Machine-learning-assisted efficient reconstruction of the quantum states generated from the Sagnac polarization-entangled photon source

Neural networks are becoming ubiquitous in various areas of physics as a successful machine learning(ML)technique for addressing different tasks.Based on ML technique,we propose and experimentally demonstrate an efficient method for state reconstruction of the widely used Sagnac polarization-entangled photon source.By properly modeling the target states,a multi-output fully connected neural network is well trained using only six of the sixteen measurement bases in standard tomography technique,and hence our method reduces the resource consumption without loss of accuracy.We demonstrate the ability of the neural network to predict state parameters with a high precision by using both simulated and experimental data.Explicitly,the mean absolute error for all the parameters is below 0.05 for the simulated data and a mean fidelity of 0.99 is achieved for experimentally generated states.Our method could be generalized to estimate other kinds of states,as well as other quantum information tasks.

Triad-displaced ULAs configuration for non-circular sources with larger continuous virtual aperture and enhanced degrees of freedom

Non-uniform linear array(NULA)configurations are well renowned due to their structural ability for providing increased degrees of freedom(DOF)and wider array aperture than uniform linear arrays(ULAs).These characteristics play a significant role in improving the direction-of-arrival(DOA)estimation accuracy.However,most of the existing NULA geometries are primarily applicable to circular sources(CSs),while they limitedly improve the DOF and continuous virtual aperture for noncircular sources(NCSs).Toward this purpose,we present a triaddisplaced ULAs(Tdis-ULAs)configuration for NCS.The TdisULAs structure generally consists of three ULAs,which are appropriately placed.The proposed antenna array approach fully exploits the non-circular characteristics of the sources.Given the same number of elements,the Tdis-ULAs design achieves more DOF and larger hole-free co-array aperture than its sparse array competitors.Advantageously,the number of uniform DOF,optimal distribution of elements among the ULAs,and precise element positions are uniquely determined by the closed-form expressions.Moreover,the proposed array also produces a filled resulting co-array.Numerical simulations are conducted to show the performance advantages of the proposed Tdis-ULAs configuration over its counterpart designs.

ESTIMATION OF THE NUMBER OF CORRELATED SOURCES WITH COMMON FREQUENCIES BASED ON POWER SPECTRAL DENSITY

Blind source separation and estimation of the number of sources usually demand that the number of sensors should be greater than or equal to that of the sources, which, however, is very difficult to satisfy for the complex systems. A new estimating method based on power spectral density （PSD） is presented. When the relation between the number of sensors and that of sources is unknown, the PSD matrix is first obtained by the ratio of PSD of the observation signals, and then the bound of the number of correlated sources with common frequencies can be estimated by comparing every column vector of PSD matrix. The effectiveness of the proposed method is verified by theoretical analysis and experiments, and the influence of noise on the estimation of number of source is simulated.

Numerical Study of Natural Convective Heat Transfer in an Air Filled Square Cavity Heated from Below and Symmetrically Cooled from the Sides with a Partition in the Hot Wall

A two-dimensional numerical study of laminar natural convection in a square enclosure filled with air with a wall partially heated on the bottom is presented.The heat source is located on the lower wall with different heated widths varied from 20 to 80%(ε=0.2–0.8)of the total width of the lower wall and different heights h=H/4 and H/2 of the partition.The effect of the partition height on the main system dynamics is investigated through solution of the two-dimensional Navier-Stokes equations and the energy equation by means of a finite volume method based on the SIMPLE algorithm.The influence of the Rayleigh number(Ra=10^(3) to 10^(6))and the hot wall length is also examined.It is shown that the average Nusselt number grows whenεincreases and when h decreases.For a given value ofεand h,the average Nusselt number increases as Ra increases.It is concluded that the partition height causes a decrease in the average Nusselt number.

Heuristic techniques for maximum likelihood localization of radioactive sources via a sensor network

Maximum likelihood estimation(MLE)is an effective method for localizing radioactive sources in a given area.However,it requires an exhaustive search for parameter estimation,which is time-consuming.In this study,heuristic techniques were employed to search for radiation source parameters that provide the maximum likelihood by using a network of sensors.Hence,the time consumption of MLE would be effectively reduced.First,the radiation source was detected using the k-sigma method.Subsequently,the MLE was applied for parameter estimation using the readings and positions of the detectors that have detected the radiation source.A comparative study was performed in which the estimation accuracy and time consump-tion of the MLE were evaluated for traditional methods and heuristic techniques.The traditional MLE was performed via a grid search method using fixed and multiple resolutions.Additionally,four commonly used heuristic algorithms were applied:the firefly algorithm(FFA),particle swarm optimization(PSO),ant colony optimization(ACO),and artificial bee colony(ABC).The experiment was conducted using real data collected by the Low Scatter Irradiator facility at the Savannah River National Laboratory as part of the Intelligent Radiation Sensing System program.The comparative study showed that the estimation time was 3.27 s using fixed resolution MLE and 0.59 s using multi-resolution MLE.The time consumption for the heuristic-based MLE was 0.75,0.03,0.02,and 0.059 s for FFA,PSO,ACO,and ABC,respectively.The location estimation error was approximately 0.4 m using either the grid search-based MLE or the heuristic-based MLE.Hence,heuristic-based MLE can provide comparable estimation accuracy through a less time-consuming process than traditional MLE.

A robust triaxial localization method of AE source using refraction path

Acoustic emission(AE)localization algorithms based on homogeneous media or single-velocity are less accurate when applied to the triaxial localization experiments.To the end,a robust triaxial localization method of AE source using refraction path is proposed.Firstly,the control equation of the refraction path is established according to the sensor coordinates and arrival times.Secondly,considering the influence of time-difference-of-arrival(TDOA)errors,the residual of the governing equation is calculated to estimate the equation weight.Thirdly,the refraction points in different directions are solved using Snell’s law and orthogonal constraints.Finally,the source coordinates are iteratively solved by weighted correction terms.The feasibility and accuracy of the proposed method are verified by pencil-lead breaking experiments.The simulation results show that the new method is almost unaffected by the refraction ratio,and always holds more stable and accurate positioning performance than the traditional method under different ratios and scales of TDOA outliers.

THE MINIMAL PROPERTY OF THE CONDITION NUMBER OF INVERTIBLE LINEAR BOUNDED OPERATORS IN BANACH SPACES

In this paper we show that in error estimates, the condition number κ(T) of any invertible linear bounded operator T in Banach spaces is minimal. We also extend the Hahn-Banach theorem and other related results.

Dynamic Direction of Arrival Estimation with an Unknown Number of Sources

Aiming at source number determination and direction of arrival(DOA) estimation under the case of time-varying source number,a method of DOA estimation with an unknown number of sources was proposed.Firstly,an algorithm based on crossvalidation technique was introduced to determine the number of sources.Then dynamic DOAs of source were estimated using an algorithm based on blind source separation(BSS) under the case that number of sources were unknown in advance and it was timevarying.The effectiveness of the proposed method was validated by simulation of time-invariant and time-varying numbers of source.Compared with other conventional methods,the proposed method has superior evaluation performances The proposed method can estimate m(the numbers of sensor) DOAs while other conventional methods estimate less than m DOAs.The R_(mse) of the proposed method in the case of low signal-to-noise ratio(SNR)(equal or lower than 30 dB) is smaller than 0.2 while R_(mse) of other conventional methods are greater than 0.8.

Thermal partition of two asymmetric discrete heat sources by cold air curtain

A partition solution implemented by a cold air curtain for two asymmetric discrete heat sources in a twodimensional rectangular enclosure was numerically studied. Main attentions were focused on the effects of Reynolds number, Grashof number, separation distance between heat sources, and buoyancy ratio. It is found that the airflow and heat transfer are not only determined by governing parameters, but also affected by boundary conditions. It is also found that nearly symmetry of flow structure corresponds to nearly thermal partition, and the symmetry can be enhanced when Reynolds number, separation distance and buoyancy ratio increase. In addition, it is observed that there is a minimum Reynolds number for obtaining nearly thermal partition, which increases when Grashof number increases.

Estimate Totel Number of the Earth Atmospheric Particle with Standard Atmosphere model

The total number of atmospheric particle (AP) is an important datum for planetary science and geoscience. Estimating entire AP number is also a familiar question in general physics. With standard atmosphere model, considering the number difference of AP caused by rough and uneven in the earth surface below, the sum of dry clean atmosphere particle is . So the whole number of AP including water vapor is . The rough estimation for the total number of AP on other planets (or satellites) in condensed state is also discussed on the base of it.

The K Method for Estimating Earthquake Activity Parameters and Effect of the Boundary Uncertainty of the Source Region:Discussion on the Seismic Zoning Method

Two aspects of a new method,which can be used for seismic zoning,are introduced in this paper.On the one hand,the approach to estimate b value and annual activity rate proposed by Kijko and Sellevoll needs to use the earthquake catalogue.The existing earthquake catalogue contains both historical and recent instrumental data sets and it is inadequate to use only one part.Combining the large number of historical events with recent complete records and taking the magnitude uncertainty into account,Kijko’s method gives the maximum likelihood estimation of b value and annual activity rate,which might be more realistic.On the other hand,this method considers the source zone boundary uncertainty in seismic hazard analysis,which means the earthquake activity rate across a boundary of a source zone changes smoothly instead of abruptly and avoids too large a gradient in the calculated results.

Estimating the Level of Asymptomatic COVID-19 Infections in Northern Ireland in 2020

The identification and understanding of COVID-19 potential routes of transmission are fundamental to informing policies and strategies to successfully control the outbreak. Various studies highlighted asymptomatic infections as one of the silent drivers of the epidemic. An accurate estimation of the asymptomatic cases and the understanding of their contribution to the spread of the disease could enhance the effectiveness of current control strategies, mainly based on the symptom onset, to curb transmission. We investigate the dynamics of the COVID-19 epidemic in Northern Ireland during the period 1st March 25th to December 2020 to estimate the proportion of the asymptomatic infections in the country. We extended our previous model to include the stage of the asymptomatic infection, and we implement the corresponding deterministic model using a publicly available dataset. We partition the data into 11 sets over the period of study and fit the model parameters on the consecutive intervals using the cumulative number of confirmed positive cases for each interval. Moreover, we assess numerically the impacts of uncertainty in testing and we provide estimates of the reproduction numbers using the fitted parameters. We found that the proportion of asymptomatically infectious subpopulations, in Northern Ireland during the period of study, ranged between 5% and 25% of exposed individuals. Also, the estimate of the basic reproduction number, R0, is 3.3089. The lower and upper estimates for herd immunity are (0.6181, 0.7243) suggesting that around 70% of the population of Northern Ireland should acquire immunity via infection or vaccination, which is in line with estimates reported in other studies.

Blind identification and DOA estimation for array sources in presence of scattering

A novel identification method for point source,coherently distributed（CD） source and incoherently distributed（ICD） source is proposed.The differences among the point source,CD source and ICD source are studied.According to the different characters of covariance matrix and general steering vector of the array received source,a second order blind identification method is used to separate the sources,the mixing matrix could be obtained.From the mixing matrix,the type of the source is identified by using an amplitude criterion.And the direction of arrival for the array received source is estimated by using the matching pursuit algorithm from the vectors of the mixing matrix.Computer simulations validate the efficiency of the method.

Vibration Source Number Estimation of A Shell Structure

It has been challenging to correctly separate the mixed signals into source components when the source number is not known a priori.To reveal the complexity of the measured vibration signals,and provide the priori information for the blind source separation,in this paper,we propose a novel source number estimation based on independent component analysis(ICA)and clustering evaluation analysis,and then carry out experiment studies with typical mechanical vibration signals from a shell structure.The results demonstrate that the proposed ICA based source number estimation performs stably and robustly for the shell structure.

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.

Impacts of the sampling design on the abundance index estimation of Portunus trituberculatus using bottom trawl

In the survey of fishery resources,the sampling design will directly impact the accuracy of the estimation of the abundance.Therefore,it is necessary to optimize the sampling design to increase the quality of fishery surveys.The distribution and abundance of fisheries resource estimated based on the bottom trawl survey data in the Changjiang River(Yangtze River)Estuary-Hangzhou Bay and its adjacent waters in 2007 were used to simulate the"true"situation.Then the abundance index of Portunus trituberculatus were calculated and compared with its true index to evaluate the impacts of different sampling designs on the abundance estimation.Four sampling methods(including fixed-station sampling,simple random sampling,stratified fixed-station sampling,and stratified random sampling)were simulated.Three numbers of stations(9,16 and 24)were assumed for the scenarios of fixed-station sampling and simple random sampling without stratification.While 16 stations were assumed for the scenarios with stratification.Three reaction distances(1.5 m,3 m and 5 m)of P.trituberculatus to the bottom line of trawl were also assumed to adapt to the movement ability of the P.trituberculatus for different ages,seasons and substrate conditions.Generally speaking,compared with unstratified sampling design,the stratified sampling design resulted in more accurate abundance estimation of P.trituberculatus,and simple random sampling design is better than fixed-station sampling design.The accuracy of the simulated results was improved with the increase of the station number.The maximum relative estimation error(REE)was 163.43%and the minimum was 49.40%for the fixed-station sampling scenario with 9 stations,while 38.62%and 4.15%for 24 stations.With the increase of reaction distance,the relative absolute bias(RAB)and REE gradually decreased.Resource-intensive area and the seasons with high density variances have significant impacts on simulation results.Thus,it will be helpful if there are prior information or pre-survey results about density distribution.The current study can provide reference for the future sampling design of bottom trawl of P.trituberculatus and other species.

Eco-environment range in the source regions of the Yangtze and Yellow rivers

Based on geographical and hydrological extents delimited, four principles are identified, as the bases for delineating the ranges of the source regions of the Yangtze and Yellow rivers in the paper. According to the comprehensive analysis of topographical characteristics, climate conditions, vegetation distribution and hydrological features, the source region ranges for eco-environmental study are defined. The eastern boundary point is Dari hydrological station in the upper reach of the Yellow River. The watershed above Dari hydrological station is the source region of the Yellow River which drains an area of 4.49×10 4 km 2 . Natural environment is characterized by the major topographical types of plateau lakes and marshland, gentle landforms, alpine cold semi-arid climate, and steppe and meadow vegetation in the source region of the Yellow River. The eastern boundary point is the convergent site of the Nieqiaqu and the Tongtian River in the upstream of the Yangtze River. The watershed above the convergent site is the source region of the Yangtze River, with a watershed area of 12.24×10 4 km 2 . Hills and alpine plain topography, gentle terrain, alpine cold arid and semi-arid climate, and alpine cold grassland and meadow are natural conditions in the source region of the Yangtze River.

Discussion on heat source mechanism and geothermal system of Qinghai Gonghe-Guide Basin

The Qinghai Gonghe-Guide Basin together with the alternatively distributed mountainous region shows characteristics that the conductive geothermal resource of the basin has high geothermal gradient, the granite occurs in the bottom of borehole for geothermal exploration, and the convective hot springs in the basin-edge uplift fracture are in zonal distribution and with high-temperature geothermal water. There are still some divergences about the heat source mechanism of the basin. In this paper, queries to the view of mantle-derived heat source have been put forward, coming up with geochemical evidences to prove that the radiogenic heat of granite is the heat source within the mantle. Additionally, temperature curve is drawn based on the geothermal boring and geochemical geothermometer has been adopted for an estimation of the temperature and depth of the geothermal reservoir, it has been found that the surrounding mountains belong to the medium-temperature geothermal system while the area within the basin belongs to the high-temperature geothermal system with the temperature of borehole bottom reaching up to 175-180 ℃. In this paper, discussions on the problems existing in the calculation of geothermal gradient and the differences generated by the geothermal system have been carried out.

ON THE SENSITIVITY OF THE LDU FACTORIZATION

In this paper,we give the sensitivity analyses by two approaches for L,D,U in factorization A=LDU of general perturbations in A which sufficiently small in norm. By the matrix vector equation approach,we derive the sharp condition number for L,D and U factors .By the matrix equation approach we derive corresponding condition estimates. When A is a symmetric matrix,the corresponding results can be obtained for LDL T factorization.

Impacts of sampling design on the abundance estimation of Portunus trituberculatus using crab pots

Fishery-independent surveys can provide high-quality data and support fishery assessment and management.Optimization of sampling design is crucial to increase the quality of fishery surveys.Crab pots are important fishing gears used to catch crabs.We analyzed the impacts of sampling design of crab pots on the abundance of Portunus trituberculatus in the Changjiang(Yangtze)River estuary to the Hangzhou Bay and its adjacent waters in East China Sea.The crab pots were cylindrical,240 mm in height and 600 mm in diameter of the iron ring.Our sampling designs(including fixed-station sampling,simple random sampling,stratified fixed-station sampling,and stratified random sampling),three number of stations(9,16,and 24),and three numbers of crab pots(500,1000,and 3000)were simulated and compared with the“true”abundance that obtained from bottom trawl surveys in the study area in 2007.The scenarios with 16 stations were set in stratification as a control group for comparison with unstratified designs.Results show that simple random sampling can obtain more stable results than fixed-station sampling in the abundance estimation of P.trituberculatus.In addition,stratified sampling resulted in more accurate abundance than unstratified sampling.The accuracy of the simulated results improved with the increase of the number of stations.No remarkable differences in the results were found among the scenarios of different number of crab pots at each station.However,resource-intensive areas exerted great impacts on simulation results.Thus,prior information or pre-survey results about resource abundance and density distribution are necessary.This study may serve as a reference for future sampling designs of crab pots of P.trituberculatus and other species.