Compact Set Of Parameters Research Articles

A combinatorial proof of a sumset conjecture of Furstenberg

We give a new proof of a sumset conjecture of Furstenberg that was first proved by Hochman and Shmerkin in 2012: if log r/log s is irrational and X and Y are times r - and times s-invariant subsets of [0, 1], respectively, then dim _{text {H}}(X + Y ) = min (1, dim _{text {H}}X + dim _{text {H}}Y ). Our main result yields information on the size of the sumset lambda X + eta Y uniformly across a compact set of parameters at fixed scales. The proof is combinatorial and avoids the machinery of local entropy averages and CP-processes, relying instead on a quantitative, discrete Marstrand projection theorem and a subtree regularity theorem that may be of independent interest.

Automated Assessment of Glottal Dysfunction Through Unified Acoustic Voice Analysis

This paper uses the recent glottal flow model for iterative adaptive inverse filtering to analyze recordings from dysfunctional speakers, namely those with larynx-related impairment such as laryngectomy. The analytical model allows extraction of the voice source spectrum, described by a compact set of parameters. This single model is used to visualize and better understand speech production characteristics across impaired and nonimpaired voices. The analysis reveals some discriminative aspects of the source model which map to a physiological class description of those impairments. Furthermore, being based on analysis of source parameters only, it is complementary to any existing techniques of vocal-tract or phonetic analysis. The results indicate the potential for future automated speech reconstruction systems that adapt to the method of reconstruction required, as well as being useful for mainstream speech systems, such as ASR, in which front-end analysis can direct back-end models to suit characteristics of impaired speech.

Testing Linear and Nonlinear Hypotheses in a Cox Proportional Hazards Model with Errors in Covariates

We investigate linear and nonlinear hypotheses testing in a Cox proportional hazards model for right-censored survival data when the covariates are subject to measurement errors. In Kukush and Chernova (2018) [Theor. Probability and Math. Statist. 96, 101–110], a consistent simultaneous estimator is introduced for the baseline hazard rate and the vector of regression parameters. Therein the baseline hazard rate belongs to an unbounded set of nonnegative Lipschitz functions, with fixed constant, and the vector of regression parameters belongs to a compact parameter set. Based on the estimator, we develop two procedures to test nonlinear and linear hypotheses about the vector of regression parameters: Wald-type and score-type tests. The latter is based on an unbiased estimating equation. The consistency of the tests is shown.

A compact multi‐frequency GNSS scintillation model

We present a scintillation model that generates complex scintillation realizations using two-dimensional phase-screen calculations. A compact parameter set simplifies the model. The parameters can be adjusted to reproduce statistically equivalent realizations of target multi-frequency GNSS intensity and phase scintillation time series or defaulted to representative values. Geometric range and TEC inputs can be incorporated to generate realizations of baseband GNSS signals for processor performance evaluation. Selecting model parameters is guided by an efficient encapsulation of the two-dimensional phase-screen theory. Motion of the propagation path through ionospheric structure generates temporal variation. The phase-screen theory incorporates space-to-time conversion via a ratio of the Fresnel scale to an effective scan velocity. A universal strength parameter adjusts the strength of the scintillation. The model is an encapsulation of results that have been used for GPS performance analysis work that is cited in the paper. A MATLAB implementation of the model with examples has been made available.

Ionospheric Scintillation Simulation on Equatorial GPS Signals for Dynamic Platforms

This paper presents a physics-based, data-consistent, multifrequency GPS scintillation signal simulator for dynamic platforms in the equatorial region. This simulator is based on a two-dimensional two-component power-law phase screen model which is described by a compact set of parameters. The time scale factor is mainly investigated in this paper, which determines the decorrelation time of the simulation signal and is affected by various factors including propagation geometry, irregularity drift velocity, and dynamics of the platform. The comparison between the initialization and simulation data for stationary receivers shows the effectiveness of the simulator. In addition, this paper examines the influence of the platform dynamics on simulation signals with respect to the geomagnetic field direction and the irregularity drift velocity. The simulator presented in this paper will provide a viable tool for dynamic GPS scintillation signal simulation and will aid the design for robust receiver processing algorithms during scintillation for dynamic platforms.

AAM Based Face Sketch Synthesis

Face sketch synthesis has many practical applications, such as law enforcement and digital entertainment. Existing face sketch synthesis methods focus on neighbor selection and/or weight reconstruction. However, these approaches did not take “interpretation through synthesis” into consideration obviously. Active appearance model (AAM) is one of “interpretation through synthesis” approaches. In this paper, we introduce AAM to “explain” face photos by generating synthetic images that are as similar as possible. Then AAM provides a compact set of parameters that are useful for face sketch synthesis. Extensive experiments on public face sketch databases demonstrate the superiority of the proposed method in comparison to state-of-the-art methods.

Worst‐case stability and performance with mixed parametric and dynamic uncertainties

SummaryThis work deals with computing the worst‐case stability and the worst‐case H∞ performance of linear time‐invariant systems subject to mixed real‐parametric and complex‐dynamic uncertainties in a compact parameter set. Our novel algorithmic approach is tailored to the properties of the nonsmooth worst‐case functions associated with stability and performance, and this leads to a fast and reliable optimization method, which finds good lower bounds of μ. We justify our approach theoretically by proving a local convergence certificate. Because computing μ is known to be NP‐hard, our technique should be used in tandem with a classical μ upper bound to assess global optimality. Extensive testing indicates that the technique is practically attractive. Copyright © 2016 John Wiley & Sons, Ltd.

Parametrized means and limit properties of their Gaussian iterations

We propose the notion of a mean depending on a parameter, define Gauss-type iterates of parametrized mean-type mapping and study their limit behaviour. Also a suitable invariance property of the limit function is established. In such a way we obtain an extension of generalized Gaussian algorithm (Theorem 2.5) to the case of a compact set of parameters. In particular, we generalize some well known results of J. Matkowski dealing with iterates of mean-type mappings not depending on parameter.

Rapid and robust traffic accident detection based on orientation map

Video-based rapid traffic accident detection is very important for intelligent transport systems. Traditional methods are either not fast enough or not stable with working environments. A rapid and environment-adaptive method is proposed. The inspiration of the method is originated from the key observation that the traffic accident brings abundant information on motion directions. This method includes three steps. First, the orientation map for each video frame is constructed based on the optical flows. Then, for each orientation map, the connected regions are formed. An entropy-like energy function is used to measure the orientation information of the connected region. The higher the energy value, the more moving directions exist. The highest measure of these connected regions in each orientation map is considered as its energy measure. Finally, based on the energy sequence of orientation maps, a Gaussian model is established to learn the normal energy fluctuation range for some environment. In the detection process, if the energy of one orientation map burst out of the normal range, it means there exists a traffic accident. The advantages of our method include the fast processing speed, a compact parameter set, and the robustness to the different environments and illuminations. Experimental results confirm the above advantages of the proposed approach.

Reverse Shape Synthesis of the Hydropump Volute Using Stereo-Photogrammetry, Parameterization, and Geometric Modeling

An automatic procedure for reverse 3D shape synthesis is proposed. Shape acquisition of an existing object involving stereo-photogrammetry, triangulation, and 3D reconstruction is applied to obtain the point clouds. Subsequent parameterization of the acquired geometry using mathematical surfaces yields a compact set of parameters as shape variables to be used in diagnostics. The developed procedure and several specific computational geometry operators are applied with a hydro-pump casing whose complex shape is processed and related to the volute design and flow theory.

A New One-Dimensional Rate-Based Phenomenological Model to Describe the Non-Linear Behaviour of Piezoelectric Actuators for Real-Time Applications

In this paper, a new rate-based phenomenological model of piezoelectric actuators for real-time applications is developed. This compact theoretical approach employs the Arrhenius equation for chemical reaction kinetics in order to describe the non-linear effect of domain switching. It needs only nine model parameters to account for the complete non-linearity of a piezoelectric actuator as well as the dependence of its non-linear effect on the electric field, the mechanical stress, and the temperature. This general validity for a wide range of operation conditions, which is based on a simplified description of the real behaviour, is the optimum prerequisite for a technically inexpensive control loop strategy for fast piezoelectric actuators as they are employed in state-of-the-art gasoline and diesel injectors for combustion engines. Moreover, other interfering physical effects, such as ageing, which may cause an injector's dosing function to deteriorate severely can be tackled by making use of this approach in electronic control units. All this is possible because the extremely compact theoretical formulation with a compact set of parameters does not need access to complex characteristic diagrams so that the most essential requirements of an automotive control unit such as a minimum computation time and a modest requirement of storage space can be fulfilled.

Adaptive detection of a high-variable function

A major difficulty arising in statistics of multi-variable functions is “the curse of dimensionality:” Rates of accuracy in estimation and separation rates in detection problems behave poorly as the number of variables increases. This difficulty arises for most popular functional classes such as Sobolev or Holder balls. In 2007, the authors considered functional classes of a new type, which were first introduced by Sloan and Woźniakowski. These classes are balls SWσ,s in weighed tensor product spaces, which are characterized by two parameters: σ> 0 is a “smoothness” parameter, and s> 0 determines the weight sequence that characterizes the “importance” of variables. In particular, it was shown that under the white Gaussian noise model, the log-asymptotics of separation rates in detection are similar to those for one-variable functions of smoothness σ* = min (s, σ) independently of the original problem dimensions; thus, the curse of dimensionality is “lifted.” However, the test procedure depends on parameters (σ, s), which are typically unknown. In the present paper, we propose a test procedure which does not depend on parameters (σ, s) and provides the same log-asymptotics of separation rates uniformly over any compact set of parameters (σ, s). In addition, we give an independent simple proof of log-asymptotics of separation rates in the problem. Bibliography: 16 titles.

A “Joint+Marginal” Approach to Parametric Polynomial Optimization

Given a compact parameter set $\mathbf{Y}\subset\mathbb{R}^p$, we consider polynomial optimization problems $(\mathbf{P}_{\mathbf{y}}$) on $\mathbb{R}^n$ whose description depends on the parameter $\mathbf{y}\in\mathbf{Y}$. We assume that one can compute all moments of some probability measure $\varphi$ on $\mathbf{Y}$, absolutely continuous with respect to the Lebesgue measure (e.g., $\mathbf{Y}$ is a box or a simplex and $\varphi$ is uniformly distributed). We then provide a hierarchy of semidefinite relaxations whose associated sequence of optimal solutions converges to the moment vector of a probability measure that encodes all information about all global optimal solutions $\mathbf{x}^*(\mathbf{y})$ of $\mathbf{P}_{\mathbf{y}}$, as $\mathbf{y}\in\mathbf{Y}$. In particular, one may approximate as closely as desired any polynomial functional of the optimal solutions like, e.g., their $\varphi$-mean. In addition, using this knowledge on moments, the measurable function $\mathbf{y}\mapsto x^*_k(\mathbf{y})$ of the $k$th coordinate of optimal solutions, can be estimated, e.g., by maximum entropy methods. Also, for a boolean variable $x_k$, one may approximate as closely as desired its persistency $\varphi(\{\mathbf{y}:x^*_k(\mathbf{y})=1\}$, i.e., the probability that in an optimal solution $\mathbf{x}^*(\mathbf{y})$, the coordinate $x^*_k(\mathbf{y})$ takes the value 1. Last but not least, from an optimal solution of the dual semidefinite relaxations, one provides a sequence of polynomial (resp., piecewise polynomial) lower approximations with $L_1(\varphi)$ (resp., $\varphi$-almost uniform) convergence to the optimal value function.

Efficient class-specific models for autoregressive processes with slowly varying amplitude in white noise

This paper describes an efficient model to describe an autoregressive (AR) signal with slowly-varying amplitude in additive white Gaussian noise (WGN). Even a simple low-order AR model becomes complicated by varying amplitude and additive white noise. However, by approximating the signal amplitude as piecewise-constant, an efficient filtering approach can be applied in order to compute the maximum likelihood (ML) estimate for the entire data record. The model is efficient both in terms of having a compact set of parameters and in the computational sense. Simulation results are provided. The algorithm has applications in signal modeling for underwater acoustic signals, particularly active wideband signals such as explosive sources.

Mathematical analysis of DICOM CT datasets: Can endograft sizing be automated for complex anatomy?

To validate the use of a novel mathematical algorithm applied to digital imaging and communication in medicine (DICOM) computed tomography (CT) data to automate the generation of complex endovascular graft planning. An algorithm was developed enabling the creation of patient-specific mathematical model based upon DICOM CT data to allow for detailed efficient geometric analysis with repeatable results. This algorithm was applied to high resolution DICOM CT datasets of 15 patients, selected at random from 350 patients with aneurysms involving the visceral arteries. The longitudinal and rotational relationships of the visceral vessels were determined by the algorithm. For comparison purposes, the same measurements were acquired manually using centerline of flow software by a blinded investigator. The distance between the renal arteries, and location of the renal origins calculated with each method were then compared. Automated results were readily created for all 15 randomly selected patients. The measured versus calculated mean inter-renal artery distances were exceptionally close, differing by a mean of only 1.3 mm with a maximal range of 3.0 mm. The rotational position of the renal origins differed by only 10.5 degrees of arc (21 clock-face minutes) on average and by 32.5 degrees in the worst case. The generation of an automated mathematical model to represent complex aortic geometry is feasible and reproducible in the context of high-resolution CT data. This process has been validated in 15 patients, where results corresponded with manual measurements that were used to successfully implant customized devices that accommodate the imaged vessels. Additional attributes include the expression of the 3D aorta in a compact form (on the order of kilobytes) for purposes of data storage, transfer, and other manipulations. The construct of mathematical representation of patient specific anatomy from CT data is both feasible and applicable, allowing for automated endograft device design even in the setting of markedly tortuous anatomy where the repair must incorporate major aortic branches. The process has been validated in 15 patients, where results corresponded with manual measurements that were used to successfully implant customized devices that accommodate the imaged vessels. The application of this technology must now be studied in a prospective manner and incorporated into a system users may readily apply to patients undergoing evaluation. Additional attributes of a mathematical representation of the arterial tree include the 3D expression from a very compact set of parameters (on the order of kilobytes) for purposes of data storage, transfer, and other manipulations.

Algebraic vs. numerical methods for analysing diatomic spectral data: a resolution of discrepancies

The past decade has seen persistent disagreements in the literature and at meetings concerning the validity and physical significance of two different approaches for the reduction of a set of diatomic molecule data to a compact set of parameters defining a potential energy curve and Born–Oppenheimer breakdown (BOB) radial functions. This paper explains the apparent discrepancies between an algebraic method championed by J.F. Ogilvie and a numerical method pioneered by J.A. Coxon. It confirms the validity of the central underlying assumption of both approaches, namely, that spectroscopic data for one or multiple isotopomers can be reduced accurately to a compact set of parameters characterizing the potential energy and BOB radial functions, and it shows that the values of those parameters should not depend on which method is used to determine them. The previously reported discrepancies arose because of a truncation convention applied in Ogilvie’s algebraic R adiatom code. Because of that convention, eigenvalues of the Schrödinger equation generated using published potential energy and BOB functions determined using R adiatom will not accurately reproduce the input data used in the analyses. However, if that truncation convention is not applied and the Dunham-type expansions are summed to convergence, algebraic analyses yield results essentially identical to those obtained from direct numerical-fit methods. Tests reported herein also support Watson’s [J. Mol. Spectrosc. 217 (2003) 157] assertion that electric dipole moments and rotational g-factors cannot be determined only from transition energy data obtained in the absence of external fields.

SOME UNIFORM ESTIMATES IN PRODUCTS OF RANDOM MATRICES

For each product of random matrices, there associated an invariant measure on the projective space. The convergence to the invariant measure is exponentially fast. In this paper we give uniform estimates on the exponential convergence when the distribution of the random matrices depends on a compact set of parameters.

Bifurcation test functions and surge control for axial flow compressors

Surge control is investigated in conjunction with rotating stall control for axial flow compressors using a bifurcation approach. Test functions are developed to determine the existence and stability of the Hopf bifurcation associated with surge for closed-loop systems under linear state feedback. A control design method is proposed for the synthesis of linear feedback laws that eliminate surge, coupled with rotating stall for any given compact parameter set. Comparisons are made with existing results. Stabilization results are demonstrated with numerical simulations.

Using random iteration function systems for reduction of rotation correlation matrix data

We suggest using Random Iteration Function Systems to describe the gross features of discrete spectroscopy of rotational nuclei. Very large matrices could thus be described by a compact set of parameters.

Effective parameter extraction using multiple-objective function for VLSI circuits

Effective parameter extraction is a crucial step in accurate simulation of microelectronic circuits and systems. A parameter extraction program, which is based on a global optimization algorithm, uses a single objective function that minimizes the drain current error between the predicted and measured data. Parameter sets extracted on this basis are adequate for the purpose of digital circuit simulation, but fall short of simulation requirements for analog circuits. The use of a multiple-objective function is proposed, which simultaneously optimizes several critical electrical quantities including the drain current, output conductance, and transconductance. Experimental results with the multiple-objective function are presented, to show the improvement in extracted parameters. The recently developed BSIM_plus MOS transistor model for sub-half-micron integrated circuits uses a compact set of parameters, which greatly enhances the ability to accurately extract parameter values. This model was implemented into the parameter extraction program and some extraction results are presented. The parameter space has several local minima within which a gradient descent method may be trapped. Simulated annealing techniques can be applied to find near-optimal solutions of problems containing multiple local minima in their solution spaces. Experimental results showing the optimization of drain current error using simulation annealing techniques are presented.