Finding the Relationship between a Search Algorithm and a Class of Functions on Discrete Space by Exhaustive Search

* The work is supported by RFBR, grant 04-01-00858-a.

Discrete solitons in coupled active lasing cavities

We examine the existence and stability of discrete spatial solitons in coupled nonlinear lasing cavities (waveguide resonators), addressing the case of active defocusing media, where the gain exceeds damping in the low-amplitude limit. A new family of stable localized structures is found: these are bright and gray cavity solitons representing the connections between homogeneous and inhomogeneous states. Solitons of this type can be controlled by discrete diffraction and are stable when the bistability of homogenous states is absent. © 2012 Optical Society of America.

Efficient HIV-1 inhibition by a 16 nt-long RNA aptamer designed by combining in vitro selection and in silico optimisation strategies

The human immunodeficiency virus type-1 (HIV-1) genome contains multiple, highly conserved structural RNA domains that play key roles in essential viral processes. Interference with the function of these RNA domains either by disrupting their structures or by blocking their interaction with viral or cellular factors may seriously compromise HIV-1 viability. RNA aptamers are amongst the most promising synthetic molecules able to interact with structural domains of viral genomes. However, aptamer shortening up to their minimal active domain is usually necessary for scaling up production, what requires very time-consuming, trial-and-error approaches. Here we report on the in vitro selection of 64 nt-long specific aptamers against the complete 5' -untranslated region of HIV-1 genome, which inhibit more than 75% of HIV-1 production in a human cell line. The analysis of the selected sequences and structures allowed for the identification of a highly conserved 16 nt-long stem-loop motif containing a common 8 nt-long apical loop. Based on this result, an in silico designed 16 nt-long RNA aptamer, termed RNApt16, was synthesized, with sequence 5'-CCCCGGCAAGGAGGGG-3-'. The HIV-1 inhibition efficiency of such an aptamer was close to 85%, thus constituting the shortest RNA molecule so far described that efficiently interferes with HIV-1 replication.

Discrete Models of Time-Fractional Diffusion in a Potential Well

Mathematics Subject Classification: 26A33, 45K05, 60J60, 60G50, 65N06, 80-99.

About Learning Discrete Mathematics at Bulgarian School

The present work is dedicated to the learning discrete mathematics at Bulgarian school. A review of syllabuses and standards has been made. A project of learning discrete mathematics elements from first to twelve class is proposed.

Optimisation of polymer optical fibre based interferometric sensors

A numerical model for studying the performance of polymer optical fibre-based interferometric sensors is presented. The strain sensitivity of Fabry-Perot and two-beam interferometric sensors is investigated by varying the physical and optical properties corresponding to frequently used wavelengths. The developed model was used to identify the regimes in which these devices offer enhanced performance over their silica counterparts when used for stress sensing. © (2015) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.

A simulation analysis of spoke-terminals operating in LTL Hub-and-Spoke freight distribution systems

DUE TO COPYRIGHT RESTRICTIONS ONLY AVAILABLE FOR CONSULTATION AT ASTON UNIVERSITY LIBRARY AND INFORMATION SERVICES WITH PRIOR ARRANGEMENT The research presented in this thesis is concerned with Discrete-Event Simulation (DES) modelling as a method to facilitate logistical policy development within the UK Less-than-Truckload (LTL) freight distribution sector which has been typified by “Pallet Networks” operating on a hub-and-spoke philosophy. Current literature relating to LTL hub-and-spoke and cross-dock freight distribution systems traditionally examines a variety of network and hub design configurations. Each is consistent with classical notions of creating process efficiency, improving productivity, reducing costs and generally creating economies of scale through notions of bulk optimisation. Whilst there is a growing abundance of papers discussing both the network design and hub operational components mentioned above, there is a shortcoming in the overall analysis when it comes to discussing the “spoke-terminal” of hub-and-spoke freight distribution systems and their capabilities for handling the diverse and discrete customer profiles of freight that multi-user LTL hub-and-spoke networks typically handle over the “last-mile” of the delivery, in particular, a mix of retail and non-retail customers. A simulation study is undertaken to investigate the impact on operational performance when the current combined spoke-terminal delivery tours are separated by ‘profile-type’ (i.e. retail or nonretail). The results indicate that a potential improvement in delivery performance can be made by separating retail and non-retail delivery runs at the spoke-terminal and that dedicated retail and non-retail delivery tours could be adopted in order to improve customer delivery requirements and adapt hub-deployed policies. The study also leverages key operator experiences to highlight the main practical implementation challenges when integrating the observed simulation results into the real-world. The study concludes that DES be harnessed as an enabling device to develop a ‘guide policy’. This policy needs to be flexible and should be applied in stages, taking into account the growing retail-exposure.

Henselian Discrete Valued Fields Admitting One-Dimensional Local Class Field Theory

2000 Mathematics Subject Classification: 11S31 12E15 12F10 12J20.

Notes on the Solution of Dynamic Optimization Problems with Explicit Controls in Discrete-Time Economic Models

Йордан Йорданов, Андрей Василев - В работата се изследват методи за решаването на задачи на оптималното управление в дискретно време с безкраен хоризонт и явни управления. Дадена е обосновка на една процедура за решаване на такива задачи, базирана на множители на Лагранж, коята често се употребява в икономическата литература. Извеждени са необходимите условия за оптималност на базата на уравнения на Белман и са приведени достатъчни условия за оптималност при допускания, които често се използват в икономиката.

Discrete Generalization of Gronwall-Bellman Inequality with Maxima and Application

Снежана Христова, Кремена Стефанова, Лиляна Ванкова - В работата са решени няколко нови видове линейни дискретни неравенства, които съдържат максимума на неизвестната функция в отминал интервал от време. Някои от тези неравенства са приложени за изучаване непрекъснатата зависимост от смущения при дискретни уравнения с максимуми.

An edge-based matching kernel through discrete-time quantum walks

In this paper, we propose a new edge-based matching kernel for graphs by using discrete-time quantum walks. To this end, we commence by transforming a graph into a directed line graph. The reasons of using the line graph structure are twofold. First, for a graph, its directed line graph is a dual representation and each vertex of the line graph represents a corresponding edge in the original graph. Second, we show that the discrete-time quantum walk can be seen as a walk on the line graph and the state space of the walk is the vertex set of the line graph, i.e., the state space of the walk is the edges of the original graph. As a result, the directed line graph provides an elegant way of developing new edge-based matching kernel based on discrete-time quantum walks. For a pair of graphs, we compute the h-layer depth-based representation for each vertex of their directed line graphs by computing entropic signatures (computed from discrete-time quantum walks on the line graphs) on the family of K-layer expansion subgraphs rooted at the vertex, i.e., we compute the depth-based representations for edges of the original graphs through their directed line graphs. Based on the new representations, we define an edge-based matching method for the pair of graphs by aligning the h-layer depth-based representations computed through the directed line graphs. The new edge-based matching kernel is thus computed by counting the number of matched vertices identified by the matching method on the directed line graphs. Experiments on standard graph datasets demonstrate the effectiveness of our new kernel.

A quantum Jensen-Shannon graph kernel using discrete-time quantum walks

In this paper, we develop a new graph kernel by using the quantum Jensen-Shannon divergence and the discrete-time quantum walk. To this end, we commence by performing a discrete-time quantum walk to compute a density matrix over each graph being compared. For a pair of graphs, we compare the mixed quantum states represented by their density matrices using the quantum Jensen-Shannon divergence. With the density matrices for a pair of graphs to hand, the quantum graph kernel between the pair of graphs is defined by exponentiating the negative quantum Jensen-Shannon divergence between the graph density matrices. We evaluate the performance of our kernel on several standard graph datasets, and demonstrate the effectiveness of the new kernel.

Integrated optimisation of surface roughness and tool performance when face milling 416 SS

Tool life is an important factor to be considered during the optimisation of a machining process since cutting parameters can be adjusted to optimise tool changing, reducing cost and time of production. Also the performance of a tool is directly linked to the generated surface roughness and this is important in cases where there are strict surface quality requirements. The prediction of tool life and the resulting surface roughness in milling operations has attracted considerable research efforts. The research reported herein is focused on defining the influence of milling cutting parameters such as cutting speed, feed rate and axial depth of cut, on three major tool performance parameters namely, tool life, material removal and surface roughness. The research is seeking to define methods that will allow the selection of optimal parameters for best tool performance when face milling 416 stainless steel bars. For this study the Taguchi method was applied in a special design of an orthogonal array that allows studying the entire parameter space with only a number of experiments representing savings in cost and time of experiments. The findings were that the cutting speed has the most influence on tool life and surface roughness and very limited influence on material removal. By last tool life can be judged either from tool life or volume of material removal.

Optimisation of random DFB Raman laser amplifier

We numerically optimise 2nd-order random DFB Raman laser amplifiers for transmission for the first time. Optical signal to noise ratio, nonlinear phase shift, signal power variation and the impact of the reflectivity of FBG are investigated in the links from 10 - 120 km.

Discrete Time Bisexual Branching Processes in Varying Environments

2000 Mathematics Subject Classification: 60J80