Multi-parameter Setting Research Articles

Finding the optimal probe state for multiparameter quantum metrology using conic programming

The ultimate precision in quantum sensing could be achieved using optimal quantum probe states. However, current quantum sensing protocols do not use probe states optimally. Indeed, the calculation of optimal probe states remains an outstanding challenge. Here, we present an algorithm that efficiently calculates a probe state for correlated and uncorrelated measurement strategies. The algorithm involves a conic program, which minimizes a linear objective function subject to conic constraints on a operator-valued variable. Our algorithm outputs a probe state that is a simple function of the optimal variable. We prove that our algorithm finds the optimal probe state for channel estimation problems, even in the multiparameter setting. For many noiseless quantum sensing problems, we prove the optimality of maximally entangled probe states. We also analyze the performance of 3D-field sensing using various probe states. Our work opens the door for a plethora of applications in quantum metrology.

Relations between general sombor index and other general indices

Abstract The Sombor Index is a topological index in graph theory used to measure the complexity of a graph, particularly in describing the connectivity and structural diversity of a graph. We utilize the Sombor index as a bridge to explore the relationships between the Sombor index and other indices (General Zeroth-Order Randić Index, General Randić Index, General Sum-connectivity Index, General Redefined First Zagreb Index) in a more general multiparameter setting, thereby establishing new upper and lower bounds. Through a detailed analysis of data visualized from the Erdős-Rényi model, we’ve pinpointed limitations in our estimation methods. Nevertheless, the majority of our estimates are praiseworthy.

Quantum steering from phase measurements with limited resources

Quantum steering captures the ability of one party, Alice, to control through quantum correlations the state at a distant location, Bob, with superior ability than allowed by a local hidden state model. Verifying the presence of quantum steering has implications for the operation of quantum communication with limited trust, and its connection to the metrological power of the quantum state has been recently proved. This link is established by means of the violation of a Cramér–Rao bound holding for non-steerable states: its direct assessment would then require operation in the asymptotic regime of a large number of repetitions. Here, we build on previous work to account explicitly for the use of a limited number of resources and put this modified approach to test in a quantum optics experiment. The imperfections in the apparatus demand an adaptation of the original test in the multiparameter setting. Our results provide guidelines to apply such a metrological approach to the validation of quantum channels.

A fiducial-based confidence interval for the linear combination of multinomial probabilities.

Across a broad set of applications, system outcomes may be summarized as probabilities in confusion or contingency tables. In settings with more than two outcomes (e.g., stages of cancer), these outcomes represent multinomial experiments. Measures to summarize system performance have been presented as linear combinations of the resulting multinomial probabilities. Statistical inference on the linear combination of multinomial probabilities has been focused on large-sample and parametric settings and not small-sample settings. Such inference is valuable, however, especially in settings such as those resulting from pilot or low-cost studies. To address this gap, we leverage the fiducial approach to derive confidence intervals around the linear combination of multinomial parameters with desirable frequentist properties. One of the original arguments against the fiducial approach was its inability to extend to multiparameter settings. Therefore, the great novelty of this work is both the derived interval and the logical framework for applying the fiducial approach in multiparameter settings. Through simulation, we demonstrate that the proposed method maintains a minimum coverage of , unlike the bootstrap and large-sample methods, at comparable interval lengths. Finally, we illustrate its use in a medical problem of selecting classifiers for diagnosing chronic allograph nephropathy in postkidney transplantpatients.

Sharp constants in inequalities admitting the Calderón transference principle

AbstractThe aim of this note is twofold. First, we prove an abstract version of the Calderón transference principle for inequalities of admissible type in the general commutative multilinear and multiparameter setting. Such an operation does not increase the constants in the transferred inequalities. Second, we use the last information to study a certain dichotomy arising in problems of finding the best constants in the weak type $(1,1)$ and strong type $(p,p)$ inequalities for one-parameter ergodic maximal operators.

Reliability prediction and evaluation of communication base stations in earthquake prone areas

One of the primary tasks for effective disaster relief after a catastrophic earthquake is robust communication. In this paper, we propose a simple logistic method based on two-parameter sets of geology and building structure for the failure prediction of the base stations in post-earthquake. Using the post-earthquake base station data in Sichuan, China, the prediction results are 96.7% and 90% for the two-parameter sets and all parameter sets, respectively, and 93.3% for the neural network method sets. The results show that the two-parameter method outweighs the whole parameter set logistic method and the neural network prediction and can effectively improve the accuracy of the prediction. The weight parameters of two-parameter set by the actual field data significantly show that the failure of base stations after earthquake is mainly due to the geological differences where the base stations are located. It can be envisioned that if the geological distribution between the earthquake source and the base station is parameterized, the multi-parameter sets logistic method can not only effectively solve the failure prediction after earthquakes and the evaluation of communication base stations under complex conditions, but also provide site selection evaluation for the construction of civil buildings and power grid towers in earthquake-prone areas.

Multi-Parameter Hardy Spaces Theory and Endpoint Estimates for Multi-Parameter Singular Integrals

The main purpose of this paper is to establish the theory of the multi-parameter Hardy spaces H p H^p ( 0 > p ≤ 1 0>p\leq 1 ) associated to a class of multi-parameter singular integrals extensively studied in the recent book of B. Street (2014), where the L p L^p ( 1 > p > ∞ ) (1>p>\infty ) estimates are proved for this class of singular integrals. This class of multi-parameter singular integrals are intrinsic to the underlying multi-parameter Carnot-Carathéodory geometry, where the quantitative Frobenius theorem was established by B. Street (2011), and are closely related to both the one-parameter and multi-parameter settings of singular Radon transforms considered by Stein and Street (2011, 2012a, 2012b, 2013). More precisely, Street (2014) studied the L p L^p ( 1 > p > ∞ ) (1>p>\infty ) boundedness, using elementary operators, of a type of generalized multi-parameter Calderón Zygmund operators on smooth and compact manifolds, which include a certain type of singular Radon transforms. In this work, we are interested in the endpoint estimates for the singular integral operators in both one and multi-parameter settings considered by Street (2014). Actually, using the discrete Littlewood-Paley-Stein analysis, we will introduce the Hardy space H p H^p ( 0 > p ≤ 1 0>p\leq 1 ) associated with the multi-parameter structures arising from the multi-parameter Carnot-Carathéodory metrics using the appropriate discrete Littlewood-Paley-Stein square functions, and then establish the Hardy space boundedness of singular integrals in both the single and multi-parameter settings. Our approach is much inspired by the work of Street (2014) where he introduced the notions of elementary operators so that the type of singular integrals under consideration can be decomposed into elementary operators.

Shape-constrained geophysical inversion

Two long-standing challenges for geophysical inverse problems are nonuniqueness (especially in the multiparameter setting) and the slow convergence of gradient-based optimization methods. We introduce shape-based inversion algorithms to address these challenges. The shape-based algorithms determine, based on the available geophysical data, the underlying subsurface structures (e.g., stratigraphic layers) and the spatially varying unknown physical parameters (e.g., velocity and density). Inverting simultaneously for geologic structures and physical parameters eliminates degeneracies between parameters and also provides a multiscale framework for decomposing the inverse problem. First, we provide a rigorous mathematical formulation of shape-based algorithms through diffuse interface approximations. Then, we demonstrate the applicability of these algorithms to a range of synthetic model problems in traveltime tomography, full-waveform inversion, gradiometry, and history matching of single-phase flow. These examples highlight the ability of shape-based inversion to mitigate nonuniqueness and improve the rate of convergence to a physically realistic solution.

Longitudinal Changes in MRI Muscle Morphometry and Composition in People With Inclusion Body Myositis.

Limited data suggest that quantitative MRI (qMRI) measures have potential to be used as trial outcome measures in sporadic inclusion body myositis (sIBM) and as a noninvasive assessment tool to study sIBM muscle pathologic processes. Our aim was to evaluate changes in muscle structure and composition using a comprehensive multiparameter set of qMRI measures and to assess construct validity and responsiveness of qMRI measures in people with sIBM. This was a prospective observational cohort study with assessments at baseline (n = 30) and 1 year (n = 26). qMRI assessments include thigh muscle volume (TMV), inter/intramuscular adipose tissue (IMAT), muscle fat fraction (FF), muscle inflammation (T2 relaxation time), IMAT from T2* relaxation (T2*-IMAT), intermuscular connective tissue from T2* relaxation (T2*-IMCT), and muscle macromolecular structure from the magnetization transfer ratio (MTR). Physical performance assessments include sIBM Physical Functioning Assessment (sIFA), 6-minute walk distance, and quantitative muscle testing of the quadriceps. Correlations were assessed using the Spearman correlation coefficient. Responsiveness was assessed using the standardized response mean (SRM). After 1 year, we observed a reduction in TMV (6.8%, p < 0.001) and muscle T2 (6.7%, p = 0.035), an increase in IMAT (9.7%, p < 0.001), FF (11.2%, p = 0.030), connective tissue (22%, p = 0.995), and T2*-IMAT (24%, p < 0.001), and alteration in muscle macromolecular structure (ΔMTR = -26%, p = 0.002). A decrease in muscle T2 correlated with an increase in T2*-IMAT (r = -0.47, p = 0.008). Deposition of connective tissue and IMAT correlated with deterioration in sIFA (r = 0.38, p = 0.032; r = 0.34, p = 0.048; respectively), whereas a decrease in TMV correlated with a decrease in quantitative muscle testing (r = 0.36, p = 0.035). The most responsive qMRI measures were T2*-IMAT (SRM = 1.50), TMV (SRM = -1.23), IMAT (SRM = 1.20), MTR (SRM = -0.83), and T2 relaxation time (SRM = -0.65). Progressive deterioration in muscle quality measured by qMRI is associated with a decline in physical performance. Inflammation may play a role in triggering fat infiltration into muscle. qMRI provides valid and responsive measures that might prove valuable in sIBM experimental trials and assessment of muscle pathologic processes. This study provides Class I evidence that qMRI outcome measures are associated with physical performance measures in patients with sIBM.

Dyadic product BMO in the Bloom setting

Ó. Blasco and S. Pott showed that the supremum of operator norms over L 2 $L^2$ of all bicommutators (with the same symbol) of one-parameter Haar multipliers dominates the biparameter dyadic product BMO norm of the symbol itself. In the present work we extend this result to the Bloom setting, and to any exponent 1 < p < ∞ $1<p<\infty$ . The main tool is a new characterization in terms of paraproducts and two-weight John–Nirenberg inequalities for dyadic product BMO in the Bloom setting. We also extend our results to the whole scale of indexed spaces between little bmo and product BMO in the general multiparameter setting, with the appropriate iterated commutator in each case.

Generalized persistence algorithm for decomposing multiparameter persistence modules

The classical persistence algorithm computes the unique decomposition of a persistence module implicitly given by an input simplicial filtration. Based on matrix reduction, this algorithm is a cornerstone of the emergent area of topological data analysis. Its input is a simplicial filtration defined over the integers $${\mathbb {Z}}$$ giving rise to a 1-parameter persistence module. It has been recognized that multiparameter version of persistence modules given by simplicial filtrations over d-dimensional integer grids $${\mathbb {Z}}^d$$ is equally or perhaps more important in data science applications. However, in the multiparameter setting, one of the main challenges is that topological summaries based on algebraic structure such as decompositions and bottleneck distances cannot be as efficiently computed as in the 1-parameter case because there is no known extension of the persistence algorithm to multiparameter persistence modules. We present an efficient algorithm to compute the unique decomposition of a finitely presented persistence module M defined over the multiparameter $${\mathbb {Z}}^d$$ . The algorithm first assumes that the module is presented with a set of N generators and relations that are distinctly graded. Based on a generalized matrix reduction technique it runs in $$O(N^{2\omega +1})$$ time where $$\omega <2.373$$ is the exponent of matrix multiplication. This is much better than the well known algorithm called Meataxe which runs in $${\tilde{O}}(N^{6(d+1)})$$ time on such an input. In practice, persistence modules are usually induced by simplicial filtrations. With such an input consisting of n simplices, our algorithm runs in $$O(n^{(d-1)(2\omega + 1)})$$ time for $$d\ge 2$$ . For the special case of zero dimensional homology, it runs in time $$O(n^{2\omega +1})$$ .

Improved model-free adaptive predictive control method for direct data-driven control of a wastewater treatment process with high performance

In this paper, an improved model-free adaptive predictive control (IMFAPC) method with controller parameters sensitivity discrimination and optimization is proposed, to solve the problem that using conventional methods is difficult to effectively control the nitrate concentration and dissolved oxygen concentration of wastewater treatment process (WWTP). First, aiming at the nonstationary dynamic characteristics of WWTP and the limitation of control accuracy of conventional MFAPC method in the nonlinear dynamic system control, a novel improved MFAPC method is proposed considering the effect of the WWTP output tracking error variation on the control of nitrate concentration and dissolved oxygen concentration. Meanwhile, in order to obtain the optimum control performance, the sensitivity discrimination and optimization for the multi-parameter set of the proposed IMFAPC method are performed by combining the Monte Carlo experiment based multi-parameter sensitivity analysis and the hybrid intelligent optimization. Then, the stability of the proposed IMFAPC scheme is analyzed and proved by the BIBO method. Finally, various data experiments are carried out to verify the proposed method. The experimental results demonstrate that the proposed method can control the nitrate nitrogen and dissolved oxygen concentration rapidly and accurately under different operating conditions.

Research on Automatic Control Method of Motor Current in Distribution Network Based on Bionic Algorithm

Due to the problems of multi-parameter identification and processing in traditional approach of current-predicting, it is difficult to control PMSM in practical complex environments. In this paper, a predictive current control method based on improved extended observer is proposed, whose mathematical model based on extended state observer is also established. Because of the problem of multi-parameter setting in ESO, the flower pollination algorithm is used to adjust the parameters with the fitness function of minimum absolute error of ESO input and output. To verify the stability of PMSM system based on predicted current control with improved ESO, MATLAB/SIMULINK is used to build the simulation model. And the results show that the control strategy can predict the accurate current ofdq, and the PMSM based on this method can output the desired current, determining the stable operation of the system.

Clusters of Ultrasound Scattering Parameters for the Classification of Steatotic and Normal Livers

The study of ultrasound tissue interactions in fatty livers has a long history with strong clinical potential for assessing steatosis. Recently we proposed alternative measures of first- and second-order statistics of echoes from soft tissues, namely, the H-scan, which is based on a matched filter approach, to quantify scattering transfer functions and the Burr distribution to model speckle patterns. Taken together, these approaches produce a multiparameter set that is directly related to the fundamentals of ultrasound propagation in tissue. To apply this approach to the problem of assessing steatotic livers, these analyses were applied to in vivo rat livers (N=21) under normal feeding conditions or after receiving a methionine- and choline-deficient diet that produces steatosis within a few weeks. Ultrasound data were acquired at baseline and again at weeks 2 and 6 before applying the H-scan and Burr analyses. Furthermore, a classification technique known as the support vector machine was then used to find clusters of the five parameters that are characteristic of the different steatotic liver conditions as confirmed by histologic processing of excised liver tissue samples. With the in vivo multiparametric ultrasound measurement approach and determination of clusters, steatotic can be discriminated from normal livers with 100% accuracy in a rat animal model.

RLD Fisher information bound for multiparameter estimation of quantum channels

One of the fundamental tasks in quantum metrology is to estimate multiple parameters embedded in a noisy process, i.e. a quantum channel. In this paper, we study fundamental limits to quantum channel estimation via the concept of amortization and the right logarithmic derivative (RLD) Fisher information value. Our key technical result is the proof of a chain-rule inequality for the RLD Fisher information value, which implies that amortization, i.e. access to a catalyst state family, does not increase the RLD Fisher information value of quantum channels. This technical result leads to a fundamental and efficiently computable limitation for multiparameter channel estimation in the sequential setting, in terms of the RLD Fisher information value. As a consequence, we conclude that if the RLD Fisher information value is finite, then Heisenberg scaling is unattainable in the multiparameter setting.

Experimental investigation on WEDM performance analysis using grey-fuzzy integrated with TLBO algorithm for Inconel 625: comparison with GA and SA

Purpose In the present study, wire electro-discharge machining (WEDM) of Inconel 625 (In-625) is performed with the machining parameter such as spark-on time, spark-off time, wire-speed, wire tension and servo voltage. The purpose of this study is to find the most favorable machining parameter setting with respect to WEDM performance such as material removal rate (MRR) and surface roughness (RA). Design/methodology/approach Taguchi’s L27 orthogonal array has been used to design the experiments with varying machining parameters into three-level four factors. A hybrid multi-optimization technique has been purposed with grey relation analysis and fuzzy inference system integrated with teaching learning-based optimization to achieve optimum machinability (MRR and RA in present case). The obtained result has been compared with two evolutionary optimization tools via a genetic algorithm and simulated annealing. Findings It has been found that proposed hybrid technique taking minimum computational time, provide better solution and avoid priority weightage calculation by decision-makers. A confirmation test has been performed at single and multi-optimal parameter settings. The decision-makers have been chosen to select any single or multi-parameter setting as per the industry’s demand. Originality/value The proposed optimization technique provides better machinability of In-625 using zinc-coated brass wire electrode during WEDM operation.

Smaller p-Values via Indirect Information

This article develops p-values for evaluating means of normal populations that make use of indirect or prior information. A p-value of this type is based on a biased frequentist hypothesis test that has optimal average power with respect to a probability distribution that encodes indirect information about the mean parameter, resulting in a smaller p-value if the indirect information is accurate. In a variety of multiparameter settings, we show how to adaptively estimate the indirect information for each mean parameter while still maintaining uniformity of the p-values under their null hypotheses. This is done using a linking model through which indirect information about the mean of one population may be obtained from the data of other populations. Importantly, the linking model does not need to be correct to maintain the uniformity of the p-values under their null hypotheses. This methodology is illustrated in several data analysis scenarios, including small area inference, spatially arranged populations, interactions in linear regression, and generalized linear models. Supplementary materials for this article are available online.

Homological Algebra for Persistence Modules

We develop some aspects of the homological algebra of persistence modules, in both the one-parameter and multi-parameter settings, considered as either sheaves or graded modules. The two theories are different. We consider the graded module and sheaf tensor product and Hom bifunctors as well as their derived functors, Tor and Ext, and give explicit computations for interval modules. We give a classification of injective, projective, and flat interval modules. We state Kunneth theorems and universal coefficient theorems for the homology and cohomology of chain complexes of persistence modules in both the sheaf and graded modules settings and show how these theorems can be applied to persistence modules arising from filtered cell complexes. We also give a Gabriel-Popescu theorem for persistence modules. Finally, we examine categories enriched over persistence modules. We show that the graded module point of view produces a closed symmetric monoidal category that is enriched over itself.

Multi-parameter setting (c,α) means with respect to one dimensional Vilenkin system

We prove that the maximal operator of the (C,?n)-means of the one dimensional Vilenkin-Fourier series is of weak type(L1, L1). Moreover, we prove the almost everywhere convergence of the (C,?n) means of integrable functions (i.e. ? ?n n f ? f ), where n ? N?,q and n ? 1 for f ? L1(Gm), Gm is a bounded Vilenkin group, for every sequence ? = (?n), 0 &lt; ?n &lt; 1.

FIVE-FOLD SYNERGY AS AN OPTIMAL INNOVATIVE MODEL

Introduction. The issue of understanding the patterns and factors of economic growth is reflected in the work of scientists, politicians, historians and publicists from antiquity to the present. The economic system is transforming, at the same time evolving partly randomly, and quantitative changes often precede qualitative ones. Systems of this type are characterized by the bifucarial nature of development, i.e. a change in the qualitative behaviour of such dynamic nonequilibrium systems with a slight alternative to their parameters, bifurcation points (transition or progress) of which are the economic crises, and the equilibrium state is only a certain moment in their movement and development. This nature of evolution is decisive for the whole set of complex multicomponent nonlinear systems, represented by a multiparameter set of dynamic systems of lower order, which include economic ones. However, this typology automatically means a logical problem of finding patterns of their movement and development, given the difficulty of predicting the reaction of this type of system to the impact and change of their parameters. The aim of the article is to substantiate the optimal innovative model of the economy based on the determination of a key factor of economic development. The methodological basis of the research is dialectical analysis, the method of studying the causality of phenomena, determinism in the study of systems, theoretical and logical generalizations and hypotheses. Results. The characterization of economic systems as complex, multicomponent and chaotic, i.e. those that can be deterministic and predictable only in theory, explains the stochastic nature of economic laws and the logical absence of a "universal" recipe for development, which proves the need to find endogenous factors. Based on the assumption of a unified nature of development and unevenness, it is determined that the core of innovative development in the modern world is the intellectualization of economic systems. The factor of unevenness and development, at the same time, in the modern sense, development innovative that is, is the intellectual capital, which produces an innovative flash, which with the appropriate working mechanism becomes the driving force of development. The study of development theories proves the need to endogenize the "Sollow residual", because the assumption of the exogenous nature of scientific and technological development, and hence economic growth, does not explain the root causes of the uneven development of individual economies, and therefore does not explain the key development factor. Naturally, the general trajectory of global development is set exogenously, at the same time, it begins with an endogenous innovation outbreak, which turns into an innovation flow and forms the technological base adopted by the rest of economic systems. The contradiction of the neoclassical paradigm and institutionalism is purely nominal, because the establishment of rules and directives by institutions can be based on "ratio" and convergence of economic agents – institutions, or their synergy can provide recursive directiveness to the system, the economic system as a whole, that is, and "irrational" rules will be organically calibrated as a result of this interaction, at the same time, the presence of rules will give the chaotic multicomponent system some additional determinism. Thus, a five-fold synergy is proposed as an innovative model of economic development, which takes into account the whole set of interactions between economic agents in their joint development and conflict, determining the optimal trajectory of overall sustainable economic growth.