Perturbation analysis of the limit cycle of the free van der Pol equation

A power series expansion in the damping parameter, epsilon, of the limit cycle of the free van der Pol equation is constructed and analyzed. Coefficients in the expansion are computed in exact rational arithmetic using the symbolic manipulation system MACSYMA and using a FORTRAN program. The series is analyzed using Pade approximants. The convergence of the series for the maximum amplitude of the limit cycle is limited by two pair of complex conjugate singularities in the complex epsilon-plane. A new expansion parameter is introduced which maps these singularities to infinity and leads to a new expansion for the amplitude which converges for all real values of epsilon. Amplitudes computed from this transformed series agree very well with reported numerical and asymptotic results. For the limit cycle itself, convergence of the series expansion is limited by three pair of complex conjugate branch point singularities. Two pair remain fixed throughout the cycle, and correspond to the singularities found in the maximum amplitude series, while the third pair moves in the epsilon-plane as a function of t from one of the fixed pairs to the other. The limit cycle series is transformed using a new expansion parameter, which leads to a new series that converges for larger values of epsilon

Dissecting Biomolecular Interactions Using Deep Learning Approaches

Immunglobuline spielen sowohl bei biologischen Prozessen als auch bei biotechnologischen Anwendungen eine wichtige Rolle, insbesondere aufgrund ihrer zentralen Bedeutung für Immunreaktionen und die Entwicklung therapeutischer Arzneimittel. Um die Immunologie voranzubringen und gezielte Therapien zu entwickeln, ist es entscheidend zu verstehen, wie diese Proteine interagieren. Trotz bedeutender Fortschritte in der Molekularbiologie bleibt die genaue Vorhersage und Beeinflussung von Protein-Protein- Interaktionen (PPIs) eine Herausforderung, die den Durchbruch in Bereichen wie der Arzneimittelentdeckung und Diagnostik behindert. Das Aufkommen fortschrittlicher Deep- Learning-Techniken eröffnet jedoch neue Möglichkeiten zur Überwindung dieser Herausforderungen, indem es schnelle und präzise Vorhersagen von PPIs ermöglicht. Diese Studie ist motiviert durch das Potenzial dieser computergestützten Werkzeuge, unser Verständnis von Immunglobulin-Interaktionen zu verbessern und dadurch zu Innovationen in der Biotechnologie und therapeutischen Entwicklung beizutragen. In dieser Studie haben wir ein weithin zugängliches neuronales Faltungsnetzwerk (Convolutional Neural Network, CNN) angepasst, um eine speziesspezifische Klassifizierung verschiedener Immunglobulin G (IgG) Komplexe zu erreichen. Wir haben Tröpfchen verschiedener Immunglobuline gemischt mit dem B-Zell-Superantigen (SAg), rekombinantem Staphylokokkenprotein A, hergestellt und auf hydrophobe Polymersubstrate aufgebracht. Diese Proteinfärbungen wurden dann mit Hilfe der Polarisationslichtmikroskopie (PLM) abgebildet. Unsere umfassende Analyse auf der Grundlage von 23.745 Bildern ergab, dass das vortrainierte CNN, InceptionV3, nicht nur IgGs aus vier verschiedenen Spezies erfolgreich kategorisierte, sondern auch ihre relative Bindungsstärke an Protein A vorhersagte. Im Durchschnitt von 36 Bindungspaaren beobachteten wir (i) eine Gesamtgenauigkeit von 81.4%, (ii) die höchste Vorhersagegenauigkeit für humanes IgG, den Antikörper mit der höchsten Bindungsaffinität für Protein A, und dass (iii) die Klassifizierungsgenauigkeit für die verschiedenen IgG/Protein A-Verhältnisse im Allgemeinen mit der Bindungsstärke des Protein-Protein-Komplexes korreliert, die mittels Circulardichroismus-Spektroskopie (CD) bestimmt wurde. Darüber hinaus wurde das CNN, das ursprünglich mit IgG/Protein AFarbbildern trainiert wurde, mit einem neuen Satz von Bildern getestet, bei denen ein anderes Superantigen, rekombinantes Protein G, verwendet wurde. Bemerkenswerterweise klassifizierte das CNN trotz des ungewohnten Superantigens die Bindungsstärke von humanem IgG und Protein G korrekt und erreichte eine Genauigkeit von 94 % über verschiedene molare Bindungsverhältnisse hinweg, da der ähnlichste IgG-Komplex im Trainingsdatensatz vorhanden war. Darüber hinaus wurde eine graphentheoretische Analyse eingesetzt, um den bildbasierten Ansatz mit einer parameterbasierten neuronalen Netzwerkstrategie zu ergänzen. Dieser innovative Ansatz wurde durch die Beobachtung von strukturellen Kristallmustern in verschiedenen Proteinproben inspiriert. Die Graphentheorie, die für ihre vielseitigen Anwendungen in verschiedenen wissenschaftlichen Disziplinen bekannt ist, wurde eingesetzt, um Bilder in Graphen umzuwandeln. Mit Hilfe des an der Universität von Michigan entwickelten Python-Pakets StructuralGT extrahierten wir aus diesen Graphen eine Reihe aussagekräftiger Merkmale, die als Eingabedatensätze dienten. Diese Methode wurde mit den Ergebnissen herkömmlicher neuronaler Faltungsnetzwerke verglichen. Die Studie ergab, dass durch die Verwendung der aus den Graphen abgeleiteten Merkmale als Eingabedatensatz für ein entwickeltes neuronales Netz die erforderliche Trainingszeit im Vergleich zur bildbasierten Klassifizierung erheblich (etwa um das Dreifache) reduziert werden konnte, wobei die Genauigkeit im optimierten Schema dennoch hoch blieb. Die Ergebnisse unterstreichen das Potenzial der Kombination von Graphentheorie und Deep Learning für die Proteininteraktionsanalyse. Geeignete graphbasierte Merkmale können zur Vorhersage von Protein-Protein-Interaktionen über den ursprünglichen Trainingsdatensatz hinaus verwendet werden. Dieser Ansatz wird durch die Verarbeitung numerischer Daten vereinfacht und ermöglicht die Klassifizierung auf nicht-GPU-abhängigen Systemen, was sowohl die Rechenkosten als auch die Trainingszeit reduziert. Die Ergebnisse deuten auf eine vielversprechende Methode zur Klassifizierung von biologischen Graphen und zur Vorhersage der Stärke von Proteininteraktionen hin, die für das Protein-Engineering, das Verständnis der Selbstaggregation und die Aufrechterhaltung der Proteinstabilität in komplexen Umgebungen von Nutzen ist

Power Series Solution to a Simple Pendulum with Oscillating Support

The problem of determining some of the effects of a small forcing term on a regular perturbation solution to a nonlinear oscillation problem is studied via a simple example. In particular, we investigate the periodic solution of a simple pendulum with an oscillating support. A power series solution is constructed in terms of c-=( )2 L,where w0 and w are the natural and driving frequencies respectively, a is the amplitude of the support oscillation, and L is the length of the pendulum. These solutions are analyzed for three cases: above resonance (w \u3e wo), below resonance (w \u3c wo), and at resonance (w = wo). In each case, the approximate location of the nearest singularities which limit the convergence of the power series are obtained by using Pad6 approximants. Using this information, a new expansion parameter 6 is introduced, where the radius of convergence of the transformed series is greater than the original series. The effects of primary and higher order resonances on the convergence of the series solution is noted and discussed

Psychometric Properties of the Persian Version of the Short Beck Depression Inventory with Iranian Psychiatric Outpatients

The short form of the Beck Depression Inventory (BDI-13) is useful for the screening and assessment of depression in clinical and research settings. The aim of the present study was to investigate the psychometric properties of the Persian (Farsi) version of BDI-13 in an Iranian clinical sample. The sample consisted of 52 Iranian psychiatric outpatients who received services at psychiatric and psychological clinics at the School of Behavioral Sciences & Mental Health-Tehran Institute of Psychiatry, Iran University of Medical Sciences (IUMS) in Tehran, Iran. The study examined the reliability, construct validity, and factor structure of the instrument. The instrument indicated good reliability with Cronbach's alpha of.85 and strong construct validity based on moderate to strong positive correlations with other measures of mental health issues. Using a Principal Component Analysis and Varimax Rotation with Kaiser Normalization, three factors were identified and labeled Affective (F1), Somatic/Vegetative (F2), and Cognitive/Loss of Functioning (F3). The current factor structure suggests that depression is a multidimensional construct in an Iranian clinical sample. This study provides further evidence that the Persian version of the BDI-13 is a psychometrically sound instrument that can be used for clinical and research purposes in Iran. Copyright © 2016 M. Dadfar and Z. Kalibatseva

The effect of Saliva officinalis extract on the menopausal symptoms in postmenopausal women: An RCT

Background: The menopausal symptoms are the most common problems in postmenopausal women. Due to the side effects of hormone replacement therapy, the use of medicinal herbs has increased for the treatment of menopausal symptoms. Objective: The aim of this study was to evaluate the effect of Saliva officinal is on the decreasing of the severity of the menopausal symptoms in postmenopausal women. Materials and Methods: The study was performed on 30 postmenopausal women aged 46–58 yr referred to the healthcare center of Darab who experienced various degrees of postmenopausal symptoms. The severity of menopausal symptoms is recorded by a Menopause Rating Scale. Participants received a 100 mg capsule of sage extract daily for 4 wk. The severity of postmenopausal symptoms was compared before and after four weeks of the consumption of sage extract. Results: The results showed the severity of hot flashes, night sweats, panic, fatigue, and concentration had significant differences before and after the consumption of sage extract. Conclusion: It was concluded that Saliva officinal is were effective to change the severity of some of the menopausal symptoms in postmenopausal women

The Impression of the Originality of Existence Philosophy Concepts in the Dramatic Literature with Emphasis on Three Plays (Nausea, Dirty Hands and the Satan and God)

Jean-Paul Sartre's point of view on the originality of existence philosophy is interleaved with concepts such as: freedom, apprehension, choice, awareness and human presence as well as everything that leading to man's liberation is reflected in his plays. Jean-Paul Sartre puts existence precede to the nature and considered the man as a potential free being that in the way of freedom he is responsible not only for himself but also for others. In the book of "Existence and Non-Existence" he is believes in deconstruction in all social and cultural fields. Sartre sees drama as a window for attitudinize the universe. The concept of existentialism in his plays is under the influence of philosophical and ideological propositions. Moral and political characteristics in the works of Jean-Paul Sartre expressed in such a way that describes a kind of worldview with philosophical propositions and dramatic, artful technique. Therefore one of the questions in this article is how did Sartre's dramatic literature benefit from the philosophy of existentialism? How does existence and non-existence appear in most of Sartre's plays? What does the concept of hell basically mean in his works? In this article, an attempt has been made to demonstrate how existence and non-existence and the critique of dialectical wisdom have been evaluated in his plays

Reliability and factorial structure of the farsi version of the Arabic scale of death anxiety in an iranian middle-aged sample

The present study aimed to explore the psychometric properties of the Arabic Scale of Death Anxiety (ASDA) in an Iranian middle-aged sample. A sample of 55 volunteer Iranian persons took part in the study. Cronbach's alpha of the ASDA was found to be high (0.91) and Spearman-Brown and Guttman Split-Half coefficients were 0.86. The factor analysis of the ASDA items yielded five factors accounting for 72.49 of the total variance and labeled (F1) fear of death and fear of dead people; (F2) fear of postmortem events and fear of tombs; (F3) fear of lethal disease; (F4) preoccupation with after death, and death fear in sleep; and (F5) fear of deprivation of own ones. The ASDA has a good validity and reliability, and it can be used in clinical, educational, and research settings. © 2016 Mahboubeh Dadfar and Fazel Bahrami

Mutual inductance instability of the tip vortices behind a wind turbine

Two modal decomposition techniques are employed to analyse the stability of wind turbine wakes. A numerical study on a single wind turbine wake is carried out focusing on the instability onset of the trailing tip vortices shed from the turbine blades. The numerical model is based on large-eddy simulations (LES) of the Navier-Stokes equations using the actuator line (ACL) method to simulate the wake behind the Tj ae reborg wind turbine. The wake is perturbed by low-amplitude excitation sources located in the neighbourhood of the tip spirals. The amplification of the waves travelling along the spiral triggers instabilities, leading to breakdown of the wake. Based on the grid configurations and the type of excitations, two basic flow cases, symmetric and asymmetric, are identified. In the symmetric setup, we impose a 120 degrees symmetry condition in the dynamics of the flow and in the asymmetric setup we calculate the full 360 degrees wake. Different cases are subsequently analysed using dynamic mode decomposition (DMD) and proper orthogonal decomposition (POD). The results reveal that the main instability mechanism is dispersive and that the modal growth in the symmetric setup arises only for some specific frequencies and spatial structures, e.g. two dominant groups of modes with positive growth (spatial structures) are identified, while breaking the symmetry reveals that almost all the modes have positive growth rate. In both setups, the most unstable modes have a non-dimensional spatial growth rate close to pi/2 and they are characterized by an out-of-phase displacement of successive helix turns leading to local vortex pairing. The present results indicate that the asymmetric case is crucial to study, as the stability characteristics of the flow change significantly compared to the symmetric configurations. Based on the constant non-dimensional growth rate of disturbances, we derive a new analytical relationship between the length of the wake up to the turbulent breakdown and the operating conditions of a wind turbine