by means of the Kullback-Leibler entropy. The departure of the distribution function from a local Maxwellian parametrized by the temperature of the electrons is also considered with a functional analogous to the Kullback-Leibler entropy. For neon and argon as moderators, we found no evidence for the formation of a local Maxwellian followed by a slower relaxation to equilibrium. The momentum-transfer cross section for e-Ne collisions is almost constant with energy, whereas the e-Ar momentum-transfer cross section has a deep Ramsauer-Townsend minimum and a strong energy dependence. The role of the Ramsauer minimum in the relaxation processes is investigated. The time-dependent Lorentz-Fokker-Planck equation is solved for the speed distribution of the electrons with a finite difference method. A pseudospectral method is also used to investigate the spectral properties of the Fokker-Planck operator. In spite of the multi-exponential time dependence of the speed distribution function, we show that a single average relaxation time can be defined to characterize the relaxation to equilibrium. © 2011 American Physical Society.

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