On the SNR Variability in Noisy Compressed Sensing

Compressed sensing (CS) is a sampling paradigm that allows to simultaneously measure and compress signals that are sparse or compressible in some domain. The choice of a sensing matrix that carries out the measurement has a defining impact on the system performance and it is often advocated to draw its elements randomly. It has been noted that in the presence of input (signal) noise, the application of the sensing matrix causes SNR degradation due to the noise folding effect. In fact, it might also result in the variations of the output SNR in compressive measurements over the support of the input signal, potentially resulting in unexpected non-uniform system performance. In this work, we study the impact of a distribution from which the elements of a sensing matrix are drawn on the spread of the output SNR. We derive analytic expressions for several common types of sensing matrices and show that the SNR spread grows with the decrease of the number of measurements. This makes its negative effect especially pronounced for high compression rates that are often of interest in CS.Comment: 4 pages + reference

A Latent Dirichlet Framework for Relevance Modeling

Abstract. Relevance-based language models operate by estimating the probabilities of observing words in documents relevant (or pseudo relevant) to a topic. However, these models assume that if a document is relevant to a topic, then all tokens in the document are relevant to that topic. This could limit model robustness and effectiveness. In this study, we propose a Latent Dirichlet relevance model, which relaxes this assumption. Our approach derives from current research on Latent Dirichlet Allocation (LDA) topic models. LDA has been extensively explored, especially for generating a set of topics from a corpus. A key attraction is that in LDA a document may be about several topics. LDA itself, however, has a limitation that is also addressed in our work. Topics generated by LDA from a corpus are synthetic, i.e., they do not necessarily correspond to topics identified by humans for the same corpus. In contrast, our model explicitly considers the relevance relationships between documents and given topics (queries). Thus unlike standard LDA, our model is directly applicable to goals such as relevance feedback for query modification and text classification, where topics (classes and queries) are provided upfront. Thus although the focus of our paper is on improving relevance-based language models, in effect our approach bridges relevance-based language models and LDA addressing limitations of both. Finally, we propose an idea that takes advantage of “bagof-words” assumption to reduce the complexity of Gibbs sampling based learning algorithm

Роль юридичних конструкцій в нормотворчій діяльності

У науковій статті розглядаються питання щодо голоної ролі юридичних конструкцій у нормотворчій діяльності. Можемо позначити, що саме юридична конструкція свою голов­ну роль відображає як один із найважливіших засобів юридичної техніки. Пропонуємо роз­глянути юридичну конструкцію в призмі нор- мотворчої діяльності Розглядаються як поня­тійна форма юридичного мислення, яка може бути виражена в системі норм, що задають кон­кретний механізм правового регулювання або його окремий елемент. На основі вищенаведеного запропоновано визначення юридичної конструкції та їх головна роль в нормотворчій діяльності. Юридичні конструкції виступають єдиним та незалежним елементом юридичної техніки . Можемо зазначити що наразі йде ви­сокий прояв вчених до вивчення, ролі юридич­них конструкцій. Це стосується переважно га­лузевих дисциплін, а не загальнотеоретичних досліджень. Нові дослідження, щодо даної ролі юридичної конструкції останнім часом базуєть­ся на сучасних поглядах науковців. Запропоновуються нові причини походження юридич­них конструкцій та їх головна роль. Можемо побачити, що відсутні чіткі думки, щодо похо­дження ролі юридичних конструкцій. Тим самим ми пропонуємо розглядати новіт­ні формування понять та їх походження і при­ділити особливу увагу визначенню ролі кон­струкцій в нормотворчій діяльності. Приділено увагу актуальній темі юриспруденції, пов'язаної із процесом визначеної ролі конструкцій право­вої діяльності з практичною складовою. Наукова новизна полягає не тільки в аналізі вітчизняної літератури, щодо поняття та головної ролі юри­дичних конструкцій, а ще й новітніх поглядів на дану дифиніцію. При цьому, проблематика юри­дичних конструкцій до теперішнього часу має здебільшого галузеве (цивільне, кримінальне, адміністративне, сімейне, фінансове, податкове, соціального забезпечення тощо) «забарвлення», що характеризує більшу частину досліджень з практичної сторони

Compressive Acquisition and Processing of Sparse Analog Signals

Since the advent of the first digital processing units, the importance of digital signal processing has been steadily rising. Today, most signal processing happens in the digital domain, requiring that analog signals be first sampled and digitized before any relevant data can be extracted from them. The recent explosion of the demands for data acquisition, storage and processing, however, has pushed the capabilities of conventional acquisition systems to their limits in many application areas. By offering an alternative view on the signal acquisition process, ideas from sparse signal processing and one of its main beneficiaries compressed sensing (CS), aim at alleviating some of these problems. In this thesis, we look into the ways the application of a compressive measurement kernel impacts the signal recovery performance and investigate methods to infer the current signal complexity from the compressive observations. We then study a particular application, namely that of sub-Nyquist sampling and processing of sparse analog multiband signals in spectral, angular and spatial domains.Seit dem Aufkommen der ersten digitalen Verarbeitungseinheiten hat die Bedeutung der digitalen Signalverarbeitung stetig zugenommen. Heutzutage findet die meiste Signalverarbeitung im digitalen Bereich statt, was erfordert, dass analoge Signale zuerst abgetastet und digitalisiert werden, bevor relevante Daten daraus extrahiert werden können. Jahrzehntelang hat die herkömmliche äquidistante Abtastung, die durch das Nyquist-Abtasttheorem bestimmt wird, zu diesem Zweck ein nahezu universelles Mittel bereitgestellt. Der kürzliche explosive Anstieg der Anforderungen an die Datenerfassung, -speicherung und -verarbeitung hat jedoch die Fähigkeiten herkömmlicher Erfassungssysteme in vielen Anwendungsbereichen an ihre Grenzen gebracht. Durch eine alternative Sichtweise auf den Signalerfassungsprozess können Ideen aus der sparse Signalverarbeitung und einer ihrer Hauptanwendungsgebiete, Compressed Sensing (CS), dazu beitragen, einige dieser Probleme zu mindern. Basierend auf der Annahme, dass der Informationsgehalt eines Signals oft viel geringer ist als was von der nativen Repräsentation vorgegeben, stellt CS ein alternatives Konzept für die Erfassung und Verarbeitung bereit, das versucht, die Abtastrate unter Beibehaltung des Signalinformationsgehalts zu reduzieren. In dieser Arbeit untersuchen wir einige der Grundlagen des endlichdimensionalen CSFrameworks und seine Verbindung mit Sub-Nyquist Abtastung und Verarbeitung von sparsen analogen Signalen. Obwohl es seit mehr als einem Jahrzehnt ein Schwerpunkt aktiver Forschung ist, gibt es noch erhebliche Lücken beim Verständnis der Auswirkungen von komprimierenden Ansätzen auf die Signalwiedergewinnung und die Verarbeitungsleistung, insbesondere bei rauschbehafteten Umgebungen und in Bezug auf praktische Messaufgaben. In dieser Dissertation untersuchen wir, wie sich die Anwendung eines komprimierenden Messkerns auf die Signal- und Rauschcharakteristiken auf die Signalrückgewinnungsleistung auswirkt. Wir erforschen auch Methoden, um die aktuelle Signal-Sparsity-Order aus den komprimierten Messungen abzuleiten, ohne auf die Nyquist-Raten-Verarbeitung zurückzugreifen, und zeigen den Vorteil, den sie für den Wiederherstellungsprozess bietet. Nachdem gehen wir zu einer speziellen Anwendung, nämlich der Sub-Nyquist-Abtastung und Verarbeitung von sparsen analogen Multibandsignalen. Innerhalb des Sub-Nyquist-Abtastung untersuchen wir drei verschiedene Multiband-Szenarien, die Multiband-Sensing in der spektralen, Winkel und räumlichen-Domäne einbeziehen.Since the advent of the first digital processing units, the importance of digital signal processing has been steadily rising. Today, most signal processing happens in the digital domain, requiring that analog signals be first sampled and digitized before any relevant data can be extracted from them. For decades, conventional uniform sampling that is governed by the Nyquist sampling theorem has provided an almost universal means to this end. The recent explosion of the demands for data acquisition, storage and processing, however, has pushed the capabilities of conventional acquisition systems to their limits in many application areas. By offering an alternative view on the signal acquisition process, ideas from sparse signal processing and one of its main beneficiaries compressed sensing (CS), have the potential to assist alleviating some of these problems. Building on the premise that the signal information rate is often much lower than what is dictated by its native representation, CS provides an alternative acquisition and processing framework that attempts to reduce the sampling rate while preserving the information content of the signal. In this thesis, we explore some of the basic foundations of the finite-dimensional CS framework and its connection to sub-Nyquist sampling and processing of sparse continuous analog signals with application to multiband sensing. Despite being a focus of active research for over a decade, there still remain signi_cant gaps in understanding the implications that compressive approaches have on the signal recovery and processing performance, especially against noisy settings and in relation to practical sampling problems. This dissertation aims at filling some of these gaps. More specifically, we look into the ways the application of a compressive measurement kernel impacts signal and noise characteristics and the relation it has to the signal recovery performance. We also investigate methods to infer the current complexity of the signal scene from the reduced-rate compressive observations without resorting to Nyquist-rate processing and show the advantage this knowledge offers to the recovery process. Having considered some of the universal aspects of compressive systems, we then move to studying a particular application, namely that of sub-Nyquist sampling and processing of sparse analog multiband signals. Within the sub-Nyquist sampling framework, we examine three different multiband scenarios that involve multiband sensing in spectral, angular and spatial domains. For each of them, we provide a sub-Nyquist receiver architecture, develop recovery methods and numerically evaluate their performance

Effect of degree of salinity on seed germination and initial growth of chickpea (Cicer arietinum)

Chickpea (Cicer arietinum L.) is one of the main pulse crops cultivated mostly in the arid and semi-arid regions of the world, very often on saline lands. The problem is that it has not been clearly determined yet what is the safe salinity degree for obtaining uniform and vigorous sprouts of the crop without significant suppression in the parameters of initial growth and development. The goal of our study was to determine the effect of different NaCl concentrations in solutions on chickpea germination and initial growth to determine the safe degree of salinity for the crop cultivation. The study was carried out in greenhouse conditions of Kherson State Agrarian University. We studied the effect of five different gradually increasing degrees of NaCl solutions on the germination percentage and initial growth of chickpea (variety Rosanna, kabuli type) that was germinated in laboratory conditions in flasks filled with sand, at the temperature of 25 oC. A significant decrease in all the studied parameters was observed with the increase of salinity degree. However, we think that a considerable decrease of the crop germination and initial growth started with NaCl concentration of 1.79 g/L: germination percentage decreased by 33.9%, plant height – by 7.8 cm, root length – by 5.5 cm in comparison to the control variant (not saline conditions). Therefore, we conclude that the chickpea can be efficiently cultivated on slightly-saline lands. Besides, the results of linear regression analysis revealed that the most susceptible stage of chickpea growth and development is germination because this stage had strong close inter-connection with the degree of salinity. Further growth of the crop was less affected by the salinity stress. We recommend cultivation of chickpea on the saline lands only with a slight salinity level

Experimental study of mechanical characteristics of support and movement of centrifuge PICO21

Експериментально досліджені механічні характеристики центрифуги та її елементів. Досліджено рух центрифуги. Дослідження дало можливість встановити реальні параметри системи, які необхідні для розрахунку її динаміки. Встановлено, що опори у першому наближенні можна вважати лінійно-пружними. Знайдені залежності власних частот від швидкості і напрямку обертання центрифуги. Встановлені додаткові частоти на яких виникає явище резонансу.Purpose. Definition of laboratory centrifuge characteristic with regard to its structural features. Design/methodology/approach. The dynamic characteristics of the centrifuge with design features that consist in fact that it is multi-mass system fixed on elastic support is determined. Contrast to the previous well-known approaches in which the centrifuge is seen as a single-mass construction and do not take into account the design features fixing is shown. Quality of work required depends on the centrifuge parameters. The dynamic behavior of a centrifuge depends on the stiffness and damping supports. To determine the stiffness of rubber supports used the method of perturbation forced vibrations using vibration stand, which allows to determine the dynamic characteristics of the supports in tension and shear. Findings. Found that support in the first approximation can be considered linear elastic. The dependences of the natural frequencies of the frequency and direction of rotation of the centrifuge. Originality/value. This research was important and original in field of vibrations of medical machines, which usually work with high values of frequencies. It shows changes of own frequencies depending on work frequencies. It can help to avoid a resonance during operation.Экспериментально исследованы механические характеристики центрифуги и ее элементов. Исследовано движение центрифуги. Исследование дало возможность выявить реальные параметры системы, которые необходимы для расчета ее динамики. Установлено, что опоры в первом приближении можно считать линейно-упругими. Получены зависимости собственных частот от скорости и направления вращения центрифуги. Определены дополнительные частоты на которых возникает явление резонанса

Estimation of a centrifuge rotor strength and analysis of the influence of constructive and technological parameters

В статті досліджена конструкційна міцність чашки центрифуги. Основними елементами дослідження являються напружено-деформований стан чашки, який визначається її конструктивними особливостями та вплив на міцність чашки технології її виготовлення. В статті приведені результати числового моделювання напружено-деформованого стану і результати мікро та макро структурного аналізу, які дозволили оцінити вплив технології виготовлення.The constructive strength of the centrifuge cup is investigated. The main parts of the study are the stress-strain state of the cup, which is determined by its design features and influence on the strength of its cups fabrication method. The results of numerical simulation of the stress-strain state and the results of micro- and macro-structural analysis were used to assess the effect of fabrication method. Most constructive elements of modern machines and mechanisms operating at variable loading, which cause vibrations. Fluctuations cause occurrence of cyclic stress that is the reason of damage and destruction as a result of fatigue especially in the case of resonance or other transitional regimes. Also critical stresses and fatigue limit strongly depend on structural and technological factors. Construction of modern tools and machines developed in the direction of increasing power and high speed while reducing weight. In connection with this increased dynamic loads, respectively, and the vibration influence on machines, tools and their parts. The most influential structural factors actually are a stress concentration and component dimensions. To technological parameters include the structure of the material, which depends on its production. High speed centrifuges are often designed as universal devices where one motor drives a wide range of different rotors. Centrifuges are used for the separation of mixtures of different densities.В статье исследована конструкционная прочность чашки центрифуги. Основными элементами исследования являются напряженно-деформированное состояние чашки, которое определяется ее конструктивными особенностями и влияние на прочность чашки технологии ее изготовления. В статье приведены результаты численного моделирования напряженно-деформированного состояния и результаты микро и макро структурного анализа позволившие оценить влияние технологии изготовления