Random Set Research Articles

Decomposed POMDP Optimization-Based Sensor Management for Multi-Target Tracking in Passive Multi-Sensor Systems

This paper presents an efficient information-theoretic sensor management method to maximize the performance of the passive multi-sensor system for multi-target tracking. We model the multi-target state as a generalized labeled multi-Bernoulli (GLMB) random finite set and formulate the dynamic sensor selection process as a partially observable Markov decision process (POMDP). The optimization objective is to maximum the information gain obtained from the observed data, which is measured by the Cauchy-Schwarz divergence. This is accomplished with two main technical innovations. The first is a tractable decomposed POMDP based sensor selection solution, in which the informative sensors are selected sequentially from the candidates based on the Cauchy-Schwarz divergence. The second is a novel dual-stage multi-sensor fusion strategy based on the iterated-corrector GLMB filter. Since the uncertainty of the passive multi-sensor system is generally large, the performance of the iterated-corrector scheme can be greatly influenced by the order of sensor updates. To fix this problem, the selected sensors are ranked in order of the Cauchy-Schwarz divergence obtained in sensor selection, followed by the iterated-corrector update. For the multi-sensor fusion, the effect of poor performance sensors is weakened and that of better performance sensors is enhanced. Simulation studies demonstrate the effectiveness and efficiency of the proposed method in challenging passive multi-target tracking scenarios.

Survival and Larynx Preservation in Early Glottic Cancer: A Randomized Trial Comparing Laser Surgery and Radiation Therapy

The prognosis of glottic T1a laryngeal squamous cell carcinoma (LSCC) is excellent with both transoral laser surgery (TLS) and radiation therapy (RT). Our aim was to compare TLS and RT treatment results in a randomized study. Of 56 male patients with glottic T1a LSCC, 31 were randomized for TLS and 25 for RT. Survival and larynx preservation data were collected from medical records. Five-year overall survival (OS) was 87%, disease-specific survival (DSS) was 97%, and recurrence-free survival (RFS) was 81% in patients treated with TLS. Five-year OS was 92%, DSS was 100%, and RFS was 88% in patients treated with RT. The primary treatment method was not associated with OS, RFS, or DSS in a log-rank test. The larynx preservation rate was similar in both groups (TLS, 97%; RT, 92%; P=.575). In a prospective randomized setting oncological outcomes of both treatment modalities (TLS or RT) for T1a LSCC were similar.

Comparative analysis of molecular signatures reveals a hybrid approach in breast cancer: Combining the Nottingham Prognostic Index with gene expressions into a hybrid signature.

The diagnosis of breast cancer—including determination of prognosis and prediction—has been traditionally based on clinical and pathological characteristics such as tumor size, nodal status, and tumor grade. The decision-making process has been expanded by the recent introduction of molecular signatures. These signatures, however, have not reached the highest levels of evidence thus far. Yet they have been brought to clinical practice based on statistical significance in prospective as well as retrospective studies. Intriguingly, it has also been reported that most random sets of genes are significantly associated with disease outcome. These facts raise two highly relevant questions: What information gain do these signatures procure? How can one find a signature that is substantially better than a random set of genes? Our study addresses these questions. To address the latter question, we present a hybrid signature that joins the traditional approach with the molecular one by combining the Nottingham Prognostic Index with gene expressions in a data-driven fashion. To address the issue of information gain, we perform careful statistical analysis and comparison of the hybrid signature, gene expression lists of two commercially available tests as well as signatures selected at random, and introduce the Signature Skill Score—a simple measure to assess improvement on random signatures. Despite being based on in silico data, our research is designed to be useful for the decision-making process of oncologists and strongly supports association of random signatures with outcome. Although our study shows that none of these signatures can be considered as the main candidate for providing prognostic information, it also demonstrates that both the hybrid signature and the gene expression list of the OncotypeDx signature identify patients who may not require adjuvant chemotherapy. More importantly, we show that combining signatures substantially improves the identification of patients who do not need adjuvant chemotherapy.

Coarse reduced model selection for nonlinear state estimation

State estimation is the task of approximately reconstructing a solu- tion u of a parametric partial differential equation when the parameter vector y is unknown and the only information is m linear measurements of u. Cohen et al. [arXiv:2009.02687, Nov. 2020] proposed a method to use a family of linear reduced spaces as a generalised nonlinear reduced model for state estimation. A computable surrogate distance is used to evaluate which linear estimate lies closest to a true solution of the pde problem. In this article we propose a strategy of coarse computation of the surrogate distance while maintaining a fine mesh reduced model, as the computational cost of the surrogate distance is large relative to the reduced modelling task. We demonstrate numerically that the error induced by the coarse distance is dominated by other approximation errors.

Certificateless Reliable and Privacy-Preserving Auditing of Group Shared Data for FOG-CPSs

FOG-enabled cyber-physical systems (FOG-CPSs) open new security challenges as the local edge devices are easier to compromise than a traditional cloud server. Remote data integrity checking (RDIC) plays an important role in safeguarding against data corruption from a storage server. Certificateless cryptography (CLPKC)-based RDIC schemes do not suffer from the drawbacks of the public key infrastructure (PKI)-based RDIC protocols. Most of the CLPKC-based RDIC schemes proposed in the literature deal with personal data. However, in a FOG-CPS, it is also important to audit a data file shared by a group of edge devices. Most of the existing group shared data auditing schemes lack mechanisms to defend against a semi-trusted data auditor applicable for a FOG-CPS scenario. In order to address these issues, in this paper, we propose a novel CLPKC-based group shared data auditing protocol tailored to the specific security requirements of a FOG-CPS. Besides, we perform a detailed cryptanalysis of two existing CLPKC-based privacy-preserving group shared data auditing schemes. The formal security analysis of our proposed protocol establishes metadata and data integrity proof unforgeability and claimed zero-knowledge privacy and reliability properties through rigorous proofs in the random oracle model setting. Performance evaluations establish the efficiency of our proposed protocol.

Titmice are a better indicator of bird density in Northern European than in Western European forests.

Population sizes of many birds are declining alarmingly and methods for estimating fluctuations in species’ abundances at a large spatial scale are needed. The possibility to derive indicators from the tendency of specific species to co‐occur with others has been overlooked. Here, we tested whether the abundance of resident titmice can act as a general ecological indicator of forest bird density in European forests. Titmice species are easily identifiable and have a wide distribution, which makes them potentially useful ecological indicators. Migratory birds often use information on the density of resident birds, such as titmice, as a cue for habitat selection. Thus, the density of residents may potentially affect community dynamics. We examined spatio‐temporal variation in titmouse abundance and total bird abundance, each measured as biomass, by using long‐term citizen science data on breeding forest birds in Finland and France. We analyzed the variation in observed forest bird density (excluding titmice) in relation to titmouse abundance. In Finland, forest bird density linearly increased with titmouse abundance. In France, forest bird density nonlinearly increased with titmouse abundance, the association weakening toward high titmouse abundance. We then analyzed whether the abundance (measured as biomass) of random species sets could predict forest bird density better than titmouse abundance. Random species sets outperformed titmice as an indicator of forest bird density only in 4.4% and 24.2% of the random draws, in Finland and France, respectively. Overall, the results suggest that titmice could act as an indicator of bird density in Northern European forest bird communities, encouraging the use of titmice observations by even less‐experienced observers in citizen science monitoring of general forest bird density.

CANONICAL THRESHOLDING FOR NON-SPARSE HIGH-DIMENSIONAL LINEAR REGRESSION.

We consider a high-dimensional linear regression problem. Unlike many papers on the topic, we do not require sparsity of the regression coefficients; instead, our main structural assumption is a decay of eigenvalues of the covariance matrix of the data. We propose a new family of estimators, called the canonical thresholding estimators, which pick largest regression coefficients in the canonical form. The estimators admit an explicit form and can be linked to LASSO and Principal Component Regression (PCR). A theoretical analysis for both fixed design and random design settings is provided. Obtained bounds on the mean squared error and the prediction error of a specific estimator from the family allow to clearly state sufficient conditions on the decay of eigenvalues to ensure convergence. In addition, we promote the use of the relative errors, strongly linked with the out-of-sample R 2. The study of these relative errors leads to a new concept of joint effective dimension, which incorporates the covariance of the data and the regression coefficients simultaneously, and describes the complexity of a linear regression problem. Some minimax lower bounds are established to showcase the optimality of our procedure. Numerical simulations confirm good performance of the proposed estimators compared to the previously developed methods.

An info-gap framework for robustness assessment of epistemic uncertainty models in hybrid structural reliability analysis

The main objective of this work is to study the impact of the choice of input uncertainty models on robustness evaluations for probabilities of failure. Aleatory and epistemic uncertainties are jointly propagated by considering hybrid models and applying random set theory. The notion of horizon of uncertainty found in the info-gap method, which is usually used to assess the robustness of a model to uncertainty, allows to compare the bounds on the probability of failure obtained from different epistemic uncertainty models at increasing levels of uncertainty. Info-gap robustness and opportuneness curves are obtained and compared for the interval model, the triangular and trapezoidal possibility distributions, the probabilistic uniform distribution and the parallelepiped convex model on two academic examples and one industrial use-case. A specific demand value, as introduced in the info-gap method, is used as a value of information metric to quantify the gain of information on the probability of failure between less informative uncertainty models and a more informative ones.

Machine learning based rate decline prediction in unconventional reservoirs

The main objective of this paper is to develop a novel machine learning based model that can accurately predict the decline curves and EUR (Estimated Ultimate Recovery) for new wells based on the data collected from nearby wells. This is because decline curves are easier and faster alternative to complex reservoir simulators which perform computationally expensive operations. In contrast to this, decline curves require only a few parameters in the equation which can be easily collected from the existing data of the wells. In this study, first we collected the well data corresponding to well parameters such as initial monthly oil flow rate ( q i ), well completion parameters (i.e., no. of fracturing stages, completed length, amount of proppant used, amount of fracturing fluid used), well location parameters (TVD Heel-Toe Difference), reservoir fluid properties (Oil API Gravity, initial 24 h period Gas-Oil Ratio (GOR), initial 24 h period Gas Produced, initial 24 h period Oil Produced), flowing tubing pressure, casing pressure tubing size,choke size from publicly available databases of the Eagle Ford Shale formation Texas RRC (Railroad Commission of Texas). Wells were selected randomly and only those wells were finally included for the study whose data of the all the required parameters were available. The model parameters were estimated by fitting the production data to the decline curve models. Artificial Neural Network (ANN) was employed to build Machine learning models as a function of the above well parameters for the corresponding model parameters. The decline curves for new or existing wells were rapidly predicted using these models. In order to estimate the predictive accuracy of these models when applied to new or test wells cross validation technique such as k-fold cross validation was employed. These models were also used to predict EUR for the test wells. Additionally, feature selection was also done using algorithms such as Chi Square Test (χ2) and Minimum Redundancy Maximum Relevance (MRMR) Algorithm to determine the relative importance of predictor variables in predicting EUR. The predictor variables were successfully linked to SEDM (Stretched Exponential Decline Model) decline curve parameters (n and τ) in a random set of oil field well data. The relative influences of various well parameters were also examined to determine the hidden relationship between them. The novelty in this study lies in the algorithm and dataset that we used for the rate decline prediction in Eagle Ford data set. Although, this paper has referenced some previous papers where machine learning has been used to make prediction, but this paper presents use of new algorithm as well as a new dataset. As more data gets available, there is definitely extra room for further data analysis and improved results using machine learning methods. In future, the number of wells can be increased and the updated results can again be submitted after investing more time. It should be noted here that data downloading and preparing takes most of the time for such study especially when dealing with oil and gas data.

Validation of rapid antibody (IgG-IgM) test kit for SARS-CoV-2 infection in Qatar.

Background: In response to the growing coronavirus disease 2019 (COVID-19) pandemic and the shortage of laboratory based molecular testing capacity and reagents, multiple diagnostic test manufacturers have developed rapid and easy to use devices to facilitate testing outside laboratory settings. These kits are either based on detection of proteins from SARS-CoV-2 virus or detection of antigen or human antibodies generated in response to the infection. However, it is important to understand their performance characteristics and they must be validated in the local population setting.Design and methods: The objective is to assess the validity of the rapid test for IgG and IgM immunoglobulins compared to the current gold standard reverse transcription polymerase chain reaction (RT-PCR) test. A total of 16951 asymptomatic individuals were tested by the Ministry of Public Health track-and-trace team using both rapid immunodiagnostic test and RT-PCR as part of screening across various random settings with potential risk of community interaction prior to gradual lifting of restrictions in Qatar. Rapid test was considered to be posiive if both IgG and IgM are positive, while only IgG/IgM positive was considered as rapid test negative. Sensitivity, specificity, positive predictive value (PPV) and negative predictive value (NPV) were calculated.Results: The sensitivity of rapid test kit was found to be 0.9%, whereas the specificity was found to be 97.8%. the PPV was found to be 0.3% whereas the NPV was found to be 99.4%.Conclusions: Based on the outcome and results of the study, it appears that the sensitivity and PPV of the rapid antibody test are low. As such, this test is not recommended for use to assist in taking clinic-based decisions or decisions related to quarantine/isolation. Significance for public health It is important to understand the performance characteristics of the Rapid Antibody (IgG-IgM) kits and they must be validated in the local population setting before they can be recommended for use.

A risk scoring system to predict the individual incidence of early-onset colorectal cancer

BackgroundThe incidence of early-onset colorectal cancer (EOCRC) is increasing at an alarming rate and further studies are needed to identify risk factors and to develop prevention strategies.MethodsRisk factors significantly associated with EOCRC were identified using meta-analysis. An individual risk appraisal model was constructed using the Rothman–Keller model. Next, a group of random data sets was generated using the binomial distribution function method, to determine nodes of risk assessment levels and to identify low, medium, and high risk populations.ResultsA total of 32,843 EOCRC patients were identified in this study, and nine significant risk factors were identified using meta-analysis, including male sex, Caucasian ethnicity, sedentary lifestyle, inflammatory bowel disease, and high intake of red meat and processed meat. After simulating the risk assessment data of 10,000 subjects, scores of 0 to 0.0018, 0.0018 to 0.0036, and 0.0036 or more were respectively considered as low-, moderate-, and high-risk populations for the EOCRC population based on risk trends from the Rothman–Keller model.ConclusionThis model can be used for screening of young adults to predict high risk of EOCRC and will contribute to the primary prevention strategies and the reduction of risk of developing EOCRC.

Bounding an archiving: assessing the relative completeness of the Jacques Toussele archive using pattern-matching and face-recognition

Archival research is haunted by the question of how complete are the archival fonds being consulted. In this article, we describe how we have used a combination of pattern-matching and face-recognition to evaluate the completeness of the Jacques Toussele photographic archive which was established as part of the Endangered Archives Programme at the British Library. A random set of scanned prints from the archive was matched with originating negatives also in the archive suggesting a survival rate of only 30%. Separately, an envelope of negatives from a single event in 1982 was analysed, looking at frame numbers from the surviving negatives. In this case, the survival rate was as high as 70%. Combinations of face-recognition and pattern-matching, for example, of fabric patterns or parts of backdrops, allow us to set some limits to the relative completeness or exhaustiveness of an otherwise relatively undocumented archive.

Best-practice severe accident uncertainty and sensitivity analysis for a short-term SBO sequence of a reference PWR using MAAP5

The integrated severe accident codes like MELCOR and MAAP5 include numerous uncertain models and parameters representing a wide range of physico-chemical phenomena for a comprehensive plant simulation, consequently making relevant uncertainty analysis a non-trivial task. In this paper, best-practice uncertainty and sensitivity analysis was performed to statistically quantify uncertainties associated with the analysis results of interest and identify potentially important uncertain parameters, based on the key modeling parameters employed in MAAP5. Three reference scenarios related to a short-term station blackout (STSBO) accident of a reference pressurized water reactor (PWR: OPR1000), were considered for the purpose: one base scenario and two mitigation scenarios to investigate the impact of dedicated severe accident mitigation (SAM) actions on the results of interest. A series of uncertainty and sensitivity analyses were carried out for these model parameters. Uncertainties for the results of interest were quantified through a random set of the Monte Carlo samples per case scenario, with values statistically sampled from the probability distributions of the individual model parameters. In addition, the relative importance of these model parameters to each relevant analysis result was then quantitatively evaluated through the sensitivity and importance analysis. Analysis results and relevant insights are summarized in terms of particular points of interest.

Cooperative-PHD Tracking Based on Distributed Sensors for Naval Surveillance Area.

Brazil has an extensive coastline and Exclusive Economic Zone (EEZ) area, which are of high economic and strategic importance. A Maritime Surveillance System becomes necessary to provide information and data to proper authorities, and target tracking is crucial. This paper focuses on a multitarget tracking application to a large-scale maritime surveillance system. The system is composed of a sensor network distributed over an area of interest. Due to the limited computational capabilities of nodes, the sensors send their tracking data to a central station, which is responsible for gathering and processing information obtained by the distributed components. The local Multitarget Tracking (MTT) algorithm employs a random finite set approach, which adopts a Gaussian mixture Probability Hypothesis Density (PHD) filter. The proposed data fusion scheme, utilized in the central station, consists of an additional step of prune & merge to the original GM PHD filter algorithm, which is the main contribution of this work. Through simulations, this study illustrates the performance of the proposed algorithm with a network composed of two stationary sensors providing the data. This solution yields a better tracking performance when compared to individual trackers, which is attested by the Optimal Subpattern Assignment (OSPA) metric and its location and cardinality components. The presented results illustrate the overall performance improvement attained by the proposed solution. Moreover, they also stress the need to resort to a distributed sensor network to tackle real problems related to extended targets.

Lattice structure of the random stable set in many-to-many matching markets

We study the lattice structure of the set of random stable matchings for a many-to-many matching market. We define a partial order on the random stable set and present two natural binary operations for computing the least upper bound and the greatest lower bound for each side of the matching market. Then we prove that with these binary operations the set of random stable matchings forms two distributive lattices for the appropriate partial order, one for each side of the market. Moreover, these lattices are dual.

Intersections of random sets

AbstractWe consider a variant of a classical coverage process, the Boolean model in $\mathbb{R}^d$ . Previous efforts have focused on convergence of the unoccupied region containing the origin to a well-studied limit C. We study the intersection of sets centered at points of a Poisson point process confined to the unit ball. Using a coupling between the intersection model and the original Boolean model, we show that the scaled intersection converges weakly to the same limit C. Along the way, we present some tools for studying statistics of a class of intersection models.

A Soft Computing-Based Analysis of Cutting Rate and Recast Layer Thickness for AZ31 Alloy on WEDM Using RSM-MOPSO.

In the present research, the AZ31 alloy is machined by wire-cut electric discharge machining (WEDM). The experiments were designed according to the Box-Behnken design (BBD) of response surface methodology (RSM). The input process variables, namely servo feed (SF), pulse on-time (Ton), servo voltage (SV), and pulse off-time (Toff), were planned by BBD, and experiments were performed to investigate the cutting rate (CR) and recast layer thickness (RCL). The analysis of variance (ANOVA) was performed to determine the influence of machining variables on response characteristics. The empirical models developed for CR and RCL were solved using Multi-Objective Particle Swarm Optimization (MOPSO). Pareto optimal front is used for the collective optimization of CR and RCL. The optimal solution suggested by the hybrid approach of RSM-MOPSO is further verified using a confirmation test on the random setting indicated by the hybrid algorithm. It is found that the minimum RCL (6.34 µm) is obtained at SF: 1700; SV: 51 V; Toff: 10.5 µs; and Ton: 0.5 µs. However, maximum CR (3.18 m/min) is predicted at SF: 1900; SV: 40 V; Toff: 7 µs; and Ton: 0.9 µs. The error percentage of ±5.3% between the experimental results and predicted solutions confirms the suitability of the proposed hybrid approach for WEDM of AZ31.

Compressive strength prediction of basalt fiber reinforced concrete via random forest algorithm

Basalt fiber is a green non-polluting material with strong tensile mechanical properties. In this paper, the strength prediction model of basalt fiber concrete is constructed by random forest method based on experiments to study the strengthening effect of basalt fiber in concrete composites and explore the impact of different fiber sizes and fiber content on the strength of basalt fiber concrete. First, the compressive strength tests of BFRC under different stress states were performed at fiber volume fractions of 0.2%, 0.4%, 0.6% and fiber lengths of 6 mm, 12 mm and 18 mm to obtain stress–strain curves and peak compressive strength. Then, 70% of the original test data is used to establish a random forest training sample set, and the remaining 30% is used as a test set. According to the error outside the bag, the appropriate number of decision trees and leaf nodes are selected, and the influencing factors are ranked by importance. Then use the Pearson correlation diagram to analyze the correlation of each influencing factor, establish a random forest training model, and output the fitting prediction results of the model training set and the prediction set. Finally, the prediction results of random forest with BP neural network and support vector regression are measured by MSE, RMSE, and R2 evaluation metrics for performance. The results show that the random forest prediction model has a good model fitting ability. Compared with other algorithms, the accuracy of the RF model in the MSE index is increased by 8% and 18.8%, which further verifies the accuracy and reliability of the model.

Mean-square invariant manifolds for ill-posed stochastic evolution equations driven by nonlinear noise

This paper discerns the invariant manifold of a class of ill-posed stochastic evolution equations driven by a nonlinear multiplicative noise. To be more precise, we establish the existence of mean-square random unstable invariant manifold and only mean-square stable invariant set. Due to the lack of the Hille-Yosida condition, we construct a modified variation of constants formula by the resolvent operator. With the price of imposing an unusual condition involving a non-decreasing map, we set up the Lyapunov-Perron method and derive the required estimates. We also emphasize that the Lyapunov-Perron map in the forward time loses the invariant due to the adaptedness, we alternatively establish the existence of mean-square random stable sets.

Star discrepancy subset selection: Problem formulation and efficient approaches for low dimensions

Motivated by applications in instance selection, we introduce the star discrepancy subset selection problem, which consists of finding a subset of m out of n points that minimizes the star discrepancy. First, we show that this problem is NP-hard. Then, we introduce a mixed integer linear formulation (MILP) and a combinatorial branch-and-bound (BB) algorithm for the star discrepancy subset selection problem and we evaluate both approaches against random subset selection and a greedy construction on different use-cases in dimension two and three. Our results show that the MILP and BB are efficient in dimension two for large and small m/n ratio, respectively, and for not too large n. However, the performance of both approaches decays strongly for larger dimensions and set sizes.As a side effect of our empirical comparisons we obtain point sets of discrepancy values that are much smaller than those of common low-discrepancy sequences, random point sets, and of Latin Hypercube Sampling. This suggests that subset selection could be an interesting approach for generating point sets of small discrepancy value.