A new source number estimation method based on the beam eigenvalue

Most source number estimation methods based on the eigenvalues are decomposed by covariance matrix in MUSIC algorithm. To develop the source number estimation method which has lower signal to noise ratio and is suitable to both correlated and uncorrelated impinging signals, a new source number estimation method called beam eigenvalue method (BEM) is proposed in this paper. Through analyzing the space power spectrum and the correlation of the line array, the covariance matrix is constructed in a new way, which is decided by the line array shape when the signal frequency is given. Both of the theory analysis and the simulation results show that the BEM method can estimate the source number for correlated signals and can be more effective at lower signal to noise ratios than the normal source number estimation methods.

Proximal-distal motor unit number estimationdynamic changes in patients with amyotrophic lateral sclerosis A one-year follow-up

BACKGROUND：Amyotrophic lateral sclerosis （ALS） is the most common of all the motor neuron diseases and the absence of a biologic marker has made both diagnosis and tracking evolution of the disease difficult, Electrodiagnostic tests play a fundamental role in quantifying pathological changes in the motor unit pool.OBJECTIVE：We assessed distal-proximal Motor Unit （MU） loss and changes using the method of motor unit number estimation （MUNE）.DESIGN, TIME AND SETTING：A case-control study was performed at the Department of Neuroscience, Pisa University Medical School, Italy from December 1999 to November 2009. PARTICIPANTS：A total of 50 ALS patients were recruited, 30 males：mean age （59.6 ± 13.3） years; 20 females：mean age （63.9 ± 11.7） years; range （30-82） years; all patients had probable or definite ALS. Thirty healthy volunteers were recruited from department staffs, including 20 males and 10 females; mean age （57.7 ± 13.8） years served as controls.METHODS：MUNE was performed for both the biceps brachii and abductor digiti minimi muscles of the same side. The technique used relayed substantially on manual incremental stimulation of the motor nerve, known as the McComas technique （50 ms sweep duration, a gain of 2 mV/Div for M wave, 0.5 mV/Div for each step; filters 10-20 kHz）.MAIN OUTCOME MEASURES：MUNE results were measured.RESULTS：Functioning MU numbers, measured by MUNE, decreased in the biceps brachii and abductor digiti minimi muscles over the entire one-year follow-up period （one assessment every three months） compared with baseline determination, the rate of MU decrease was similar in both muscles, but steeper distally.CONCLUSION：MUNE is a feasible method for ALS patients both proximally and distally to track changes over time in muscle MUs during the disease＇s evolution.

Fast algorithm for coherent source number estimation

In order to estimate the number of coherent sources, a Hankel matrix with the size of half the number of the received arrays is constructed using snapshot data of observed vectors. And the rank of the Hankel matrix is only related with the number of signal sources, no matter the signals are uncorrelated or coherent. We can get the signal and noise eigenvalues by conducting the singular value decomposition （SVD） to the Hankel matrix, the source number can be obtained by calculating the maximum ratio of each eigenvalue pair. The complexity of the algorithm is reduced greatly as only part of the observed data （single snapshot） is used. The Monte-Carlo simulation results demonstrate the feasibility of the algorithm.

Analysis of the outbreak of COVID-19 in Japan by SIQR model

The SIQR model is exploited to analyze the outbreak of COVID-19 in Japan where the number of the daily confirmed new cases is explicitly treated as an observable.It is assumed that the society consists of four compartments;susceptible individuals(S),infected individuals at large(I),quarantined patients(Q)and recovered individuals(R),and the time evolution of the pandemic is described by a set of ordinary differential equations.It is shown that the quarantine rate can be determined from the time dependence of the daily confirmed new cases,from which the number of infected individuals can be estimated.The infection rate and quarantine rate are determined for the period from mid-February to mid-April in Japan and transmission characteristics of the initial stages of the outbreak in Japan are analyzed in connection with the policies employed by the government.The effectiveness of different measures is discussed for controlling the outbreak and it is shown that identifying patients through PCR(Polymerase Chain Reaction)testing and isolating them in a quarantine is more effective than lockdown measures aimed at inhibiting social interactions of the general population.An effective reproduction number for infected individuals at large is introduced which is appropriate to epidemics controlled by quarantine measures.

Number estimation of controllers for pinning a complex dynamical network

Number estimation of controllers is a fundamental question in pinning synchronization of complex networks. This paper studies the problem of controller number in synchronizing a complex network of coupled dynamical systems by means of pinning. For a complex network with a symmetric coupling matrix and full coupling between the nodes, we formulate network synchronization via pinning as a linear matrix inequality criterion, and provide a lower bound and an upper bound of the controller number for a given complex network with fixed architecture. Several numerical examples with Barabási-Albert network topologies are provided to verify our theoretical results.

Effects of multiple transmission pathways on Zika dynamics

Although the Zika virus is transmitted to humans primarily through the bite of infected female Aedes aegypti mosquitoes,it can also be sexually and vertically transmitted within both populations.In this study,we develop a new mathematical model of the Zika virus which incorporates sexual transmission in humans and mosquitos,vertical transmission in mosquitos,and mosquito to human transmission through bites.Analysis of this deterministic model shows that the secondary transmission routes of Zika increase the basic reproductive number(R0)of the virus by 5%,shift the peak time of an outbreak to occur 10%sooner,increase the initial growth of an epidemic,and have important consequences for control strategies and estimates of R0.Furthermore,sensitivity analysis show that the basic reproductive number is most sensitive to the mosquito biting rate and transmission probability parameters and reveal that the dynamics of juvenile mosquito stages greatly impact the peak time of an outbreak.These discoveries deepen our understanding of the complex transmission routes of ZIKV and the consequences that they may hold for public health officials.

THE STRONG LAW OF LARGE NUMBER AND PARAMETER ESTIMATION OF ONE CLASS OF NON-NEGATIVE INTEGER-VALUED TIME SERIES

In [7], a general integer-valued time series model, the generalization of the model proposedby Al-Osh and Al..id[1], has been proposed. Its stationarity and spectral representation hasbeen investigated. In this paper, we make a further study of the model. Its strong law of largenumbers and parameter estimstion are obtained. At the end of the paper, we give a few openproblems to be researched further.