Arbitrary Basis Research Articles

Note on the differentiability of singular Lebesgue–Stieltjes measures

Abstract For an arbitrary translation invariant basis B which does not differentiate an integral of some function, we construct a singular Lebesgue–Stieltjes measure having non-vanishing means with respect to B at almost every point.

A sensitivity analysis on the parameter of the GLS method for a second‐gradient theory of incompressible flow

SummaryUsing a non‐conforming C0‐interior penalty method and the Galerkin least‐square approach, we develop a continuous–discontinuous Galerkin finite element method for discretizing fourth‐order incompressible flow problems. The formulation is weakly coercive for spaces that fail to satisfy the inf‐sup condition and consider discontinuous basis functions for the pressure field. We consider the results of a stability analysis through a lemma which indicates that there exists an optimal or quasi‐optimal least‐square stability parameter that depends on the polynomial degree used to interpolate the velocity and pressure fields, and on the geometry of the finite element in the mesh. We provide several numerical experiments illustrating such dependence, as well as the robustness of the method to deal with arbitrary basis functions for velocity and pressure, and the ability to stabilize large pressure gradients. We believe the results provided in this paper contribute for establishing a paradigm for future studies of the parameter of the Galerkin least square method for second‐gradient theory of incompressible flow problems. Copyright © 2015 John Wiley & Sons, Ltd.

Compressed Representation of Kohn–Sham Orbitals via Selected Columns of the Density Matrix

Given a set of Kohn-Sham orbitals from an insulating system, we present a simple, robust, efficient, and highly parallelizable method to construct a set of optionally orthogonal, localized basis functions for the associated subspace. Our method explicitly uses the fact that density matrices associated with insulating systems decay exponentially along the off-diagonal direction in the real space representation. We avoid the usage of an optimization procedure, and the localized basis functions are constructed directly from a set of selected columns of the density matrix (SCDM). Consequently, the core portion of our localization procedure is not dependent on any adjustable parameters. The only adjustable parameters present pertain to the use of the SCDM after their computation (for example, at what value should the SCDM be truncated). Our method can be used in any electronic structure software package with an arbitrary basis set. We demonstrate the numerical accuracy and parallel scalability of the SCDM procedure using orbitals generated by the Quantum ESPRESSO software package. We also demonstrate a procedure for combining the orthogonalized SCDM with Hockney's algorithm to efficiently perform Hartree-Fock exchange energy calculations with near-linear scaling.

Refusal to Deal, Abuse of Right and Competition Law in Electronic Markets and Digital Communities

Abstract: Economic activity is today to a great extent, totally or partially, developed in the electronic realm. Commercial transactions are more and more frequently concluded within electronic markets and other trading platforms, supplementing or even entirely replacing traditional negotiating channels and marketplaces. Likewise, non-commercial activities and professional and social interaction increasingly take place in digital spaces from P2P systems to social networks. These closed, network-based and community-building platforms compete with each other for gaining and retaining users, clients or participants. With such a purpose, electronic markets and platforms may be tempted to impose exclusivity obligations to ensure a minimum efficient scale or adopt leveraging and exploitative practices. At the same time, for certain disclosed reasons or merely on an arbitrary basis, platforms' managers may refuse to accept the application of a user or the offer of a business entity willing to join the network and become a member. As a premise, it can be argued that the electronic market is so exercising the right to run business activities, decide whom to deal with, and on which commercial conditions, under the free enterprise principle. Notwithstanding, such a refusal to deal can entail an abusive exercise of right ignoring constitutional principles and involve in practice an anticompetitive exclusionary behaviour resulting in market foreclosure or an effective social marginalization of the user, especially in the case of excessive concentration, market dominance or even essential facilities. Therefore, private autonomy in dealing with decisions, specifically in refusing admission, has to be carefully examined under public policy principles, considering, in particular, the specific features of the 'electronic markets' market' and the rules of the digital economy.

Some Sharp Estimates for the Haar System and Other Bases In $L^1(0,1)$

Let $h=(h_k)_{k\geq 0}$ denote the Haar system of functions on $[0,1]$. It is well known that $h$ forms an unconditional basis of $L^p(0,1)$ if and only if $1<p<\infty$, and the purpose of this paper is to study a substitute for this property in the case $p=1$. Precisely, for any $\lambda>0$ we identify the best constant $\beta=\beta_h(\lambda)\in [0,1]$ such that the following holds. If $n$ is an arbitrary nonnegative integer and $a_0$, $a_1$, $a_2$, $\ldots$, $a_n$ are real numbers such that $\bigl\|\sum_{k=0}^n a_kh_k\bigr\|_1\leq 1$, then \[ \Bigl|\Bigl\{x\in [0,1]:\Bigl|\sum_{k=0}^n \varepsilon_ka_kh_k(x)\Bigr|\geq \lambda\Bigr\}\Bigr|\leq \beta, \] for any sequence $\varepsilon_0, \varepsilon_1, \varepsilon_2,\ldots, \varepsilon_n$ of signs. A related bound for an arbitrary basis of $L^1(0,1)$ is also established. The proof rests on the construction of the Bellman function corresponding to the problem.

A Consistent and Stable Approach to Generalized Sampling

We consider the problem of generalized sampling, in which one seeks to obtain reconstructions in arbitrary finite dimensional spaces from a finite number of samples taken with respect to an arbitrary orthonormal basis. Typical approaches to this problem consider solutions obtained via the consistent reconstruction technique or as solutions of an overcomplete linear systems. However, the consistent reconstruction technique is known to be non-convergent and ill-conditioned in important cases, such as the recovery of wavelet coefficients from Fourier samples, and whilst the latter approach presents solutions which are convergent and well-conditioned when the system is sufficiently overcomplete, the solution becomes inconsistent with the original measurements. In this paper, we consider generalized sampling via a non-linear minimization problem and prove that the minimizers present solutions which are convergent, stable and consistent with the original measurements. We also provide analysis in the case of recovering wavelets coefficients from Fourier samples. We show that for compactly supported wavelets of sufficient smoothness, there is a linear relationship between the number of wavelet coefficients which can be accurately recovered and the number of Fourier samples available.

Uncertainty quantification in natural frequencies and radiated acoustic power of composite plates: Analytical and experimental investigation

In this study, the impact of elastic parameter uncertainty on the natural frequency and the radiated acoustic power of laminated composite plates is investigated. Due to structure complexity, composites exhibit great variability in mechanical properties. We adopt a model to develop stochastic natural frequencies and the equivalent radiated power of rectangular laminated plates where elastic parameters, natural frequencies and acoustic power density are represented using generalized polynomial chaos expansions with arbitrary random basis. Available experimental data are used to realize the distribution type of the parameters by utilizing the Pearson model. This realization is then employed to identify orthogonal random basis for each uncertain parameter. A non-intrusive collocation based method is conducted in order to calculate the deterministic polynomial chaos coefficients of the natural frequencies and the acoustic power density. Numerical results show that the natural frequencies and as well as the radiated acoustic powers are strongly affected from uncertainty in input parameters.

Computational approaches to finding and measuring inconsistency in arbitrary knowledge bases

There is extensive theoretical work on measures of inconsistency for arbitrary formulae in knowledge bases. Many of these are defined in terms of the set of minimal inconsistent subsets (MISes) of the base. However, few have been implemented or experimentally evaluated to support their viability, since computing all MISes is intractable in the worst case. Fortunately, recent work on a related problem of minimal unsatisfiable sets of clauses (MUSes) offers a viable solution in many cases. In this paper, we begin by drawing connections between MISes and MUSes through algorithms based on a MUS generalization approach and a new optimized MUS transformation approach to finding MISes. We implement these algorithms, along with a selection of existing measures for flat and stratified knowledge bases, in a tool called mimus. We then carry out an extensive experimental evaluation of mimus using randomly generated arbitrary knowledge bases. We conclude that these measures are viable for many large and complex random instances. Moreover, they represent a practical and intuitive tool for inconsistency handling.

Optimized quantum state transfer through anXYspin chain

Quantum state transfer along a one-dimensional spin chain has become a fundamental ingredient for quantum communication between distant nodes in a quantum network. We study the average fidelity of quantum state transfer (QST) along an $XY$ spin chain by adjusting the basis identification between the first spin and the last spin. In a proper choice of the basis identification, we find that the QST fidelity depends only on the average parity of the initial state linearly. We propose a simple scheme to adjust the basis identification to optimize the average fidelity such that it depends linearly on the absolute value of the average parity. In the case where the absolute value of the average parity is 1 we prove that the fidelity takes the maximum at any time over arbitrary initial state and basis identification.

Light vectorlike fermions in a minimalSU(5)setup

The Standard Model fermion sector is enlarged by either one light singlet vectorlike down-type quark or one light vectorlike lepton doublet, which might be accommodated within a five-dimensional representation of $SU(5)$. At low energies the inclusion of these states affects precisely measured observables in flavor physics, as well as electroweak precision measurements. These experimental results strongly constrain couplings of vectorlike states to the Standard Model particles. Having these bounds, we investigate the impact of vectorlike fermions on the mass matrices for down-type quarks and charged leptons in an $SU(5)$ setting. We find that unitary transformations relating an arbitrary flavor basis to the mass eigenstate basis depend only on three free parameters. Then we discuss the parameter space constrained by low-energy data, assuming vectorlike quark and vectorlike lepton masses to be 800 GeV and 400 GeV, respectively. We demonstrate that these two scenarios generate unique patterns for relevant proton decay widths. A further improvement of experimental bounds on proton decay modes would thus differentiate the allowed parameter space. We finally present two full-fledged $SU(5)$ models that allow for gauge coupling unification with light vectorlike fermions under consideration and discuss their viability.

A matrix based method for two dimensional nonlinear Volterra-Fredholm integral equations

In this paper, a matrix based method is considered for solving a class of 2DNVFIEs (Two Dimensional Nonlinear Volterra-Fredholm Integral Equations) of the second kind based on the operational Tau method. We developed this method with arbitrary polynomial bases (Standard, Legendre or Chebyshev polynomials) to obtain numerical solution of these equations. Some theoretical results are given to simplify and reduce the computation costs. In addition, L 2-convergence of the proposed method is proved when the given data are sufficiently smooth. Finally, some numerical examples are given to illustrate efficiency and accuracy of the proposed method.

Identification of multivariable nonlinear systems in the presence of colored noises using iterative hierarchical least squares algorithm

This paper presents an efficient method for identification of nonlinear Multi-Input Multi-Output (MIMO) systems in the presence of colored noises. The method studies the multivariable nonlinear Hammerstein and Wiener models, in which, the nonlinear memory-less block is approximated based on arbitrary vector-based basis functions. The linear time-invariant (LTI) block is modeled by an autoregressive moving average with exogenous (ARMAX) model which can effectively describe the moving average noises as well as the autoregressive and the exogenous dynamics. According to the multivariable nature of the system, a pseudo-linear-in-the-parameter model is obtained which includes two different kinds of unknown parameters, a vector and a matrix. Therefore, the standard least squares algorithm cannot be applied directly. To overcome this problem, a Hierarchical Least Squares Iterative (HLSI) algorithm is used to simultaneously estimate the vector and the matrix of unknown parameters as well as the noises. The efficiency of the proposed identification approaches are investigated through three nonlinear MIMO case studies.

Computation of the topological type of a real Riemann surface

We present an algorithm for the computation of the topological type of a real compact Riemann surface associated to an algebraic curve, i.e., its genus and the properties of the set of fixed points of the anti-holomorphic involution τ \tau , namely, the number of its connected components, and whether this set divides the surface into one or two connected components. This is achieved by transforming an arbitrary canonical homology basis to a homology basis where the A \mathcal {A} -cycles are invariant under the anti-holomorphic involution τ \tau .

Arbitrary order Trefftz-like basis functions on polygonal meshes and realization in BEM-based FEM

Polygonal meshes appear in more and more applications and the BEM-based Finite Element Method (FEM) turns out to be a forward-looking approach. The method uses Trefftz-like basis functions which are defined implicitly and are treated locally by means of Boundary Element Methods (BEMs). The BEM-based Finite Element Method is applicable on a variety of meshes including hanging nodes. The aim of this presentation is to give a rigorous construction of H1-conforming basis functions of a given arbitrary order yielding optimal rates of convergence in a Finite Element Method for elliptic equations. With the help of an interpolation operator, approximation properties are proven which guarantee optimal rates of convergence in the H1- as well as in the L2-norm for Finite Element simulations. These theoretical results are illustrated and verified by several numerical examples on polygonal meshes.

A realisation of the quantum supergroup [formula omitted

We reconstruct the quantum enveloping superalgebra U(glm|n) over Q(υ) via (finite dimensional) quantum Schur superalgebras. In particular, we obtain a new basis containing the standard generators for U(glm|n) and explicit multiplication formulas of an arbitrary basis element by a generator.

Reconfigurable spatially-diverse optical vector network analyzer

We present a spatially-diverse optical vector network analyzer which is capable of measuring the partial or complete mode transfer matrix of a system as a function of wavelength in an arbitrary mode basis using single or multiple sweeps.

Comparative Analysis between Risk Based Capital (RBC) and Solvency-II Framework-An Impact on Life Insurer

Risk-based capital is the theoretical amount of capital needed to absorb the risks involved in the operation of a business. Different companies face different risks and, therefore, should have different levels of capital based on those different risks, rather than on some arbitrary basis. The major areas of risk facing a life insurance company & property-casualty insurance company include asset risk, reserve risk, interest risk, business risk and credit risk. Risk based capital information also helps to customers, creditors and investors. The present paper compares the global and Indian scenario with regard to the capital adequacy frameworks for life insurance companies. It provides a comparative analysis of the Risk Based Capital framework used in the US with Solvency II being adopted by the European nations in terms of their implications for the life insurers.

Method of synthesis of easily testable circuits admitting single fault detection tests of constant length

It is constructively proved that any nonconstant Boolean function may be realized (over an arbitrary complete basis of gates) by a testable combinational circuit admitting (under single inverse or arbitrary constant faults at outputs of gates) a single fault detection test set whose cardinality does not exceed 4.

A Unified Approach to Structured Covariances: Fast Generalized Sliding Window RLS Recursions for Arbitrary Basis

This paper extends the existing fast RLS recursions originally intended to exponentially windowed problems for general models, to a generalized sliding window formulation (GSWRLS). From a matrix algebra perspective, we show explicitly how the displacement rank of the underlying inverse covariance matrix associated to any operator is defined as a function of the number of window breakpoints and how the fast GSWRLS calculates these rank factors in a fast manner. The recursions hold regardless of the (first order) data structure induced and show that fast fixed order and order recursive RLS algorithms can still be obtained for unwindowed data matrices exhibiting a fixed arbitrary relation between successive regressors. Our approach highlights the existence of a certain degree of freedom inherent to structured data matrices induced by general models, showing that efficient representations of their inverse covariances are not limited to factor circulants, but rather constructed from any arbitrary operator. These Bezoutians, usually expressed via reproducing kernel relations, can be represented exactly in matrix form, along with a precise correspondence to variables of a GSWRLS. As a fallout, we obtain a vector relation stating the so-called minimality property, for extended models and windows, as opposed to analogous generating function arguments normally seen in original approaches. These results pave the way to a more general framework of polynomial Vandermonde covariance decompositions which arise naturally via a proper choice of recurrence related polynomials. This has further impact on several signal processing applications, including superfast realization of equalizers in communications scenarios.

Holographic spatial coherence analysis of a laser

We show that the second-order coherent-mode representation of a stationary quasi-monochromatic scalar light beam can be experimentally characterized by dual-mode holographic interference using an arbitrary basis. Analysis of the laser beam emitted from a stable spherical mirror cavity, using a mismatched Hermite-Gaussian basis, recovered the profiles and powers of a set of cavity modes with the expected spot size, including a hybrid of frequency degenerate modes. Observed near- and far-field irradiance transverse profiles and associated M2 parameter measures confirmed the results.