Simplified Variants of Penalty Function Methods

Penalty function methods have several disadvantages. The main ones are as follows: (1) The methods are time-consuming. They~do require multiple solving of unconstrained minimization sub-problems; (2) Solution of minimization sub-problems becomes exceedingly cumbersome when the penalty coefficient increases, since a minimization function becomes ill-conditioned; (3) The usual penalty methods cannot be used for determining a solution with great accuracy. These methods are subject to numerical instabilities because the derivatives of the penalty functions increase without bound near the solution as computation proceeds. The methods suggested in this paper essentially simplify standard penalty function procedure and remove, to some extent, the first two shortcomings

Electron Beam Diagnostic at the ELBE Free Electron Laser

The radiation source ELBE is a scientific user facility able to generate electromagnetic radiation as well as beams of secondary particles. The figure below shows the layout of the facility. ELBE is based on a superconducting electron linac. The linac consists of two accelerating modules and uses TESLA type nine-cell niobium cavities, two cavities in each module. The cavities were developed at DESY in the framework of the TESLA linear collider project and the X-ray free electron laser (FEL) project. The ELBE linac is designed to operate with an accelerating field gradient of 10 MV/m so that the maximum design electron beam energy at the exit of the second module is 40 MeV. The essential difference of the ELBE linac from the future TESLA and X-ray FEL linacs is that ELBE operates in the continuous wave (CW) mode. ELBE delivers an electron beam with an average current of up to 1 mA. The electron source is a DC thermionic triode delivering beam with energy of 250 keV. The gun beam quality predefines the accelerated beam quality. One application of the electron beam is the generation of bremsstrahlung in the MeV energy range. The bremsstrahlung is used for nuclear spectroscopy experiments. Another application of the electron beam is the generation of quasi-monochromatic X-rays via channeling radiation in a single crystal. Thus X-rays with an energy from 10 keV through 100 keV can be generated. The channeling radiation is used for radio-biological and bio-medical experiments. In the future the ELBE electron beam will be used to produce monoenergetic positrons for material research. One more future application of the beam is the production of neutrons by bremsstrahlung via reactions. The neutrons will be used for material research oriented toward construction of future nuclear fusion reactors. In the author’s opinion, the most exciting and elegant application of the electron beam at ELBE is the infrared FEL. There are two FELs planned to run simultaneously at ELBE. The first one, with an undulator period of 27 mm, is going to operate in the wavelength range from 3 µm through 30 µm. The second one is in the design stage only but it will be built to work at longer wavelengths from 25 µm to 150 µm where the FEL has no competition from conventional quantum lasers. While an infrared FEL makes possible a great variety of experiments it is the device most sensitive to the electron beam quality. This dissertation is dedicated to the development of beam instrumentation and the measurement of electron beam parameters at ELBE. - In Chapter #1 we review fundamentals of FEL operation, discuss the importance of the electron beam quality for the FEL and lay down the requirements imposed by the FEL on the electron beam parameters. - Chapter #2 describes measurements of the transverse emittance we did at ELBE including an explanation of the experimental methods and the measurement error analysis. The transverse emittance was measured with the multislit method in the injector where the beam is space charge dominated. The transverse emittance of the accelerated beam was measured with the quadrupole scan method since the beam is emittance dominated. - Measurements of the electron bunch length, which is in the picosecond range, are described in Chapter #3. The bunch length was estimated from a frequency domain fit of a specially constructed analytical function to the measured power spectrum of the bunch. The power spectrum was obtained as a Fourier transform of the measured autocorrelation function of the coherent transition radiation (CTR). The CTR autocorrelation function was measured with the help of a Martin-Puplett interferometer. - A system of beam position monitors was designed, built, and commissioned in the framework of this effort. The design of our stripline BPM, the corresponding electronics and software is described in Chapter #4 along with the system performance as measured with the ELBE beam

From a metal vapor laser projection microscope to a laser monitor (by the 50 year-anniversary of metal vapor lasers)

The paper presents the history of active optical systems development from a laser projection microscope to a laser monitor. The examples of object visualization and diagnostics of high speed processes hidden by the intense background radiation are discussed. These are the processes of laser-surface interaction, self-propagating high-temperature synthesis (SHS), the corona discharge in the air, the nanoparticle production process using a high-power fiber laser, and etc. The results obtained by different research groups suggest that high-speed metal vapor brightness amplifiers and active optical systems based on them need further research, development and novel applications. © (2015) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only

Digital Technologies in Providing Development of Algorithms Surgical Treatment of Supraventricular Arrhythmias

The aim of the study was the development and clinical application of patient selection algorithm for surgical treatment of longlasting persistent atrial fibrillation. The study included 235 patients with acquired heart disease and coronary artery disease, which in the period from 1999 to 2015 performed surgical treatment of long-term persistent atrial fibrillation (RF “MAZE III” procedure) in conjunction with the correction of the underlying heart disease. The patients were divided into 2 groups according to the method of operation: the group 1 – 135 patients (76 women and 59 men) who have applied an integrated approach to surgery for atrial fibrillation, including penetrating method of RF effects on atrial myocardium and the study of the function of the sinus node before and after the operation (these patients were operated on from 2008 to 2015). The group 2 – 100 patients (62 women and 38 men) with a “classical” method of monopolar RF “MAZE III”, which the sinus node function was not studied. We used the combined (epi- and endocardial) method of RF "MAZE". This algorithm is decreasing of possible permanent pacemaker postoperatively. The initial sinus node function in these patients, measured using the original method, the basic line of this algorithm was taken. The results showed that use this algorithm for selection of patients allows significantly reduce the possibility of pacemaker implantation in the postoperative perio

High Prf metal vapor laser active media for visual and optical monitoring

In this paper the feasibility of using metal vapor lasers for visual and optical monitoring of fast processes is discussed. The theoretical calculations consistent with the experimental study have been performed. The possibility of visualizing objects with pulse repetition frequency of the brightness amplifier up to 60 kHz has been demonstrated. The visualization results of the corona discharge are also given

Node-based Generalized Friendship Paradox fails

The Friendship Paradox--the principle that ``your friends have more friends than you do''--is a combinatorial fact about degrees in a graph; but given that many Web-based social activities are correlated with a user's degree, this fact has been taken more broadly to suggest the empirical principle that ``your friends are also more active than you are.'' This Generalized Friendship Paradox, the notion that any attribute positively correlated with degree obeys the Friendship Paradox, has been established mathematically in a network-level version that essentially aggregates uniformly over all the edges of a network. Here we show, however, that the natural node-based version of the Generalized Friendship Paradox--which aggregates over nodes, not edges--may fail, even for degree-attribute correlations approaching 1. Whether this version holds depends not only on degree-attribute correlations, but also on the underlying network structure and thus can't be said to be a universal phenomenon. We establish both positive and negative results for this node-based version of the Generalized Friendship Paradox and consider its implications for social-network data.Comment: 8 pages, 5 figures, 1 tabl

Non-Linear Programming Approaches to National Settlement System Planning

Three rather aggregate approaches to modeling interregional migration processes within a national urban settlement systems context are described. General, modified penalty function methods of non-linear programming are developed and then adapted for application to the simplest of the three migration models. The numerical convergence properties of the procedure are discussed. Some of the numerical results for a Canadian urban system case study-are interpreted. Finally, some extensions to the procedures used in this study as well as alternative approaches to the same or similar problems are suggested

Again On Holling's Puzzle

In a recent IIASA Research Report, C. Holling introduces a new concept of Resilience as an important characteristic of the behavior of complex ecological systems. He writes (1) In mathematical analyses, stability has tended to assume definitions that relate to conditions very near equilibrium points. (2) Resilience determines the persistence of relationships within a system and is a measure of the ability of these systems to absorb changes of state variables, driving variables, and parameters, and still persist. In this definition resilience is the property of the system and persistence of probability of extinction is the result. (3) Stability on the other hand, is the ability of a system to return to an equilibrium state after a temporary disturbance. (4) The more rapidly it returns, and with the least fluctuation, the more stable it is. In this definition stability is the stability is the property of the system and the degree of fluctuation around specific states the result. With these definitions in mind a system can be very resilient and still fluctuate greatly, i.e. have low stability. These forms of definitions are rather vague and underestimate the achievements of modern stability theory. The subsequent examples do little to clarify the definitions. Meanwhile, defining stability as behavior not only near equilibrium but also in the large and allowing for existing oscillations even in stable systems, the concept of stability may be extended to a broader class of problems and in particular to Holling's concept of resilience. These broad definitions are in current use in stability theory. The vague nature of Holling's approach resulted in the appearance of several mathematical definitions of resilience when this topic was discussed among the IIASA methodology staff in February, 1975. This note is another attempt to solve a loosely specified problem and it is certainly open for any criticism and comments. As the concepts of stability and resilience appear very often together in Holling's presentation we shall try to relate them directly through rigorous concepts of stability theory

Community Structure of Spiders (Aranei) of Ground Tier of Four Shatsky National Nature Park Typical Biotopes

Різноманітність та специфічність видового складу павуків (Aranei) можна використовувати як індикаційні показники стану природних екосистем. Для вивчення структури угруповань павуків приґрунтового ярусу на території Шацького національного природного парку (Волинська область, Україна) методом ґрунтових пасток досліджували видовий склад та кількісне співвідношення павуків соснового, мішаного, дубово-грабового лісів і сфагнового болота. Зареєстровано 90 видів павуків із 15 родин. Установлено, що всі біотопи характеризуються своїми оригінальними угрупованнями павуків. Отримані дані слід ураховувати під час проведення природоохоронних заходів на території парку. A variety and specificity of species structure of spiders (Aranei) can be used as indicators of a natural ecosystems condition. The species structure and a quantitative ratio of spiders of pine, mixed, oak-hornbeam woods and a sphagnum bog was investigated with the method of soil traps for studying the structure of ground spiders communities on the territory of Shatsky National Nature Park (Volyn region, Ukraine). A total of 90 species of spiders from 15 families are registered. It is established that all biotopes are characterized by the special communities of spiders. The obtained data have to be considered when carrying out nature protection actions in the park territory.Роботу виконано у відділі акарології ІЗ ім. І. І. Шмальгаузена НАН Україн