Complete Set Of Functions Research Articles

(1+1) genetic programming with functionally complete instruction sets can evolve Boolean conjunctions and disjunctions with arbitrarily small error

Recently it has been proven that simple GP systems can efficiently evolve a conjunction of n variables if they are equipped with the minimal required components. In this paper, we make a considerable step forward by analysing the behaviour and performance of a GP system for evolving a Boolean conjunction or disjunction of n variables using a complete function set that allows the expression of any Boolean function of up to n variables. First we rigorously prove that a GP system using the complete truth table to evaluate the program quality, and equipped with both the AND and OR operators and positive literals, evolves the exact target function in O(ℓnlog2⁡n) iterations in expectation, where ℓ≥n is a limit on the size of any accepted tree. Additionally, we show that when a polynomial sample of possible inputs is used to evaluate the solution quality, conjunctions or disjunctions with any polynomially small generalisation error can be evolved with probability 1−O(log2⁡(n)/n). The latter result also holds if GP uses AND, OR and positive and negated literals, thus has the power to express any Boolean function of n distinct variables. To prove our results we introduce a super-multiplicative drift theorem that gives significantly stronger runtime bounds when the expected progress is only slightly super-linear in the distance from the optimum.

Spsur: An R Package for Dealing with Spatial Seemingly Unrelated Regression Models

Spatial seemingly unrelated regression (spatial SUR) models are a useful multiequational econometric specification to simultaneously incorporate spatial effects and correlated error terms across equations. The purpose of the spsur R package is to supply a complete set of functions to test for spatial structures in the residual of a SUR model; to estimate the most popular specifications by applying different methods and test for linear restrictions on the parameters. The package also facilitates the estimation of socalled spatial impacts, conveniently adapted to a SUR framework. The package includes functions to simulate datasets with the features decided by the user, which may be useful in teaching activities or in more general research projects. The article concludes with a real data application showing the potential that spsur has to examine the relation of individual mobility over geographic areas and the incidence of COVID-19 in Spain during the first lockdown.

(Invited) Logic-in-Memory Based on an Atomically Thin Semiconductor

The growing importance of applications based on machine learning is driving the need to develop dedicated, energy-efficient electronic hardware. Compared with von-Neumann architectures, brain-inspired in-memory computing uses the same basic device structure for logic operations and data storage, thus promising to reduce the energy cost of data-centric computing significantly. Two-dimensional materials such as semiconducting MoS2 could stand out as a promising candidate to face this obstacle thanks to their exceptional electrical and mechanical properties. Here, we show that wafer-scale grown MoS2 can be used as an active channel material for developing logic-in-memory devices and circuits based on floating-gate field-effect transistors (FGFET). The conductance of our FGFETs can be precisely and continuously tuned, allowing us to use them as building blocks for reconfigurable logic circuits where logic operations can be directly performed using the memory elements. We show that this design can be simply extended to implement more complex programmable logic and functionally complete sets of functions. Our findings highlight the potential of atomically thin semiconductors for the development of next-generation low-power electronics.

Effect of electric field on photoionisation cross-section of impurity in multilayered quantum dot

The electron - impurity binding energy and photoionization cross-section of hydrogenic impurity are studied in spherical multilayered quantum dot AlxGa1-xAs/GaAs/AlyGa1-yAs driven by external electric field. The problem is solved in the framework of the effective mass approximation and rectangular potential profiles for wells and barriers, using the method of wave function expansion over a complete set of functions obtained as exact solutions of Schrodinger equation in nanostructure without impurity and electric field.

МЕТОД ОЦЕНКИ НАДЁЖНОСТИ ИНТЕГРИРОВАННЫХ РАДИОЭЛЕКТРОННЫХ СИСТЕМ УПРАВЛЕНИЯ КОСМИЧЕСКИМИ АППАРАТАМИ НА СТАДИИ ЭКСПЛУАТАЦИИ

Modern and perspective radio-electronic control systems for spacecraft are considered, which have such features as multifunctionality, high integration of hardware and software, high requirements for reliability and availability, structural redundancy, low-series, etc. A review of existing models and methods for assessing the reliability of hardware and software providing electronic systems at various stages of their life cycle, including at the operational stage. The complexity of a reliable assessment of the reliability of such systems using existing models and methods in an independent approach to assessing the reliability of hardware and software is shown. The task of combining the reliability models of hardware and software for integrated electronic systems in order to more fully take into account their mutual influence in the context of ensuring the reliability of structurally complex systems as a whole has been set. The characteristic of logical and probabilistic methods of system modeling and analysis is given, and, in particular, the capabilities of the general logical and probabilistic method, as having advanced capabilities compared to classical logical and probabilistic methods. It is proposed to use the apparatus of the general logical and probabilistic method for modeling, analysis and a comprehensive assessment of the reliability of integrated electronic systems. The proposed method consists in using a complete set of functions of the algebra of logic, both for a graphical description of the structure of systems and for the analytical recording of the conditions for their operability, as well as the development of methods for moving from logical functions that are a criterion for the functioning of systems to probabilistic functions characterizing the properties of the systems under study. It is shown that for reliable assessment of the reliability of integrated radio-electronic spacecraft control systems, a methodological apparatus is necessary that takes into account both the features of their use and the fact of the joint, interdependent functioning of hardware and software.

Trefftz method in solving the pennes’ and single-phase-lag heat conduction problems with perfusion in the skin

Purpose The purpose of this paper is to derive the Trefftz functions (T-functions) for the Pennes’ equation and for the single-phase-lag (SPL) model (hyperbolic equation) with perfusion and then comparing field of temperature in a flat slab made of skin in the case when perfusion is taken into account, with the situation when a Fourier model is considered. When considering the process of heat conduction in the skin, one needs to take into account the average values of its thermal properties. When in biological bodies relaxation time is of the order of 20 s, the thermal wave propagation appears. The initial-boundary problems for Pennes’ model and SPL with perfusion model are considered to investigate the effect of the finite velocity of heat in the skin, perfusion and thickness of the slab on the rate of the thermal wave attenuation. As a reference model, the solution of the classic Fourier heat transfer equation for the considered problems is calculated. A heat flux has direction perpendicular to the surface of skin, considered as a flat slab. Therefore, the equations depend only on time and one spatial variable. Design/methodology/approach First of all the T-functions for the Pennes’ equation and for the SPL model with perfusion are derived. Then, an approximate solutions of the problems are expressed in the form of a linear combination of the T-functions. The T-functions satisfy the equation modeling the problem under consideration. Therefore, approximating a solution of a problem with a linear combination of n T-functions one obtains a function that satisfies the equation. The unknown coefficients of the linear combination are obtained as a result of minimization of the functional that describes an inaccuracy of satisfying the initial and boundary conditions in a mean-square sense. Findings The sets of T-functions for the Pennes’ equation and for the SPL model with perfusion are derived. An infinite set of these functions is a complete set of functions and stands for a base functions layout for the space of solutions for the equation used to generate them. Then, an approximate solutions of the initial-boundary problem have been found and compared to find out the effect of finite velocity of heat in the skin, perfusion and thickness of the slab on the rate of the thermal wave attenuation. Research limitations/implications The methods used in the literature to find an approximate solution of any bioheat transfer problems are more complicated than the one used in the presented paper. However, it should be pointed out that there is some limitation concerning the T-function method, namely, the greater number of T-function is used, the greater condition number becomes. This limitation usually can be overcome using symbolic calculations or conducting calculations with a large number of significant digits. Originality/value The T-functions for the Pennes’ equation and for the SPL equation with perfusion have been reported in this paper for the first time. In the literature, the T-functions are known for other linear partial differential equations (e.g. harmonic functions for Laplace equation), but for the first time they have been derived for the two aforementioned equations. The results are discussed with respect to practical applications.

Ploidy- and Purity-Adjusted Allele-Specific DNA Analysis Using CLONETv2.

High‐throughput DNA sequencing technology provides base‐level and statistically rich information about the genomic content of a sample. In the contexts of cancer research and precision oncology, thousands of genomes from paired tumor and matched normal samples are profiled and processed to determine somatic copy‐number changes and single‐nucleotide variations. Higher‐order informative analyses, in the form of allele‐specific copy‐number assessments or subclonality quantification, require reliable estimates of tumor DNA ploidy and tumor cellularity. CLONETv2 provides a complete set of functions to process matched normal and tumor pairs using patient‐specific genotype data, is independent of low‐level tools (e.g., aligner, segmentation algorithm, mutation caller) and offers high‐level functions to compute allele‐specific copy number from segmented data and to identify subclonal population in the input sample. CLONETv2 is applicable to whole‐genome, whole‐exome and targeted sequencing data generated either from tissue or from liquid biopsy samples. © 2019 The Authors.

Master integrals for the NNLO virtual corrections to \u03bce scattering in QED: the non-planar graphs

We evaluate the master integrals for the two-loop non-planar box-diagrams contributing to the elastic scattering of muons and electrons at next-to-next-to-leading order in QED. We adopt the method of differential equations and the Magnus exponential to determine a canonical set of integrals, finally expressed as a Taylor series around four space-time dimensions, with coefficients written as combination of generalised polylogarithms. The electron is treated as massless, while we retain full dependence on the muon mass. The considered integrals are also relevant for crossing-related processes, such as di-muon production at e+e− colliders, as well as for the QCD corrections to top-pair production at hadron colliders. In particular our results, together with the planar master integrals recently computed, represent the complete set of functions needed for the evaluation of the photonic two-loop virtual next-to-next-to-leading order QED corrections to μe → μe and e+e− → μ+μ−.

Exact series model of axially polarized hollow piezoelectric ceramic cylinders of finite length.

An analytical model is presented of axisymmetric circular hollow piezoelectric ceramic cylinders with arbitrary dimensions and boundary conditions. Forced vibrations of the cylinders with specified potentials on the electroded surfaces and displacement or stress on the boundaries are considered. The exact, linearized, axisymmetric governing equations are used in the analysis. Three series solutions are used, and each term in each series is an exact solution to the exact governing equations of motion. The terms in the series expressions for components of displacement, stress, electric potential, and electrical displacement are products of Bessel and sinusoidal functions and are orthogonal to other terms. Complete sets of functions in the radial and axial directions are formed by terms in the first series and the other two, respectively. It is, therefore, possible to satisfy arbitrary boundary conditions on all surfaces of the hollow piezoelectric cylinder. Numerical results are presented for hollow piezoelectric cylinders of various dimensions. Input electrical admittance and displacements are computed for three special cases in bands that include several resonance frequencies, and they are in excellent agreement with those computed using atila-a finite element package.

Cylindrical Plasma Antenna with Large Longitudinal Density Irregularity

The efficiency of operation of a cylindrical plasma antenna as a function of the degree of longitudinal nonuniformity of the plasma density is examined. The study is based on the method of spectral field expansion into a complete set of functions comprising surface and pseudosurface waves of the plasma column. The system of integrodifferential equations for expansion coefficients determining radiation patterns and the amplitudes of transmitted, reflected, and scattered waves is solved in the case of rapid variation in the plasma density. Dependences of the coefficients of conversion of the surface-wave energy on the plasma-density gradient, the electric length of the section of plasma nonuniformity, and the electric radius of the plasma cylinder are calculated. It is demonstrated by examples that the portion of energy of the surface wave converted into radiation may exceed 50%. It has been found that the radiation patterns are narrow with a single lobe whose maximum is at an angle of several degrees to the direction of propagation of the surface wave. As the plasma-density gradient increases, the lobe width decreases and the lobe itself shifts toward 0°.

Architecture for software-assisted quantity calculus

A quantity value, such as 5 kg, consists of a number and a reference (often an International System of Units (SI) unit) that together express the magnitude of a quantity. Many software libraries, packages, and ontologies that implement “quantities and units” functions are available. Although all of them begin with SI and associated practices, they differ in how they address issues such as ad hoc counting units, ratios of two quantities of the same kind, and uncertainty. This short article describes an architecture that addresses the complete set of functions in a simple and consistent fashion. Its goal is to encourage more convergent thinking about the functions and the underlying concepts so that the many disparate implementations, present and future, will become more consistent with one another.

Analytical model of mechanically excited piezoelectric unimorph beams.

A model is presented of a composite beam with one elastic and one piezoelectric layer. A reduced set of piezoelectric equations of state that has only the longitudinal components of stress and strain and the transverse components of electric field and charge density is consistently used to include the effect of piezoelectric coupling in all the equations. The equi-potential boundary conditions on the electrodes, the open-circuit condition, and the Gauss condition are satisfied. The position of the neutral axis and the dynamic equilibrium equation are derived after including the effect of piezoelectric coupling. All equations are combined to derive an equation of motion that contains only the displacement and the mechanical excitation. The solution to the equation is expressed in terms of a complete set of functions and an auxiliary function that contains the electric potential. The latter is needed to satisfy piezoelectric boundary conditions at the ends of the beam. The electric potential varies along the length of the beam and has a quadratic variation between the electrodes. Analytical expressions for displacement and potential, and numerical results at low frequencies and in the neighborhood of resonance, are presented for certain sets of boundary conditions.

P22. Evaluation and implementation of the module myQA Machines for a standard Elekta Synergy accelerator, with setup of acceptance criteria according to the guidelines defined by the decision of the ANSM of July 27th, 2007, and setting in routine

Introduction myQA platform and devices is a computer program hosting applications developed by IBA. It provides different modules for dosimetry qality assurance (QA) including machine QA, patient QA, and radiotherapy QA. This project regards myQA Machines which provides a complete set of functions to plan, perform, analyze and document quality assurance of treatment units, imaging devices and their accessories. All QA activities are based on customizable protocols. The objective of this project is to implement a protocol according to ANSM decision of July 27th, 2007 in order to evaluate the application myQA Machines for a setting in routine in the service. Methods We use an Elekta Synergy MLC80 accelerator delivering X-ray beams of 6 and 18 MV and electron beams from 6 to 18 MeV. It has a system of Portal and CBCT imagery. In myQA Machines, there are two possible types of tests: Generic tests , when the measurements are carried out without the software and results are manually entered, and Plugin tests , when the complete QA procedure is performed with the software using the multi detector MatriXX for example. The results of dosimetry and MLC tests will be compared respectively with those obtained in reference conditions (water phantom standard MP3 PTW) and with the Aquilab solution. A study of influence of mechanical, physical and dosimetric parameters of the accelerator is carried out in the aim of evaluating the performances and the limits of the system myQA Machines as well as defined acceptability criteria. Results The template related to the QA according to ANSM decision is operational on myQA Machines software. Results of Plugin tests are conforms. The largest difference between constancy measurements and references for homogeneity and symmetry, of all the beams available on the machine, is lower than 1%. The study on the sensitivity of the system shows the importance to choose the tolerances well because a variation of more than 1 mm in the centering of MatriXX induces a non-conformity of at least one of the controlled parameters. Conclusion The application myQA Machines is operational for the quality controls on machines. The analysis of QA results and sensitivity study’s results will enable us to determine the feasibility, reliability and adaptability of myQA Machines software for a setting in routine in an external service of radiotherapy. This implementation would make it possible to have control of data by connecting all the applications of QA on a single platform.

Construction and use of numerical-analytical approximating functions

The article goes over the methodology of constructing numerical-analytical approximating functions, satisfying the given boundary conditions for the function of its derivatives in the circuit areas of various shapes. The methodology is based on presenting the unknown function as a series in a complete set of functions that do not satisfy the given boundary conditions on the contour of the area, but additionally numerically defined near the contour to satisfy the boundary conditions. The additional definition of the functions near the area contour is performed numerically based on finite-difference relations. The main advantage of the stated method is the ability to build a relatively simple approximating functions satisfying the given boundary conditions on the boundary of complex shaped areas. The examples of applying the described method for solving the boundary value problem of a plate of different shapes. The possibility of using numerical-analytical functions for solving boundary value problems that contain higher derivatives up to fourth order is shown.

Revisiting CFHTLenS cosmic shear: optimal E/B mode decomposition using COSEBIs and compressed COSEBIs

We present a re-analysis of the CFHTLenS weak gravitational lensing survey using Complete Orthogonal Sets of E/B-mode Integrals, known as COSEBIs. COSEBIs provide a complete set of functions to efficiently separate E-modes from B-modes and hence allow for robust and stringent tests for systematic errors in the data. This analysis reveals significant B-modes on large angular scales that were not previously seen using the standard E/B decomposition analyses. We find that the significance of the B-modes is enhanced when the data is split by galaxy type and analysed in tomographic redshift bins. Adding tomographic bins to the analysis increases the number of COSEBIs modes, which results in a less accurate estimation of the covariance matrix from a set of simulations. We therefore also present the first compressed COSEBIs analysis of survey data, where the COSEBIs modes are optimally combined based on their sensitivity to cosmological parameters. In this tomographic CCOSEBIs analysis we find the B-modes to be consistent with zero when the full range of angular scales are considered.

Satisficing Game Approach to Collaborative Decision Making Including Airport Management

Collaborative decision making (CDM) has been used as an essential paradigm to increase the efficiency of air traffic flow management (ATFM), including takeoff or landing operations at airports. Air traffic control (ATC) services and airlines have been involved in the current CDM, but airport management service, an important stakeholder, has not been involved yet, generally. This paper proposes a new CDM model, which is named satisficing CDM, that is based on the satisficing game theory. This model includes three main entities (ATC, airlines, and airport management) in ATFM. The complete set of functions (preference, rejectability, and selectability) is established for each of the entities. Because the delay due to ground or air holding potentially alters the takeoff or the landing order of a flight, the sequence of takeoff and landing is determined through the satisficing negotiation process. To demonstrate the utility of the developed intelligent system, experiments are run with real air traffic in the terminal area of Sao Paulo. The experimental results show the importance and effectiveness of including airport management services in CDM. The sequences of takeoff and landing determined by the proposed model mostly meet the preferences of the three stakeholders in the given real traffic scenarios.

Free and forced vibrations of hollow elastic cylinders of finite length.

An analytical model of axisymmetric vibrations of hollow elastic circular cylinders with arbitrary boundary conditions is presented. Free vibrations of cylinders with free or fixed boundaries and forced vibrations of cylinders with specified non-uniform displacement or stress on the boundaries are considered. Three series solutions are used and each term in each series is an exact solution to the exact governing equations of motion. The terms in the expressions for components of displacement and stress are products of Bessel and sinusoidal functions and are orthogonal to each other. Complete sets of functions in the radial and axial directions are formed by terms in the first series and the other two, respectively. It is therefore possible to satisfy arbitrary boundary conditions. It is shown that just two terms in each series are sufficient to determine several resonance frequencies of cylinders with certain specified boundary conditions. The error is less than 1%. Numerical results are also presented for forced vibration of hollow steel cylinders of length 10 mm and outer diameter 10 mm with specified normal displacement or stress. Excellent agreement with finite element results is obtained at all frequencies up to 1 MHz. Convergence of the series is also discussed.

Free and forced vibrations of hollow elastic cylinders of finite length

An analytical model of axisymmetric vibrations of hollow elastic circular cylinders with arbitrary boundary conditions is presented. Free vibrations of cylinders with free or fixed boundaries and forced vibrations of cylinders with specified non-uniform displacement or stress on the boundaries are considered. Three series solutions are used and each term in each series is an exact solution to the exact governing equations of motion. The terms in the expressions for components of displacement and stress are products of Bessel and sinusoidal functions and are orthogonal to each other. Complete sets of functions in the radial and axial directions are formed by terms in the first series and the other two, respectively. It is therefore possible to satisfy arbitrary boundary conditions. It is shown that two terms in each series are sufficient to determine several resonance frequencies of cylinders with certain specified boundary conditions. The error is less than 1% for free cylinders. Numerical results are also presented for forced vibration of hollow steel cylinders of length 10 mm and outer diameter 10 mm with specified normal displacement or stress. Excellent agreement with finite element results is obtained at all frequencies up to 1 MHz. Convergence of the series is also discussed.

Image Reconstruction From Finite Number of Projections: Method of Transferring Geometry

This paper introduces a novel method of image reconstruction from a finite number of projections by processing the image along parallel rays. The geometry from the image plane is transferred to the Cartesian lattice by means of using the original image's line-integrals to calculate the line-sums of the discrete image to be reconstructed. Such a transformation of geometry allows for the 2D discrete paired transform, whose complete set of functions is defined by directions, to be effectively used in the exact reconstruction of the original image. The model of image reconstruction is described, and both examples and experimental results of implementation of the proposed method are provided for reconstruction on the Cartesian lattice of size 2(r) × 2(r), where r ≥ 2.

A literature survey of benchmark functions for global optimisation problems

Test functions are important to validate and compare the performance of optimisation algorithms. There have been many test or benchmark functions reported in the literature; however, there is no standard list or set of benchmark functions. Ideally, test functions should have diverse properties to be truly useful to test new algorithms in an unbiased way. For this purpose, we have reviewed and compiled a rich set of 175 benchmark functions for unconstrained optimisation problems with diverse properties in terms of modality, separability, and valley landscape. This is by far the most complete set of functions so far in the literature, and it can be expected that this complete set of functions can be used for validation of new optimisation in the future.