Framework Of Approximation Research Articles

Theoretical modeling of nonlinear optical properties in spheroidal CdTe/ZnTe core/shell quantum dot embedded in various dielectric matrices

The theoretical investigation of the electronic and nonlinear optical properties in spheroid-shaped CdTe/ZnTe core/shell quantum dots (CSQDs) embedded into two commonly adopted dielectric matrices (PVA, SiO2) is done in the framework of the Effective Mass Approximation (EMA). The discrete intra-band confined energy levels and their matching wave functions were calculated by solving the stationary Schrödinger equation taking into account the Compact Density Matrix (CDM) approach. The effect of the dielectric mismatch between the system and the capped matrix has been studied and discussed. Our numerical results revealed that the third-order nonlinear (TON) optical susceptibility χ3 is strongly influenced by the geometrical parameters and the dielectric environment.

Unification: Emergent universe followed by inflation and dark epochs from multi-field theory

A two scalar field model that incorporates non Riemannian Measures of integration or usually called Two Measures Theory (TMT) is introduced, in order to unify the early and present universe. In the Einstein frame a K-essence is generated and as a consequence for the early universe, we can have a Non Singular Emergent universe followed by Inflation and for the present universe dark epochs with consistent generation of dark energy (DE), dark matter (DM) and stiff matter. The scale invariance is introduced and then is spontaneously broken from the integration of the degrees of freedom associated with the modified measures. The resulting effective potentials and K-essence in the Einstein frame produce three flat regions corresponding to the different epochs mentioned before. For the first flat region we can associate an emergent and an inflationary universe. Here for a parameter-space region this flat plateau possesses a non singular stable emergent universe solution which characterizes an initial epoch of evolution that precedes the inflationary scenario. Also assuming this first plateau, we study the inflation in the framework of the slow-roll approximation. In this scenario under the slow roll approximation we obtain a linear combination that is a constant. The corresponding cosmological perturbations in our model are determined and we also obtain the different constrains on the parameter-space from the Planck data.In the following flat region DE and also the DM, which does not need to be introduced separately, it is instead a result of a K-essence induced by the multi measures, multi field theory. Also stiff matter component is automatically generated from the K-essence theory from two scalar fields. From the perturbative analysis associated to the perturbation solution of background, we find a correlation between the two scalars. Besides, we obtain that our model during the dark epoch has a behavior of tracking freezing model.

Scalable Approximate Butterfly and Bi-triangle Counting for Large Bipartite Networks

A bipartite graph is a graph that consists of two disjoint sets of vertices and only edges between vertices from different vertex sets. In this paper, we study the counting problems of two common types of em motifs in bipartite graphs: (i) butterflies (2x2 bicliques) and (ii) bi-triangles (length-6 cycles). Unlike most of the existing algorithms that aim to obtain exact counts, our goal is to obtain precise enough estimations of these counts in bipartite graphs, as such estimations are already sufficient and of great usefulness in various applications. While there exist approximate algorithms for butterfly counting, these algorithms are mainly based on the techniques designed for general graphs, and hence, they are less effective on bipartite graphs. Not to mention that there is still a lack of study on approximate bi-triangle counting. Motivated by this, we first propose a novel butterfly counting algorithm, called one-sided weighted sampling, which is tailored for bipartite graphs. The basic idea of this algorithm is to estimate the total butterfly count with the number of butterflies containing two randomly sampled vertices from the same side of the two vertex sets. We prove that our estimation is unbiased, and our technique can be further extended (non-trivially) for bi-triangle count estimation. Theoretical analyses under a power-law random bipartite graph model and extensive experiments on multiple large real datasets demonstrate that our proposed approximate counting algorithms can reach high accuracy, yet achieve up to three orders (resp. four orders) of magnitude speed-up over the state-of-the-art exact butterfly (resp. bi-triangle) counting algorithms. Additionally, we present an approximate clustering coefficient estimation framework for bipartite graphs, which shows a similar speed-up over the exact solutions with less than 1% relative error.

Efficient Approximation Framework for Attribute Recommendation

Trend analysis is a fundamental type of analytical query in online analytical processing (OLAP) systems. In trend analysis, a key step is to identify k valuable attributes whose distributions in two subsets under different predicates significantly differ for further investigation, where the difference is measured by metric functions. However, the exact solution that involves scanning all records is prohibitively expensive, particularly when handling large datasets in the era of big data. To minimize unnecessary data access, the existing state-of-the-art solution TopKAttr adopts sampling to avoid the expensive data scan. However, their solution still has two main drawbacks. Firstly, their solution is tailored only for two limited metric functions: the Earth Mover distance and Euclidean distance, and cannot be generalized to more complicated metric functions. Besides, their solution still aims to return the exact top-k answers via the sampling method, which still causes high running costs as shown in our experiment. Motivated by these limitations, we propose a general approximation framework for attribute recommendation that efficiently returns the top-k attributes with theoretical guarantees while supporting an extensive range of metric functions, such as the Kolmogorov-Smirnov test (KS-test), Chebyshev distance, the Earth Mover distance, Euclidean distance, and with the potential to more metrics. The key to our framework is a new bound estimation strategy that can be applied to a wide spectrum of metrics, as we listed above. Based on our estimation framework, we further devise an efficient approximation algorithm with theoretical guarantees to answer the top-k queries, which is widely used in attribute recommendation. Extensive experiments on four real large datasets show that our framework gains up to an order of magnitude speed-up and consistently high accuracy compared to TopKAttr, providing a promising alternative for attribute recommendation in OLAP systems.

Effects of the magnetic field and the off-center displacement on the third-order nonlinear optical susceptibility of inverted core/shell spherical one-electron quantum dots

The third order nonlinear optical susceptibility (TONOS) of an inverted ZnS/CdSe core–shell spherical quantum dot embedded in SiO 2-matrix with or without impurity, and subjected to an external magnetic field is investigated. Within the framework of effective mass approximation and using B-splines basis functions, the energy levels, the dipole matrix elements and the TONOS are computed. The dielectric mismatch in the interface dots as well as the effective mass dependence on the core and shell regions are taken into account. It is revealed that, simultaneously the shell size, magnetic field and off-center displacement have a noticeable effect on the positions and the heights of the peaks of the TONOS. Moreover, we have shown that, due to the magnetic field and the off-center displacement effects, the TONOS takes different profiles associated with the polarization direction (parallel and perpendicular). In the perpendicular polarization, two peaks of the nonlinear optical properties appear for each off-center displacement value corresponding to the two transversal allowed transitions. The shift towards higher energies of the peak position and the reduction of the intensity of the peak when the magnetic field increases are recorded in the transversal transition case. Furthermore, in the longitudinal transition, as increasing the magnetic field strength, the intensity of the peak of the TONOS grows and the position of the peak is shifted towards lower frequencies. The dielectric constant, effective mass and conduction band offset of the materials that constitute the core and shell are equally found to modify significantly the main features of the susceptibility.

Twist decomposition of non-linear effects in Balitsky–Kovchegov evolution of proton structure functions

Effects of non-linear small-x evolution of the gluon distribution given by the Balitsky–Kovchegov equation are analyzed within the collinear approximation framework. We perform a twist decomposition of the proton structure functions F2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$F_2$$\\end{document} and FL\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$F_{\ extrm{L}}$$\\end{document} obtained from the Balitsky–Kovchegov equation using the Mellin representation of the scattering cross-sections at high energies. In both the structure functions we find strong corrections coming from the non-linear effects in the gluon evolution at twist 2, and strongly suppressed higher twist effects. This implies that unitarization effects of high energy scattering amplitudes are mostly the leading twist effect. Furthermore we consider the double logarithmic limit of the Balitsky–Kovchegov equation for the collinear gluon distribution, and compare the result to the Gribov–Levin–Ryskin equation. We find that these two equations differ by two powers of the hard scale logarithm for the large scales.

Electronic and optical properties of the exponential and hyperbolic Rosen–Morse types quantum wells under applied magnetic field

In this study, we considered the electronic and optical properties of quantum wells with the exponential and hyperbolic Rosen–Morse potentials under an applied magnetic field. Calculations are made within the framework of effective mass and parabolic band approximations. We have used the diagonalization method by choosing a wave function based on the trigonometric orthonormal function to find eigenvalues and eigenfunctions of the confined electron. Our results show that the magnetic field, asymmetry, and confinement parameters cause a significant increase in electron energies and energy differences between the electron states and the blue shift in the absorption peaks. These results can be used to probe materials’ electronic and structural properties and develop new materials with tailored optical properties.

A mathematical model of Marburg virus disease outbreaks and the potential role of vaccination in control

BackgroundMarburg virus disease is an acute haemorrhagic fever caused by Marburg virus. Marburg virus is zoonotic, maintained in nature in Egyptian fruit bats, with occasional spillover infections into humans and nonhuman primates. Although rare, sporadic cases and outbreaks occur in Africa, usually associated with exposure to bats in mines or caves, and sometimes with secondary human-to-human transmission. Outbreaks outside of Africa have also occurred due to importation of infected monkeys. Although all previous Marburg virus disease outbreaks have been brought under control without vaccination, there is nevertheless the potential for large outbreaks when implementation of public health measures is not possible or breaks down. Vaccines could thus be an important additional tool, and development of several candidate vaccines is under way.MethodsWe developed a branching process model of Marburg virus transmission and investigated the potential effects of several prophylactic and reactive vaccination strategies in settings driven primarily by multiple spillover events as well as human-to-human transmission. Linelist data from the 15 outbreaks up until 2022, as well as an Approximate Bayesian Computational framework, were used to inform the model parameters.ResultsOur results show a low basic reproduction number which varied across outbreaks, from 0.5 [95% CI 0.05–1.8] to 1.2 [95% CI 1.0–1.9] but a high case fatality ratio. Of six vaccination strategies explored, the two prophylactic strategies (mass and targeted vaccination of high-risk groups), as well as a combination of ring and targeted vaccination, were generally most effective, with a probability of potential outbreaks being terminated within 1 year of 0.90 (95% CI 0.90–0.91), 0.89 (95% CI 0.88–0.90), and 0.88 (95% CI 0.87–0.89) compared with 0.68 (0.67–0.69) for no vaccination, especially if the outbreak is driven by zoonotic spillovers and the vaccination campaign initiated as soon as possible after onset of the first case.ConclusionsOur study shows that various vaccination strategies can be effective in helping to control outbreaks of MVD, with the best approach varying with the particular epidemiologic circumstances of each outbreak.

A COMPOSITE MODEL OF MICROWAVE SCATTERING FROM WATER SURFACE IN EXTREME WIND SPEED CONDITION

Experiments were carried out in the wind-wave flume of Large Thermo-Stratified Wind-Wave Tank of IAP RAS aimed at studying the mechanisms of cross-polarized microwave radiation scattering from water surface under conditions of extremely high wind speeds. It is shown that the normalized radar cross-section (NRCS) can be represented as the result of an incoherent addition of contributions from breaking wave crests and from non-breaking wind waves. The effect of smoothing the water surface after passing the breaking crest made it possible to measure the NRCS of the breaking area on cross-polarization, while no dependence of the NRCS on wind speed and incidence angle was revealed. NRCS on non-breaking wind waves was calculated within the framework of the small slope approximation (SSA) using experimentally measured wind wave spectra. It is shown that the NRCS on cross-polarization increases monotonically with increasing wind speed, including hurricane conditions. In this case, the contribution of non-breaking wind waves to the NRCS saturates at wind speeds above 25 m/s. The monotonous increasing NRCS at higher wind speeds is associated with a breaking area increasing. A composite model of microwave radiation scattering from wave-covered water surface has been constructed, which has been verified on the basis of comparison with measurement data. The possibility of constructing a geophysical model function for ocean conditions based on the proposed composite model is shown, which can be used for remote sensing of sea storms and hurricanes.

Natural Vibrations of a Gas in a Helmholtz Resonator with a Periodically Varying Cross-section

Within the framework of the long-wave approximation, the frequencies and shapes of gas natural oscillations in a Helmholtz resonator having the shape of a pipe of periodic cross-section have been studied. The problem is reduced to the Sturm–Liouville problem with boundary conditions of the first kind, the solution of which is carried out by the method of accelerated convergence. A detailed analysis of the dependences of eigenvalues and eigenfunctions on pipe parameters was carried out. A “self-similar” type of dependence of the natural frequency for various modes has been revealed. The values of the resonator periodicity parameters at which a sharp change in the natural frequency occurs are determined.

Display optimization under the multinomial logit choice model: Balancing revenue and customer satisfaction

In this paper, we consider an assortment optimization problem in which a platform must choose pairwise disjoint sets of assortments to offer across a series of T stages. Arriving customers begin their search process in the first stage, and progress sequentially through the stages until their patience expires, at which point they make a multinomial logit–based purchasing decision from among all products they have viewed throughout their search process. The goal is to choose the sequential displays of product offerings to maximize expected revenue. Additionally, we impose stage‐specific constraints that ensure that as each customer progresses farther and farther through the T stages, there is a minimum level of “desirability” met by the collections of displayed products. We consider two related measures of desirability: purchase likelihood and expected utility derived from the offered assortments. In this way, the offered sequence of assortments must be both high earning and well liked, which breaks from the traditional assortment setting, where customer‐centric considerations are generally not explicitly accounted for. We show that our assortment problem of interest is strongly NP‐Hard, thus ruling out the existence of a fully polynomial‐time approximation scheme (FPTAS). From an algorithmic standpoint, as a warm‐up, we develop a simple constant factor approximation scheme in which we carefully stitch together myopically selected assortments for each stage. Our main algorithmic result consists of a polynomial‐time approximation scheme (PTAS), which combines a handful of structural results related to the make‐up of the optimal assortment sequence within an approximate dynamic programming framework. We also provide an additional approximation scheme, which, under mild assumptions, can handle a cardinality constraint that enforces that an exact number of new products are introduced at each stage. Using an extensive set of numerical experiments, we demonstrate that both algorithms exhibit excellent practical performance, producing sequences of assortments that are, on average, always within 2% of optimal.

Model-to-Circuit Cross-Approximation For Printed Machine Learning Classifiers

Printed electronics (PE) promises on-demand fabrication, low non-recurring engineering costs, and sub-cent fabrication costs. It also allows for high customization that would be infeasible in silicon, and bespoke architectures prevail to improve the efficiency of emerging PE machine learning (ML) applications. Nevertheless, large feature sizes in PE prohibit the realization of complex ML models in PE, even with bespoke architectures. In this work, we present an automated, cross-layer approximation framework tailored to bespoke architectures that enable complex ML models, such as Multi-Layer Perceptrons (MLPs) and Support Vector Machines (SVMs), in PE. Our framework adopts cooperatively a hardware-driven coefficient approximation of the ML model at algorithmic level, a netlist pruning at logic level, and a voltage over-scaling at the circuit level. Extensive experimental evaluation on 12 MLPs and 12 SVMs and more than 6000 approximate and exact designs demonstrates that our model-to-circuit cross-approximation delivers power and area optimal designs that, compared to the state-of-the-art exact designs, feature on average 51% and 66% area and power reduction, respectively, for less than 5% accuracy loss. Finally, we demonstrate that our framework enables 80% of the examined classifiers to be battery-powered with almost identical accuracy with the exact designs, paving thus the way towards smart complex printed applications.

Nucleation Work on Curved Substrates

Nucleation is the initial phase transition process when nuclei of a new phase form within an undercooled or supersaturated parent phase under appropriate conditions. Nucleation most often occurs through a heterogeneous process on active centers on which the probability of nucleus formation is high. In general, the origin of active centers may be difficult to distinguish. In this work, we consider the formation of crystalline nuclei in a melt on various curved substrates. Knowledge of excess free energy plays a key role in understanding the process of formation of clusters and it is not easy to express this quantity in a considered system. Excess free energy is often approximated within the framework of capillarity approximation based on interfacial energy, which depends on interatomic interactions near the interface, as well as the misfit between melts, surface roughness, temperature, composition, etc., near the phase interface. The formation of nuclei requires overcoming a certain energy (nucleation) barrier that is a consequence of balancing the volume and the interfacial free energy. Knowing the nucleation barrier (W) is crucial for understanding this process, as nuclei predetermine the physical properties of a newly formed phase. W is typically expressed as a function of the nucleus radius; however, in nucleation kinetics, one needs to determine (W) as a function of the number of molecules forming the nucleus. We analyze nucleation work on various substrates (flat, convex, and concave) for crystallization from an aluminum melt to show that the formation of nuclei is the most probable on concave substrates. An analytical expression for W can be easily applied to other systems under consideration. We show that under the same conditions, the critical radius of nuclei is identical for various substrate, in contrast with the critical number of molecules forming a nucleus.

GaAs Quantum Dot Confined with a Woods–Saxon Potential: Role of Structural Parameters on Binding Energy and Optical Absorption

We present the first detailed study of optical absorption coefficients (OACs) in a GaAs quantum dot confined with a Woods–Saxon potential containing a hydrogenic impurity at its center. We use a finite difference method to solve the Schrödinger equation within the framework of the effective mass approximation. First, we compute energy levels and probability densities for different parameters governing the confining potential. We then calculate dipole matrix elements and energy differences, E1p−E1s, and discuss their role with respect to the OACs. Our findings demonstrate the important role of these parameters in tuning the OAC to enable blue or red shifts and alter its amplitude. Our simulations provide a guided path to fabricating new optoelectronic devices by adjusting the confining potential shape.

A Broken FEEC Framework for Electromagnetic Problems on Mapped Multipatch Domains

We present a framework for the structure-preserving approximation of partial differential equations on mapped multipatch domains, extending the classical theory of finite element exterior calculus (FEEC) to discrete de Rham sequences which are broken, i.e., fully discontinuous across the patch interfaces. Following the Conforming/Nonconforming Galerkin (CONGA) schemes developed in Campos Pinto and Sonnendrücker (Math Comput 85:2651–2685, 2016) and Campos Pinto and Güçlü (Broken-FEEC discretizations and Hodge Laplace problems. arXiv:2109.02553, 2022), our approach is based on: (i) the identification of a conforming discrete de Rham sequence with stable commuting projection operators, (ii) the relaxation of the continuity constraints between patches, and (iii) the construction of conforming projections mapping back to the conforming subspaces, allowing to define discrete differentials on the broken sequence. This framework combines the advantages of conforming FEEC discretizations (e.g. commuting projections, discrete duality and Hodge–Helmholtz decompositions) with the data locality and implementation simplicity of interior penalty methods for discontinuous Galerkin discretizations. We apply it to several initial- and boundary-value problems, as well as eigenvalue problems arising in electromagnetics. In each case our formulations are shown to be well posed thanks to an appropriate stabilization of the jumps across the interfaces, and the solutions are extremely robust with respect to the stabilization parameter. Finally we describe a construction using tensor-product splines on mapped cartesian patches, and we detail the associated matrix operators. Our numerical experiments confirm the accuracy and stability of this discrete framework, and they allow us to verify that expected structure-preserving properties such as divergence or harmonic constraints are respected to floating-point accuracy.

Characteristics of an Ising-like Model with Ferromagnetic and Antiferromagnetic Interactions.

In the framework of mean field approximation, we consider a spin system consisting of two interacting sub-ensembles. The intra-ensemble interactions are ferromagnetic, while the inter-ensemble interactions are antiferromagnetic. We define the effective number of the nearest neighbors and show that if the two sub-ensembles have the same effective number of the nearest neighbors, the classical form of critical exponents (α=0, β=1/2, γ=γ'=1, δ=3) gives way to the non-classical form (α=0, β=3/2, γ=γ'=0, δ=1), and the scaling function changes simultaneously. We demonstrate that this system allows for two second-order phase transitions and two first-order phase transitions. We observe that an external magnetic field does not destroy the phase transitions but only shifts their critical points, allowing for control of the system's parameters. We discuss the regime when the magnetization as a function of the magnetic field develops a low-magnetization plateau and show that the height of this plateau abruptly rises to the value of one when the magnetic field reaches a critical value. Our analytical results are supported by a Monte Carlo simulation of a three-dimensional layered model.

Reconstructing inflation and reheating in [formula omitted] gravity

In this work we study the reconstruction of an inflationary universe in the context of a theory of gravity f(ϕ)T, in which T corresponds to the trace of energy momentum tensor. To realize this reconstruction during the inflationary epoch, we consider as attractor the scalar spectral index ns in terms of the number of e-folds N, in the framework of the slow-roll approximation. By assuming a specific function f(ϕ) together with the simplest attractor ns(N), we find different expressions for the reconstructed effective potential V(ϕ). Additionally, we analyze the era of reheating occurs after of the reconstruction obtained during the inflationary epoch. In this scenario we determine the duration and temperature during the reheating epoch, in terms of the equation of state parameter and of the observational parameters. In this context, the different parameters associated to the reconstructed model are restricted during the scenarios of inflation and reheating by considering the recent astronomical observations.

Spatially Dependent Bayesian Modeling of Geostatistics Data and Its Application for Tuberculosis (TB) in China

Geostatistics data in regions always have highly spatial heterogeneous, yet the regional features of the data itself cannot be ignored. In this paper, a novel latent Bayesian spatial model is proposed, which incorporates the spatial dependence of different subjects and the spatial random effects to further analysis the influence of spatial effect. The model is verified to be compatible with the integrated nested Laplace approximation (INLA) framework and is fitted using INLA and stochastic partial differential equation (SPDE). The posterior marginal distribution of parameters is estimated with high precision. Additionally, a practical application of the model is presented using tuberculosis (TB) incidence data in China from 2015 to 2019. The results show that the fitting accuracy of our model is higher than the general Bayesian spatial model using INLA-SPDE.

Backscattering properties of randomly oriented hexagonal hollow columns for lidar application.

The study of the optical properties of cirrus clouds is necessary to improve the accuracy of interpreting data from space lidars and ground-based lidar networks. Existing databases of backscattering properties do not include data on hollow columns. In this paper, the backscattering properties of randomly oriented hollow column ice crystal particles in cirrus at wavelengths of 355 nm, 532 nm, and 1064 nm have been investigated. The backscattering cross section (M11), depolarization ratio (δ), lidar ratio (S), and color ratio (χ) of randomly oriented hollow columns with sizes ranging from 10-316.23 µm are calculated within the framework of the physical optical approximation (PO). For the first time, we introduce the concept of modal hollow columns (MHC) suitable for mid-latitude regions, which simplifies the description of hollow ice crystals in nature. It is found that when the mixing proportion of MHC and solid columns (SC) reaches 50%, the mixing ratio can be distinguished by the lidar ratio for a wavelength of 1064 nm and by the χ(1064,532)-δ(532) relation.

In English

Using a variational method within the framework of the effective mass approximation, using a triangular coordinate system of an electron, hole, and exciton moving in a titanium dioxide quantum dot, the exciton energy spectrum was obtained as a function of the radius a of the quantum dot. The variational wave function of the exciton contained factors that took into account the motion of an electron and a hole in a potential well of infinite depth of a quantum dot, as well as the form of a hydrogen-like wave function. It is shown that the occurrence of an exciton in a quantum dot has a threshold character. An exciton, as a bound state of an electron and a hole, is formed starting from a certain critical radius ac, the value of which exceeds the Bohr radius of the exciton in titanium dioxide. The exciton energy levels are located in the band gap of the titanium dioxide quantum dot. In this case, with an increase in the radius a of the quantum dot (so that a≥ac), a band of exciton states appears in the band gap of the titanium dioxide quantum dot. The mechanism for the formation of optical absorption spectra in nanosystems containing titanium dioxide nanocrystals are presented. It is found that the optical absorption of anatase NC, which was observed under the experimental conditions, was due to the appearance of an exciton in the NC. Using the variational calculation of the energy spectrum of an exciton in NC, the position of the absorption peak of NC anatase was determined. This absorption peak differs slightly from the absorption peak, which was obtained in the experimental work.