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Transport in multilayered nanostructures : the dynamical mean-field theory approach
\"Over the last 25 years, dynamical mean-field theory (DMFT) has emerged as one of the most powerful new developments in many-body physics. Written by one of the key researchers in the field, this book presents the first comprehensive treatment of this ever-developing topic. Transport in Mutlilayered Nanostructures is varied and modern in its scope, and: Develops the formalism of many-body Green's functions using the equation-of-motion approach Applies DMFT to study transport in multilayered nanostructures, which is likely to be one of the most prominent applications of nanotechnology in the coming years Develops formalism first for the bulk and then for the inhomogeneous multilayered systems Describes in great detail the science behind the metal-insulator transition, electronic charge reconstruction, strongly correlated contributions to capacitance, and superconductivity Includes complete derivations and emphasizes how to carry out numerical calculations, including discussions of parallel programming algorithms Provides descriptions of the crossover from tunneling to thermally activated transport, of the properties of Josephson junctions with barriers tuned near the metal-insulator transition of thermoelectric coolers and power generators and of nonequilibrium extensions to determine current-voltage characteristics as applications of the theory A series of over 40 problems help develop the skills to allow readers to reach the level of being able to contribute to research. This book is suitable for an advanced graduate course in DMFT, and for individualized study by graduate students, postdoctoral fellows and advanced researchers wishing to enter the field\"-- Provided by publisher.
Book
Improvements of bounds for the Sándor–Yang means
In the article, we provide new bounds for two Sándor–Yang means in terms of the arithmetic and contraharmonic means. Our results are the improvements of the previously known results.
Journal Article
On approximating the quasi-arithmetic mean
In this article, we prove that the double inequalities α1[7C(a,b)16+9H(a,b)16]+(1−α1)[3A(a,b)4+G(a,b)4]0\\(a, b>0\\) with a≠b\\(a b\\) if and only if α1≤3/16=0.1875\\(_1 3/16=0.1875\\), β1≥64/π2−6=0.484555…\\(_164/^2-6= 0.484555\\), α2≤3/16=0.1875\\(_23/16=0.1875\\) and β2≥(5log2−log3−2logπ)/(log7−log6)=0.503817…\\(_2(52-3-2 )/(7-6)= 0.503817\\), where E(a,b)=(2π∫0π/2acos2θ+bsin2θdθ)2\\(E(a,b)= (2ınt^/2_0a^2 +b^2\\,d )^2\\), H(a,b)=2ab/(a+b)\\(H(a,b)=2ab/(a+b)\\), G(a,b)=ab\\(G(a,b)=ab\\), A(a,b)=(a+b)/2\\(A(a,b)=(a+b)/2\\) and C(a,b)=(a2+b2)/(a+b)\\(C(a,b)=(a^2+b^2)/(a+b)\\) are the quasi-arithmetic, harmonic, geometric, arithmetic and contra-harmonic means of a and b, respectively.
Journal Article
Sharp bounds for the Toader mean of order 3 in terms of arithmetic, quadratic and contraharmonic means
In the article, we present the best possible parameters α1, β1, α2, β2 ∈ ℝ and α3, β3 ∈ [1/2, 1] such that the double inequalitiesα1C(a,b)+(1−α1)A(a,b) 0 with a ≠ b, and provide new bounds for the complete elliptic integral of the second kind, where A(a, b) = (a + b)/2 is the arithmetic mean, Q(a,b)=a2+b2/2 $\\begin{array}{}\\displaystyleQ(a, b)=\\sqrt{\\left(a^{2}+b^{2}\\right)/2}\\end{array}$is the quadratic mean, C(a, b) = (a2 + b2)/(a + b) is the contra-harmonic mean, C(p; a, b) = C[pa + (1 – p)b, pb + (1 – p)a] is the one-parameter contra-harmonic mean and T3(a,b)=(2π∫0π/2a3cos2θ+b3sin2θdθ)2/3 $\\begin{array}{}T_{3}(a,b)=\\Big(\\frac{2}{\\pi}\\int\\limits_{0}^{\\pi/2}\\sqrt{a^{3}\\cos^{2}\\theta+b^{3}\\sin^{2}\\theta}\\text{d}\\theta\\Big)^{2/3}\\end{array}$is the Toader mean of order 3.
Journal Article
Beyond publication numbers: a novel approach to academic ranking using evolutionary programming
Evaluating the impact of researchers within a scientific community remains a complex and debated issue. Traditional metrics, such as publication and citation counts, often fail to capture the multifaceted nature of scholarly influence. While several indices, such as the h-index and its variants have been proposed, they too face limitations in reflecting qualitative and longitudinal aspects of academic contributions. This study introduces a novel researcher ranking framework that integrates four distinct parameters: Normalized Citation Score (NCS), Complete Career Contribution (CCC), Temporal Citation Input (TCI), and Collaborative Prestige (CP). These parameters are combined using two ranking mechanisms: the Statistical Ranking System (SRS), based on mathematical models, and the Comprehensive Ranking System (CRS), which employs Genetic Programming (GP) to evolve domain-specific ranking formulas. The methodology was evaluated across five datasets, Computer Science, Mathematics, Neuroscience, Civil Engineering, and a combined dataset, each balanced with equal numbers of awardees and non-awardees. In SRS, models such as the Lehmer Mean and Logarithmic Mean performed effectively in highlighting awardees. In CRS, the evolved models achieved fitness values of up to 0.96 in Computer Science and 0.88 in Mathematics, with slightly lower scores in other domains. The reduced performance on the combined dataset highlights the importance of domain-sensitive modeling. The results suggest that the proposed framework offers a flexible and comprehensive approach to researcher evaluation that can adapt to domain-specific impact patterns, providing an alternative to conventional ranking metrics.
Journal Article
The coefficient of determination R-squared is more informative than SMAPE, MAE, MAPE, MSE and RMSE in regression analysis evaluation
Regression analysis makes up a large part of supervised machine learning, and consists of the prediction of a continuous independent target from a set of other predictor variables. The difference between binary classification and regression is in the target range: in binary classification, the target can have only two values (usually encoded as 0 and 1), while in regression the target can have multiple values. Even if regression analysis has been employed in a huge number of machine learning studies, no consensus has been reached on a single, unified, standard metric to assess the results of the regression itself. Many studies employ the mean square error (MSE) and its rooted variant (RMSE), or the mean absolute error (MAE) and its percentage variant (MAPE). Although useful, these rates share a common drawback: since their values can range between zero and +infinity, a single value of them does not say much about the performance of the regression with respect to the distribution of the ground truth elements. In this study, we focus on two rates that actually generate a high score only if the majority of the elements of a ground truth group has been correctly predicted: the coefficient of determination (also known as R -squared or R 2 ) and the symmetric mean absolute percentage error (SMAPE). After showing their mathematical properties, we report a comparison between R 2 and SMAPE in several use cases and in two real medical scenarios. Our results demonstrate that the coefficient of determination ( R -squared) is more informative and truthful than SMAPE, and does not have the interpretability limitations of MSE, RMSE, MAE and MAPE. We therefore suggest the usage of R -squared as standard metric to evaluate regression analyses in any scientific domain.
Journal Article
Sharp bounds for Neuman means in terms of two-parameter contraharmonic and arithmetic mean
In the article, we prove that λ1=1/2+[(2+log(1+2))/2]1/ν−1/2\\( _1=1/2+ [ (2+ (1+2) )/2 ]^1/ -1/2\\), μ1=1/2+6ν/(12ν)\\( _1=1/2+6 /(12 )\\), λ2=1/2+[(π+2)/4]1/ν−1/2\\( _2=1/2+ [( +2)/4 ] ^1/ -1/2\\) and μ2=1/2+3ν/(6ν)\\( _2=1/2+3 /(6 )\\) are the best possible parameters on the interval [1/2,1]\\([1/2, 1]\\) such that the double inequalities Cν[λ1x+(1−λ1)y,λ1y+(1−λ1)x]A1−ν(x,y)0\\(x, y>0\\) with x≠y\\(x y\\) and ν∈[1/2,∞)\\( ın [1/2, ınfty )\\), where A(x,y)\\(A(x, y)\\) is the arithmetic mean, C(x,y)\\(C(x, y)\\) is the contraharmonic mean, and RQA(x,y)\\(R_QA(x, y)\\) and RAQ(x,y)\\(R_AQ(x, y)\\) are two Neuman means.
Journal Article
Forecasting standardized precipitation index using data intelligence models: regional investigation of Bangladesh
A noticeable increase in drought frequency and severity has been observed across the globe due to climate change, which attracted scientists in development of drought prediction models for mitigation of impacts. Droughts are usually monitored using drought indices (DIs), most of which are probabilistic and therefore, highly stochastic and non-linear. The current research investigated the capability of different versions of relatively well-explored machine learning (ML) models including random forest (RF), minimum probability machine regression (MPMR), M5 Tree (M5tree), extreme learning machine (ELM) and online sequential-ELM (OSELM) in predicting the most widely used DI known as standardized precipitation index (SPI) at multiple month horizons (i.e., 1, 3, 6 and 12). Models were developed using monthly rainfall data for the period of 1949–2013 at four meteorological stations namely, Barisal, Bogra, Faridpur and Mymensingh, each representing a geographical region of Bangladesh which frequently experiences droughts. The model inputs were decided based on correlation statistics and the prediction capability was evaluated using several statistical metrics including mean square error (
MSE
), root mean square error (
RMSE
), mean absolute error (
MAE
), correlation coefficient (
R
), Willmott’s Index of agreement (
WI
), Nash Sutcliffe efficiency (
NSE
), and Legates and McCabe Index (
LM
). The results revealed that the proposed models are reliable and robust in predicting droughts in the region. Comparison of the models revealed ELM as the best model in forecasting droughts with minimal
RMSE
in the range of 0.07–0.85, 0.08–0.76, 0.062–0.80 and 0.042–0.605 for Barisal, Bogra, Faridpur and Mymensingh, respectively for all the SPI scales except one-month SPI for which the RF showed the best performance with minimal
RMSE
of 0.57, 0.45, 0.59 and 0.42, respectively.
Journal Article
Keep Calm and Learn Multilevel Logistic Modeling: A Simplified Three-Step Procedure Using Stata, R, Mplus, and SPSS
This paper aims to introduce multilevel logistic regression alysis in a simple and practical way. First, we introduce the basic principles of logistic regression alysis (conditiol probability, logit transformation, odds ratio). Second, we discuss the two fundamental implications of running this kind of alysis with a nested data structure: In multilevel logistic regression, the odds that the outcome variable equals one (rather than zero) may vary from one cluster to another (i.e. the intercept may vary) and the effect of a lower-level variable may also vary from one cluster to another (i.e. the slope may vary). Third and filly, we provide a simplified three-step “turnkey” procedure for multilevel logistic regression modeling:-Prelimiry phase: Cluster- or grand-mean centering variables -Step #1: Running an empty model and calculating the intraclass correlation coefficient (ICC) -Step #2: Running a constrained and an augmented intermediate model and performing a likelihood ratio test to determine whether considering the cluster-based variation of the effect of the lower-level variable improves the model fit -Step #3 Running a fil model and interpreting the odds ratio and confidence intervals to determine whether data support your hypothesisCommand syntax for Stata, R, Mplus, and SPSS are included. These steps will be applied to a study on Justin Bieber, because everybody likes Justin Bieber.1
Journal Article
Short-Term Forecasting of the Output Power of a Building-Integrated Photovoltaic System Using a Metaheuristic Approach
The rapidly increasing use of renewable energy resources in power generation systems in recent years has accentuated the need to find an optimum and efficient scheme for forecasting meteorological parameters, such as solar radiation, temperature, wind speed, and sun exposure. Integrating wind power prediction systems into electrical grids has witnessed a powerful economic impact, along with the supply and demand balance of the power generation scheme. Academic interest in formulating accurate forecasting models of the energy yields of solar energy systems has significantly increased around the world. This significant rise has contributed to the increase in the share of solar power, which is evident from the power grids set up in Germany (5 GW) and Bavaria. The Spanish government has also taken initiative measures to develop the use of renewable energy, by providing incentives for the accurate day-ahead forecasting. Forecasting solar power outputs aids the critical components of the energy market, such as the management, scheduling, and decision making related to the distribution of the generated power. In the current study, a mathematical forecasting model, optimized using differential evolution and the particle swarm optimization (DEPSO) technique utilized for the short-term photovoltaic (PV) power output forecasting of the PV system located at Deakin University (Victoria, Australia), is proposed. A hybrid self-energized datalogging system is utilized in this setup to monitor the PV data along with the local environmental parameters used in the proposed forecasting model. A comparison study is carried out evaluating the standard particle swarm optimization (PSO) and differential evolution (DE), with the proposed DEPSO under three different time horizons (1-h, 2-h, and 4-h). Results of the 1-h time horizon shows that the root mean square error (RMSE), mean relative error (MRE), mean absolute error (MAE), mean bias error (MBE), weekly mean error (WME), and variance of the prediction errors (VAR) of the DEPSO based forecasting is 4.4%, 3.1%, 0.03, −1.63, 0.16, and 0.01, respectively. Results demonstrate that the proposed DEPSO approach is more efficient and accurate compared with the PSO and DE.
Journal Article