Arbitrary Joint Research Articles

Analytical Method for Segmental Tunnel Linings Reinforced by Secondary Lining Considering Interfacial Slippage and Detachment

The reinforcement of shield tunnels with secondary linings is a widely used method to enhance the overall rigidity of tunnels; therefore, ensuring tunnel safety during construction and operational periods. According to a new composite curved Euler beam theory, an analytical method will be proposed to analyze a shield tunnel that is reinforced by a secondary lining, in which the radial joints and the interaction between the segmental lining and the surrounding soil will be simulated by a series of concentrated and distributed springs, respectively. In contrast to the radial rigid connection that was assumed in previous studies, radial detachment and tangential slippage between the segmental and secondary linings will be allowed. The solutions for the internal forces and deformations will be derived using the state-space method with arbitrary loads and joint distributions. In addition, the proposed method will be extended to cases with partial reinforcement that have a segment of secondary lining and a reinforcement connected by bolts. The proposed method will be validated using finite element numerical simulations. In addition, the variations in the internal forces and deformation for the soil reaction stiffness under different joint and interfacial stiffnesses will be examined. The results indicate that the internal forces and deformations of the linings decreased with the increase of soil reaction spring stiffness, and the interfacial radial spring stiffness had a more significant influence on the axial force transfer between the linings.

Stability and tail behavior of redundancy systems with processor sharing

We investigate the stability condition for redundancy-d systems where each of the servers follows a processor-sharing (PS) discipline. We allow for generally distributed job sizes, with possible dependence among the d replica sizes being governed by an arbitrary joint distribution. We establish that for homogeneous servers the stability condition for the associated fluid-limit model is characterized by the expectation of the minimum of d replica sizes being less than the mean interarrival time per server. In the special case of identical replicas, the stability condition is insensitive to the job size distribution given its mean, and the stability threshold is inversely proportional to the number of replicas. In the special case of i.i.d. replicas, the stability threshold decreases (increases) in the number of replicas for job size distributions that are NBU (NWU). We also discuss the extension to heterogeneous servers.For heavy-tailed job sizes we characterize the tail behavior of the response time distribution. In particular, for regularly varying job sizes with tail index −ν it is shown that the tail index of the response time equals −ν and −dν for identical and i.i.d. replicas, respectively.

Bodyweight distribution between limbs, muscle strength, and proprioception in traumatic transtibial amputees: a cross-sectional study

OBJECTIVES:To evaluate how transtibial amputation (TT) affects bodyweight distribution, voluntary knee joint position sense (JPS), and quadriceps (QUA) and hamstrings (HAM) strength in prosthetized patients.METHODS:Only TT patients who had been prosthetized for more than one year were included, and an age-paired able-bodied group was used as control. The participants stood on force plates with their eyes open to measure bodyweight distribution between the limbs. Knee voluntary JPS was assessed by actively reproducing a set of given arbitrary joint angles using a video analysis approach, and QUA and HAM strength were assessed isometrically with a hand-held dynamometer.RESULTS:Sixteen TT subjects (age: 39.4±4.8 years) and sixteen age-paired control subjects (age: 38.4±4.3 years) participated in the study. The amputees supported their bodyweight majorly on the sound limb (54.8±8.3%, p<0.001). The proprioceptive performance was similar between the amputated (absolute error (AE): 2.2±1.6°, variable error (VE): 1.9±1.6°, constant error (CE): -0.7±2.0°) and non-amputated limbs (AE: 2.6±0.9°, VE: 2.1±0.9°, CE: 0.02±2.3°), and was not different from that of control subjects (AE: 2.0±0.9°, VE: 1.4±0.4°, CE: -1.1±1.7°). There was a considerable weakness of the QUA and HAM in the amputated limb compared with the sound limb and control subjects (p<0.001 both).CONCLUSIONS:The asymmetric bodyweight distribution in the transtibial amputees was not accompanied by a reduction in knee proprioception. There was significant weakness in the amputated limb, which could be a potential issue when designing rehabilitation programs.

First-order linear differential equations whose data are complex random variables: Probabilistic solution and stability analysis via densities

&lt;abstract&gt;&lt;p&gt;Random initial value problems to non-homogeneous first-order linear differential equations with complex coefficients are probabilistically solved by computing the first probability density of the solution. For the sake of generality, coefficients and initial condition are assumed to be absolutely continuous complex random variables with an arbitrary joint probability density function. The probability of stability, as well as the density of the equilibrium point, are explicitly determined. The Random Variable Transformation technique is extensively utilized to conduct the overall analysis. Several examples are included to illustrate all the theoretical findings.&lt;/p&gt;&lt;/abstract&gt;

Quantification of Joint Space Width Difference on Radiography Via Phase-Only Correlation (POC) Analysis: a Phantom Study Comparing with Various Tomographical Modalities Using Conventional Margin-Contouring.

Several visual scoring methods are currently used to assess progression of rheumatoid arthritis (RA) on radiography. However, they are limited by its subjectivity and insufficient sensitivity. We have developed an original measurement system which uses a technique called phase-only correlation (POC). The purpose of this study is to validate the system by using a phantom simulating the joint of RA patients.A micrometer measurement apparatus that can adjust arbitrary joint space width (JSW) in a phantom joint was developed to define true JSW. The phantom was scanned with radiography, 320 multi detector CT (MDCT), high-resolution peripheral quantitative CT (HR-pQCT), cone beam CT (CBCT), and tomosynthesis. The width was adjusted to the average size of a women's metacarpophalangeal joint, from 1.2 to 2.2mm with increments of 0.1mm and 0.01mm. Radiographical images were analyzed by the POC-based system and manual method, and images from various tomographical modalities were measured via the automatic margin detection method. Correlation coefficients between true JSW difference and measured JSW difference were all strong at 0.1mm intervals with radiography (POC-based system and manual method), CBCT, 320MDCT, HR-pQCT, and tomosynthesis. At 0.01mm intervals, radiography (POC-based system), 320MDCT, and HR-pQCT had strong correlations, while radiography (manual method) and CBCT had low correlations, and tomosynthesis had no statistically significant correlation. The smallest detectable changes for radiography (POC-based system), radiography (manual method), 320MDCT, HR-pQCT, CBCT, and tomosynthesis were 0.020mm, 0.041mm, 0.076mm, 0.077mm, 0.057mm, and 0.087mm, respectively. We conclude that radiography analyzed with the POC-based system might sensitively detect minute joint space changes of the finger joint.

Information-disturbance trade-off in generalized entanglement swapping

We study information-disturbance trade-off in generalized entanglement swapping protocols wherein starting from Bell pairs $\left(1,2\right)$ and $\left(3,4\right)$, one performs an arbitrary joint measurement on $\left(2,3\right)$, so that $\left(1,4\right)$ now becomes correlated. We obtain trade-off inequalities between information gain in correlations of $\left(1,4\right)$ and residual information in correlations of $\left(1,2\right)$ and $\left(3,4\right)$ respectively and argue that information contained in correlations (information) is conserved if each inequality is an equality. We show that information is conserved for a maximally entangled measurement but is not conserved for any other complete orthogonal measurement and Bell measurement mixed with white noise. However, rather surprisingly, we find that information is conserved for rank-two Bell diagonal measurements, although such measurements do not conserve entanglement. We also show that a separable measurement on $\left(2,3\right)$ can conserve information, even if, as in our example, the post-measurement states of all three pairs $\left(1,2\right)$, $\left(3,4\right)$, and $\left(1,4\right)$ become separable. This implies correlations from an entangled pair can be transferred to separable pairs in nontrivial ways so that no $information$ is lost in the process.

Intertemporal Pricing via Nonparametric Estimation: Integrating Reference Effects and Consumer Heterogeneity

We consider intertemporal pricing in the presence of reference effects and consumer heterogeneity. Our research question encompasses how to estimate heterogeneous consumer reference effects from data and how to efficiently compute the optimal pricing policy. Understanding reference effects is essential for designing pricing policies in modern retailing. Our work contributes to this area by further incorporating consumer heterogeneity under arbitrary distributions. We propose a demand model that allows arbitrary joint distributions of valuations, responsiveness to prices, and responsiveness to reference prices among consumers. To learn consumer heterogeneity from transaction data, we use a nonparametric estimation method. We formulate the pricing optimization as an infinite horizon dynamic programming problem and solve it by applying a modified policy iteration algorithm. We investigate the structure of optimal pricing policies and prove the sub-optimality of constant pricing policies even when all consumers are loss-averse according to the classical definition. Our numerical studies further show that our estimation and optimization framework improves the expected revenue of retailers via accounting for heterogeneity. We validate our model using real data from JD.com, a large E-commerce retailer, and find empirical evidence of consumer heterogeneity. In practice, ignoring consumer heterogeneity may lead to a significant loss of revenue. Furthermore, the existence of heterogeneous reference effects offers a strong motive for promotions and price fluctuations.

Joint measurability structures realizable with qubit measurements: Incompatibility via marginal surgery

Measurements in quantum theory exhibit incompatibility, i.e., they can fail to be jointly measurable. An intuitive way to represent the (in)compatibility relations among a set of measurements is via a hypergraph representing their joint measurability structure: its vertices represent measurements and its hyperedges represent (all and only) subsets of compatible measurements. Projective measurements in quantum theory realize (all and only) joint measurability structures that are graphs. On the other hand, general measurements represented by positive operator-valued measures (POVMs) can realize arbitrary joint measurability structures. Here we explore the scope of joint measurability structures realizable with qubit POVMs. We develop a technique that we term marginal surgery to obtain nontrivial joint measurability structures starting from a set of compatible measurements. We show explicit examples of marginal surgery on a special set of qubit POVMs to construct joint measurability structures such as N-cycle and N-Specker scenarios for any integer N≥3. We also show the realizability of various joint measurability structures with N∈{4,5,6} vertices. In particular, we show that all possible joint measurability structures with N=4 vertices are realizable. We conjecture that all joint measurability structures are realizable with qubit POVMs. This contrasts with the unbounded dimension required in R. Kunjwal et al. [Phys. Rev. A 89, 052126 (2014)]. Our results also render this previous construction maximally efficient in terms of the required Hilbert space dimension. We also obtain a sufficient condition for the joint measurability of any set of binary qubit POVMs which powers many of our results and should be of independent interest.25 MoreReceived 13 March 2020Revised 4 August 2020Accepted 5 October 2020DOI:https://doi.org/10.1103/PhysRevResearch.2.043147Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasQuantum information processingQuantum Information

Networks with degree–degree correlations are special cases of the edge-coloured random graph

Abstract In complex networks, the degrees of adjacent nodes may often appear dependent—which presents a modelling challenge. We present a working framework for studying networks with an arbitrary joint distribution for the degrees of adjacent nodes by showing that such networks are a special case of edge-coloured random graphs. We use this mapping to study bond percolation in networks with assortative mixing and show that, unlike in networks with independent degrees, the sizes of connected components may feature unexpected sensitivity to perturbations in the degree distribution. The results also indicate that degree–degree dependencies may feature a vanishing percolation threshold even when the second moment of the degree distribution is finite. These results may be used to design artificial networks that efficiently withstand link failures and indicate the possibility of super spreading in networks without clearly distinct hubs.

An efficient stress and deformation model for arbitrary elastic-perfectly plastic adhesive lap joints

The present work introduces an efficient general sandwich-type model that allows for stress analyses of arbitrarily shaped adhesive lap joints with composite adherends with an elastic-perfectly plastic adhesive layer obeying the von Mises yield criterion. For the analysis of the nonlinear adhesive layer the plastic zone approach is applied. The model is applicable to various joint configurations, as e.g. single-lap joints, T-joints, L-joints, reinforcement patches or balanced double-lap joints. It considers only the overlap region of the joint with any combination of section forces and moments and is therefore denoted as sandwich-type model. First Order Shear Deformation Theory is employed to account for shear deformations of the composite adherends. Bending extension coupling is covered. The adhesive layer is assumed to be very thin compared to the thickness of the adherends and the shear and peel stress distributions are assumed as constant through the bondline thickness. To allow for a comparison of several different structural situations a two-dimensional Finite Element model of the overlap region is used. The stress distributions predicted by the present model are in good agreement with the results of detailed Finite Element analyses.

Portfolio optimization with two coherent risk measures

We provide analytical results for a static portfolio optimization problem with two coherent risk measures. The use of two risk measures is motivated by joint decision-making for portfolio selection where the risk perception of the portfolio manager is of primary concern, hence, it appears in the objective function, and the risk perception of an external authority needs to be taken into account as well, which appears in the form of a risk constraint. The problem covers the risk minimization problem with an expected return constraint and the expected return maximization problem with a risk constraint, as special cases. For the general case of an arbitrary joint distribution for the asset returns, under certain conditions, we characterize the optimal portfolio as the optimal Lagrange multiplier associated to an equality-constrained dual problem. Then, we consider the special case of Gaussian returns for which it is possible to identify all cases where an optimal solution exists and to give an explicit formula for the optimal portfolio whenever it exists.

Analytical solution for a jointed shield tunnel lining reinforced by secondary linings

Based on the curved Euler beam theory, an analytical solution is proposed for a jointed shield tunnel lining reinforced by secondary linings, which can be idealized as a partial-interaction composite curved beam. The effect of joints and the interaction between linings and surrounding soils are simulated by a series of linear mechanical springs and Winkler type springs, respectively. The solutions for the internal forces and deformations can be derived by the state space method for conditions involving arbitrary loadings and variable joint distributions. The capability of the proposed analytical solution is verified by the finite element method and other existing analytical solutions. Furthermore, the effect of bending-direction-dependent joint stiffness is discussed, and the variation trends of internal forces and deformations, varying with soil reaction stiffness, are examined under different joint stiffness conditions.

Topological junction states and their crystalline network in systems with chiral symmetry: Application to graphene nanoribbons

We develop a general theoretical framework based on $Z$ classification to count the number of topological bound states at a junction of chiral-symmetric one-dimensional systems. The formulation applies to general multiway junctions composed of an arbitrary number of channels and an arbitrary joint structure. By using the formula, we calculate the zero-energy bound states in various types of two-way and three-way junctions of semiconducting graphene nanoribbons. We then consider periodic two-dimensional networks of graphene nanoribbons and show that the topological junction states form isolated energy bands inside the bulk energy gap, which can be viewed as a two-dimensional crystal of the effective atoms. Depending on the $Z$ number of a single junction, we have a different set of effective atomic orbitals, resulting in various types of nanoscale metamaterials, which are often accompanied by flat bands. The system would provide an ideal platform for quantum simulator to emulate a strongly-interacting fermion system on various types of lattices.

Wandering subspaces and inner operators

A noncommutative domain Bφ(H)⊂B(H)n generated by the certain class of n-tuples φ=(φ1,⋯,φn) of formal power series in noncommutative indeterminates Z1,⋯,Zn, admits a universal model MZ=(MZ1,⋯, MZn), acting on a model space H2(φ). In this paper, we provide an explicit description of the wandering subspace W(Q)=Q⊖∑i=1n(MZi⊗IG)Q, where Q is an arbitrary joint invariant subspace under the operators MZ1⊗IG,⋯,MZn⊗IG. Moreover, we also provide a transfer function type characterization of the MZ-inner operators. This extends to the noncommutative setting the corresponding result obtained by Olofsson [7], [8] (when n=1) and by Eschmeier [3] in the multivariable commutative case.

Feedback Control to a Static Target Angle in the Middle Finger Metacarpophalangeal Joint Using Functional Electrical Stimulation

ABSTRACT In this study, we proposed a feedback control method for a finger joint angle, which has been considered difficult, via functional electrical stimulation using the surface electrode method. If detailed finger movement can be realized by functional electrical stimulation using the surface electrode method, this can be applied in various situations such as musical instrument performance, daily movements, and so on. The control method was designed based on the following three proposals. First, the non-linear relationship between the electrical stimulation intensity and joint angle change was absorbed by constructing polygonal line regression models of the relationship between the electrical stimulation intensity reaching each muscle and the flexion and extension force of the middle finger’s metacarpophalangeal joint. Second, the concepts of the muscle antagonist ratio and muscle antagonist sum were adopted to translate the input/output relationship to a single-input/single-output system while maintaining joint stiffness. Finally, the proportional–integral–derivative control parameters were determined using the Ziegler–Nichols ultimate sensitivity method. Using the control method based on the aforementioned three proposals, we conducted feedback control experiments for three static target angles in the middle finger’s metacarpophalangeal joint. Results show that at all target angles, greater than 80% of the participants were able to control the joint with nearly no error. Therefore, the control method proposed in this study can be used to control an arbitrary static target joint angle with high accuracy via functional electrical stimulation.

Rate-Memory Trade-Off for Caching and Delivery of Correlated Sources

This paper studies the fundamental limits of content delivery in a cache-aided broadcast network for correlated content generated by a discrete memoryless source with arbitrary joint distribution. Each receiver is equipped with a cache of equal capacity, and the requested files are delivered over a shared error-free broadcast link. A class of achievable correlation-aware schemes based on a two-step source coding approach is proposed. Library files are first compressed, and then cached and delivered using a combination of multiple-request caching schemes that are agnostic to the content correlations. The first step uses Gray-Wyner source coding to represent the library via private descriptions and descriptions that are common to more than one file. The second step then becomes a multiple-request caching problem, where the demand structure is dictated by the configuration of the compressed library, and it is interesting in its own right. The performance of the proposed two-step scheme is evaluated by comparing its achievable rate with a lower bound on the optimal peak and average rate-memory trade-offs in a two-file multiple-receiver network, and in a three-file two-receiver network. Specifically, in a network with two files and two receivers, the achievable rate matches the lower bound for a significant memory regime and it is within half of the conditional entropy of files for all other memory values. In the three-file two-receiver network, the two-step strategy achieves the lower bound for large cache capacities, and it is within half of the joint entropy of two of the sources conditioned on the third one for all other cache sizes.

Modeling and simulation study of the stoichiometric niche space and niche overlap based on the copula method

To qualify niche space and niche overlap, the current methods are based on a strict assumption of the normal distribution and restrict dependence to the linear structure between resource axes. In this study, we propose a new method for measuring the stoichiometric niche space and niche overlap based on copula theory. Our method does not require the resource axes to obey the multivariate normal distribution and only assumes that each dimension of resource availability follows a one-dimensional normal distribution. Based on the dependence structure presented by the three resource axes, an appropriate copula is selected to couple the normal assumptions and thus determine a joint distribution that fits the carbon, nitrogen and phosphorus concentration data. Additional simulation studies were conducted to calculate niche space and niche overlap. We applied our method to qualify the stoichiometric niche space and niche overlap between seven grassland plants in Inner Mongolia, North China. Our results demonstrate that, except for a positive correlation, symmetrical tail correlations existed between nitrogen and phosphorus concentrations, which had a significant influence on the shape of the niche space. The new method presented in our work extends types of joint distribution fitting resource axes from a multivariate normal distribution to an arbitrary joint distribution determined by copulas and normal margins, and it has the advantage of describing the complex dependence between resource axes.

Analytical approach for circular‐jointed shield tunnel lining based on the state space method

SummaryThis paper presents a new analytical solution to the circular segmental tunnel lining subjected to overburden and surrounding earth pressures. The governing equations are derived by adopting the curved Euler beam theory and the principle of minimum potential energy. Based on the state space method, the displacements and the relevant energy‐conjugated internal forces are treated as the fundamental unknown state vector and can be obtained by solving the state function. The inter‐segment joints on the lining are modeled by a set of linear springs, including shear, compression, and rotation. The presented method allows for the arbitrary distribution of the segmented joints and loads along the circumferential direction. The most striking advantages of the proposed method include the rigid body displacement treatment, lining‐displacement‐dependent soil reaction, and internal force direction dependency of the joint stiffness. Using this method, the displacements and internal forces of the entire lining can be obtained conveniently and simultaneously under the arbitrary loading and joint distribution conditions. The verification of the analytical solutions is provided by several examples.

Analysis of approximations of GUM supplement 2 based non-Gaussian PDFs of measurement models with Rosenblatt Gaussian transformation mappings

In scientific metrology practise the application of Monte Carlo simulations with the aid of the GUM Supplement 2 (GS2) technique for performing multivariate uncertainty analyses is now more prevalent, however a key remaining challenge for metrologists in many laboratories is the implicit assumption of Gaussian characteristics for summarizing and analysing measurement model results. Whilst non-Gaussian probability density functions (PDFs) may result from Monte Carlo simulations when the GS2 is applied for more complex non-linear measurement models, in practice results are typically only reported in terms of multivariate expected and covariance values. Due to this limitation the measurement model PDF summary is implicitly restricted to a multivariate Gaussian PDF in the absence of additional higher order statistics (HOS) information. In this paper an earlier classical theoretical result by Rosenblatt that allows for an arbitrary multivariate joint distribution function to be transformed into an equivalent system of Gaussian distributions with mapped variables is revisited. Numerical simulations are performed in order to analyse and compare the accuracy of the equivalent Gaussian system of mapped random variables for approximating a measurement model’s PDF with that of an exact non-Gaussian PDF that is obtained with a GS2 Monte Carlo statistical simulation. Results obtained from the investigation indicate that a Rosenblatt transformation offers a convenient mechanism to utilize just the joint PDF obtained from the GS2 data in order to both sample points from a non-Gaussian distribution, and also in addition which allows for a simple two-dimensional approach to estimate coupled uncertainties of random variables residing in higher dimensions using conditional densities without the need for determining parametric based copulas.

Magnetometer-free inertial motion tracking of arbitrary joints with range of motion constraints

In motion tracking of connected multi-body systems, Inertial Measurement Units (IMUs) are used in a wide variety of applications, since they provide a low-cost easy-to-use method for orientation estimation. However, in indoor environments or near ferromagnetic material, the magnetic field is inhomogeneous, which limits the accuracy of tracking algorithms using magnetometers. Methods that use only accelerometers and gyroscopes on the other hand yield no information on the absolute heading of the tracked object. For objects connected by rotational joints with range of motion constraints, a method is proposed that provides a magnetometer-free, long-term stable relative orientation estimate based on a non-linear, window-based cost function. The method can be used for real-time estimation as well as post-processing. It is validated experimentally with a mechanical joint and compared to other methods that are commonly used in motion tracking. It is shown that for the used test object, the proposed method yields the best results with a total angle error of less than 4◦ for all experiments.