Nonlinear Measurement Function in the Ensemble Kalman Filter

ABSTRACT The optimal Kalman gain was analyzed in a rigorous statistical framework. Emphasis was placed on a comprehensive understanding and interpretation of the current algorithm, especially when the measurement function is nonlinear. It is argued that when the measurement function is nonlinear, the current ensemble Kalman Filter algorithm seems to contain implicit assumptions： the forecast of the measurement function is unbiased or the nonlinear measurement function is linearized. While the forecast of the model state is assumed to be unbiased, the two assumptions are actually equivalent. On the above basis, we present two modified Kalman gain algorithms. Compared to the current Kalman gain algorithm, the modified ones remove the above assumptions, thereby leading to smaller estimated errors. This outcome was confirmed experimentally, in which we used the simple Lorenz 3-component model as the test-bed. It was found that in such a simple nonlinear dynamical system, the modified Kalman gain can perform better than the current one. However, the application of the modified schemes to realistic models involving nonlinear measurement functions needs to be further investigated.

Determination of the degree 120 time-variable gravity field in the Sichuan-Yunnan region using Slepian functions and terrestrial measurements

The terrestrial time-variable gravity measurements are characterized by a high signal-to-noise ratio and sensitivity to the sources of mass change in the Earth's crust.These gravity data have many applications,such as surface deformation,groundwater storage changes,and mass migration before and after earthquakes.Based on repeated terrestrial gravity measurements at 198 gravity stations in the Sichuan-Yunnan region(SYR)from 2015 to 2017,we determine a time series of degree 120 gravity fields using the localized spherical harmonic(Slepian)basis functions.Our results show that adopting the first 6 Slepian basis functions is sufficient for effective localized Slepian modeling in the SYR.The differences between two gravity campaigns at the same time of year show an obvious correlation with tectonic features.The degree 120 timevariable gravity models presented in this paper will benefit the study of the regional mass migration inside the crust of the SYR and supplement the existing geophysical models for the China Seismic Experimental Site.

Establishing minimum clinically important difference values for the Patient-Reported Outcomes Measurement Information System Physical Function, hip disability and osteoarthritis outcome score for joint reconstruction, and knee injury and osteoarthritis out

AIM To establish minimum clinically important difference(MCID) for measurements in an orthopaedic patient population with joint disorders.METHODS Adult patients aged 18 years and older seeking care for joint conditions at an orthopaedic clinic took the Patient-Reported Outcomes Measurement Information System Physical Function(PROMIS~? PF) computerized adaptive test(CAT), hip disability and osteoarthritis outcome score for joint reconstruction(HOOS JR), and the knee injury and osteoarthritis outcome score for joint reconstruction(KOOS JR) from February 2014 to April 2017. MCIDs were calculated using anchorbased and distribution-based methods. Patient reports of meaningful change in function since their first clinic encounter were used as an anchor.RESULTS There were 2226 patients who participated with a mean age of 61.16(SD = 12.84) years, 41.6% male, and 89.7% Caucasian. Mean change ranged from 7.29 to 8.41 for the PROMIS~? PF CAT, from 14.81 to 19.68 for the HOOS JR, and from 14.51 to 18.85 for the KOOS JR. ROC cut-offs ranged from 1.97-8.18 for the PF CAT, 6.33-43.36 for the HOOS JR, and 2.21-8.16 for the KOOS JR. Distribution-based methods estimated MCID values ranging from 2.45 to 21.55 for the PROMIS~? PF CAT; from 3.90 to 43.61 for the HOOS JR, and from 3.98 to 40.67 for the KOOS JR. The median MCID value in the range was similar to the mean change score for each measure and was 7.9 for the PF CAT, 18.0 for the HOOS JR, and 15.1 for the KOOS JR.CONCLUSION This is the first comprehensive study providing a wide range of MCIDs for the PROMIS? PF, HOOS JR, and KOOS JR in orthopaedic patients with joint ailments.

Scattering of Geometric Algebra Wave Functions and Collapse in Measurements

The research considers wavelike objects that are elements of even subalgebra of geometric algebra in three dimensions. The used formalism particularly eliminates long existing confusion about the reasons behind the appearance of the imaginary unit in quantum mechanics and introduces clear definition of wave functions. When a wave function acts through the Hopf fibration on a localized geometric algebra element, that is executing a measurement, the result can be named as “collapse” of the wave function.

Clinical value of predictive models based on liver stiffness measurement in predicting liver reserve function of compensated chronic liver disease

BACKGROUND Assessment of liver reserve function(LRF)is essential for predicting the prognosis of patients with chronic liver disease(CLD)and determines the extent of liver resection in patients with hepatocellular carcinoma.AIM To establish noninvasive models for LRF assessment based on liver stiffness measurement(LSM)and to evaluate their clinical performance.METHODS A total of 360 patients with compensated CLD were retrospectively analyzed as the training cohort.The new predictive models were established through logistic regression analysis and were validated internally in a prospective cohort(132 patients).RESULTS Our study defined indocyanine green retention rate at 15 min(ICGR15)≥10%as mildly impaired LRF and ICGR15≥20%as severely impaired LRF.We constructed predictive models of LRF,named the mLPaM and sLPaM,which involved only LSM,prothrombin time international normalized ratio to albumin ratio(PTAR),age and model for end-stage liver disease(MELD).The area under the curve of the mLPaM model(0.855,0.872,respectively)and sLPaM model(0.869,0.876,respectively)were higher than that of the methods for MELD,albumin bilirubin grade and PTAR in the two cohorts,and their sensitivity and negative predictive value were the highest among these methods in the training cohort.In addition,the new models showed good sensitivity and accuracy for the diagnosis of LRF impairment in the validation cohort.CONCLUSION The new models had a good predictive performance for LRF and could replace the indocyanine green(ICG)clearance test,especially in patients who are unable to undergo ICG testing.

Study on the Effect of Repetitive Peripheral Magnetic Stimulation Combined with Conventional Rehabilitation Measures on Shoulder Dysfunction in Early Stroke

Objective:To study the effect of repetitive peripheral magnetic stimulation(rPMS)combined with conventional rehabilitation measures on shoulder dysfunction in early stroke.Methods:60 patients with shoulder dysfunction in early stroke were selected,and all of them were admitted to our hospital from August 2021 to August 2023.The patients were randomly grouped into a control group(conventional rehabilitation measures intervention,30 cases)and an intervention group(rPMS and conventional rehabilitation measures intervention,30 cases)according to the lottery method.The pain scores,shoulder mobility,and motor function scores of the two groups were compared.Results:The pain score was lower in the intervention group,and the shoulder mobility and motor function scores were higher in the intervention group(P<0.05)as compared to that of the control group.Conclusion:The effect of combining rPMS and conventional rehabilitation measures in treating shoulder dysfunction in early stroke was remarkable and should be popularized.

Hardness Measurement of (TiB_2-TiAl)/TiAl Symmetrically Function Gradient Materials

( TiB2-TiAl)/TiAl symmetrically function gradient materials ( FGM) were prepared by spark plasma sintering ( SPS). Owing to the difference, of the thermal expansion coefficients between TiB2 and TiAl, a compressive surface stress was introduced to the FGM fry the thermal expansion mismatch. The hardness values of the uniform materials and the FGM were tested, respectively. For the FGM with a compressive surface stress, hardness is obviously superior to that of the uniform material. When the FGM was subjected to heat treatment, the hardness decreased due to a partial relaxation of the compressive surface stress.

Scheme for direct measurement of Wigner function in two-mode cavity QED driven by classical fields

We propose a scheme for the direct measurement of Wigner function in two-mode cavity QED. The atoms are sent to resonantly interact with two orthogonally polarized cavity modes in the presence of strong classical field. The probability of measuring the atom in the ground state directly gives the useful information of the cavity field. This method can be used for quantum non-demolition measurement of the photon number.

Multiple Scattering Between Adjacent Sound Sources in Head-Related Transfer Function Measurement System

To accelerate head-related transfer functions(HRTFs)measurement,two or more independent sound sources are usually employed in the measurement system.However,the multiple scattering between adjacent sound sources may influence the accuracy of measurement.On the other hand,the directivity of sound source could induce measurement error.Therefore,a model consisting of two spherical sound sources with approximate omni-directivity and a rigid-spherical head is proposed to evaluate the errors in HRTF measurement caused by multiple scattering between sources.An example of analysis using multipole re-expansion indicates that the error of ipsilateral HRTFs are within the bound of±1.0 dB below a frequency of 20 kHz,provided that the sound source radius does not exceed 0.025 m,the source distance relative to head center is not less than 0.5 m,and the angular interval between two adjacent sources is not less than 20 degrees.Similar conclusions under different conditions can also be analyzed and discussed by using this calculation method.Furthermore,the results are verified by measurements of HRTFs for a rigid sphere and a KEMAR artificial head.

Functional safety verification and performance measurement of train-train communication link

The short-range wireless communication technology has advanced considerably and provides the feasibility of train-train(T2T)communication link in the communication-based train control system.The introduction of the T2T link would reduce the headway and improve operational efficiency.Formal methods are system design techniques that use rigorously specified mathematical models to ensure all behaviors work as expected.And it is exactly the functional safety verification needed.Therefore,to deal with the functional safety verification of the T2T link,an untimed colored petri net model is first constructed.Secondly,the verification process is performed.Conclusions can be drawn from the state space report and the computation tree logic queries.Lastly,the model is parameterized,and then data log files are obtained for further performance measurement.Results show that the proposed criteria are satisfied and there are no defects in the basic design requirements.The transmission delay has considered the reconnection,transmission errors and the interruption.The probability of the delay lower than 150 ms accounts for 98.106%,which meets the specification and the previous field test.

Selection of a Minimal Complexity of a Transformation Functions of Pressure Sensors with a Maintained Given Measurement Accuracy

For series manufacture of pressure sensors, stage of technological tests is performed, related to a definition of the manufacturing accuracy of the sensors. Technological test plan of pressure sensors involves testing the sensors on certain fixed temperature and pressure points available in the table. According to a test results, we determine transformation function mathematical model coefficients of sensors and accordance by the claimed accuracy class, of the manufactured sensors. The cost of pressure sensors mostly depends on the cost of this step and determined by the complexity of the used transformation function model. The analysis of a contemporary works associated with the choice of transformation functions for smart pressure sensors. A new proposed indicator of model complexity of a sensor transformation function. In details shown features of the complexity indicator use and given an example. In the article was set and resolved the task to reduce the cost of the tests for commercially available sensors, by reducing the number of temperature points, without compromising the accuracy of the sensor measurement ability.

Functions of “Marriage” in Shakespeare's Measure for Measure

Marriage is usually associated with happiness and harmony. But in Shakespear's Measure for Measure, it seems it is infused with power of law. Is it a clear-cut punishment or reward? Its qualities revolve around the individual situations in which it occurs, which is interpreted and deployed by characters in the play in different ways.

SDNMS: A Software Defined Network Measurement System for NFV Networks

As a promising technology to completely transform how we architect, deploy, operate and manage various networks, software-based Network Function Virtualization(NFV) enables hardware-independent, flexible, fast and efficient network service provision. With the increasing popularity of NFV paradigm, the Internet has also transformed to be a hybrid environment where NFV-based network entities coexist with traditional network devices. To facilitate our understanding, design, evaluate and manage of such novel network environment, there is a great need for a new NFV-compatible network measurement system which is still in absent so far. To bridge this gap, a system, named Software Defined Network Measurement System(SDNMS), is presented in this paper. Firstly, the architecture of SDNMS is proposed. In this architecture, a formal method to describe the working mode of the network measurement is defined. This method can also be utilized to generate a network measurement middle box(NMMB) in a specific location of the NFV network according to the customized description file, and to flexibly deploy the network measurement function. Secondly, the technology of virtual network measurement function(VNMF) combined with LXC is studied to form NMMB function. Thirdly, a control method is presented to control the start, stop, and update NMMB to form a specific network measurement system function. Finally, a prototype of SDNMS with network monitoring function to monitor network performance anomalies and locate faults is introduced. Experimental results have shown that SDNMS architecture and related technologies are feasible and effective to deploy and control network measurement functions in NFV networks. We hope SDNMS could provide a new method for practitioners to conduct network management and research at the age of NFV.

The pig as a preclinical traumatic brain injury model:current models,functional outcome measures,and translational detection strategies

Traumatic brain injury(TBI) is a major contributor of long-term disability and a leading cause of death worldwide. A series of secondary injury cascades can contribute to cell death, tissue loss, and ultimately to the development of functional impairments. However, there are currently no effective therapeutic interventions that improve brain outcomes following TBI. As a result, a number of experimental TBI models have been developed to recapitulate TBI injury mechanisms and to test the efficacy of potential therapeutics. The pig model has recently come to the forefront as the pig brain is closer in size, structure, and composition to the human brain compared to traditional rodent models, making it an ideal large animal model to study TBI pathophysiology and functional outcomes. This review will focus on the shared characteristics between humans and pigs that make them ideal for modeling TBI and will review the three most common pig TBI models–the diffuse axonal injury, the controlled cortical impact, and the fluid percussion models. It will also review current advances in functional outcome assessment measures and other non-invasive, translational TBI detection and measurement tools like biomarker analysis and magnetic resonance imaging. The use of pigs as TBI models and the continued development and improvement of translational assessment modalities have made significant contributions to unraveling the complex cascade of TBI sequela and provide an important means to study potential clinically relevant therapeutic interventions.

The Exact Measure Functions of the Images for a Class of Self-Similar Processes

Let X= (Ω, ■, ■_t, X_t,, θ_t, p~x) be a self-similar Markov process on (0,∞) with non-decreasing path. The exact Hausdorff and Packing measure functions of the image X([0,t] ) are obtained.

Rough law energy and measurement of ■-decomposition rough law

By employing function one-direction S-rough sets and rough law generation method based on function S-rough sets, ^-f-decomposition law and ^-F-decomposition rough law are proposed, and the measurement of rough law variation in the process of rough law ^-F-decomposition is researched. The concepts of law energy and attdbute ^-f-interference degree are presented, which make the variation of rough law become measurable. ^-f-decomposition law energy characteristic theorem, ^-f- decomposition law energy inequality theorem, ^-F-decomposition rough law energy characteristic theorem, and ^-f-decomposition law energy mean value theorem are presented.

Analytical Evaluation of Non-Elementary Integrals Involving Some Exponential, Hyperbolic and Trigonometric Elementary Functions and Derivation of New Probability Measures Generalizing the Gamma-Type and Gaussian-Type Distributions

The non-elementary integrals involving elementary exponential, hyperbolic and trigonometric functions, and where α,η and β are real or complex constants are evaluated in terms of the confluent hypergeometric function 1F1 and the hypergeometric function 1F2. The hyperbolic and Euler identities are used to derive some identities involving exponential, hyperbolic, trigonometric functions and the hypergeometric functions 1F1 and 1F2. Having evaluated, these non-elementary integrals, some new probability measures generalizing the gamma-type and Gaussian distributions are also obtained. The obtained generalized probability distributions may, for example, allow to perform better statistical tests than those already known (e.g. chi-square (x2) statistical tests and other statistical tests constructed based on the central limit theorem (CLT)), while avoiding the use of computational approximations (or methods) which are in general expensive and associated with numerical errors.

Consensus for High-Order Linear Multi-Agent Systems with Unknown but Bounded Measurement Noises

The staticε-consensus problem for a high-order linear multi-agent system is studied over a connected undirected communication topology,in which the state measurements of neighbors are affected by unknown but bounded(UBB)noises.Using the dead-zone function and binomial coefficients,we propose a distributed consensus protocol.Under this protocol,all agents achieve staticε-consensus,i.e.,the first components of the states for each agent reachε-consensus,and the remaining components reach agreement at zero.Numerical examples illustrate the validity of the theoretical results.

MEASUREMENT AND COMPUTATION OF THE PSEUDO-RESONANCE AND ANTI-RESONANCE

This paper presents a phenomenon of“Pseudo-resonance”of beams androds discovered from experiments and computations,and gives the definition of“Pseudo-resonance”.The relationship of distribution between the frequency of pseu-do-resonance and that of anti-resonance is found,and an analytic solution for thetransfer function between any two points on a beam or rod is established.The law ofdistribution of the anti-resonant frequencies,as well as the relation between the fre-quency distribution and the nodes of vibration is also proposed.

A Study of Model for Distributed Measurement and Control System

This paper is concerned with a method for forming distributed measurement and control system.A three-layer structure model based on network,physical node layer and func-tion node layer is discussed.It is designed on object-oriented software method.The model has a fine application prospect.