Search results for: negative differential conductance

Authors: Rafia Rafique, Mutmina Zainab

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The present study investigated the relationship between fear of negative evaluation (FNE), social support and well-being in people with Vitiligo. It was hypothesized that low level of FNE and greater social support is likely to predict well-being. It was also hypothesized that social support is likely to moderate the relationship between FNE and well-being. Correlational research design was used for the present study. Non-probability purposive sampling technique was used to collect a sample (N=122) of people with Vitiligo. Hierarchical Moderated Regression analysis was used to test prediction and moderation. Brief Fear of Negative Evaluation Scale, Multidimensional Scale of Perceived Social Support (MSPSS) and Mental Health Continuum-Short form (MHC-SF) were used to evaluate the study variables. Fear of negative evaluation negatively predicted well-being (emotional and psychological). Social support from significant others and friends predicted social well-being. Social Support from family predicted emotional and psychological well-being. It was found that social support from significant others moderated the relationship between FNE and emotional well-being and social support from family moderated the relationship between FNE and social well-being. Dermatologists treating people with Vitiligo need to educate them and their families about the buffering role of social support (family and significant others). Future studies need to focus on other important mediating factors that can possibly explain the relationship between fear of negative evaluation and wellbeing.

Keywords: fear of negative evaluation, hierarchical moderated regression, vitiligo, well-being

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Authors: Ayaz Ahmad

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In this work, we present the effect of noise on the solution of a partial differential equation (PDE) in three different setting. We shall first consider random initial condition for two nonlinear dispersive PDE the non linear Schrodinger equation and the Kortteweg –de vries equation and analyse their effect on some special solution , the soliton solutions.The second case considered a linear partial differential equation , the wave equation with random initial conditions allow to substantially decrease the computational and data storage costs of an algorithm to solve the inverse problem based on the boundary measurements of the solution of this equation. Finally, the third example considered is that of the linear transport equation with a singular drift term, when we shall show that the addition of a multiplicative noise term forbids the blow up of solutions under a very weak hypothesis for which we have finite time blow up of a solution in the deterministic case. Here we consider the problem of wave propagation, which is modelled by a nonlinear dispersive equation with noisy initial condition .As observed noise can also be introduced directly in the equations.

Keywords: drift term, finite time blow up, inverse problem, soliton solution

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Authors: Han Xue, Zhang Lanyue

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In order to seek more effective feature extraction technology, feature extraction method based on MFCC combined with vector hydrophone is exposed in the paper. The sound pressure signal and particle velocity signal of two kinds of ships are extracted by using MFCC and its evolution form, and the extracted features are fused by using fisher-ratio and correlated distance criterion. The features are then identified by BP neural network. The results showed that MFCC, First-Order Differential MFCC and Second-Order Differential MFCC features can be used as effective features for recognition of underwater targets, and the fusion feature can improve the recognition rate. Moreover, the results also showed that the recognition rate of the particle velocity signal is higher than that of the sound pressure signal, and it reflects the superiority of vector signal processing.

Keywords: vector information, MFCC, differential MFCC, fusion feature, BP neural network

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Authors: Johnson Oladele Fatokun, I. P. Akpan

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In this paper, the one-dimensional time dependent Schrödinger equation is discretized by the method of lines using a second order finite difference approximation to replace the second order spatial derivative. The evolving system of stiff ordinary differential equation (ODE) in time is solved numerically by an L-stable trapezoidal-like integrator. Results show accuracy of relative maximum error of order 10-4 in the interval of consideration. The performance of the method as compared to an existing scheme is considered favorable.

Keywords: Schrodinger’s equation, partial differential equations, method of lines (MOL), stiff ODE, trapezoidal-like integrator

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Authors: C. A. Bradley, D. Patsios, D. Berridge

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This paper presents evidence to better understand the risk and protective factors related to sibling conflict and the patterns of association between sibling conflict and negative adjustment outcomes by incorporating additional familial and societal factors within statistical models of risk and adjustment. It was conducted through the secondary analysis of a large representative cross-sectional dataset of children in the UK. The original study includes proxy interviews for young children and self-report interviews for adolescents. The study applies an ecological systems framework for the analyses. Hierarchical regression models assess risk and protective factors and adjustment outcomes associated with sibling conflict. Interactions reveal differential effect between contextual risk factors and the social context of influence. The general pattern of findings suggested that, although factors affecting likelihood of experiencing sibling conflict were often determined by child age, some remained consistent across childhood. These factors were often conditional on each other, reinforcing the importance of an ecological framework. Across both age-groups, sibling conflict was associated with siblings closer in age; male sibling groups; most advantaged socio-economic group; and exposure to community violence, such as witnessing violent assault or robbery. The study develops the evidence base on the influence of ethnicity and socio-economic group on sibling conflict by exploring interactions between social context. It also identifies key new areas of influence – such as family structure, disability, and community violence in exacerbating or reducing risk of conflict. The study found negative associations between sibling conflict and young children’s mental well-being and adolescents' mental well-being and anti-social behaviour, but also more context specific associations – such as sibling conflict moderating the negative impact of adversity and high risk experiences for young children such as parental violence toward the child.

Keywords: adjustment, conflict, ecological systems, family systems, risk and protective factors, sibling

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Authors: N. Senu, I. A. Kasim, F. Ismail, N. Bachok

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In this paper zero-dissipative explicit Runge-Kutta method is derived for solving second-order ordinary differential equations with periodical solutions. The phase-lag and dissipation properties for Runge-Kutta (RK) method are also discussed. The new method has algebraic order three with dissipation of order infinity. The numerical results for the new method are compared with existing method when solving the second-order differential equations with periodic solutions using constant step size.

Keywords: dissipation, oscillatory solutions, phase-lag, Runge-Kutta methods

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Authors: Alaa Sheta

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Economic Load Dispatch (ELD) is one of the vital optimization problems in power system planning. Solving the ELD problems mean finding the best mixture of power unit outputs of all members of the power system network such that the total fuel cost is minimized while sustaining operation requirements limits satisfied across the entire dispatch phases. Many optimization techniques were proposed to solve this problem. A famous one is the Quadratic Programming (QP). QP is a very simple and fast method but it still suffer many problem as gradient methods that might trapped at local minimum solutions and cannot handle complex nonlinear functions. Numbers of metaheuristic algorithms were used to solve this problem such as Genetic Algorithms (GAs) and Particle Swarm Optimization (PSO). In this paper, another meta-heuristic search algorithm named Differential Evolution (DE) is used to solve the ELD problem in power systems planning. The practicality of the proposed DE based algorithm is verified for three and six power generator system test cases. The gained results are compared to existing results based on QP, GAs and PSO. The developed results show that differential evolution is superior in obtaining a combination of power loads that fulfill the problem constraints and minimize the total fuel cost. DE found to be fast in converging to the optimal power generation loads and capable of handling the non-linearity of ELD problem. The proposed DE solution is able to minimize the cost of generated power, minimize the total power loss in the transmission and maximize the reliability of the power provided to the customers.

Keywords: economic load dispatch, power systems, optimization, differential evolution

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Authors: Romaric Desbrousses, Lan Lin

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The objective of this study is to determine how Canadian seismic design provisions affect the column axial load resistance of moment-resisting frame reinforced concrete buildings subjected to the differential settlement of their foundation. To do so, two four-storey buildings are designed in accordance with the seismic design provisions of the Canadian Concrete Design Standards. One building is located in Toronto, which is situated in a moderate seismic hazard zone in Canada, and the other in Vancouver, which is in Canada’s highest seismic hazard zone. A finite element model of each building is developed using SAP 2000. A 100 mm settlement is assigned to the base of the building’s center column. The axial load resistance of the column is represented by the demand capacity ratio. The analysis results show that settlement-induced tensile axial forces have a particularly detrimental effect on the conventional settling columns of the Toronto buildings which fail at a much smaller settlement that those in the Vancouver buildings. The results also demonstrate that particular care should be taken in the design of columns in short-span buildings.

Keywords: Columns, Demand, Foundation differential settlement, Seismic design, Non-linear analysis

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Authors: Arash Jafari, Mehdi Taghaddosi, Azin Parvin

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In this study, a vibrational differential equation governing on swinging single-degree-of-freedom pendulum in a viscous fluid has been investigated. The damping process is characterized according to two different regimes: at first, damping in stationary viscous fluid, in the second, damping in flowing viscous fluid with constant velocity. Our purpose is to enhance the ability of solving the mentioned nonlinear differential equation with a simple and innovative approach. Comparisons are made between new method and Numerical Method (rkf45). The results show that this method is very effective and simple and can be applied for other nonlinear problems.

Keywords: oscillating systems, angular frequency and damping ratio, pendulum at fluid, locus of maximum

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Authors: Abhigna Bhatt, Arnab Banerjee

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A periodic system with only a single coupling degree of freedom is called a monocoupled system. Monocoupled systems with mechanisms like mass in the mass system generates effective negative mass, mass connected with rigid links generates inertial amplification, and spring-mass connected with a rigid link generateseffective negative stiffness. In this paper, the representative unit cell is introduced, considering all three mechanisms combined. Further, the dynamic stiffness matrix of the unit cell is constructed, and the dispersion relation is obtained by applying the Bloch theorem. The frequency response function is also calculated for the finite length of periodic unit cells. Moreover, the input displacement signal is given to the finite length of periodic structure and using inverse Fourier transform to visualize the wave propagation in the time domain. This visualization explains the sudden attenuation in metamaterial due to energy dissipation by an embedded resonator at the resonance frequency. The visualization created for wave propagation is found necessary to understand the insights of physics behind the attenuation characteristics of the system.

Keywords: mono coupled system, negative effective mass, negative effective stiffness, inertial amplifier, fourier transform

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Authors: Emanuel Guariglia

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In this paper we deal with Chebyshev wavelets. We analyze their properties computing their Fourier transform. Moreover, we discuss the differential properties of Chebyshev wavelets due the connection coefficients. The differential properties of Chebyshev wavelets, expressed by the connection coefficients (also called refinable integrals), are given by finite series in terms of the Kronecker delta. Moreover, we treat the p-order derivative of Chebyshev wavelets and compute its Fourier transform. Finally, we expand the mother wavelet in Taylor series with an application both in fractional calculus and fractal geometry.

Keywords: Chebyshev wavelets, Fourier transform, connection coefficients, Taylor series, local fractional derivative, Cantor set

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Authors: Pan Lee Ching, Chua Bee Seok

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The experience of negative work-life interaction often confronted with work related stress includes workload. The appraisal of challenge and hindrance jobs depend on the type of workload to stimulate stress response. Nevertheless, the effects of challenge and hindrance jobs on distress and negative work-life interaction are scarcely explored. Thus, research objective was to examine the relationship among challenge appraisal job (qualitative workload), hindrance appraisal job (quantitative workload), and negative work-life interaction with the mediating role of distress. A survey with random sampling method was performed on current serving public secondary school teachers in Sabah. Collected data showed 447 respondents completed three questionnaires, namely Challenge-hindrance Appraisal Scale, Stress Professional Positive and Negative Questionnaire, and Survey Work-home Interaction-Nijmegan. Partial Least Square-Structural Equation Modeling (PLS-SEM) was used to analyse mediation effect. Results showed distress fully mediates the relationship between challenge appraisal job (qualitative workload) and negative work-life interaction. The indirect effect was significant and negative. While distress partially mediates the relationship between hindrance appraisal job (quantitative workload) and negative work-life interaction. The indirect effect was significant and positive. The study implied that challenge appraisal job could be a positive resource for teacher to facilitate work and life, whereas hindrance appraisal job could disengage the facilitation. Hence, strengthen challenge appraisal job and control hindrance appraisal job could curb distress at work and underpin life interaction among the teachers.

Keywords: challenge-hindrance job, distress, work-life, workload

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Authors: Hassan Manouzi

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We present in this paper a useful strategy to solve stochastic partial differential equations (SPDEs) involving stochastic coefficients. Using the Wick-product of higher order and the Wiener-Itˆo chaos expansion, the SPDEs is reformulated as a large system of deterministic partial differential equations. To reduce the computational complexity of this system, we shall use a decomposition-coordination method. To obtain the chaos coefficients in the corresponding deterministic equations, we use a least square formulation. Once this approximation is performed, the statistics of the numerical solution can be easily evaluated.

Keywords: least squares, wick product, SPDEs, finite element, wiener chaos expansion, gradient method

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Authors: Xuezhang Hou

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In the present paper, a hybrid hyperbolic dynamic system formulated by partial differential equations with initial and boundary conditions is considered. First, the system is transformed to an abstract evolution system in an appropriate Hilbert space, and spectral analysis and semigroup generation of the system operator is discussed. Subsequently, a sliding model control problem is proposed and investigated, and an equivalent control method is introduced and applied to the system. Finally, a significant result that the state of the system can be approximated by an ideal sliding mode under control in any accuracy is derived and examined.

Keywords: hyperbolic dynamic system, sliding model control, semigroup of linear operators, partial differential equations

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Authors: Tudor Barbu

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We present a robust nonlinear parabolic partial differential equation (PDE)-based denoising scheme in this article. Our approach is based on a second-order anisotropic diffusion model that is described first. Then, a consistent and explicit numerical approximation algorithm is constructed for this continuous model by using the finite-difference method. Finally, our restoration experiments and method comparison, which prove the effectiveness of this proposed technique, are discussed in this paper.

Keywords: anisotropic diffusion, finite differences, image denoising and restoration, nonlinear PDE model, anisotropic diffusion, numerical approximation schemes

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Authors: Abdel-Maksoud Abdel-Kader Soliman

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The General Regularized Long Wave (GRLW) equation is solved numerically by giving a new algorithm based on collocation method using quartic B-splines at the mid-knot points as element shape. Also, we use the Fourth Runge-Kutta method for solving the system of first order ordinary differential equations instead of finite difference method. Our test problems, including the migration and interaction of solitary waves, are used to validate the algorithm which is found to be accurate and efficient. The three invariants of the motion are evaluated to determine the conservation properties of the algorithm.

Keywords: generalized RLW equation, solitons, quartic b-spline, nonlinear partial differential equations, difference equations

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Authors: Sook Ching Yee, Angela Siew Hoong Lee

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Big data technologies have become a trend to exploit business opportunities and provide valuable business insights through the analysis of big data. However, there are still many organizations that have yet to adopt big data technologies especially small and medium organizations (SME). This study uses the technology acceptance model (TAM) to look into several constructs in the TAM and other additional constructs which are positive affect, negative affect, organizational factor and motivational factor. The conceptual model proposed in the study will be tested on the relationship and influence of positive affect, negative affect, organizational factor and motivational factor towards the intention to use big data technologies to produce an outcome. Empirical research is used in this study by conducting a survey to collect data.

Keywords: big data technologies, motivational factor, negative affect, organizational factor, positive affect, technology acceptance model (TAM)

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Authors: Asim Qureshi, R. S. Jangid

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Seismic response control of structures is generally achieved by using control devices which either dissipate the input energy or modify the dynamic properties of structure.In this paper, the response of a 20-storey benchmark building supplemented by viscous dampers and Negative Stiffness Device (NSD) is assessed by numerical simulations using the Newmark-beta method. True negative stiffness is an adaptive passive device which assists the motion unlike positive stiffness. The structure used in this study is subjected to four standard ground motions varying from moderate to severe, near fault to far-field earthquakes. The objective of the present study is to show the effectiveness of the adaptive negative stiffness device (NSD and passive dampers together) relative to passive dampers alone. This is done by comparing the responses of the above uncontrolled structure (i.e., without any device) with the structure having passive dampers only and also with the structure supplemented with adaptive negative stiffness device. Various performance indices, top floor displacement, top floor acceleration and inter-storey drifts are used as comparison parameters. It is found that NSD together with passive dampers is quite effective in reducing the response of aforementioned structure relative to structure without any device or passive dampers only. Base shear and acceleration is reduced significantly by incorporating NSD at the cost of increased inter-storey drifts which can be compensated using the passive dampers.

Keywords: adaptive negative stiffness device, apparent yielding, NSD, passive dampers

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Authors: Rahul Singha, D. Vakula

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This paper presents a corrugated antipodal vivaldi antenna with improved performance by using negative index metamaterial (NIM) of the Archimedean spiral design. A single layer NIM piece is placed perpendicular middle of the two arm of the proposed antenna. The antenna size is 30×60×0.787 mm3 operating at 8GHz. The simulated results of NIM corrugated antipodal vivaldi antenna show that the gain and directivity has increased up to 1.2dB and 1dB respectively. The HPBW is increased by 90 with the reflection coefficient less than ‒10 dB from 4.7 GHz to 11 GHz for UWB application.

Keywords: Negative Index Metamaterial (NIM), Ultra Wide Band (UWB), Half Power Beam Width (HPBW), vivaldi antenna

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Authors: G. Akgun, I. Algul, H. Kurtaran

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In this paper geometrically nonlinear static behavior of laminated composite hollow super-elliptic beams is investigated using generalized differential quadrature method. Super-elliptic beam can have both oval and elliptic cross-sections by adjusting parameters in super-ellipse formulation (also known as Lamé curves). Equilibrium equations of super-elliptic beam are obtained using the virtual work principle. Geometric nonlinearity is taken into account using von-Kármán nonlinear strain-displacement relations. Spatial derivatives in strains are expressed with the generalized differential quadrature method. Transverse shear effect is considered through the first-order shear deformation theory. Static equilibrium equations are solved using Newton-Raphson method. Several composite super-elliptic beam problems are solved with the proposed method. Effects of layer orientations of composite material, boundary conditions, ovality and ellipticity on bending behavior are investigated.

Keywords: generalized differential quadrature, geometric nonlinearity, laminated composite, super-elliptic cross-section

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Authors: Hellal Abdelkader, Chafaa Salah, Boudjemaa Fouzia

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A new, convenient, and high yielding procedure for the preparation of diethyl α-aminophosphonates in water via Kabachnik-Fields reaction by one-pot reaction of aromatic aldehydes, ortho-aminophenols, and dialkylphosphites in the presence of a low catalytic amount of citric, malic, tartaric, and oxalic acids as a natural, bi-functional, and highly stable catalyst is described, the obtained products were characterized by elemental analyses, molar conductance, magnetic susceptibility, FTIR, Uv-Vis spectral data, NMR-C, NMR-H, and NMR-P analyses.

Keywords: α-aminophosphonates, aminophenols, natural acids, aqueous media, Kabachnik-Fields reaction

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Authors: H. Ozbasaran

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IPN and IPE sections, which are commonly used European I shapes, are widely used in steel structures as cantilever beams to support overhangs. A considerable number of studies exist on calculating lateral torsional buckling load of I sections. However, most of them provide series solutions or complex closed-form equations. In this paper, a simple equation is presented to calculate lateral torsional buckling load of IPN and IPE section cantilever beams. First, differential equation of lateral torsional buckling is solved numerically for various loading cases. Then a parametric study is conducted on results to present an equation for lateral torsional buckling load of European IPN and IPE beams. Finally, results obtained by presented equation are compared to differential equation solutions and finite element model results. ABAQUS software is utilized to generate finite element models of beams. It is seen that the results obtained from presented equation coincide with differential equation solutions and ABAQUS software results. It can be suggested that presented formula can be safely used to calculate critical lateral torsional buckling load of European IPN and IPE section cantilevers.

Keywords: cantilever, IPN, IPE, lateral torsional buckling

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Authors: Hossein Arfaeinia, Azam Nadali, Zahra Asadgol, Mohammad Fahiminia

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Indoor and outdoor particulate matters (PM) were monitored in 20 residential buildings in a two-part study. In part I, the levels of indoor and outdoor PM₁₀, PM₂.₅ and PM₁ was measured using real time GRIMM dust monitors. In part II, the effect of negative air ions (NAIs) method was investigated on the reduction of indoor concentration of PM in these residential buildings. Hourly average concentration and standard deviation (SD) of PM₁₀ in indoor and outdoor at residential buildings were 90.1 ± 33.5 and 63.5 ± 27.4 µg/ m3, respectively. Indoor and outdoor concentrations of PM₂.₅ in residential buildings were 49.5 ± 18.2 and 39.4± 18.1 µg/ m3 and for PM₁ the concentrations were 6.5 ± 10.1and 4.3 ± 7.7 µg/ m3, respectively. Indoor/outdoor (I/O) ratios and concentrations of all size fractions of PM were strongly correlated with wind speed and temperature whereas a good relationship was not observed between humidity and I/O ratios of PM. We estimated that nearly 71.47 % of PM₁₀, 79.86 % of PM₂.₅ and of 61.25 % of PM₁ in indoor of residential buildings can be removed by negative air ions.

Keywords: particle matter (PM), indoor air, negative air ions (NAIs), residential building

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Authors: Magdalena Jablonska, Andrzej Falkowski

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The negativity effect is one of the most intriguing and well-studied psychological phenomena that can be observed in many areas of human life. The aim of the following study is to investigate how valence framing and positive and negative information about political candidates affect judgments about similarity to an ideal and bad politician. Based on the theoretical framework of features of similarity, it is hypothesized that negative features have a stronger effect on similarity judgments than positive features of comparable value. Furthermore, the mediating role of affect is tested. Method: One hundred sixty-one people took part in an experimental study. Participants were divided into 6 research conditions that differed in the reference point (positive vs negative framing) and the number of favourable and unfavourable information items about political candidates (a positive, neutral and negative candidate profile). In positive framing condition, the concept of an ideal politician was primed; in the negative condition, participants were to think about a bad politician. The effect of independent variables on similarity judgments, affective evaluation, and voting intention was tested. Results: In the positive condition, the analysis showed that the negative effect of additional unfavourable features was greater than the positive effect of additional favourable features in judgements about similarity to the ideal candidate. In negative framing condition, ANOVA was insignificant, showing that neither the addition of positive features nor additional negative information had a significant impact on the similarity to a bad political candidate. To explain this asymmetry, two mediational analyses were conducted that tested the mediating role of affect in the relationship between similarity judgments and voting intention. In both situations the mediating effect was significant, but the comparison of two models showed that the mediation was stronger for a negative framing. Discussion: The research supports the negativity effect and attempts to explain the psychological mechanism behind the positive-negative asymmetry. The results of mediation analyses point to a stronger mediating role of affect in the relationship between cognitive evaluation and voting intention. Such a result suggests that negative comparisons, leading to the activation of negative features, give rise to stronger emotions than positive features of comparable strength. The findings are in line with positive-negative asymmetry, however, by adopting Tversky’s framework of features of similarity, the study integrates the cognitive mechanism of the negativity effect delineated in the contrast model of similarity with its emotional component resulting from the asymmetrical effect of positive and negative emotions on decision-making.

Keywords: affect, framing, negativity effect, positive-negative asymmetry, similarity judgements

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Authors: Serkan Caliskan

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The aim of this study is to understand the spin-resolved properties of ZnO armchair and zigzag nanoribbons. The spin polarization can be induced by either geometry of the nanoribbons or ferromagnetic electrodes. Hence, spin-dependent behavior is revealed in these nanostructures in the absence of external magnetic field. Both electronic structure and magnetic properties of the nanoribbons are analyzed, employing first-principles calculations through Density Functional Theory. The relevant properties using the spin-dependent band structure, conductance, transmission, density of states and magnetic moment are elucidated. These results can be utilized to describe the nanoscale structures and stimulate the experimental works.

Keywords: first principles, spin polarized transport, ZnO device, ZnO nanoribbons

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Authors: J. J. Cetina-Denis, R. M. López-Gutiérrez, R. Ramírez-Ramírez, C. Cruz-Hernández

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This work addresses the problem of designing an algorithm capable of generating chaotic trajectories for mobile robots. Particularly, the chaotic behavior is induced in the linear and angular velocities of a Khepera III differential mobile robot by infusing them with the states of the H´enon chaotic map. A possible application, using the properties of chaotic systems, is patrolling a work area. In this work, numerical and experimental results are reported and analyzed. In addition, two quantitative numerical tests are applied in order to measure how chaotic the generated trajectories really are.

Keywords: chaos, chaotic trajectories, differential mobile robot, Henon map, Khepera III robot, patrolling applications

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Authors: Deva Kanta Phukan

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An attempt is made where an electrically conducting fluid is injected from a fixed outer cylindrical casing onto an inner moving cylindrical rod. A magnetic field is applied parallel to the axis of the cylindrical rod. The basic governing set of partial differential equations for conservation of mass and momentum are reduced to a set of non-linear ordinary differential equation by introducing similarity transformation, which are integrated numerically. A perturbation solution for the case of large magnetic parameter is derived for constant Reynolds number.

Keywords: annular axi-symmetric stagnation flow, conducting fluid, magnetic field, moving cylinder

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Authors: Razi Khalafi

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Brain is the information processing center of the human body. Stimuli in form of information are transferred to the brain and then brain makes the decision on how to respond to them. In this research we propose a new partial differential equation which analyses the EEG signals and make a relationship between the incoming stimuli and the brain response to them. In order to test the proposed model, a set of external stimuli applied to the model and the model’s outputs were checked versus the real EEG data. The results show that this model can model the EEG signal well. The proposed model is useful not only for modeling of the EEG signal in case external stimuli but it can be used for the modeling of brain response in case of internal stimuli.

Keywords: Brain, stimuli, partial differential equation, response, eeg signal

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Authors: Jurriaan Gillissen

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This work is concerned with stabilizing the numerical integration of the Navier-Stokes equation (NSE), backwards in time. Applications involve the detection of sources of, e.g., sound, heat, and pollutants. Stable reverse numerical integration of parabolic differential equations is also relevant for image de-blurring. While the literature addresses the reverse integration problem of the advection-diffusion equation, the problem of numerical reverse integration of the NSE has, to our knowledge, not yet been addressed. Owing to the presence of viscosity, the NSE is irreversible, i.e., when going backwards in time, the fluid behaves, as if it had a negative viscosity. As an effect, perturbations from the perfect solution, due to round off errors or discretization errors, grow exponentially in time, and reverse integration of the NSE is inherently unstable, regardless of using an implicit time integration scheme. Consequently, some sort of filtering is required, in order to achieve a stable, numerical, reversed integration. The challenge is to find a filter with a minimal adverse affect on the accuracy of the reversed integration. In the present work, we explore an adjoint gradient method (AGM) to achieve this goal, and we apply this technique to two-dimensional (2D), decaying turbulence. The AGM solves for the initial velocity field u0 at t = 0, that, when integrated forward in time, produces a final velocity field u1 at t = 1, that is as close as is feasibly possible to some specified target field v1. The initial field u0 defines a minimum of a cost-functional J, that measures the distance between u1 and v1. In the minimization procedure, the u0 is updated iteratively along the gradient of J w.r.t. u0, where the gradient is obtained by transporting J backwards in time from t = 1 to t = 0, using the adjoint NSE. The AGM thus effectively replaces the backward integration by multiple forward and backward adjoint integrations. Since the viscosity is negative in the adjoint NSE, each step of the AGM is numerically stable. Nevertheless, when applied to turbulence, the AGM develops instabilities, which limit the backward integration to small times. This is due to the exponential divergence of phase space trajectories in turbulent flow, which produces a multitude of local minima in J, when the integration time is large. As an effect, the AGM may select unphysical, noisy initial conditions. In order to improve this situation, we propose two remedies. First, we replace the integration by a sequence of smaller integrations, i.e., we divide the integration time into segments, where in each segment the target field v1 is taken as the initial field u0 from the previous segment. Second, we add an additional term (regularizer) to J, which is proportional to a high-order Laplacian of u0, and which dampens the gradients of u0. We show that suitable values for the segment size and for the regularizer, allow a stable reverse integration of 2D decaying turbulence, with accurate results for more then O(10) turbulent, integral time scales.

Keywords: time reversed integration, parabolic differential equations, adjoint gradient method, two dimensional turbulence

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Authors: Lola T. Alimkhodjaeva, Lola T. Zakirova, Soniya S. Ziyavidenova

Abstract:

Background: Breast cancer occupies the first place among the cancer in women in the world. It is urgent today to study the role of molecular markers which are capable of predicting the dynamics and outcome of the disease. The aim of this study is to define the prognostic value of the content of estrogen receptor (ER), progesterone receptor (PgR), and amplification of HER-2 / neu oncoprotein by studying 3 and 5-year overall and relapse-free survival in 470 patients with primary operable and 280 patients with locally–advanced breast cancer. Materials and methods: Study results of 3 and 5-year overall and relapse-free survival, depending on the content of RE, PgR in primary operable patients showed that ER positive (+) and PgR (+) survival was 100 (96.2%) and 97.3 (94.6%), for ER negative (-) and PgR (-) - 69.2 (60.3%) and 65.4 (57.7%), for ER positive (+) and negative PgR (-) 87.4 (80.1%) and 81.5 (79.3%), for ER negative (-) and positive PgR (+) - 97.4 (93.4%) and 90.4 (88.5%), respectively. Survival results depended also on the level of HER-2 / neu expression. In patients with HER-2 / neu negative the survival rates were as follows: 98.6 (94.7%) and 96.2 (92.3%). In group of patients with the level of HER-2 / neu (2+) expression these figures were: 45.3 (44.3%) and 45.1 (40.2%), and in group of patients with the level of HER-2 / neu (3+) expression - 41.2 (33.1%) and 34.3 (29.4%). The combination of ER negative (-), PgR (-), HER-2 / neu (-) they were 27.2 (25.4%) and 19.5 (15.3%), respectively. In patients with locally-advanced breast cancer the results of 3 and 5-year OS and RFS for ER (+) and PgR (+) were 76.3 (69.3%) and 62.2 (61.4%), for ER (-) and RP (-) 29.1 (23.7%) and 18.3 (12.6%), for ER (+) and PgR (-) 61.2 (47.2%) and 39.4 (25.6%), for ER (-) and PgR (+) 54.3 (43.1%) and 41.3 (18.3%), respectively. The level of HER-2 / neu expression also affected the survival results. Therefore, in HER-2/ neu negative patients the survival rate was 74.1 (67.6%) and 65.1 (57.3%), with the level of expression (2+) 20.4 (14.2%) and 8.6 (6.4%), with the level of expression (3+) 6.2 (3.1%) and 1.2 (1.5%), respectively. The combination for ER, PgR, HER-2 / neu negative was 22.1 (14.3%) and 8.4 (1.2%). Conclusion: Thus, the presence of steroid hormone receptors in breast tumor tissues at primary operable and locally- advanced process as the lack of HER-2/neu oncoprotein correlates with the highest rates of 3- and 5-year overall and relapse-free survival. The absence of steroid hormone receptors as well as of HER-2/neu overexpression in malignant breast tissues significantly degrades the 3- and 5-year overall and relapse-free survival. Tumors with ER, PgR and HER-2/neu negative have the most unfavorable prognostics.

Keywords: breast cancer, estrogen receptor, oncoprotein, progesterone receptor

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