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This paper presents the results of a laboratory experiment on transmission, reflection, and dissipation of irregular waves over smooth impermeable submerged breakwaters. Experiments included 75 JONSWAP-based irregular waves with five different wave characteristics generated at three water depths in a 2D wave flume. The investigated breakwater sections were three rectangular breakwaters with different widths, a toothed rectangular breakwater, and a trapezoidal breakwater with a slope of 1:2. A new comprehensive dimensionless parameter (β) was proposed representing both wave hydrodynamic and breakwater geometry characteristics. This parameter could be employed as a suitable descriptive option to make an accurate estimate of the hydraulic performances of submerged breakwaters. The β parameter is composed of four conventional simple dimensionless variables. However, the results revealed that the relative submergence depth significantly affects the hydraulic responses of submerged breakwaters. The transmission, reflection and dissipation of waves show a logarithmic growth, a logarithmic reduction, and a quadratic decreasing trend against the increasing of β parameter, respectively. The verifications of results revealed the high efficiency of β parameter for data reported by Carevic et al. (2013) with R2 = 0.88 and high agreement with predictions made by Van der Meer et al. (2005) formulation with R2 = 0.93.

Graphical abstract, Mutual Exclusivity analysis of genomic aberrations contributes to the exploration of potential synthetic lethal (SL) relationships thus guiding the nomination of specific cancer cells vulnerabilities. When multiple classes of genomic aberrations and large cohorts of patients are interrogated, exhaustive genome-wide analyses are not computationally feasible with commonly used approaches. Here we present Fast Mutual Exclusivity (FaME), an algorithm based on matrix multiplication that employs a logarithm-based implementation of the Fisher’s exact test to achieve fast computation of genome-wide mutual exclusivity tests; we show that brute force testing for mutual exclusivity of hundreds of millions of aberrations combinations can be performed in few minutes. We applied FaME to allele-specific data from whole exome experiments of 27 TCGA studies cohorts, detecting both mutual exclusivity of point mutations, as well as allele-specific copy number signals that span sets of contiguous cytobands. We next focused on a case study involving the loss of tumor suppressors and druggable genes while exploiting an integrated analysis of both public cell lines loss of function screens data and patients’ transcriptomic profiles. FaME algorithm implementation as well as allele-specific analysis output are publicly available at https://github.com/demichelislab/FaME.

In this work, self-absorption correction factor related to the variation of the composition and the density of soil samples were evaluated using the p-type HPGe detector. The validated MCNP5 simulation model of this detector was used to evaluate its Full Energy Peak Efficiency (FEPE) under the variation of the composition and the density of the analysed samples. The results indicates that FEPE calculation of low gamma ray is affected by the composition and the density of soil samples. The self-absorption correction factors for different gamma-ray energies which was fitted as a function of FEPEs via density and energy and fitting parameters as polynomial function for the logarithm neper of gamma ray energy help to calculate quickly the detection efficiency of detector. Factor Analysis for the influence of the element composition in analysed samples on the FEPE indicates the FEPE distribution changes from non-metal to metal groups when the gamma ray energy increases from 92 keV to 238 keV. At energies above 238 keV, the FEPE primarily depends only on the metal elements and is significantly affected by aluminium and silicon composition in soil samples.

In this note, we propose a new class of orthogonal polynomials (named Bachok–Hasham polynomials H 1 n k ( x ) ), which is an extension of the Chebyshev polynomials. Eigenfunctions and corresponding eigenvalues are found for the homogeneous second kind of Logarithmic Singular Integral Equations (LogSIEs). For non-homogeneous LogSIEs truncated series of the first kind Bachok–Hasham polynomials are used to find approximate solution. It is found that first kind of Bachok–Hasham polynomials ( H 1 n k ( x ) ) are orthogonal with weight w k ( x ) = x k - 1 1 - x 2 k , where k is positive odd integer. Properties of first kind of Bachok–Hasham polynomials are also proved. Finally, two examples are presented to show the validity and accuracy of the proposed method.

One of the fundamental traits of quantum entanglement is the restricted shareability among multipartite quantum systems, namely monogamy of entanglement, while it is well known that monogamy inequalities are always satisfied by entanglement measures with convexity. Here we present a measure of entanglement, logarithmic convex-roof extended negativity (LCREN) satisfying important characteristics of an entanglement measure, and investigate the monogamy relation for logarithmic negativity and LCREN both without convexity. We show exactly that the α th power of logarithmic negativity, and a newly defined good measure of entanglement, LCREN, obey a class of general monogamy inequalities in multiqubit systems, 2 ⊗ 2 ⊗ 3 systems and 2 ⊗ 2 ⊗ 2 n systems for α ≥ 4 ln 2 . We provide a class of general polygamy inequalities of multiqubit systems in terms of logarithmic convex-roof extended negativity of assistance (LCRENoA) for 0 ≤ β ≤ 2 . Given that the logarithmic negativity and LCREN are not convex, these results are surprising. Using the power of the logarithmic negativity and LCREN, we further establish a class of tight monogamy inequalities of multiqubit systems, 2 ⊗ 2 ⊗ 3 systems and 2 ⊗ 2 ⊗ 2 n systems in terms of the α th power of logarithmic negativity and LCREN for α ≥ 4 ln 2 . We also show that the β th power of LCRENoA obeys a class of tight polygamy inequalities of multiqubit systems for 0 ≤ β ≤ 2 .

Physical characteristics: Original contains color illustrations, Accepted: 2018-11-19, 資料番号: PA1920038000

Log D the logarithm (log10) of the distribution coefficient (D), is one of the important parameters used in Lipinski's rule to assess the druggability of a molecule in pharmaceutical formulations. The distribution of a molecule between a hydrophobic organic phase and an aqueous buffer phase is influenced by the pH of the buffer system. In this work, we used both the conventional algebraic method and the generalized ‘dynamic’ approach to model the distribution coefficient of amphoteric, diamino-monoprotic molecule and monoprotic acid in the presence of salt or co-solvent. We have shown the equivalence of these methods by analysing the recently reported experimental data of amphoteric molecules such as nalidixic acid, mebendazole, benazepril and telmisartan., Graphical abstract fx1, Highlights • Modelled the effect of salt and co-solvent in log D analysis. • log10D analysis of diamino-monoprotic acid using both algebraic and dynamic approach is provided. • Shown how analogous kinetic mechanisms simplifies analysis of complex multi-species at equilibrium.

Upon investigating whether the variation of the antineutron-nucleus annihilation cross-sections at very low energies satisfy Bethe-Landau's power law of $\sigma_{\rm ann} (p) \propto 1/p^{\alpha}$ behavior as a function of the antineutron momentum $p$, we uncover unexpected regular oscillatory structures in the low antineutron energy region from 0.001 to 10 MeV, with small amplitudes and narrow periodicity in the logarithm of the antineutron energies, for large-$A$ nuclei such as Pb and Ag. Subsequent semiclassical analyses of the $S$ matrices reveal that these oscillations are pocket resonances that arise from quasi-bound states inside the pocket and the interference between the waves reflecting inside the optical potential pockets with those from beyond the potential barriers, implicit in the nuclear Ramsauer effect. They are the continuation of bound states in the continuum. Experimental observations of these pocket resonances will provide vital information on the properties of the optical model potentials and the nature of the antineutron annihilation process., Comment: 10 pages, 5 figures

This study established the preciseness of the robust MLP-firefly optimizer (MLP-FFA) artificial intelligence algorithm coupled with satellite-derived photosynthetic active radiation (PAR) data in order to forecast PAR itself using historical values for a regional Queensland location (Toowoomba). To optimize the MLP-FFA model, (1) hidden and output transfer functions; (2) number of hidden neurons; (3) training, cross-validation, and test percentage splits; and (4) number of historical lags were trialled, such that the logarithmic sigmoid hidden function and tangent sigmoid output function, with 120 hidden neurons, nine lags as inputs and a 60% training, 20% cross-validation, and 20% testing set, was finally adopted for thre forecasting of PAR. To meet the objective (Section 7.1), the MLP-FFA objective model was benchmarked with the MLP, RF, and MLR models for PAR forecasting. The findings of this study are that the performance of the MLP-FFA model, according to forecasting error directly, as well as association and error performance metrics, outperformed the MLP and RF models. MLR generally outperformed MLP-FFA, but this is most likely a result of nonstochastic monthly PAR data, and it is recommended for future work to investigate lower temporal resolution data (which in turn is more stochastic), which a more robust model like MLP-FFA is known to handle, but a poor model like MLR cannot. A lower resolution such as daily or hourly was not found at the time of this study, and manual data collection was not appropriate due to the time and cost limits of this research. Albeit, the MLP-FFA model has still been very effective in modeling PAR with very high accuracy and low error, leading to a significant contribution to research which is confirming something unknown—that the MLP-FFA model is in fact very effective at satellite-based PAR modeling with historical data as inputs for learning for a regional Queensland location. The results of this study are a significant research contribution, which can be used to forecast PAR conditions, a vital requirement for the growth of algal biofuel; these algae can be farmed in the ideal location of the sunny, subtropical Toowoomba region.

The Volterra function μ(t,β,α) was introduced by Vito Volterra in 1916 as the solution to certain integral equations with a logarithmic kernel. Despite the large number of applications of the Volterra function, the only known analytic representations of this function are given in terms of integrals. In this paper we derive several convergent expansion of μ(t,β,α) in terms of incomplete gamma functions. These expansions may be used to implement numerical evaluation techniques for this function. As a particular application, we derive a numerical series representation of the Fransén–Robinson constant F := µ(1, 1, 0) = R ∞ 0 1 Γ(x) dx. Some numerical examples illustrate the accuracy of the approximations This research was supported by the Ministerio de Economía y Competitividad (MTM2017-83490-P) and the Universidad Pública de Navarra, Spain.

A compact formulation has been developed to efficiently optimize early-stage field development planning of multi-reservoir fields. The proposed formulation is a mixed-integer linear programming model which employs piecewise-linear functions to approximate the model non-linearities. The project economic value is maximized by optimizing the production allocation and the drilling schedule. The field production profiles are estimated with production potential curves calculated from simulated data of an integrated reservoir and surface facilities model. The novelties of this work are: a scalable model for the well combination selection, a logarithmic piecewise-linear model to approximate the well production potential curves, and the modeling and solution of realistic field development optimization problems. Through simulation analysis of a real field case study, the logarithmic and standard SOS2 formulations are compared in terms of computational performance and accuracy. The results show that the logarithmic formulation has significantly reduced the computational time and achieved improved accuracy over SOS2.

This paper studies nonparametric estimation of the infinite order regression E ( Y t k | F t − 1 ) , k ∈ Z with stationary and weakly dependent data. We propose a Nadaraya–Watson type estimator that operates with an infinite number of conditioning variables. We propose a bandwidth sequence that shrinks the effects of long lags, so the influence of all conditioning information is modelled in a natural and flexible way, and the issues of omitted information bias and specification error are effectively handled. We establish the asymptotic properties of the estimator under a wide range of static and dynamic regressions frameworks, thereby allowing various kinds of conditioning variables to be used. We establish pointwise/uniform consistency and CLTs. We show that the convergence rates are at best logarithmic, and depend on the smoothness of the regression, the distribution of the marginal regressors and their dependence structure in a non-trivial way via the Lambert W function. We apply our methodology to examine the intertemporal risk-return relation for the aggregate stock market, and some new empirical evidence is reported. For the S&P 500 daily data from 1950 to 2017 using our estimator we report an overall positive risk-return relation. We also find evidence of strong time variation and counter-cyclical behaviour in risk aversion. These conclusions are possibly attributable to the allowance of further flexibility and the inclusion of otherwise neglected information in our method.

We derive the k T resummation for a transverse-momentum-dependent charmonium wave function, which involves the bottom quark mass m b , the charm quark mass m c , and the charm quark transverse momentum k T , up to the next-to-leading-logarithm (NLL) accuracy under the hierarchy m b ≫ m c ≫ k T . The resultant Sudakov factor is employed in the perturbative QCD (PQCD) approach to the B c → J / ψ transition form factor A 0 B c → J / Ψ ( 0 ) and the B c + → J / ψ π + decay. We compare the NLL resummation effect on these processes with the leading-logarithm one in the literature, and find a ( 5 − 10 ) % enhancement to the form factor A 0 B c → J / Ψ ( 0 ) and a ( 10 − 20 ) % enhancement to the decay rate B R ( B c + → J / Ψ π + ) . The improved k T resummation formalism is applicable to the PQCD analysis of heavy meson decays to other charmonia.

From the entropy argument for the dS swampland conjecture which connects the Gibbons-Hawking entropy bound with the distance conjecture, we find the entropic quasi-dS instability time given by $1/(\sqrt{\epsilon_H}H)\log(m_{\rm Pl}/H)$ as the lifetime of quasi-dS spacetime. It depends on the slow-roll parameter, and contains the logarithmic factor $\log(m_{\rm Pl}/H)$ which can be found in the scrambling (or decoherence) time as well. Such a logarithmic factor enhances the geodesic distance of the modulus from the mere Planck scale, and also possibly relaxes the bound on $m_{\rm Pl}^2 \nabla^2 V/V$., Comment: 5 pages, 2 figures, version published in Phys. Lett. B

The holographic entanglement entropy is computed for an entangling surface that coincides with the horizon of a boundary de Sitter metric. This is achieved through an appropriate slicing of anti-de Sitter space and the implementation of a UV cutoff. The entropy is equal to the Wald entropy for an effective action that includes the higher-curvature terms associated with the conformal anomaly. The UV cutoff can be expressed in terms of the effective Planck mass and the number of degrees of freedom of the dual theory. The entanglement entropy takes the expected form of the de Sitter entropy, including logarithmic corrections., Comment: 5 pages, 1 figure, acknowledgment added

The Bekenstein-Hawking (BH) entropy is expected to be modified by certain correction terms in the quantum loop expansion. As is well known the logarithmic terms in the entropy of black holes appear as a one-loop addition to the classical BH entropy. In this note we study the further modifications of the logarithmic terms in the entropy of the Schwarzschild black holes due to higher quantum loops: up to three loops in a general renormalizable theory of gauge fields, scalars and fermions and two loops in quantum gravity. For a large class of field multiplets (including that of the Standard Model) that include graviton and for a certain range in the values of the couplings these modifications manifest themselves in cooling down the black holes at later stages of evaporation and, respectively, in increasing the life time of the black hole. If this picture persists to even higher loops, then the small black holes formed in the early stages of the cosmic evolution do not evaporate completely by now as is predicted in the standard picture. Instead, their long-lived (Planckian mass) remnants should present in abundance in today's Universe., Comment: 12 pages; more comments and references added, to appear in Phys. Lett. B

In precision agriculture, data-intelligent algorithms applied for predicting wheat yield can generate crucial information about enhancing crop production and strategic decision-making. In this chapter, artificial neural network (ANN) model is trained with three neighboring station-based wheat yields to predict the yield for two nearby objective stations that share a common geographic boundary in the agricultural belt of Pakistan. A total of 2700 ANN models (with a combination of hidden neurons, training algorithm, and hidden transfer/output functions) are developed by trial-and-error method, attaining the lowest mean square error, in which the 90 best-ranked models for 3-layered neuronal network are utilized for wheat prediction. Models such as learning algorithms comprised of pure linear, tangent, and logarithmic sigmoid equations in hidden transfer/output functions, executed by Levenberg–Marquardt, scaled conjugate gradient, conjugate gradient with Powell-Beale restarts, Broyden–Fletcher–Goldfarb–Shanno quasi-Newton, Fletcher-Reeves update, one-step secant, conjugate gradient with Polak-Ribiere updates, gradient descent with adaptive learning, gradient descent with momentum, and gradient descent with momentum adaptive learning method are trained. For the predicted wheat yield at objective station 1 (i.e., Toba Taik Singh), the optimal architecture was 3-14-1 (input-hidden-output neurons) trained with the Levenberg–Marquardt algorithm and logarithmic sigmoid as activation and tangent sigmoid as output function, while at objective station 2 (i.e., Bakkar), the Levenberg–Marquardt algorithm provided the best architecture (3-20-1) with pure liner as activation and tangent sigmoid as output function. The results are benchmarked with those from minimax probability machine regression (MPMR) and genetic programming (GP) in accordance with statistical analysis of predicted yield based on correlations (r), Willmott's index (WI), Nash-Sutcliffe coefficient (EV), root mean-squared error (RMSE), and mean absolute error (MAE). For objective station 1, the ANN model attained the r value of approximately 0.983, with WI ≈ 0.984 and EV ≈ 0.962, while the MPMR model attained r ≈ 0.957, WI ≈ 0.544, and EV ≈ 0.527, with the results attained by GP model, r ≈ 0.982, WI ≈ 0.980, and EV ≈ 0.955. For optimal ANN model, a relatively low value of RMSE ≈ 192.02 kg/ha and MAE ≈ 162.75 kg/ha was registered compared with the MPMR (RMSE ≈ 614.46 kg/ha; MAE ≈ 431.29 kg/ha) and GP model (RMSE ≈ 209.25 kg/ha; MAE ≈ 182.84 kg/ha). For both objective stations, ANN was found to be superior, as confirmed by a larger Legates-McCabe's (LM) index used in conjunction with relative RMSE and MAE. Accordingly, it is averred that ANN is considered as a useful data-intelligent contrivance for predicting wheat yield by using nearest neighbor yield.

In this paper, we present an approach to global optimization of bilinear programs based on a transformation of bilinear terms to elementary functions of single variables. The substitutions relocate bilinear terms to additional equality constraints. The complicating variables in these constraints are separated by logarithm operations. Finally, the log-linear constraints are relaxed by piecewise linear approximations and/or linearizations. The transformation produces a lower-bounding mixed-integer linear program, which is used in conjunction with the original bilinear program in a global optimization algorithm. The approach was tested by pooling problems from the literature. The global optimum was obtained in all the test problems; however, more elaborate algorithmic schemes would be needed to make the proposed approach computationally efficient.

Newmark displacement estimation is generally computed using empirical models. These models are estimated from large datasets that mainly comprise moderate-to-high magnitude events (Mw > 6.0). In this work, we study the performance of several of these models to study moderate-to-low magnitude scenarios. For this purpose, data from the Betic Cordillera, S Spain, with magnitudes ranging from Mw 3.5 to 6.3, were used to compare with model predictions. The results show that errors in the estimates depend on the magnitude of events or on the yielding acceleration considered to estimate the displacement. The availability of an appropriate range of data (magnitude and yielding acceleration), when defining the regression model, may overcome the differences due to specific characteristics of the seismotectonic context of the area where data derives from. The results also show that performance of models including several ground motion predictors is better than those based on a single parameter, regardless of the combination these predictors. Furthermore, regression models with polynomial forms present a better performance than other functions based on the logarithm of these predictors. Finally, new specific models for the Betic Cordillera are proposed, especially suitable for low magnitude events (< 5.0) and low critical accelerations (< 0.1 g), based on simplified polynomial forms of models. This work was partially founded by the Spanish Ministry of Economy and EU FEDER funds (project EPILATES, CGL2015-65602-R) and by the Research Group VIGROB-184 (University of Alicante). Research was also partially funded by the Consejería de Economía, Conocimiento, Empresa y Universidad (Junta de Andalucía), in the frame of the Programa Operativo FEDER Andalucía 2014-2020 – call made by the University of Jaén 2018.

Traffic signal cycle lengths are traditionally optimized to minimize vehicle delay at intersections using the Webster formulation. This study continues previous work by the authors to enhance the Webster model and develop new formulations to compute the optimum cycle length, considering vehicle delay, fuel consumption, and tailpipe emissions. The microscopic simulation software INTEGRATION is used to simulate two-phase and four-phase isolated intersections over a wide range of traffic demand levels, traffic demand distributions, cycle lengths, and signal timing lost times. Intersection delay, fuel consumption levels, and emissions of carbon dioxide (CO2), hydrocarbon (HC), carbon monoxide (CO), and oxides of nitrogen (NOx) are derived from the simulation software. The optimum cycle lengths for various measures of effectiveness are then used to develop the proposed formulations. The simulation results demonstrate that the Webster method overestimates the optimum cycle length and produces unrealistically long cycle length estimates when the traffic volume-to-capacity ratio exceeds 50%. A new logarithmic delay model is proposed herein to address the shortcomings of the Webster model. This model is then calibrated to compute the optimum cycle lengths considering vehicle fuel consumption and emission levels. The estimated optimum cycle lengths for emissions are shown to be longer than the optimum cycle lengths for vehicle delay for lower levels of congestion. The paper demonstrates how a multi-objective cycle length can be computed to simultaneously minimize vehicle delays and fuel consumption levels. After computing the optimum cycle length, the optimum phase split can then be computed using the traditional approach of equating the degree of saturation across all phases. It is anticipated that the proposed formulations will produce significant savings in vehicle delay and fuel consumption levels.

We study the effective field theory of two intersecting D3-branes with one common dimension along the lines recently proposed in ref. [1] . We introduce a systematic way of deriving the classical effective action to arbitrary orders in perturbation theory. Using a proper renormalization prescription to handle logarithmic divergencies arising at all orders in the perturbation series, we recover the first order renormalization group equation of ref. [1] plus an infinite set of higher order equations. We show the consistency of the higher order equations with the first order one and hence interpret the first order result as an exact RG flow equation in the classical theory.

The relationship of the built environment to human travel is one of the mainstream themes in urban studies. It provides a foundation for transport prediction. The existing literature is limited in accuracy when predicting spatial temporal travels from built environment. Understanding the scaling laws of spatial visitation frequency sheds new light on the issue. The scaling laws connect travel and the built environment by ordered-rankings, which make it possible to predict the number of arrivals from environmental variables. This research analyses the scaling laws of dynamic spatial visitation frequency using taxis' global positioning system (GPS) records, and proposes a model to predict spatial temporal arrivals from points of interest (POIs). The results show that: (i) the scaling law of spatial visitation frequency is exponential; (ii) the exponential scaling law is explained by the linear preferential attachment effect and a logarithmic travel growth process; (iii) the exponential scaling law is not sensitive to time; (iv) the proposed model predicts spatial temporal arrivals with high accuracy (R2 > 0.6).

We develop a new formalism to describe the inclusive production of small radius jets in heavy-ion collisions, which is consistent with jet calculations in the simpler proton-proton system. Only at next-to-leading order (NLO) and beyond, the jet radius parameter $R$ and the jet algorithm dependence of the jet cross section can be studied and a meaningful comparison to experimental measurements is possible. We are able to consistently achieve NLO accuracy by making use of the recently developed semi-inclusive jet functions within Soft Collinear Effective Theory (SCET). In addition, single logarithms of the jet size parameter $\alpha_s^n\ln^n R$ are resummed to next-to-leading logarithmic (NLL$_R$) accuracy. The medium modified semi-inclusive jet functions are obtained within the framework of SCET with Glauber gluons that describe the interaction of jets with the medium. We present numerical results for the suppression of inclusive jet cross sections in heavy ion collisions at the LHC and the formalism developed here can be extended directly to corresponding jet substructure observables., Comment: 8 pages, 5 figures

We suggest a novel view on non-renormalizable interactions. It is based on the usual BPHZ R-operation which is equally applicable to any local QFT independently whether it is renormalizable or not. As a playground we take the phi^4_D theory in D dimensions for D=4,6,8,10 and consider the four-point scattering amplitude on shell. We derive the generalized RG equation and find the solution valid for any D that sums up the leading logarithms in all orders of PT in full analogy with the renormalizable case. It is found that the scattering amplitude in the phi^4_D theory possesses the Landau pole at high energy for any D. We discuss the application of the proposed procedure to other non-renormalizable theories., 9 pages, 2 figures, pdflatex

Analytical Hierarchical Process (AHP) along with fuzzy set theory has been used extensively in the Multi-Criteria Decision Making (MCDM) process in which fuzzy numbers are utilized to represent human judgments more realistically. Over the past couple of decades, numerous articles have been published proposing algorithms through which priority vector (or weight vector) can be calculated from fuzzy comparison matrices. The aim of this study is to conduct a comprehensive performance analysis of the most popular algorithms proposed in this domain in terms of accuracy of weights calculated from fuzzy comparison matrices. Such an analysis is much needed by the researchers and practitioners. However none is available. An experimental analysis is conducted and the performance of various algorithms are evaluated with varying three parameters i.e., the size of the comparison matrix, the level of fuzziness and the level of inconsistency. We found that modified Logarithmic Least Squares Method and Fuzzy Inverse of Column Sum Method (FICSM) generally outperformed other algorithms, while Fuzzy Extent Analysis (FEA) which is the most frequently used algorithm in the literature provides the least accurate results. Furthermore, it was observed that a modified version of FEA method significantly improved its performance.

Publisher Summary Binomial trees serve as an intuitive approach to explain the logic behind option pricing models and also as a versatile computational technique. The binomial model assumes that, over a short period of time Δt, a financial asset's price S either rises by a small amount or goes down a small amount. The probability of an uptick is p, while a downtick occurs with probability 1 - p. Probabilities here are generally risk-neutral ones. A model for price movements may either be additive (i.e., absolute movements) or multiplicative (i.e., relative movements). “Additive” and “multiplicative” here refer to units of the observed price; computationally, taking logarithms can change a multiplicative model. There are two objections against additive models: a price could become negative, and the magnitude (in currency units) of a price change does not depend on the current price.

A chloralkali membrane cell process is modeled based on a macro-homogeneous approach. The Poisson-Nernst-Planck (PNP) equation is applied to model the multi-ion transport in the system. A steep gradient problem arises at the membrane’s interfaces. The finite differences method, Hermite collocation on finite elements, and the Galerkin finite elements method are compared to determine the most efficient method to tackle the problem. A logarithmic reformulation is also investigated to evaluate its compatibility to solve the problem. The finite differences method and the Hermite collocation method turnout the best results, respectively in terms of the compuational time and accuracy. Afterwards, the finite differences method is applied to model a solution-membrane system based on the 1D PNP equation, whose results are discussed further regarding their subsequent applicability for extensive simulation studies.

WOS: 000457264700008, 30712606, Background and objective: ECG is one of the biometric signals that has been studied in peer-reviewed over past years. The developments on the signal analysis methods show that the studies on the ECG would continue unabatedly. It has a common use on cardiac diseases with high rates of classification performances by integrating it with signal analysis methods. The aim of the study is to utilize the ECG for human identification. Methods: Second Order Difference Plot (SODP) is a non-linear time-series analysis method that allows determining the features using the statistical analysis of the wave distributions. The SODP features were extracted using different quantification methods for ECG-based human identification. A new quantification approach has been proposed on the SODP for ECG-based human identification. The proposed method, Logarithmic Grid Analysis, was compared with the existing quantification methods on the SODP. The region of the SODP was divided into sub-regions with logarithmically increasing distances and the numbers of data points in each logarithmic sub regions were calculated in the proposed method. Three different databases were used to test the validity of the method. These records have been tested with the conventional feature extraction methods on the SODP. The long-term ECG signals were divided into 5-s short-term ECG signals. Results: The Logarithmic Grid Analysis features that were counted from short-time ECG signals were classified with k-Nearest Neighbor algorithm using 10-fold cross validation, and the identification performance of the proposed model was evaluated. Consequently, high accuracy rates of 91.96%, 99.86% and 95.12% were achieved on ECG-based human identification using the Logarithmic Grid Analysis method on the SODP. Conclusions: The density score of data points at the center of the SODP is too high. This case increases the importance of the regions close the center in order to find the detailed and significant features from the SODP. The number of data points at the center has been extracted in more detail and the vertex areas of the major axes of the SODP can be interpreted in the aggregate sub-regions by using logarithmically increasing distances with a small number of feature size. (C) 2019 Elsevier B.V. All rights reserved.

Two fundamental approaches to information averaging are based on linear and logarithmic combination, yielding the arithmetic average (AA) and geometric average (GA) of the fusing data, respectively. In the context of multisensor target tracking, the two most common formats of data to be fused are random variables and probability density functions, namely v-fusion and f-fusion, respectively. In this work, we analyze and compare the second-order statistics (including variance and mean square error) of AA and GA in terms of both v-fusion and f-fusion. The case of weighted Gaussian mixtures representing multitarget densities in the presence of false alarms and missed detections (whose weight sums are not necessarily unit) is also considered, the result of which turns out to be significantly different from that of a single target. In addition to exact derivation, exemplifying analyses and illustrations are also provided. This work was supported in part by the Marie Skłodowska-Curie Individual Fellowship under Grant 709267, in part by Shaanxi Natural Fund under Grant 2018MJ6048, in part by the Northwestern Polytechnical University, and in part by Junta Castilla y León, Consejería de Educación and FEDER funds under project SA267P18.

The Virasoro logarithmic minimal models were intensively studied by several groups over the last ten years with much attention paid to the fusion rules and the structures of the indecomposable representations that fusion generates. The analogous study of the fusion rules of the $N=1$ superconformal logarithmic minimal models was initiated in arXiv:1504.03155 as a continuum counterpart to the lattice explorations of arXiv:1312.6763. These works restricted fusion considerations to Neveu-Schwarz representations. Here, this is extended to include the Ramond sector. Technical advances that make this possible include a fermionic Verlinde formula applicable to logarithmic conformal field theories and a twisted version of the fusion algorithm of Nahm and Gaberdiel-Kausch. The results include the first construction and detailed analysis of logarithmic structures in the Ramond sector., Comment: 42 pages, 7 figures; v2 fixed minor typos and added a little more explanatory material

Human performance in selection tasks is frequently described by Fitts' law, which states that the average time needed to move to a target and select it is linearly related to the index of difficulty for the task, which is the logarithm of the task characteristic C=A/W, where A is the target distance and W is the target width. The coefficients in this linear relationship can vary across interaction conditions, such as when using distinct interaction devices, and can for instance be used to define throughput, which is a standardized measure to compare interaction conditions. Although Fitts' law has proven very useful in the field of human-computer interaction (HCI) over the past 50 years, there are several issues with Fitts' law that argue in favor of more advanced statistical modeling of experimental data. More specifically, we propose two generalizations of Fitts' law. The first generalization is not to limit the data analysis to average movement times, but to consider the distributions of the observed times instead. The second generalization is to extend Fitts' law to a more general relationship between task characteristics and index of difficulty and to use this generalized model to come up with additional measures that can be used alongside throughput.We use data from an experiment with both selection and tracing tasks to illustrate the proposed analysis method. The primary goal of the experiment is to compare the task performance in four experimental conditions, corresponding to all combinations of interaction device (mouse or pen) and target orientation (horzizontal/vertical versus oblique movements). First, we show that non-linear transformations on the measured task completion times are indeed advised to resolve problems with the normality and homoscedasticity of the data, especially in case of the tracing task. Second, we show that in case of the selection task the data supports a linear relationship between the logarithm of the task characteristic C and the logarithm of the movement time, which corresponds to a power-law between movement time and task characteristic, an alternative to Fitts' law that has previously been proposed by several authors. In case of the tracing task, the data supports a power-law function in between a linear and a logarithmic function. We conclude by demonstrating how multiple performance measures can be used simultaneously when comparing interaction conditions. HighlightsTwo generalizations of Fitts' law: modeling data distributions and modified index of difficultyMulti-model selection is used to compare alternative models for the observed data.Advanced data modeling accomplishes closer data approximation and higher contrasts between conditions.Performance rate measure includes the form of speed-accuracy relationship.

For displacement convex functionals in the probability space equip\-ped with the Monge-Kantorovich metric we prove the equivalence between the gradient and functional type \L oja\-sie\-wicz inequalities. \chg{We also discuss the more general case of $\lambda$-convex functions and we provide a general convergence theorem for the corresponding gradient dynamics. Specialising our results to the Boltzmann entropy, we recover Otto-Villani's theorem asserting the equivalence between logarithmic Sobolev and Talagrand's inequalities. The choice of power-type entropies shows a new equivalence between Gagliardo-Nirenberg inequality and a nonlinear Talagrand inequality. Some nonconvex results and other types of equivalences are discussed.

This article describes and compares methods for simulating the component counts of random logarithmic combinatorial structures such as permutations and mappings. We exploit the Feller coupling for simulating permutations to provide a very fast method for simulating logarithmic assemblies more generally. For logarithmic multisets and selections, this approach is replaced by an acceptance/rejection method based on a particular conditioning relationship that represents the distribution of the combinatorial structure as that of independent random variables conditioned on a weighted sum. We show how to improve its acceptance rate. We illustrate the method by estimating the probability that a random mapping has no repeated component sizes, and establish the asymptotic distribution of the difference between the number of components and the number of distinct component sizes for a very general class of logarithmic structures.

We develop the first systematic theoretical approach to dijet asymmetries in hadron-hadron collisions based on the perturbative QCD (pQCD) expansion and the Sudakov resummation formalism. We find that the pQCD calculation at next-to-leading order is indispensable to describe the experimental data, while the Sudakov resummation formalism is vital near the end points where the pQCD expansion fails to converge due to the appearance of large Sudakov logarithms. Utilizing our resummation improved pQCD approach, we obtain good agreement with the most up-to-date fully corrected ATLAS data on dijet asymmetry in $pp$ collisions. Combining with the BDMPS jet energy loss formalism, we extract the value of jet transport coefficient $\hat{q}_0 \sim 2$-$6~\textrm{GeV}^2/\textrm{fm}$ for the quark-gluon-plasma created in $PbPb$ collisions at 2.76A TeV. This work paves the way for a more complete and deeper understanding of the properties of strongly-coupled QCD medium via the studies of dijet asymmetries in relativistic heavy-ion collisions., Comment: 5 pages, 4 figures

The contribution of this work is the introduction of a multivariate circular-linear (or poly- cylindrical) distribution obtained by combining the projected and the skew-normal. We show the flexibility of our proposal, its property of closure under marginalization and how to quantify multivariate dependence. Due to a non-identifiability issue that our proposal inherits from the projected normal, a compu- tational problem arises. We overcome it in a Bayesian framework, adding suitable latent variables and showing that posterior samples can be obtained with a post-processing of the estimation algo- rithm output. Under specific prior choices, this approach enables us to implement a Markov chain Monte Carlo algorithm relying only on Gibbs steps, where the updates of the parameters are done as if we were working with a multivariate normal likelihood. The proposed approach can be also used with the projected normal. As a proof of concept, on simulated examples we show the ability of our algorithm in recovering the parameters values and to solve the identification problem. Then the proposal is used in a real data example, where the turning-angles (circular variables) and the logarithm of the step-lengths (linear variables) of four zebras are jointly modelled.

We work with spaces ( A 0 , A 1 ) θ , q , A which are logarithmic perturbations of the real interpolation spaces. We determine the dual of ( A 0 , A 1 ) θ , q , A when 0 q 1 . As we show, if θ = 0 or 1 then the dual space depends on the relationship between q and A . Furthermore we apply the abstract results to compute the dual space of Besov spaces of logarithmic smoothness and the dual space of spaces of compact operators in a Hilbert space which are close to the Macaev ideals.

We present a simple proof of the $C^1$ regularity of $p$-anisotropic functions in the plane for $2\leq p, Comment: 9 pages

Financial ratios are often used in cluster analysis to classify firms according to the similarity of their financial structures. Besides the dependence of distances on ratio choice, ratios themselves have a number of serious problems when subject to a cluster analysis such as skewed distributions, outliers, and redundancy. Some solutions to overcome those drawbacks have been proposed in the literature, but have proven problematic. In this work we put forward an alternative financial statement analysis method for classifying firms which aims at solving the above mentioned shortcomings and draws from compositional data analysis. The method is based on the use of existent clustering methods with standard software on transformed data by means of the so-called isometric logarithms of ratios. The method saves analysis steps (outlier treatment and data reduction) while defining distances among firms in a meaningful way which does not depend on the particular ratios selected. We show examples of application to two different industries and compare the results with those obtained from standard ratios This work was supported by the Catalan Autonomous Government [grant number 2014SGR551], the Spanish Health Ministry [grant number CB06/02/1002], FEDER/Spanish Economy and Competitiveness Ministry [grant number MTM2015-65016-C2-1-R], and the University of Girona [grant numbers MPCUdG2016/069, MPCUdG2016/098, and MPCUdG2016/107]

Biological networks are open systems that can utilize nutrients and energy from their environment in their metabolic processes and produce metabolic products. System entropy is defined as the difference between input and output signal entropy, that is, the net signal entropy of the biological system. System entropy is an important indicator for living or nonliving biological systems as biological systems can maintain or decrease their system entropy, which is found to be related to network evolution of biological systems. In this chapter, system entropy is determined for the first time for stochastic biological networks, and a computation method is proposed to measure the system entropy of nonlinear stochastic biological networks that are subject to intrinsic random fluctuations and environmental disturbances. We find that intrinsic random fluctuations could increase the system entropy, and that the system entropy is inversely proportional to the robustness and stability of the biological networks but is proportional to the evolvability of biological networks in a logarithmic scale, that is, system entropy is a logarithmic measurement of network evolvability. It is also determined that adding feedback loops to shift all eigenvalues to the farther left plane of the complex s-domain could decrease the system entropy and evolvability of a biological network.

In the presence of a sharp corner in the boundary of the entanglement region, the entanglement entropy (EE) and Renyi entropies for 3d CFTs have a logarithmic term whose coefficient, the corner function, is scheme-independent. In the limit where the corner becomes smooth, the corner function vanishes quadratically with coefficient $\sigma$ for the EE and $\sigma_n$ for the Renyi entropies. For a free real scalar and a free Dirac fermion, we evaluate analytically the integral expressions of Casini, Huerta, and Leitao to derive exact results for $\sigma$ and $\sigma_n$ for all $n=2,3,\dots$. The results for $\sigma$ agree with a recent universality conjecture of Bueno, Myers, and Witczak-Krempa that $\sigma/C_T = \pi^2/24$ in all 3d CFTs, where $C_T$ is the central charge. For the Renyi entropies, the ratios $\sigma_n/C_T$ do not indicate similar universality. However, in the limit $n \to \infty$, the asymptotic values satisfy a simple relationship and equal $1/(4\pi^2)$ times the asymptotic values of the free energy of free scalars/fermions on the $n$-covered 3-sphere., Comment: 10 pages, 2 figures. v2: typos corrected, references added, asymptotics updated

Within the heavy baryon chiral perturbation theory approach, we have studied the leading logarithm behaviour of the nucleon mass up to four-loop order exactly and we present some results up to six-loop order as well as an all-order conjecture. The same methods allow to calculate the main logarithm multiplying the terms with fractional powers of the quark mass. We calculate thus the coefficients of $m^{2n+1}\log^{(n-1)}(\mu^2/m^2)$ and $m^{2n+2}\log^n(\mu^2/m^2)$, with $m$ the lowest-order pion mass. A side result is the leading divergence for a general heavy baryon loop integral., Comment: 24p, misprints corrected, some minor reformulations

In his affirmative answer to the Edelman-Reiner conjecture, Yoshinaga proved that the logarithmic derivation modules of the cones of the extended Shi arrangements are free modules. However, all we know about the bases is their existence and degrees. In this article, we introduce two distinguished bases for the modules. More specifically, we will define and study the simple-root basis plus (SRB+) and the simple-root basis minus (SRB-) when a primitive derivation is fixed. They have remarkable properties relevant to the simple roots and those properties characterize the bases.

We study the parabolic integral kernel associated with the weighted Laplacian and the Feynman-Kac kernels. For manifold with a pole we deduce formulas and estimates for them and for their derivatives, given in terms of a Gaussian term and the semi-classical bridge. Assumptions are on the Riemannian data.

Recent advances in knot polynomial calculus allowed us to obtain a huge variety of LMOV integers counting degeneracy of the BPS spectrum of topological theories on the resolved conifold and appearing in the genus expansion of the plethystic logarithm of the Ooguri-Vafa partition functions. Already the very first look at this data reveals that the LMOV numbers are randomly distributed in genus (!) and are very well parameterized by just three parameters depending on the representation, an integer and the knot. We present an accurate formulation and evidence in support of this new puzzling observation about the old puzzling quantities. It probably implies that the BPS states, counted by the LMOV numbers can actually be composites made from some still more elementary objects., Comment: 23 pages

This chapter is focused on defect evaluation using longitudinal and lateral heat conduction of eddy current pulsed thermography (ECPT). In the first section, characterization of wall thinning defects and inner defects in steel is investigated in the time domain. Characterization was performed under transmission and reflection modes through 1D analytical analysis, 3D numerical studies, and experimental studies. In the second section, logarithmic analysis to quantify the depth of subsurface defects is proposed and verified through numerical and experimental studies. Results show that temperature-time curves in the logarithm domain can be used to detect subsurface defects, and separation time can measure defect depth. The third section introduces lateral heat conduction (LHC) for the detection of cracks parallel to the inductive coil (parallel cracks) and natural oblique cracks. Due to the significant temperature gradient, the spatial derivative and gradient were proposed to improve detectability of natural oblique cracks in rail.

Parametric population PK/PD models must assume that the model parameter values in a population of patients have a normal or Gaussian shape, or a lognormal one, in which the logarithms of the parameter values have a normal distribution. Other distributions such as bimodal ones, can be accommodated, but must always be assumed and specified in advance of the analysis. However, such assumptions are unnecessary. The nonparametric (NP) approach makes no such assumptions. The shape of the distribution is entirely determined by the data. The NP approach also obtains results that are more likely given the data, as it is not constrained by any assumptions of shape. NP models also permit development of dosage regimens which are maximally precise, something parametric models cannot do. Parametric technology approaches cannot even perceive the issue of precision, as they deal only with estimating the single valued central tendency of an assumed distribution in developing a dosage regimen.

Exponentials and logarithms are important basic mathematical functions. This chapter introduces the basic exponential and logarithmic functions and their properties.

Chapter 2 presents more advanced applications of the partition method for a power series expansion than those of the previous chapter. In presenting these applications, the method is both extended and adapted, thereby enabling a general theory to be developed in Chapter 4. The chapter begins by applying the method to the Bell polynomials of the first kind, denoted by Bk(x)Bk(x). From this study a general formula for the Stirling numbers of the second kind S(k,j)S(k,j), which represent the number of ways of partitioning k objects into j subgroups, is derived as a sum over the partitions summing to k. By setting j equal to several values from k down to k−3k−3, explicit formulas are derived for the four highest order Stirling numbers of the second kind. In the following section the cosecant and secant numbers of Chapter 1 are generalized by introducing an arbitrary power of ρ to the trigonometric functions that generate them. As a consequence, the cosecant and secant numbers turn into polynomials of degree k in ρ that reduce to the results of Chapter 1 for ρ=1ρ=1. In particular, the generalized cosecant numbers for integer values, viz. c2v,kc2v,k where v is an integer, are shown to be related to the k -th symmetric polynomial s(v,k)s(v,k) obtained by summing the squares of the integers up to v−1v−1. The next example deals with the generalization of the reciprocal logarithm numbers in Chapter 1 whereby a power s appears in the logarithm that generates them. Again, the numbers, which are denoted by Ak(s)Ak(s), are polynomials of degree k in s with many interesting properties. As in the case of the Bell polynomials, general expressions in k are obtained for the four highest order terms in the Ak(s)Ak(s). The section concludes by studying the power series expansion for the doubly-nested logarithm ln⁡ln⁡(1+z)ln⁡ln⁡(1+z), whose coefficients are represented by Ak(2). These numbers are found to be related to the reciprocal logarithm numbers and thus converge in a similar manner to zero as k→∞k→∞. The final application in the chapter is concerned with the generalization of the integrands in the elliptic integrals F(x,κ)F(x,κ) and E(x,κ)E(x,κ). First the partition method for a power series expansion is applied to f(x)=(1+acos⁡x)−ρf(x)=(1+acos⁡x)−ρ in Theorem 2.4. Again, general formulas are derived for the three highest and lowest order terms in powers of a+1a+1, while in a corollary the recurrence relation for the coefficients is derived. By putting a=−κ2/(κ2−2)a=−κ2/(κ2−2) and integrating the expansion over x , we obtain power series expansions for the elliptic integral of the first kind F(x,κ)F(x,κ) and the second kind E(x,κ)E(x,κ) when ρ equals 1/2 and −1/2−1/2, respectively. Then the power series expansion for the elliptic integral of the third kind Π(n,x,κ)Π(n,x,κ) is derived by combining these results. Finally, similar analyses are carried out when the cosine in f(x)f(x) is replaced by other trigonometric functions such as sin⁡xsin⁡x, tan⁡xtan⁡x and cot⁡xcot⁡x.