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Corporate boards, experts panels, parliaments, cabinets, and even nations all take important decisions as a group. Selecting an efficient decision rule to aggregate individual opinions is paramount to the decision quality of these groups. In our experiment we measure revealed preferences over and efficiency of several important decision rules. Our results show that: (1) the efficiency of the theoretically optimal rule is not as robust as simple majority voting, and efficiency rankings in the lab can differ from theory; (2) participation constraints often hinder implementation of more efficient mechanisms; (3) these constraints are relaxed if the less efficient mechanism is risky; (4) participation preferences appear to be driven by realized rather than theoretic payoffs of the decision rules. These findings highlight the difficulty of relying on theory alone to predict what mechanism is better and acceptable to the participants in practice.

We consider the heat equation defined by a generalized measure theoretic Laplacian on $[0,1]$. This equation describes heat diffusion in a bar such that the mass distribution of the bar is given by a non-atomic Borel probabiliy measure $\mu$, where we do not assume the existence of a strictly positive mass density. We show that weak measure convergence implies convergence of the corresponding generalized Laplacians in the strong resolvent sense. We prove that strong semigroup convergence with respect to the uniform norm follows, which implies uniform convergence of solutions to the corresponding heat equations. This provides, for example, an interpretation for the mathematical model of heat diffusion on a bar with gaps in that the solution to the corresponding heat equation behaves approximately like the heat flow on a bar with sufficiently small mass on these gaps., Comment: 22 pages, 1 figure

In this paper, we study approximation properties of single hidden layer neural networks with weights varying on finitely many directions and thresholds from an open interval. We obtain a necessary and at the same time sufficient measure theoretic condition for density of such networks in the space of continuous functions. Further, we prove a density result for neural networks with a specifically constructed activation function and a fixed number of neurons., 12 pages

Pearson’s correlation coefficient is considered a measure of linear association between bivariate random variables X and Y. It is recommended not to use it for other forms of associations. Indeed, for nonlinear monotonic associations alternative measures like Spearman’s rank and Kendall’s tau correlation coefficients are considered more appropriate. These views or opinions on the estimation of association are strongly rooted in the statistical and other empirical sciences. After defining linear and monotonic associations, we will demonstrate that these opinions are incorrect. Pearson’s correlation coefficient should not be ruled out a priori for measuring nonlinear monotonic associations. We will provide examples of practically relevant families of bivariate distribution functions with nonlinear monotonic associations for which Pearson’s correlation is preferred over Spearman’s rank and Kendall’s tau correlation in testing the dependency between X and Y. Alternatively, we will provide a family of bivariate distributions with a linear association between X and Y for which Spearman’s rank and Kendall’s tau are preferred over Pearson’s correlation. Our examples show that existing views on linear and monotonic associations are myths.

This paper is devoted to studying the transcendental directions of entire solutions of $ f^{(n)}+A_{n-1}f^{(n-1)}+...+A_0f = 0 $, where $ n(\geq 2) $ is an integer and $ A_i(z)(i = 0, 1, ..., n-1) $ are entire functions of finite lower order. With some additional conditions, the set of common transcendental directions of non-trivial solutions, their derivatives and their primitives must have a definite range of measure. Moreover, we obtain the lower bound of the measure of the set defined by the common transcendental directions of Jackson difference operator of non-trivial solutions.

Various strategies for active learning have been proposed in the machine learning literature. In uncertainty sampling, which is among the most popular approaches, the active learner sequentially queries the label of those instances for which its current prediction is maximally uncertain. The predictions as well as the measures used to quantify the degree of uncertainty, such as entropy, are traditionally of a probabilistic nature. Yet, alternative approaches to capturing uncertainty in machine learning, alongside with corresponding uncertainty measures, have been proposed in recent years. In particular, some of these measures seek to distinguish different sources and to separate different types of uncertainty, such as the reducible (epistemic) and the irreducible (aleatoric) part of the total uncertainty in a prediction. The goal of this paper is to elaborate on the usefulness of such measures for uncertainty sampling, and to compare their performance in active learning. To this end, we instantiate uncertainty sampling with different measures, analyze the properties of the sampling strategies thus obtained, and compare them in an experimental study.

Contains fulltext : 285105.pdf (Publisher’s version ) (Open Access) Discrete Markov chains are frequently used to analyse transition behaviour in sequential data. Here, the transition probabilities can be estimated using varying order Markov chains, where order k specifies the length of the sequence history that is used to model these probabilities. Generally, such a model is fitted to the entire dataset, but in practice it is likely that some heterogeneity in the data exists and that some sequences would be better modelled with alternative parameter values, or with a Markov chain of a different order. We use the framework of Exceptional Model Mining (EMM) to discover these exceptionally behaving sequences. In particular, we propose an EMM model class that allows for discovering subgroups with transition behaviour of varying order. To that end, we propose three new quality measures based on information-theoretic scoring functions. Our findings from controlled experiments show that all three quality measures find exceptional transition behaviour of varying order and are reasonably sensitive. The quality measure based on Akaike’s Information Criterion is most robust for the number of observations. We furthermore add to existing work by seeking for subgroups of sequences, as opposite to subgroups of transitions. Since we use sequence-level descriptive attributes, we form subgroups of entire sequences, which is practically relevant in situations where you want to identify the originators of exceptional sequences, such as patients. We show this relevance by analysing sequences of blood glucose values of adult persons with diabetes type 2. In the experiments, we find subgroups of patients based on age and glycated haemoglobin (HbA1c), a measure known to correlate with average blood glucose values. Clinicians and domain experts confirmed the transition behaviour as estimated by the fitted Markov chain models. 35 p.

Change point detection plays a fundamental role in many real-world applications, where the goal is to analyze and monitor the behaviour of a data stream. In this paper, we study change detection in binary streams. To this end, we use a likelihood ratio between two models as a measure for indicating change. The first model is a single bernoulli variable while the second model divides the stored data in two segments, and models each segment with its own bernoulli variable. Finding the optimal split can be done in \( \mathcal {O} \mathopen {}\left( n\right) \) time, where n is the number of entries since the last change point. This is too expensive for large n. To combat this we propose an approximation scheme that yields \((1 - \epsilon )\) approximation in \( \mathcal {O} \mathopen {}\left( \epsilon ^{-1} \log ^2 n\right) \) time. The speed-up consists of several steps: First we reduce the number of possible candidates by adopting a known result from segmentation problems. We then show that for fixed bernoulli parameters we can find the optimal change point in logarithmic time. Finally, we show how to construct a candidate list of size \( \mathcal {O} \mathopen {}\left( \epsilon ^{-1} \log n\right) \) for model parameters. We demonstrate empirically the approximation quality and the running time of our algorithm, showing that we can gain a significant speed-up with a minimal average loss in optimality.

We report on a timing programme of 74 young pulsars that have been observed by the Parkes 64-m radio telescope over the past decade. Using modern Bayesian timing techniques, we have measured the properties of 124 glitches in 52 of these pulsars, of which 74 are new. We demonstrate that the glitch sample is complete to fractional increases in spin-frequency greater than $\Delta\nu^{90\%}_{g}/\nu \approx 8.1 \times 10^{-9}$. We measure values of the braking index, $n$, in 33 pulsars. In most of these pulsars, their rotational evolution is dominated by episodes of spin-down with $n > 10$, punctuated by step changes in the spin-down rate at the time of a large glitch. The step changes are such that, averaged over the glitches, the long-term $n$ is small. We find a near one-to-one relationship between the inter-glitch value of $n$ and the change in spin-down of the previous glitch divided by the inter-glitch time interval. We discuss the results in the context of a range of physical models., Comment: 24 pages, 9 figures and 9 tables. Published in MNRAS. (Fixed typo in the abstract and conclusion)

In this note, we obtain a reverse version of the integral Hardy inequality on metric measure spaces. Moreover, we give necessary and sufficient conditions for the weighted reverse Hardy inequality to be true. The main tool in our proof is a continuous version of the reverse Minkowski inequality. Also, we present some consequences of the obtained reverse Hardy inequality on the homogeneous groups, hyperbolic spaces and Cartan-Hadamard manifolds., 23 pages

Ion thermodiffusion coefficients are crucial to analyse effects of thermodiffusion in thermocells and these values are difficult to measure experimentally. To determine these coefficients, this paper adopts parameter identification and studies their identifiability. Time dependence of open-circuit voltage is measured in an aqueous potassium ferri/ferrocyanide thermocell as data set. A one-dimensional numerical model is established according to theories of electrochemistry and non-equilibrium thermodynamics. Identification of thermodiffusion coefficients is conducted using genetic algorithm in eight parameter spaces, which are divided according to signs of three parameters. Thermodiffusion is suggested to induce a 9.38% drop in voltage. The best identification results are −8.30 × 10−12, −6.56 × 10−12, −3.48 × 10−12 m2/(s K) for ferricyanide, ferrocyanide and potassium ion, respectively. However, five optimal parameters in other parameter spaces have close fitness, implying multimodality of identification. And only one of these parameters is practically identifiable using this method. To improve identification results, more accurate estimation of inner temperature difference and determination of ion mobilities are necessary. Besides, electric current data has the potential to determine the actual combination of thermodiffusion coefficients from these six optimal results.

Spatial systems that experience congestion can be modeled as weighted networks whose weights dynamically change over time with the redistribution of flows. This is particularly true for urban transportation networks. The aim of this work is to find appropriate network measures that are able to detect critical zones for traffic congestion and bottlenecks in a transportation system. We propose for both single and multi-layered networks a path-based measure, called dynamical efficiency, which computes the travel time differences under congested and free-flow conditions. The dynamical efficiency quantifies the reachability of a location embedded in the whole urban traffic condition, in lieu of a myopic description based on the average speed of single road segments. In this way, we are able to detect the formation of congestion seeds and visualize their evolution in time as well-defined clusters. Moreover, the extension to multilayer networks allows us to introduce a novel measure of centrality, which estimates the expected usage of inter-modal junctions between two different transportation means. Finally, we define the so-called dilemma factor in terms of number of alternatives that an interconnected transportation system offers to the travelers in exchange for a small increase in travel time. We find macroscopic relations between the percentage of extra-time, number of alternatives and level of congestion, useful to quantify the richness of trip choices that a city offers. As an illustrative example, we show how our methods work to study the real network of a megacity with probe traffic data.

In this work, we consider a generalized quantum fractional Sturm–Liouville–Langevin difference problem with terminal boundary conditions. The relevant results rely on Mönch’s fixed point theorem along with a theoretical method by terms of Kuratowski measure of noncompactness (MNC) and the Banach contraction principle (BCP). Furthermore, two dynamical notions of Ulam–Hyers (UH) and generalized Ulam–Hyers (GUH) stability are addressed for solutions of the supposed Sturm–Liouville–Langevin quantum boundary value problem (q-FBVP). Two examples are presented to show the validity and also the effectiveness of theoretical results. In the last part of the paper, we conclude our exposition with some final remarks and observations.

Carotid-femoral pulse transit time (cfPTT) is a widely accepted measure of central arterial stiffness. The cfPTT is commonly calculated from two synchronized pressure waves. However, measurement of synchronized pressure waves is technically challenging. In this paper, a method of decomposing the radial pressure wave is proposed for estimating cfPTT. From the radial pressure wave alone, the pressure wave can be decomposed into forward and backward waves by fitting a double triangular flow wave. The first zero point of the second derivative of the radial pressure wave and the peak of the dicrotic segment of radial pressure wave are used as the peaks of the fitted double triangular flow wave. The correlation coefficient between the measured wave and the estimated forward and backward waves based on the decomposition of the radial pressure wave was 0.98 and 0.75, respectively. Then from the backward wave, cfPTT can be estimated. Because it has been verified that the time lag estimation based on of backward wave has strong correlation with the measured cfPTT. The corresponding regression function between the time lag estimation of backward wave and measured cfPTT is y = 0.96x + 5.50 (r = 0.77; p

The key process used in nuclear industries for the management of radiotoxicity associated with spent fuel in a closed fuel cycle is solvent extraction. An understanding of hydrodynamics and mass transfer is of primary importance for the design of mass transfer equipment used in solvent extraction processes. Understanding the interfacial phenomenon and the associated hydrodynamics of the liquid drops is essential for model-based design of mass transfer devices. In this work, the phenomenon of drop formation at the tip of a nozzle submerged in quiescent immiscible liquid phase is revisited. Previously reported force balance based models and empirical correlations are analyzed. Experiments are carried out to capture the process of drop formation using high-speed imaging technique. The images are digitally processed to measure the average drop diameter. A correlation based on the force balance model is proposed to estimate drop diameter and jet length. The average drop diameter obtained from the proposed model is in good agreement with experimental data with an average error of 6.3%. The developed model is applicable in both the necking as well as jetting regime and is validated for liquid-liquid systems having low, moderate and high interfacial tension.

The velocity distribution function is a statistical description that connects particle kinetics and macroscopic parameters in many-body systems. Laser-induced fluorescence (LIF) spectroscopy is utilized to measure the local velocity distribution function in spatially inhomogeneous plasmas. However, the analytic form of such a function for the system of interest is not always clear under the intricate factors in non-equilibrium states. Here, we propose a novel approach to select the valid form of the velocity distribution function based on Bayesian statistics. We formulate the Bayesian inference of ion velocity distribution function and apply it to LIF spectra locally observed at several positions in a linear magnetized plasma. We demonstrate evaluating the spatial inhomogeneity by verifying each analytic form of the local velocity distribution function. Our approach is widely applicable to experimentally establish the velocity distribution function in plasmas and fluids, including gases and liquids.

In this paper, we study the eigenvalue problem of poly-drifting Laplacian on complete smooth metric measure space ( M , ⟨ , ⟩ , e − ϕ d v ) \left(M,\langle ,\rangle ,{e}^{-\phi }{\rm{d}}v) , with nonnegative weighted Ricci curvature Ric ϕ ≥ 0 {{\rm{Ric}}}^{\phi }\ge 0 for some ϕ ∈ C 2 ( M ) \phi \in {C}^{2}\left(M) , which is uniformly bounded from above, and successfully obtain several universal inequalities of this eigenvalue problem.

We study the boundary behaviour of open, light mappings satisfying generalized modular inequalities in general metric measure spaces. We extend in this way known facts from the theory of quasiregular mappings and from their recent generalizations, namely the mappings of finite distortion and the so called ring mappings.

For the dynamic spectrum sharing (DSS), this paper proposes a spectrum sensing scheme that measures packet lengths of interfering systems. DSS requires spectrum sensing techniques to measure a length of time for which the interfering systems use a channel during observation time. A ratio of the length of time to the observation time is referred to as the channel occupation ratio (COR). When the observation time is limited, a conventional estimation scheme suffers from large errors of the measured COR. To cope with this problem, another conventional scheme divides the observation time into multiple short slots so as to estimate mean squared estimation errors of COR. However, this conventional scheme cannot accurately estimate errors, because it does not consider the time length of packets. Therefore, this paper proposes a scheme to estimate the variance of measured COR by measuring how long packets from the interfering systems can be observed, which can estimate errors much more accurately than the conventional scheme. Computer simulations evaluate how the observation time affects the standard deviation of the measured COR. It is also demonstrated that the theoretical results of the proposed scheme agree with those of the simulations when the true value of COR is less than 0.4.

Fractal is a common feature of many deterministic complex networks. The complex networks with fractal features have interesting structure and good performance. The network based on hypergraph is named hypernetwork. In this paper, we construct a hypernetwork model with fractal properties, and obtain its topological properties. Moreover, according to the exact controllability theory, we obtain the node controllability and the hyperedge controllability of the fractal hypernetwork. The simulation results show that the measure of hyperedge controllability is smaller than that of node in the fractal hypernetwork. In addition, We compare the controllability of three types of hypernetwork, which are easier to control by their hyperedges. It is shown the fractal hypernetwork constructed in this paper has the best controllability. Because of the good controllability of our fractal hypernetwork model, it is suitable for the topology structure of many real systems.

Indeterminacy associated with probing of a quantum state is commonly expressed through spectral distances (metric) featured in the outcomes of repeated experiments. Here we express it as an effective amount (measure) of distinct outcomes instead. The resulting $\mu$-uncertainties are described by the effective number theory [1] whose central result, the existence of a minimal amount, leads to a well-defined notion of intrinsic irremovable uncertainty. We derive $\mu$-uncertainty formulas for arbitrary set of commuting operators, including the cases with continuous spectra. The associated entropy-like characteristics, the $\mu$-entropies, convey how many degrees of freedom are effectively involved in a given measurement process. In order to construct quantum $\mu$-entropies, we are led to quantum effective numbers designed to count independent, mutually orthogonal states effectively comprising a density matrix. This concept is basis-independent and leads to a measure-based characterization of entanglement., Comment: 14 pages; v2: typos fixed, minor improvements; v3: 18 pages, appendices added, published version

In two celebrated experiments of quantum mechanics, the Stern-Gerlach (SG) and Heisenberg microscope (HM) experiments, the electron spin ${s}_{z}$ and spatial $\mathbit{r}$ coordinates are measured separately. In this paper, the combined $\mathrm{SG}+\mathrm{HM}$ experiment is proposed to measure the full electron coordinate $\mathbit{x}={\mathbit{r},{s}_{z}}$. To this end, noninterfering and (virtually) simultaneous SG and HM experiments are proposed to apply to the individual fragments A and B of an entangled dissociating system $\mathrm{A}\text{\ensuremath{-}}\mathrm{B}$. The theoretical description of a spin-collapsed and partially spatially collapsed state of the $\mathrm{SG}+\mathrm{HM}$ experiment is given for the prototype ``perfectly'' entangled system, the dissociating ${\mathrm{H}}_{2}$ molecule.

Although wavelet decompositions of functions in Besov spaces have been extensively investigated, those involved with mild decay bases are relatively unexplored. In this paper, we study wavelet bases of Besov spaces and the relation between norms and wavelet coefficients. We establish the $l^{p}$ l p -stability as a measure of how effectively the Besov norm of a function is evaluated by its wavelet coefficients and the $L^{p}$ L p -completeness of wavelet bases. We also discuss wavelets with decay conditions and establish the Jackson inequality.

Scalar coupling constant (SCC), directly measured by nuclear magnetic resonance (NMR) spectroscopy, is a key parameter for molecular structure analysis, and widely used to predict unknown molecular structure. Restricted by the high cost of NMR experiments, it is impossible to measure the SCC of unknown molecules on a large scale. Using density functional theory (DFT) to theoretically calculate the SCC of molecules is incredibly challenging, due to the cost of substantial computational time and space. Graph neural networks (GNN) of artificial intelligence (AI) have great potential in constructing molecul ar-like topology models, which endows them the ability to rapidly predict SCC through data-driven machine learning methods, and avoiding time-consuming quantum chemical calculations. With a priori knowledge of angles, we propose a graph angle-attention neural network (GAANN) model to predict SCC by means of some easily accessible related information. GAANN, with a multilayer message-passing network and a self-attention mechanism, can accurately simulate the molecular-like topological structure and predict molecular properties. Our simulations show that the prediction accuracy by GAANN, with the log(MAE) = −2.52, is close to that by DFT calculations. Different from conventional AI methods, GAANN combining the AI method with quantum chemistry theory (Karplus equation) has a strong physicochemical interpretability about angles. From an AI perspective, we find that bond angle has the highest correlation with the SCC among all angle features (dihedral angle, bond angle, geometric angles) about multiple coupling types in the small molecule datasets.

This paper presents a new methodology for characterising the evolving behaviour of the time-varying causality between multivariate time series, from the perspective of change in the structure of the causality pattern. We propose that such evolutionary behaviour should be tracked by means of a complex network whose nodes are causality patterns and edges are transitions between those patterns of causality. In our new methodology each edge has a weight that includes the frequency of the given transition and two metrics relating to the gross and net structural change in causality pattern, which we call $$\alpha$$ α and $$\beta$$ β . To characterise aspects of the behaviour within this network, five approaches are presented and motivated. To act as a demonstration of this methodology an application of sample data from the international oil market is presented. This example illustrates how our new methodology is able to extract information about evolving causality behaviour. For example, it reveals non-random time-varying behaviour that favours transitions resulting in predominantly similar causality patterns, and it discovers clustering of similar causality patterns and some transitional behaviour between these clusters. The example illustrates how our new methodology supports the inference that the evolution of causality in the system is related to the addition or removal of a few causality links, primarily keeping a similar causality pattern, and that the evolution is not related to some other measure such as the overall number of causality links.

This paper deals with the blow-up phenomena of solution to a reaction-diffusion equation with gradient absorption terms under nonlinear boundary flux. Based on the technique of modified differential inequality and comparison principle, we establish some conditions on nonlinearities to guarantee the solution exists globally or blows up at finite time. Moreover, some bounds for blow-up time are derived under appropriate measure in higher dimensional spaces $ \left({N \ge 2} \right). $

In this work, we solve the system of integro-differential equations (in terms of Caputo–Fabrizio calculus) using the concepts of the best proximity pair (point) and measure of noncompactness. We first introduce the concept of cyclic (noncyclic) Θ-condensing operator for a pair of sets using the measure of noncompactness and then establish results on the best proximity pair (point) on Banach spaces and strictly Banach spaces. In addition, we have illustrated the considered system of integro-differential equations by three examples and discussed the stability, efficiency, and accuracy of solutions.

Magnetic Resonance Fingerprinting (MRF) is a novel technique that simultaneously estimates multiple tissue-related parameters, such as the longitudinal relaxation time T1, the transverse relaxation time T2, off resonance frequency B0 and proton density, from a scanned object in just tens of seconds. However, the MRF method suffers from aliasing artifacts because it significantly undersamples the k-space data. In this work, we propose a compressed sensing (CS) framework for simultaneously estimating multiple tissue-related parameters based on the MRF method. It is more robust to low sampling ratio and is therefore more efficient in estimating MR parameters for all voxels of an object. Furthermore, the MRF method requires identifying the nearest atoms of the query fingerprints from the MR-signal-evolution dictionary with the L2 distance. However, we observed that the L2 distance is not always a proper metric to measure the similarities between MR Fingerprints. Adaptively learning a distance metric from the undersampled training data can significantly improve the matching accuracy of the query fingerprints. Numerical results on extensive simulated cases show that our method substantially outperforms state-of-the-art methods in terms of accuracy of parameter estimation.

Distance measure is one of the research hotspot in Pythagorean fuzzy environment due to its quantitative ability of distinguishing Pythagorean fuzzy sets (PFSs). Various distance functions for PFSs are introduced in the literature and have their own pros and cons. The common thread of incompetency for these existing distance functions is their inability to distinguish highly uncertain PFSs distinctly. To tackle this point, we introduce a novel distance measure for PFSs. An added advantage of the measure is its simple mathematical form. Moreover, superiority and reasonability of the prescribed definition are demonstrated through proper numerical examples. Boundedness and nonlinear behaviour of the distance measure is established and verified via suitable illustrations. In the current scenario, selecting an antivirus face-mask as a preventive measure in the COVID-19 pandemic and choosing the best school in private sector for children are some of the burning issues of a modern society. These issues are addressed here as multi-attribute decision-making problems and feasible solutions are obtained using the introduced definition. Applicability of the distance measure is further extended in the areas of pattern recognition and medical diagnosis.

Background Proteins form various complexes to carry out their versatile functions in cells. The dynamic properties of protein complex formation are mainly characterized by the association rates which measures how fast these complexes can be formed. It was experimentally observed that the association rates span an extremely wide range with over ten orders of magnitudes. Identification of association rates within this spectrum for specific protein complexes is therefore essential for us to understand their functional roles. Results To tackle this problem, we integrate physics-based coarse-grained simulations into a neural-network-based classification model to estimate the range of association rates for protein complexes in a large-scale benchmark set. The cross-validation results show that, when an optimal threshold was selected, we can reach the best performance with specificity, precision, sensitivity and overall accuracy all higher than 70%. The quality of our cross-validation data has also been testified by further statistical analysis. Additionally, given an independent testing set, we can successfully predict the group of association rates for eight protein complexes out of ten. Finally, the analysis of failed cases suggests the future implementation of conformational dynamics into simulation can further improve model. Conclusions In summary, this study demonstrated that a new modeling framework that combines biophysical simulations with bioinformatics approaches is able to identify protein–protein interactions with low association rates from those with higher association rates. This method thereby can serve as a useful addition to a collection of existing experimental approaches that measure biomolecular recognition.

Let $(\mathcal{X}, d, \mu )$ ( X , d , μ ) be a non-homogeneous metric measure space, which satisfies the geometrically doubling condition and the upper doubling condition. In this paper, the authors prove the boundedness in $L^{p} (\mu )$ L p ( μ ) of mth-order commutators $\mathcal{M}^{\rho }_{b,m}$ M b , m ρ generated by the Log-Dini-type parametric Marcinkiewicz integral operators with RBMO functions on $(\mathcal{X}, d, \mu )$ ( X , d , μ ) . In addition, the boundedness of the mth-order commutators $\mathcal{M}^{\rho }_{b,m}$ M b , m ρ on Morrey spaces $M^{q}_{p}(\mu )$ M p q ( μ ) , $1< p \leq q< \infty $ 1 < p ≤ q < ∞ , is also obtained for the parameter $0 0 < ρ < ∞ .

We study the maximal operator on continuous functions in the setting of metric measure spaces. The boundedness is proven for metric measure spaces satisfying an annular decay property.

Background: Researchers frequently use the responses of individuals in clusters to measure cluster-level constructs. Examples are the use of student evaluations to measure teaching quality, or the use of employee ratings of organizational climate. In earlier research, Stapleton and Johnson (2019) provided advice for measuring cluster-level constructs based on a simulation study with inadvertently confounded design factors. We extended their simulation study using both Mplus and lavaan to reveal how their conclusions were dependent on their study conditions. Methods: We generated data sets from the so-called configural model and the simultaneous shared-and-configural model, both with and without nonzero residual variances at the cluster level. We fitted models to these data sets using different maximum likelihood estimation algorithms. Results: Stapleton and Johnson’s results were highly contingent on their confounded design factors. Convergence rates could be very different across algorithms, depending on whether between-level residual variances were zero in the population or in the fitted model. We discovered a worrying convergence issue with the default settings in Mplus, resulting in seemingly converged solutions that are actually not. Rejection rates of the normal-theory test statistic were as expected, while rejection rates of the scaled test statistic were seriously inflated in several conditions. Conclusions: The defaults in Mplus carry specific risks that are easily checked but not well advertised. Our results also shine a different light on earlier advice on the use of measurement models for shared factors.

The main aim of this paper is to evaluate the effects of installing speed-humps on the safety and mobility of the unconventional median U-turn, three-leg intersections, using the VISSIM microscopic traffic simulation model. The average delay was used as the measure of mobility, while the simulated conflict ratio based on the time-to-collision (TTC) surrogate safety measure, was used as an indicator of safety performance. The surrogate safety assessment model (SSAM) was applied to extract traffic conflicts, with TTC ≤ 1.50 s, which represent less severe conflicts, and TTC ≤ 0.50 s, that represent severe conflicts. The results show that hump speeds of 5.0 km/h significantly increase the intersection average delay by 109–448% and severely increase traffic conflicts, regardless of the hump location. While hump speeds of 20.0 km/h increase the average delay by 2–36%, based on the traffic conditions. Moreover, the 20.0 km/h humps could potentially reduce serve conflicts by about 11–20%.

In this paper, we study a class of nonlinear boundary value problems (BVPs) consisting of a more general class of sequential hybrid fractional differential equations (SHFDEs) together with a class of nonlinear boundary conditions at both end points of the domain. The nonlinear functions involved depend explicitly on the fractional derivatives. We study the necessary conditions required for the unique solution to the suggested BVP under the Caratheodory conditions using the technique of measure of noncompactness and degree theory. We also develop conditions for uniqueness results and also on stability analysis.

Multicriteria Decision Making (MCDM) has a huge role to play while ruling out one suitable alternative among a pool of alternatives governed by predefined multiple criteria. Some of the factors like imprecision, lack of information/data, etc., which are present in traditional MCDM processes have showcased their lack of efficiency and hence eventually it has paved the ways for the development of Fuzzy multicriteria decision making (FMCDM). In FMCDM processes, the decision makers can model most of the real-life phenomena by fuzzy information-based preferences. The availability of a wide literature on similarity measure (SM) emphasizes the vital role of SM of generalized fuzzy numbers (GFNs) to conduct accurate and precise decision making in FMCDM problems. Despite having few advantages, most of the existing approaches possessed a certain degree of counter intuitiveness and discrepancies. Thus, we have attempted to propose a novel SM for generalized trapezoidal fuzzy numbers (GTrFNs) which could deliberately overcome the impediments associated with the earlier existing approaches. Moreover, a meticulous comparative study with the existing approaches is also presented. This paper provides us with an improved method to obtain the similarity values between GTrFNs and the proposed SM consists of calculating the prominent features of fuzzy numbers such as expected value and variance. We use fourteen different sets of GTrFNs, to compare the fruition of the present approach with the existing SM approaches. Furthermore, to show the utility and applicability of our proposed measure, we illustrate few practical scenarios such as the launching of an electronic gadget by a company, a problem of medical diagnosis and finally, a proper anti-virus mask selection in light of the recent COVID-19 pandemic. The obtained results with our proposed SM, for the mentioned FMCDM problems, are analytically correct and they depict the efficiency and novelty of the present article.

Proteins are dynamic entities that intermittently depart from their ground-state structures and undergo conformational transitions as a critical part of their functions. Central to understanding such transitions are the structural rearrangements along the connecting pathway, where the transition state plays a special role. Using NMR relaxation at variable temperature and pressure to measure aromatic ring flips inside a protein core, we obtain information on the structure and thermodynamics of the transition state. We show that the isothermal compressibility coefficient of the transition state is similar to that of short-chain hydrocarbon liquids, implying extensive local unfolding of the protein. Our results further indicate that the required local volume expansions of the protein can occur not only with a net positive activation volume of the protein, as expected from previous studies, but also with zero activation volume by compaction of remote void volume, when averaged over the ensemble of states.

In this paper, we mainly investigate the existence, continuous dependence, and the optimal control for nonlocal fractional differential evolution equations of order (1,2) in Banach spaces. We define a competent definition of a mild solution. On this basis, we verify the well-posedness of the mild solution. Meanwhile, with a construction of Lagrange problem, we elaborate the existence of optimal pairs of the fractional evolution systems. The main tools are the fractional calculus, cosine family, multivalued analysis, measure of noncompactness method, and fixed point theorem. Finally, an example is propounded to illustrate the validity of our main results.

We discuss the concept of pseudo almost automorphic solution to fractional neutral differential equation with impulses using measure theory. Our principal results are obtained via semigroup theory and the fixed point theorem due to Krasnoselskii and their combination with the properties of measure theory. An example is provided to outline the thought developed on this work.

In practical applications of graph theory, indeterminacy factors always appear in graphs. Uncertain random graph was proposed via chance theory, in which some edges exist with degrees in probability measure and others exist with degrees in uncertain measure. This paper discusses the contributions of edges for connectivity of an uncertain random graph and proposes concepts about significance of edges, according to which edges are classified. In addition, this paper presents algorithms for calculating connectivity index and significance of edges of an uncertain random graph. Examples are given to illustrate algorithms and methods.

We present the results regarding the analysis of the fast X-ray/infrared (IR) variability of the black-hole transient MAXI J1535$-$571. The data studied in this work consist of two strictly simultaneous observations performed with XMM-Newton (X-rays: 0.7$-$10 keV), VLT/HAWK-I ($K_{\rm s}$ band, 2.2 $\mu$m) and VLT/VISIR ($M$ and $PAH2$_$2$ bands, 4.85 and 11.88 $\mu$m respectively). The cross-correlation function between the X-ray and near-IR light curves shows a strong asymmetric anti-correlation dip at positive lags. We detect a near-IR QPO (2.5 $\sigma$) at $2.07\pm0.09$ Hz simultaneously with an X-ray QPO at approximately the same frequency ($f_0=2.25\pm0.05$). From the cross-spectral analysis a lag consistent with zero was measured between the two oscillations. We also measure a significant correlation between the average near-IR and mid-IR fluxes during the second night, but find no correlation on short timescales. We discuss these results in terms of the two main scenarios for fast IR variability (hot inflow and jet powered by internal shocks). In both cases, our preliminary modelling suggests the presence of a misalignment between disk and jet., Comment: 12 pages, 7 figures. Accepted for publication in MNRAS

Recent technological advances, such as single-cell RNA sequencing (scRNA-seq), allow the measurement of gene expression profiles of individual cells. These expression profiles typically exhibit substantial variations even across seemingly homogeneous populations of cells. Two main different sources contribute to this measured variability: actual differences between the biological activity of the cells and technical measurement errors. Analysis of the biological variability may provide information about the underlying gene regulation of the cells, yet distinguishing it from the technical variability is a challenge. Here, we apply a recently developed computational method for measuring the global gene coordination level (GCL) to systematically study the cell-to-cell variability in numerical models of gene regulation. We simulate ‘biological variability’ by introducing heterogeneity in the underlying regulatory dynamic of different cells, while ‘technical variability’ is represented by stochastic measurement noise. We show that the GCL decreases for cohorts of cells with increased ‘biological variability’ only when it is originated from the interactions between the genes. Moreover, we find that the GCL can evaluate and compare—for cohorts with the same cell-to-cell variability—the ratio between the introduced biological and technical variability. Finally, we show that the GCL is robust against spurious correlations that originate from a small sample size or from the compositionality of the data. The presented methodology can be useful for future analysis of high-dimensional ecological and biochemical dynamics.

The search for alien life is hard because we do not know what signatures are unique to life. We show why complex molecules found in high abundance are universal biosignatures and demonstrate the first intrinsic experimentally tractable measure of molecular complexity, called the molecular assembly index (MA). To do this we calculate the complexity of several million molecules and validate that their complexity can be experimentally determined by mass spectrometry. This approach allows us to identify molecular biosignatures from a set of diverse samples from around the world, outer space, and the laboratory, demonstrating it is possible to build a life detection experiment based on MA that could be deployed to extraterrestrial locations, and used as a complexity scale to quantify constraints needed to direct prebiotically plausible processes in the laboratory. Such an approach is vital for finding life elsewhere in the universe or creating de-novo life in the lab., The search for life in the universe is difficult due to issues with defining signatures of living systems. Here, the authors present an approach based on the molecular assembly number and tandem mass spectrometry that allows identification of molecules produced by biological systems, and use it to identify biosignatures from a range of samples, including ones from outer space.

Both small-angle scattering methods, X-rays (SAXS) and neutrons (SANS) rank among the methods that facilitate the determination of the molar mass of nanoparticles. Using this measure, aggregation or degradation processes are easy to follow. Mono- and multichain assemblies of nanoparticles in solution could be resolved, swelling ratio can also be obtained. In this work, we present a method that allows extraction of additional information, including molecular weight, from a single scattering curve, even on a relative scale. The underlying theory and step-by-step procedure are described.

Diverse many-body systems, from soap bubbles to suspensions to polymers, learn and remember patterns in the drives that push them far from equilibrium. This learning may be leveraged for computation, memory, and engineering. Until now, many-body learning has been detected with thermodynamic properties, such as work absorption and strain. We progress beyond these macroscopic properties first defined for equilibrium contexts: We quantify statistical mechanical learning using representation learning, a machine-learning model in which information squeezes through a bottleneck. By calculating properties of the bottleneck, we measure four facets of many-body systems’ learning: classification ability, memory capacity, discrimination ability, and novelty detection. Numerical simulations of a classical spin glass illustrate our technique. This toolkit exposes self-organization that eludes detection by thermodynamic measures: Our toolkit more reliably and more precisely detects and quantifies learning by matter while providing a unifying framework for many-body learning.

We introduce a mathematical model, namely, ∗-fuzzy measure model for COVID-19 disease and consider some properties of ∗-fuzzy measure such as Lebesque–Radon–Nikodym theorem.

Guiding the working population to evenly explore the valuable areas which are not dominated by feasible solutions is important in the process of dealing with constrained multi-objective optimization problems (CMOPs). To this end, according to the angular distance and $ \ell_p $-norm, this paper introduces a new compound distance to measure individual's search diameter in the objective space. After that, we propose a constraint handling technique using the compound distance and embed it in evolutionary algorithm for solving CMOPs. In the proposed algorithm, the individuals with large search diameters in the valuable areas are given priority to be preserved. This can prevent the working population from getting stuck in the local areas and then find the optimal solutions for CMOPs more effectively. A series of numerical experiments show that the proposed algorithm has better performance and robustness than several existing state-of-the-art constrained multi-objective evolutionary algorithms in dealing with different CMOPs.

A class of the boundary value problem is investigated in this research work to prove the existence of solutions for the neutral fractional differential inclusions of Katugampola fractional derivative which involves retarded and advanced arguments. New results are obtained in this paper based on the Kuratowski measure of noncompactness for the suggested inclusion neutral system for the first time. On the one hand, this research concerns the set-valued analogue of Mönch fixed point theorem combined with the measure of noncompactness technique in which the right-hand side is convex valued. On the other hand, the nonconvex case is discussed via Covitz and Nadler fixed point theorem. An illustrative example is provided to apply and validate our obtained results.

We analyze networks of functional correlations between brain regions to identify changes in their structure caused by Attention Deficit Hyperactivity Disorder (adhd). We express the task for finding changes as a network anomaly detection problem on temporal networks. We propose the use of a curvature measure based on the Forman–Ricci curvature, which expresses higher-order correlations among two connected nodes. Our theoretical result on comparing this Forman–Ricci curvature with another well-known notion of network curvature, namely the Ollivier–Ricci curvature, lends further justification to the assertions that these two notions of network curvatures are not well correlated and therefore one of these curvature measures cannot be used as an universal substitute for the other measure. Our experimental results indicate nine critical edges whose curvature differs dramatically in brains of adhd patients compared to healthy brains. The importance of these edges is supported by existing neuroscience evidence. We demonstrate that comparative analysis of curvature identifies changes that more traditional approaches, for example analysis of edge weights, would not be able to identify.

Intersections appear where one street crosses another, acting as fundamental nodes embedded in the network of urban public space. Though discussed in configurational and perceptive studies, limited attention has been paid to the morphological aspects of intersections. This study proposes and tested a new approach to modeling the urban intersection form. First, effective cylinder was introduced to define the related space for each intersection based on its scale. Second, a set of morphological indicators were presented to measure the physical properties of the intersection form. Third, the affinity propagation algorithm was used to examine the patterns of intersection form. Using the Old City of Nanjing, China as the study area, 844 intersections were analyzed to test this new method. As a result, we were able to classify the intersections into eight types. This study shows that the intersection can be modelled as a volumetric and integral spatial unit of urban form, which may demand more attention from urban designers and architects in the future for shaping the built environment. The quantitative nature of our method could also open more possibilities for intersection-based studies.