Linear Restrictions Research Articles

Enhanced Underwater Single Vector-Acoustic DOA Estimation via Linear Matched Stochastic Resonance Preprocessing

Underwater acoustic vector sensors (UAVSs) are increasingly utilized for remote passive sonar detection, but the accuracy of direction-of-arrival (DOA) estimation remains a challenging problem, particularly under low signal-to-noise ratio (SNR) conditions and complex background noise. In this paper, a comprehensive theoretical analysis is conducted on UAVS signal preprocessing subjected to gain-phase uncertainties for average acoustic intensity measurement (AAIM) and complex acoustic intensity measurement (CAIM)-based vector DOA estimation, aiming to explain the theoretical restrictions of intensity-based vector acoustic preprocessing approaches. On this basis, a generalized vector acoustic preprocessing optimization model is established in which the principle can be described as “maximizing the denoising performance under the constraints of an equivalent amplitude-gain response and phase-bias response”. A novel vector acoustic preprocessing method named linear matched stochastic resonance (LMSR) is proposed within the framework of matched stochastic resonance theory, which can naturally guarantee the linear gain-phase restrictions, as well achieving effective denoising performance. Numerical analyses demonstrate the superior vector DOA estimation performance of our proposed LMSR-AAIM and LMSR-CAIM methods in comparison to classical intensity-based AAIM and CAIM methods, especially under low-SNR conditions and non-Gaussian impulsive noise circumstances. Experimental verification conducted in the South China Sea further verifies its the effectiveness for practical application. This work can lay a solid foundation to break through the challenges of underwater remote vector acoustic DOA estimation under low-SNR conditions and complex ocean ambient noise and can provide important guidance for future research work.

Universal enzymatic numerical P systems with small number of enzymatic rules

Enzymatic Numerical P Systems (ENPSs) are a model of membrane computing that is well-suited for the simulation of physical processes and that has been used for the design and the implementation of motion controllers for wheeled robots and flying drones. The ENPSs model has been proven to be Turing universal and the theoretical effort was focused on minimizing various descriptional complexity parameters. In this paper, we explore the minimum number of enzymatic rules needed to achieve universality in ENPSs, specifically focusing on the all-parallel derivation mode where all applicable rules are applied at the same time. We show that in the case of a linear restriction for production functions, the universality can be obtained using 21 enzymatic rules, substantially improving previously known results. If production functions are allowed to be polynomials of degree 2, we show that a single enzymatic rule is sufficient to achieve universality. To obtain these results, a new proof method is introduced based on the translation of ENPSs to systems of conditional recurrences.

DESARROLLO DE MÉTODOS BASADOS EN REDES NEURONALES EN LA ESTIMACIÓN DE RECURSOS MINERALES

Due to economic and physical limitations, our understanding of mineral resources in a specific area of interest is limited and fragmented. Traditionally, this problem has been solved using the Kriging geostatistical method, where the ore grade is estimated at unmeasured locations using known values of the grade at surrounding points. The advantage of this method lies in the calculation of weights through a spatial variability model known as a variogram. However, the method is imperfect, as it is based on the assumption of stationarity, aditivity, linearity and potential subjectivity in variographic modelling. This study proposes to approach the mineral resource estimation problem as a regression problem using neural networks, which are not subject to the restrictions of stationarity, aditivity, linearity and spatial modelling of geostatistics methods. Kriging and a radial basis function neural network and a multilayer perceptron have been compared using different validation metrics. The results show that a properly trained neural network model, with appropriate labelling of the mineral grade and its input characteristics, achieves similar results to the geostatistical approach, with a significant reduction in time, while avoiding all the aforementioned assumptions. However, neural networks do not consider the spatial correlation of ore grade or reproduce it at the locations where it was measured, characteristics that have marked distrust in its industrial implementation and that are discussed in this article, finally proposing an adjustment between both approaches at a minimum sacrifice of time and labor costs. Keywords Neural networks; machine learning; geostatistics.

On the variance estimator and its bounds in general linear models under linear restrictions

In the article, the error variance estimator σ ^ 2 and its finite sample size bounds are investigated in the framework of a general linear model under linear restrictions (gLMLR) where no distributions are assumed except for some moment conditions and the covariance matrix of the response may be singular, which extends the results in Lindholm and Wahl (2020). In particular, we overcome the difficulty that the matrix of quadratic form in σ ^ 2 is not idempotent. The estimator is obtained by the proposed restricted and proxy-type generalized least square procedure. Meanwhile, the estimable function of the regression coefficient β is estimated, too. Besides, the finite sample properties of these estimators and their consistency are also established. In the end, a simulation study and a real data analysis are done to examine the finite performance of these estimators.

Asymptotics for the conditional self‐weighted M$$ M $$ estimator of GRCA(p$$ p $$) models and its statistical inference

SummaryUnder the ‐order generalised random coefficient autoregressive (GRCA()) model with random coefficients we propose a conditional self‐weighted estimator of . We investigate the asymptotic normality of this estimator with possibly heavy‐tailed random variables. Furthermore, a Wald test statistic is constructed for the linear restriction on the parameters. In addition, the simulation experiments are carried out to assess the finite sample performance of theoretical results. Finally, a real data analysis about the increase (%) in the number of construction projects this year over the same period of last year is provided.

Research of direct and inverse problems of sensitivity using methods of practical stability by direction

The general statements of the problems of construction of extreme ranges of tolerances on parameters for a linear system of differential equations in the presence of dynamic restrictions on the spread of the state vector are considered. It was found that such sensitivity problems are closely related to the problems of estimating the maximum area of stability in the corresponding function space. In order to obtain upper estimates of the sought values, the problem of estimating tolerances from the positions of stability in a single direction is formalized. The cases of linear and nonlinear restrictions on the spread of the phase coordinate vector with initial linear initial conditions relative to the vector of the system parameters are studied. Necessary and sufficient conditions are formulated in the form of criteria for estimating tolerances on parameters covering the case of fixed initial conditions. The tasks of estimating the maximum volume of the stability region with respect to the deviations of the state vectors and system parameters are considered. For the case of compatible admissible constraints, the paper gives the corresponding numerical calculations for the upper estimates. In particular, for fixed initial conditions, the maximum set of tolerances for system parameters with compatible dynamic restrictions on fluctuations of state vectors and parameters are determined according to these evaluation criteria. From the standpoint of practical stability in direction, direct sensitivity problems are investigated, numerical estimates of the spread of the phase coordinate vector of the system in the presence of linear and fixed initial conditions relative to the parameter vector are given. It has been demonstrated that in the given specification of the problem of maximum estimation of tolerances it is completely covered by problem statements of practical stability by direction. Thus, to calculate areas of guaranteed sensitivity, the concept of practical stability in a single direction is extended to the space of sensitivity functions at the initial moment of time. The above algorithms are used to estimate the range of tolerances for the adjustment parameters of the discrete model of the induction acceleration system with the given limitations on the spread of the quality criterion; the variation of the quality indicator within the tolerance field is presented in the form of a linear form relative to the spread of the parameter vector.

High-dimensional IV cointegration estimation and inference

A semiparametric triangular systems approach shows how multicointegrating linkages occur naturally in an I(1) cointegrated regression model when the long run error variance matrix in the system is singular. Under such singularity, cointegrated I(1) systems embody a multicointegrated structure that makes them useful in many empirical settings. Earlier work shows that such systems may be analyzed and estimated without appealing to the associated I(2) system but with suboptimal convergence rates and potential asymptotic bias. The present paper develops a robust approach to estimation and inference of such systems using high dimensional IV methods that have appealing asymptotic properties like those known to apply in the optimal estimation of cointegrated systems (Phillips, 1991). The approach uses an extended version of high-dimensional trend IV (Phillips, 2006, 2014) estimation with deterministic orthonormal instruments. The methods and derivations involve new results on high-dimensional IV techniques and matrix normalization in the limit theory that are of independent interest. Wald tests of general linear restrictions are constructed using a fixed-b long run variance estimator that leads to robust pivotal HAR inference in both cointegrated and multicointegrated cases. Simulations show good properties of the estimation and inferential procedures in finite samples. An empirical illustration to housing stocks, starts and completions is provided.

Inequality restricted estimator for gamma regression: Bayesian approach as a solution to the multicollinearity

In this article, we consider the multicollinearity problem in the gamma regression model when model parameters are bounded linearly restricted. The linear restrictions are available from prior information to ensure the validity of scientific theories or structural consistency based on physical phenomena. To make relevant statistical inference for a model, any available knowledge and prior information on the model parameters should be taken into account. This article proposes therefore an algorithm to acquire Bayesian estimator for the parameters of a gamma regression model subjected to some linear inequality restrictions. We then show that the proposed estimator outperforms the ordinary estimators such as the maximum likelihood and ridge estimators in terms of pertinence and accuracy through Monte Carlo simulations and application to a real dataset.

Restricted Liu estimator under stochastic linear restrictions in generalized linear models: theory and applications

It is a fact that the problem of multicollinearity adversely effects the estimation of parameters not only in normal linear models but also in generalized linear models (GLMs). In this study, we propose a new estimator by imposing the stochastic restrictions on the parameters and combining the Liu estimator in GLMs to address the problem of multicollinearity. The new estimator is referred to as the stochastic restricted Liu estimator. The novel estimator’s first order approximated form (FOA) is presented to compare it to its competitors using the asymptotic mean square error criterion. Furthermore, two empirical applications using a response variable from the Poisson and Gamma distributions are studied to evaluate the performance of estimators. In addition, a simulation study is conducted by considering a response variable from Binomial distribution for comparisons. Based on simulation study and empirical applications, it is found that the performance of the proposed estimator is better than ML, Liu, and mixed estimators for the appropriate selected biasing parameter.

Pseudopartitive constructions are not a subtype of nominal juxtaposition in Beserman

Abstract Juxtaposition as a machinery of building noun phrases is well-known to be widespread in Uralic languages: the modifier is left-adjoined to the head and does not bear any morphological marker of syntactic dependency. This strategy is used to attach adjectives, cardinals and modifying nominals to nouns (like in Beserman ǯ́aǯ́eg siĺ ‘goose meat’), and to build constructions with measure nouns (like Beserman odig kə̑də̑ gibi ‘one basket of mushrooms’, lit. one basket mushroom). However, there remains a question whether all these constructions share the same syntactic structure. We consider pseudopartitive constructions with measure nouns in comparison with NPs containing non-marked modifying nominals and NPs with adjectives, showing that they do not share the same syntactic structure. Constructions with unmarked modifying nominals show properties of compounding, while pseudopartitives arguably have a measure phrase (a cardinal with a measure noun) and a noun phrase (the quantified nominal), which is the head of the pseudopartitive construction. The syntactic properties we analyze include constituent properties, branching, pronominalization, fragment questions, linear ordering restrictions, particular properties of head ellipsis, and information structure effects.

Complexity of The Systems of Linear Restrictions over a Finite Field

This paper continues the results obtained in [1]. In the previous paper, we formulated the problem of the unknown vector recovering from linear dependencies with this vector, which act as constraints on it. The next step, after finding out some algebraic and combinatorial properties, is to give basic estimates of complexity for the main problem as well as for related problems. Such related problems can be obtained by fixing some parameters of the main problem or applying constraints on the number of restrictions in the system. Such an analysis makes possible to arrange the problem of recovering an unknown vector based on partial information into the general computational complexity framework in order to approach existing theoretical results to its solution. The obtained theoretical results can be used in algebraic cryptanalysis of stream ciphers and cryptosystems based on linear codes.

Restriction estimates in a conical singular space: Schrödinger equation

Abstract This paper continues our previous program to study the restriction estimates in a class of conical singular spaces X = C ⁢ ( Y ) = ( 0 , ∞ ) r × Y {X=C(Y)=(0,\infty)_{r}\times Y} equipped with the metric g = d ⁢ r 2 + r 2 ⁢ h {g=\mathrm{d}r^{2}+r^{2}h} , where the cross section Y is a compact ( n - 1 ) {(n-1)} -dimensional closed Riemannian manifold ( Y , h ) {(Y,h)} . Assuming the initial data possesses additional regularity in the angular variable θ ∈ Y {\theta\in Y} , we prove some linear restriction estimates for the solutions of Schrödinger equations on the cone X. The smallest positive eigenvalue of the operator Δ h + V 0 + ( n - 2 ) 2 / 4 {\Delta_{h}+V_{0}+(n-2)^{2}/4} plays an important role in the result. As applications, we prove local energy estimates and Keel–Smith–Sogge estimates for the Schrödinger equation in this setting.

Adjustment coefficients and exact rational expectations in cointegrated vector autoregressive models

In this article, we consider the cointegrated vector autoregressive model with adjustment parameters and cointegration vectors . We discuss estimation of the model under the exact linear rational expectations, when we also have linear restrictions on the adjustment parameters . In particular we consider the same restriction on all vectors in and the hypothesis that some vectors in are known.

An Improved Inferential Procedure to Evaluate Item Discriminations in a Conditional Maximum Likelihood Framework

A modified and improved inductive inferential approach to evaluate item discriminations in a conditional maximum likelihood and Rasch modeling framework is suggested. The new approach involves the derivation of four hypothesis tests. It implies a linear restriction of the assumed set of probability distributions in the classical approach that represents scenarios of different item discriminations in a straightforward and efficient manner. Its improvement is discussed, compared to classical procedures (tests and information criteria), and illustrated in Monte Carlo experiments as well as real data examples from educational research. The results show an improvement of power of the modified tests of up to 0.3.

Evaluation of the noise immunity of the navigation equipment of consumers of the global navigation satellite system with spatial adaptation based on the algorithm of maintaining the level of the useful signal

Problem statement. The use of spatial filtering of signals in adaptive antenna arrays (AAR) of consumer navigation equipment (NAP) of the global navigation satellite system (GNSS) in conditions of intentional interference is an effective means of ensuring stability and continuity of positioning of mobile objects. The specifics of solving this problem is the low level of navigation signals received from the upper hemisphere of space against the background of powerful concentrated interference, significantly exceeding noise. Most compact L-band AARs consist of 4-8 elements, and the algorithms used optimize compensation indicators without the presence of a priori information about the position of useful and interfering signals. At the same time, the formed dips on the sources of interference in width can lead to a loss of the availability of spacecraft signals for subsequent processing. This circumstance determines the relevance and practical orientation of the task of evaluating the effectiveness of the diagram formation algorithm, taking into account the integration of interference attenuation indicators and maintaining the level of the useful signal. Purpose. Investigation of the characteristics of the spatial interference compensation algorithm with a linear restriction on the direction of reception of the useful signal, as well as an assessment of its impact on the performance of the equipment of consumers of the global navigation satellite system. Results. The level of compensation of spatially distributed interference sources is analyzed using a processing algorithm that minimizes the average power of the adaptive antenna array with the exception of the direction of reception of the useful signal to the zenith. The influence of the spatial compensator on the availability of spacecraft signals for subsequent processing, depending on the number, level and angular coordinates of interference sources, is investigated. Practical significance. A model is proposed for evaluating an algorithm that maintains constant gain at the zenith and minima in the interference directions for a four-element L-band antenna array. The given values of interference attenuation depending on the number, level, angle of location and azimuth of the impact make it possible to clarify the indicators of noise immunity of the equipment of consumers of a global navigation satellite system equipped with a spatial compensator.

Lattices-Inspired CP-ABE from LWE Scheme for Data Access and Sharing Based on Blockchain

To address the quantum attacks on number theory-based ciphertext policy attribute-based encryption (CP-ABE), and to avoid private key leakage problems by relying on a trustworthy central authority, we propose a lattice-inspired CP-ABE scheme for data access and sharing based on blockchain in this paper. Firstly, a CP-ABE-based algorithm using learning with errors (LWE) assumption is constructed, which is selective security under linear independence restriction in the random oracle model. Secondly, the blockchain nodes can act as a distributed key management server to offer control over master keys used to generate private keys for different data users that reflect their attributes through launching transactions on the blockchain system. Finally, we develop smart contracts for proving the correctness of proxy re-encryption (PRE) and provide auditability for the whole data-sharing process. Compared with the traditional CP-ABE algorithm, the post-quantum CP-ABE algorithm can significantly improve the computation speed according to the result of the functional and experimental analysis. Moreover, the proposed blockchain-based CP-ABE scheme provides not only multi-cryptography collaboration to enhance the security of data access and sharing but also reduces average transaction response time and throughput.

Giardia hinders growth by disrupting nutrient metabolism independent of inflammatory enteropathy

Giardia lamblia (Giardia) is among the most common intestinal pathogens in children in low- and middle-income countries (LMICs). Although Giardia associates with early-life linear growth restriction, mechanistic explanations for Giardia-associated growth impairments remain elusive. Unlike other intestinal pathogens associated with constrained linear growth that cause intestinal or systemic inflammation or both, Giardia seldom associates with chronic inflammation in these children. Here we leverage the MAL-ED longitudinal birth cohort and a model of Giardia mono-association in gnotobiotic and immunodeficient mice to propose an alternative pathogenesis of this parasite. In children, Giardia results in linear growth deficits and gut permeability that are dose-dependent and independent of intestinal markers of inflammation. The estimates of these findings vary between children in different MAL-ED sites. In a representative site, where Giardia associates with growth restriction, infected children demonstrate broad amino acid deficiencies, and overproduction of specific phenolic acids, byproducts of intestinal bacterial amino acid metabolism. Gnotobiotic mice require specific nutritional and environmental conditions to recapitulate these findings, and immunodeficient mice confirm a pathway independent of chronic T/B cell inflammation. Taken together, we propose a new paradigm that Giardia-mediated growth faltering is contingent upon a convergence of this intestinal protozoa with nutritional and intestinal bacterial factors.

From Double Pushout Grammars to Hypergraph Lambek Grammars With and Without Exponential Modality

We study how to relate well-known hypergraph grammars based on the double pushout (DPO) approach and grammars over the hypergraph Lambek calculus HL (called HL-grammars). It turns out that DPO rules can be naturally encoded by types of HL using methods similar to those used by Kanazawa for multiplicative-exponential linear logic. In order to generalize his reasonings we extend the hypergraph Lambek calculus by adding the exponential modality, which results in a new calculus HMEL0; then we prove that any DPO grammar can be converted into an equivalent HMEL0-grammar. We also define the conjunctive Kleene star, which behaves similarly to this exponential modality, and establish a similar result. If we add neither the exponential modality nor the conjunctive Kleene star to HL, then we can still use the same encoding and show that any DPO grammar with a linear restriction on the length of derivations can be converted into an equivalent HL-grammar.

Systems of Linear Restrictions Over a Finite Field


 
 
 This paper considers the problem of recovering an unknown vector based on partial information presented in the form of certain linear dependencies. Such problem is an alternative to the standard one of solving a system of polynomial equations over a finite field, which arises in the context of algebraic cryptanalysis of stream ciphers, and it models a situation when it’s not possible to formulate specific equations with an unknown vector, but certain restrictions on linear dependencies with this vector. To formalize such linear dependencies, the notation of the system of linear restrictions over a finite field is introduced, and the problem of recovering the unknown vector is replaced by the problem of solving the system of linear restrictions over a finite field. In this paper, we researched some properties of this problem using its equivalent forms and important partial cases.
 
 

Программа построения вполне интерпретируемых элементарных и неэлементарных квазилинейных регрессионных моделей

A quite interpretable linear regression satisfies the following conditions: the signs of its coefficients correspond to the meaningful meaning of the factors; multicollinearity is negligible; coefficients are significant; the quality of the model approximation is high. Previously, to construct such models, estimated using the ordinary least squares, the QInter-1 program was developed. In it, according to the given initial parameters, the mixed integer 0-1 linear programming task is automatically generated, as a result of which the most informative regressors are selected. The mathematical apparatus underlying this program was significantly expanded over time: non-elementary linear regressions were developed, linear restrictions on the absolute values of intercorrelations were proposed to control multicollinearity, assumptions appeared about the possibility of constructing not only linear, but also quasi-linear regressions. This article is devoted to the description of the developed second version of the program for constructing quite interpretable regressions QInter-2. The QInter-2 program allows, depending on the initial parameters selected by the user, to automatically formulate for the LPSolve solver the mixed integer 0-1 linear programming task for constructing both elementary and non-elementary quite interpretable quasi-linear regressions. It is possible to set up to nine elementary functions and control such parameters as the number of regressors in the model, the number of signs in real numbers after the decimal point, the absolute contributions of variables to the overall determination, the number of occurrences of explanatory variables in the model, and the magnitude of intercorrelations. In the process of working with the program, you can also control the number of elementary and non-elementarily transformed variables that affect the speed of solving the mixed integer 0-1 linear programming task. The QInter-2 program is universal and can be used to construct quite interpretable mathematical dependencies in various subject areas.