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The main goal in group testing is to recover a small subset of defective items from a larger population while efficiently reducing the total number of (possibly noisy) required tests/measurements. Under the assumption that the input-output statistical relationship (i.e., channel law) is known to the recovery algorithm, the fundamental as well as the computational limits of the group testing problem are relatively better understood than when these statistical relationships are unknown. Practical considerations, however, render this assumption inapplicable, and “blind” recovery/estimation procedures, independent of the input-output statistics, are desired. In this paper, we analyze the fundamental limits of a general noisy group testing problem, when this relationship is unknown. Specifically, in the first part of this paper, we propose an efficient scheme, based on the idea of separate-decoding of items (where each item is recovered separately), for which we derive sufficient conditions on the number of tests required for exact recovery. The difficulty in obtaining these conditions stems from the fact that we allow the number of defective items to grow with the population size, which in turn requires delicate concentration analysis of certain probabilities. Furthermore, we show that in several scenarios, our proposed scheme achieves the same performance as that of the corresponding non-blind recovery algorithm (where the input-output statistics are known), implying that the proposed blind scheme is robust/universal. Finally, in the second part of this paper, we propose also an inefficient combinatorial-based scheme (or, “joint-decoding”), for which we derive similar sufficient conditions. [ABSTRACT FROM AUTHOR]

The coronavirus disease 2019 (COVID-19) epidemic continues to spread rapidly around the world and nearly 20 millions people are infected. This paper utilises both single-locus analysis and joint-SNPs analysis for detection of significant single nucleotide polymorphisms (SNPs) in the phenotypes of symptomatic versus asymptomatic, the early collection time versus the late collection time, the old versus the young, and the male versus the female. Also, this paper analyses the relationship between any two SNPs via linkage disequilibrium analysis, and visualises the patterns of cumulative mutations of SNPs over collection time. The results are in three folds. First, the SNP which locates at the nucleotide position 4321 is found to be an independent significant locus associated with all the first three phenotypes. Moreover, 12 significant SNPs are found in the first two studies. Second, gene orf1ab containing SNP-4321 is detected to be significantly associated with the first three phenotypes, and the three genes S, ORF3a, and N, are detected to be significant in the first two phenotypes. Third, some of the detected genes or SNPs are related to the SARS-COV-2 as supported by literature survey, which indicates that the results here may be helpful for further investigation. [ABSTRACT FROM AUTHOR]

The conventional model of disjunctive group testing assumes that there are several defective elements (or defectives) among a large population, and a group test yields the positive response if and only if the testing group contains at least one defective element. The basic problem is to find all defectives using a minimal possible number of group tests. However, when the number of defectives is unknown there arises an additional problem, namely: how to estimate the random number of defective elements. In this paper, we concentrate on testing the hypothesis $H_0$ : the number of defectives $\leq s_1$ against the alternative hypothesis $H_1$ : the number of defectives $\geq s_2$. We introduce a new decoding algorithm based on the comparison of the number of tests having positive responses with an appropriate fixed threshold. For some asymptotic regimes on $s_1$ and $s_2$ , the proposed algorithm is shown to be order-optimal. Additionally, our simulation results verify the advantages of the proposed algorithm such as low complexity and a small error probability compared with known algorithms. [ABSTRACT FROM AUTHOR]

This paper considers the problem of adaptive group testing for isolating up to $k$ defective items from a population of size $n$. There exist restrictions or preferences which determine how the items can be pooled for testing. A graphical model formalizes the pooling restrictions and preferences. Such graph-constrained group testing is investigated in three settings: populations with defectives, populations facing the potential presence of inhibitors, and populations with community structures. Adaptive group testing frameworks are provided for each setting. In populations without inhibitors, existing non adaptive frameworks can isolate the defective items perfectly with $\Theta(k \log n/k)$ number of tests, where is the $\beta$ -mixing time of a random walk over the underlying graph. This paper provides a two-stage framework that can perfectly isolate up to $k$ defective items for a regular graph using $\Theta(k2 \log n k + k)$ number of tests, thus achieving an approximate gain of a factor of $k$ over the non-adaptive frameworks. This twostage framework's principles are extended to community-structured graphs and graphs with up to $r$ inhibitor items. In particular, when inhibitors are present in the graph, a four-stage group testing framework is proposed. The results show that in the regime $r= O(k)$ for a fully connected graph, $\Theta ((k+r)\log n/(k+r) + r\log n)$ tests are sufficient for isolating the defective items. This matches the corresponding necessary condition on tests which scales $(k+r)\log n$. The adaptive graphconstrained group testing framework is also empirically evaluated. [ABSTRACT FROM AUTHOR]

Stochastic gradient descent (SGD) has become the method of choice for training highly complex and nonconvex models since it can not only recover good solutions to minimize training errors but also generalize well. Computational and statistical properties are separately studied to understand the behavior of SGD in the literature. However, there is a lacking study to jointly consider the computational and statistical properties in a nonconvex learning setting. In this paper, we develop novel learning rates of SGD for nonconvex learning by presenting high-probability bounds for both computational and statistical errors. We show that the complexity of SGD iterates grows in a controllable manner with respect to the iteration number, which sheds insights on how an implicit regularization can be achieved by tuning the number of passes to balance the computational and statistical errors. As a byproduct, we also slightly refine the existing studies on the uniform convergence of gradients by showing its connection to Rademacher chaos complexities. [ABSTRACT FROM AUTHOR]

Group testing refers to the process of testing pooled samples to reduce the total number of tests. Given the current pandemic, and the shortage of test supplies for COVID-19, group testing can play a critical role in time and cost efficient diagnostics. In many scenarios, samples collected from users are also accompanied with auxiliary information (such as demographics, history of exposure, onset of symptoms). Such auxiliary information may differ across patients, and is typically not considered while designing group testing algorithms. In this paper, we abstract such heterogeneity using a model where the population can be categorized into clusters with different prevalence rates. The main result of this work is to show that exploiting knowledge heterogeneity can further improve the efficiency of group testing. Motivated by the practical constraints and diagnostic considerations, we focus on two-stage group testing algorithms, where in the first stage, the goal is to detect as many negative samples by pooling, whereas the second stage involves individual testing to detect any remaining samples. For this class of algorithms, we prove that the gain in efficiency is related to the concavity of the number of tests as a function of the prevalence. We also show how one can choose the optimal pooling parameters for one of the algorithms in this class, namely, doubly constant pooling. We present lower bounds on the average number of tests as a function of the population heterogeneity profile, and also provide numerical results and comparisons. [ABSTRACT FROM AUTHOR]

The basic goal of threshold group testing is to identify up to $d$ defective items among a population of $n$ items, where $d$ is usually much smaller than $n$. The outcome of a test on a subset of items is positive if the subset has at least $u$ defective items, negative if it has up to $\ell $ defective items, where $0 \leq \ell < u$ , and arbitrary otherwise. This is called threshold group testing. The parameter $g = u - \ell - 1$ is called the gap. In this paper, we focus on the case $g > 0$ , i.e., threshold group testing with a gap. Note that the results presented here are also applicable to the case $g = 0$ ; however, the results are not as efficient as those in related work. Currently, a few reported studies have investigated test designs and decoding algorithms for identifying defective items. Most of the previous studies have not been feasible because there are numerous constraints on their problem settings or the decoding complexities of their proposed schemes are relatively large. Therefore, it is compulsory to reduce the number of tests as well as the decoding complexity, i.e., the time for identifying the defective items, for achieving practical schemes. The work presented here makes five contributions. The first is a more accurate theorem for a non-adaptive algorithm for threshold group testing proposed by Chen and Fu. The second is an improvement in the construction of disjunct matrices, which are the main tools for tackling (threshold) group testing and other tasks such as constructing cover-free families or learning hidden graphs. Specifically, we present a better exact upper bound on the number of tests for disjunct matrices compared with that in related work. The third and fourth contributions are a reduced exact upper bound on the number of tests and a reduced asymptotic bound on the decoding time for identifying defective items in a noisy setting on test outcomes. The fifth contribution is a simulation on the number of tests of the resulting improvements for previous work and the proposed theorems. [ABSTRACT FROM AUTHOR]

This paper studies the problem of developing an efficient signal sampling framework for distributed blind spectrum sensing, together with the corresponding local cognitive radio (CR) decision and fusion rules. A novel collaborative sampling and binary output (CSBO) generating scheme is proposed to overcome the disadvantage of traditional energy detectors for blind spectrum sensing, in which the signal-to-noise ratio (SNR) and level of noise power at the CRs are unknown and thus the decision threshold of local energy detectors cannot be specified. In designing the fusion rule in conjunction with the proposed CSBO scheme, both fixed-sample-size tests and sequential tests are considered. It is theoretically shown that the proposed CSBO scheme outperforms traditional blind cooperative energy detectors with uniform sampling schemes in terms of its ability to increase the amount of information acquired under a given number of samples. Simulation results confirm the theoretical analyses, and demonstrate that, compared with the fixed-sample-size test, the sequential test requires fewer observations on average to achieve comparable detection performance. The reduction in the expected sample size needed in the sequential CSBO test when compared to the fixed-sample-size CSBO can reach 50% when primary signal is present. [ABSTRACT FROM AUTHOR]

In the classical non-adaptive group testing setup, pools of items are tested together, and the main goal of a recovery algorithm is to identify the complete defective set given the outcomes of different group tests. In contrast, the main goal of a non-defective subset recovery algorithm is to identify a subset of non-defective items given the test outcomes. In this paper, we present a suite of computationally efficient and analytically tractable non-defective subset recovery algorithms. By analyzing the probability of error of the algorithms, we obtain bounds on the number of tests required for non-defective subset recovery with arbitrarily small probability of error. Our analysis accounts for the impact of both the additive noise (false positives) and dilution noise (false negatives). By comparing with information theoretic lower bounds, we show that the upper bounds on the number of tests are orderwise tight up to a \log ^2K factor, where $K$ is the number of defective items. We also provide simulation results that compare the relative performance of the different algorithms and reveal insights into their practical utility. The proposed algorithms significantly outperform the straightforward approaches of testing items one-by-one, and of first identifying the defective set and then choosing the non-defective items from the complement set, in terms of the number of measurements required to ensure a given success rate. [ABSTRACT FROM PUBLISHER]

In group testing, simple binary-output tests are designed to identify a small number $t$ of defective items that are present in a large population of $N$ items. Each test takes as input a group of items and produces a binary output indicating whether the group is free of the defective items or contains one or more of them. In this paper, we study a relaxation of the combinatorial group testing problem. A matrix is called $(t,\epsilon )$ -disjunct if it gives rise to a nonadaptive group testing scheme with the property of identifying a uniformly random $t$ -set of defective subjects out of a population of size $N$ with false positive probability of an item at most $\epsilon $ . We establish a new connection between $(t,\epsilon )$ -disjunct matrices and error correcting codes based on the dual distance of the codes and derive estimates of the parameters of codes that give rise to such schemes. Our methods rely on the moments of the distance distribution of codes and inequalities for moments of sums of independent random variables. We also provide a new connection between group testing schemes and combinatorial designs. [ABSTRACT FROM PUBLISHER]

A standard procedure for evaluating the performance of classification algorithms is k-fold cross validation. Since the training sets for any pair of iterations in k-fold cross validation are overlapping when the number of folds is larger than two, the resulting accuracy estimates are considered to be dependent. In this paper, the overlapping of training sets is shown to be irrelevant in determining whether two fold accuracies are dependent or not. Then a statistical method is proposed to test the appropriateness of assuming independence for the accuracy estimates in k-fold cross validation. This method is applied on 20 data sets, and the experimental results suggest that it is generally appropriate to assume that the fold accuracies are independent. The cross validation of non-overlapping training sets can make fold accuracies to be dependent. However, this dependence almost has no impact on estimating the sample variance of fold accuracies, and hence they can generally be assumed to be independent. [ABSTRACT FROM PUBLISHER]

Recognizing human activity is very useful for an investigator about a patient’s behavior and can aid in prescribing activity in future recommendations. The use of body worn accelerometers has been demonstrated to be an accurate measure of human activity; however, research looking at the use of multiple body worn accelerometers in a free living environment to recognize a wide range of activities is not evident. This paper aimed to successfully recognize activity and sub-category activity types through the use of multiple body worn accelerometers in a free-living environment. Ten participants (Age = 23.1 ± 1.7 years, height =171.0 ± 4.7 cm, and mass = 78.2 ± 12.5 Kg) wore nine body-worn accelerometers for a day of free living. Activity type was identified through the use of a wearable camera, and subcategory activities were quantified through a combination of free-living and controlled testing. A variety of machine learning techniques consisting of preprocessing algorithms, feature, and classifier selections were tested, accuracy, and computing time were reported. A fine k-nearest neighbor classifier with mean and standard deviation features of unfiltered data reported a recognition accuracy of 97.6%. Controlled and free-living testing provided highly accurate recognition for sub-category activities (>95.0%). Decision tree classifiers and maximum features demonstrated to have the lowest computing time. Results show that recognition of activity and sub-category activity types is possible in a free-living environment through the use of multiple body worn accelerometers. This method can aid in prescribing recommendations for activity and sedentary periods for healthy living. [ABSTRACT FROM PUBLISHER]

Dependence degree (DD) and importance degree (ID) of patterns are crucial for pattern appraisement and model reconstruction. In rough set data analysis (RSDA), DD and ID lack robustness because the lower approximation set is terribly unstable under the indiscernibility relation perturbation. Statistical inference is a good way to deal with this instability. However, the fixed-value hypothesis testing and interval estimation of DD and ID were only discussed by the $\chi ^2$ test, which merely suits for two contingency tables (CT) with the same number of elements, and their nonzero elements must exist at the same positions. These requirements are too strict for practical applications. In this paper, the Kolmogorov–Smirnov (K–S) goodness-of-fit test is introduced to generalize the statistical inferences of DD and ID. As the bridge between data and corresponding measures, CT lies at the core of RSDA. By transforming CT to a random sample of a hypothesized random variable, the elementary algorithm for the goodness-of-fit test of contingency tables and the advanced algorithm for the goodness-of-fit test of contingency tables are proposed based on K–S statistic to implement goodness-of-fit tests of CTs. Better than $\chi ^2$ test, all CTs, even with different numbers and different positions of nonzero elements, are permitted. Subsequently, by generating a CT with expected DD value, the fixed-value hypothesis of DD is transformed to the goodness-of fit test between the original and expected CTs. Three algorithms, i.e., hypothesis test of dependence degree based on the K–S test, region estimation of the dependence degree, and significance test and region estimation of importance degree of attribute set, are proposed as fixed-value hypothesis tests and region estimations of DD and ID. These algorithms can be used to verify the importance of attributes and choose the attribute subset with the highest likelihood of maintaining the original discrimination ability. Experiments verify that the discrimination ability, disturbance tolerance ability, and stability under varying discretization strategies of DD and ID are significantly enhanced by the proposed algorithms. [ABSTRACT FROM PUBLISHER]

In 2009 Tausch developed a simple equation to predict the cumulative probability of a single uncorrectable (double bit) error occurring within Hamming protected memory as the number of random upsets increase. This paper furthers that work by: 1) developing a simplified equation that predicts the number of failing addresses vs. random upsets in Hamming protected memories, 2) showing the range over which this simplified equation matches more complicated, 3) proving the validity of this equation through radiation testing, 4) showing how this equation can be used to improve test techniques in various simulator environments and 5) showing how this equation can be used to better analyze test results and to understand and predict the behavior of Hamming memories in radiation environments. An approach will be described to better calculate upset cross-sections of Hamming protected SRAMs in heavy ion environments. [ABSTRACT FROM AUTHOR]

In this paper, we derive mutual information based upper bounds on the number of nonadaptive group tests required to identify a given number of “non-defective” items from a large population containing a small number of “defective” items. In the asymptotic regime with the population size $N \rightarrow \infty$ , to identify $L$ nondefective items out of a population containing $K$ defective items, our results show that $\frac{C_s K}{1-o(1)} (\Phi (\alpha _0, \beta _0) + o(1))$ measurements are sufficient when the tests are reliable. Here, $C_s$ is a constant independent of $N, K$ , and $L$ , and $\Phi (\alpha _0, \beta _0)$ is a bounded function of $\alpha _0 \triangleq \lim _{N\rightarrow \infty } \frac{L}{N-K}$ and $\beta _0 \triangleq \lim _{N\rightarrow \infty } \frac{K}{N-K}$. In contrast, the necessary number of tests using the conventional approach of first identifying the $K$ defective items and picking the required number of nondefective items from the complement set grows with $N$ as $O\left(K \log N \right)$. We also derive upper bounds on the number of tests under both dilution and additive noise models. Our results are obtained under a very general sparse signal model, by virtue of which, they are also applicable to other important sparse signal based applications such as compressive sensing. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of testing the equality of $M$ covariance matrices. We first identify a suitable group of transformations leaving the problem invariant and obtain the corresponding maximal invariant statistic. Then, the Generalized Likelihood Ratio Test (GLRT) is recalled and explicit expressions for Rao, Wald, Gradient, and Durbin tests are provided. Also, equivalences among them and with other well-known tests proposed in open literature (mostly for the real-valued case) are analyzed and compared. Finally, the application of the proposed framework to the relevant signal processing application of multipass Coherent Change Detection (CCD) in polarimetric synthetic aperture radar is demonstrated both on simulated and on live data. [ABSTRACT FROM PUBLISHER]

Published by the Combined DNA Index System (CODIS) program of the Federal Bureau of Investigation (FBI) in 1997, the 13 core short tandem repeat (STR) loci are widely adopted as genetic markers in forensic applications, e.g., identity testing and paternity testing. However, these loci may be biased and suffer from reduced sensitivities toward specific population groups. In addition, the rapid growth of entries in forensic databases raises the chance of random hits, which can cause false recognitions of criminal suspects. A solution to these problems is to introduce more effective STR markers. The availability of whole genome sequencing enables us to identify more reliable STRmarkers for forensic applicationscomputationally. In this paper, we proposed an algorithm to identify STR markers with high discriminative abilities from the next-generation sequencing data. Our algorithm could select a customized set of loci for a given population with pre-specified discriminative thresholds. We have applied the method to 320 Chinese individuals from the 1000 Genomes Project and obtained various numbers of loci, which were able to statistically identify an individualworldwide and had higher combined powers of discrimination and combined probabilities of exclusion than the existing CODIS 13 loci. For identity testing, themean frequencyofDNAprofile (FDP) with the selected 11 STRs was smaller than that with CODIS 13 STRs by student’s t-test. With more loci, much smaller FDPs were obtained. The databasematching probabilities for selected loci were also lower than that for CODIS 13 STRs in a database with 10 billion entries. Moreover, the selected loci were able to provide considerably low chance of random profile matches so that statistically no false positives could occur. The selected loci also reduced the risk of random allele matches when doing the familial search, with lower random allele matching probabilities. In addition, the selected STRs were statistically better than CODIS STRs for paternity testing in our simulated data, with lower probabilities of false inclusions and exclusions. [ABSTRACT FROM PUBLISHER]

Traditional reliability analysis and prediction are performed by utilizing observed failure or degradation data of test units or field observations. Reliability testing is usually performed to predict reliability or performed as acceptance testing or reliability demonstration test. Moreover, in many cases, reliability tests are performed repeatedly during the entire life of the system by testing different samples with different characteristics in the system. At the end of each test, available data only show the number and combination of failed units which are then used for reliability estimation and prediction. This paper investigates several effective approaches to obtain expressions for system reliability metrics under different scenarios, considering the mixture characteristics of the units. The proposed approaches apply to general cases when the population size, as well as the mixture of units, increase over time. A simulation model is utilized to validate the proposed models. [ABSTRACT FROM AUTHOR]

A way to reduce the cost of regression testing consists of selecting or prioritizing subsets of test cases from a test suite according to some criteria. Besides greedy algorithms, cost cognizant additional greedy algorithms, multi-objective optimization algorithms, and multi-objective genetic algorithms (MOGAs), have also been proposed to tackle this problem. However, previous studies have shown that there is no clear winner between greedy and MOGAs, and that their combination does not necessarily produce better results. In this paper we show that the optimality of MOGAs can be significantly improved by diversifying the solutions (sub-sets of the test suite) generated during the search process. Specifically, we introduce a new MOGA, coined as DIversity based Genetic Algorithm (DIV-GA), based on the mechanisms of orthogonal design and orthogonal evolution that increase diversity by injecting new orthogonal individuals during the search process. Results of an empirical study conducted on eleven programs show that DIV-GA outperforms both greedy algorithms and the traditional MOGAs from the optimality point of view. Moreover, the solutions (sub-sets of the test suite) provided by DIV-GA are able to detect more faults than the other algorithms, while keeping the same test execution cost. [ABSTRACT FROM PUBLISHER]

Establishment of structural and functional correspondences of human brain that can be quantitatively encoded and reproduced across different subjects and populations is one of the key issues in brain mapping. As an attempt to address this challenge, our recently developed Dense Individualized and Common Connectivity-based Cortical Landmarks (DICCCOL) system reported 358 connectional landmarks, each of which possesses consistent DTI-derived white matter fiber connection pattern that is reproducible in over 240 healthy brains. However, the DICCCOL system can be substantially improved by integrating anatomical and morphological information during landmark initialization and optimization procedures. In this paper, we present a novel anatomy-guided landmark discovery framework that defines and optimizes landmarks via integrating rich anatomical, morphological, and fiber connectional information for landmark initialization, group-wise optimization and prediction, which are formulated and solved as an energy minimization problem. The framework finally determined 555 consistent connectional landmarks. Validation studies demonstrated that the 555 landmarks are reproducible, predictable, and exhibited reasonably accurate anatomical, connectional, and functional correspondences across individuals and populations and thus are named anatomy-guided DICCCOL or A-DICCCOL. This A-DICCCOL system represents common cortical architectures with anatomical, connectional, and functional correspondences across different subjects and would potentially provide opportunities for various applications in brain science. [ABSTRACT FROM AUTHOR]

The problem of classifying graphs with respect to connectivity via partial observations of nodes is posed as a composite hypothesis testing problem with controlled sensing. An observation at a node is a subset of edges incident to the node on the complete graph drawn according to a probability model, which is a function of a fixed underlying graph. Connectivity is measured through average node degree and is classified with respect to a threshold. A simple approximation of the controlled sensing test is derived and simulated on Erdös-Rènyi graphs to characterize the error probabilities as a function of the expected stopping times. The test is also experimentally validated on a real-world example of the social structure of Long-Tailed Manakins. It is shown that the proposed test achieves favorable tradeoffs between the classification error and the number of measurements. Furthermore, the test outperforms existing approaches, especially at low target error rates. In addition, the proposed test achieves the optimal error exponent. [ABSTRACT FROM PUBLISHER]

We consider non-adaptive threshold group testing for identification of up to $d$ defective items in a set of $n$ items, where a test is positive if it contains at least $2 \leq u \leq d$ defective items, and negative otherwise. The defective items can be identified using $t = O \left ({\left ({\frac {d}{u} }\right)^{u} \left ({\frac {d}{d - u} }\right)^{d-u} \left ({u \log {\frac {d}{u}} + \log {\frac {1}{\epsilon }} }\right) \cdot d^{2} \log {n} }\right)$ tests with probability at least $1 - \epsilon $ for any $\epsilon > 0$ or $t = O \left ({\left ({\frac {d}{u} }\right)^{u} \left ({\frac {d}{d -u} }\right)^{d - u} d^{3} \log {n} \cdot \log {\frac {n}{d}} }\right)$ tests with probability 1. The decoding time is $t \times (d^{2} \log {n})$. This result significantly improves the best known results for decoding non-adaptive threshold group testing: $O\left({n\log {n} + n \log {\frac {1}{\epsilon }}}\right)$ for probabilistic decoding, where $\epsilon > 0$ , and $O(n^{u} \log {n})$ for deterministic decoding. [ABSTRACT FROM AUTHOR]

Multiple-input multiple-output technology brings new challenges for detecting signal parameters in some intelligent systems. An accurate estimation of the transmit-antenna number is the prerequisite for estimating other signal parameters. Employing random matrix theory, we propose two hypothesis testing based algorithms to blindly estimate the transmit-antenna number. By exploiting hypothesis testing, the blind estimation problem is converted to a location problem, which seeks the location of the boundary between the signal subspace and the noise subspace of the received sample covariance matrix. Then, the estimated transmit-antenna number is determined by the dimension of the signal subspace. Extensive simulations verify that the two proposed algorithms perform better under a wide range of signal-to-noise ratios and sample lengths, compared with conventional algorithms based on Akaike information criterion, minimum description length, and predicted eigenvalue threshold. [ABSTRACT FROM AUTHOR]

Robust estimators and Wald-type tests are developed for the multinomial logistic regression based on $\phi $ -divergence measures. We compute the influence function of the proposed estimators and tests and discuss some consequences. Their robustness is illustrated by an extensive simulation study and two real examples. [ABSTRACT FROM AUTHOR]

In order to identify the infected individuals of a population, their samples are divided in equally sized groups called pools and a single laboratory test is applied to each pool. Individuals whose samples belong to pools that test negative are declared healthy, while each pool that tests positive is divided into smaller, equally sized pools which are tested in the next stage. In the $(k+1)$ -th stage all remaining samples are tested. If $p< 1-3^{-1/3}$ , we minimize the expected number of tests per individual as a function of the number $k+1$ of stages, and of the pool sizes in the first $k$ stages. We show that for each $p\in (0, 1-3^{-1/3})$ the optimal choice is one of four possible schemes, which are explicitly described. We conjecture that for each $p$ , the optimal choice is one of the two sequences of pool sizes $(3^{k} \text {or }3^{k-1}4,3^{k-1}, {\dots },3^{2},3)$ , with a precise description of the range of $p$ ’s where each is optimal. The conjecture is supported by overwhelming numerical evidence for $p>2^{-51}$. We also show that the cost of the best among the schemes $(3^{k}, {\dots },3)$ is of order $O\big (p\log (1/p)\big)$ , comparable to the information theoretical lower bound $p\log _{2}(1/p)+(1-p)\log _{2}(1/(1-p))$ , the entropy of a Bernoulli $(p)$ random variable. [ABSTRACT FROM AUTHOR]

Throughout the COVID-19 pandemic, nonpharmaceutical interventions, such as mobility restrictions, have been globally adopted as critically important strategies to curb the spread of infection. However, such interventions come with immense social and economic costs and the relative effectiveness of different mobility restrictions are not well understood. Some recent works have used telecoms data sources that cover fractions of a population to understand behavioral changes and how these changes have impacted case growth. This study analyzed uniquely comprehensive datasets in order to examine the relationship between mobility and transmission of COVID-19 in the country of Andorra. The data consisted of spatio-temporal telecoms data for all mobile subscribers in the country, serology screening results for 91% of the population, and COVID-19 case reports. A comprehensive set of mobility metrics was developed using the telecoms data to indicate entrances to the country, contact with tourists, stay-at-home rates, trip-making and levels of crowding. Mobility metrics were compared to infection rates across communities and transmission rate over time. All metrics dropped sharply at the start of the country's lockdown and gradually rose again as the restrictions were gradually lifted. Several of these metrics were highly correlated with lagged transmission rate. There was a stronger correlation for measures of indoor crowding and inter-community trip-making, and a weaker correlation for total trips (including intra-community trips) and stay-at-homes rates. These findings provide support for policies which aim to discourage gathering indoors while lifting the most restrictive mobility limitations. [ABSTRACT FROM AUTHOR]

Common reporting styles for statistical results in scientific articles, such as $p$ p -values and confidence intervals (CI), have been reported to be prone to dichotomous interpretations, especially with respect to the null hypothesis significance testing framework. For example when the $p$ p -value is small enough or the CIs of the mean effects of a studied drug and a placebo are not overlapping, scientists tend to claim significant differences while often disregarding the magnitudes and absolute differences in the effect sizes. This type of reasoning has been shown to be potentially harmful to science. Techniques relying on the visual estimation of the strength of evidence have been recommended to reduce such dichotomous interpretations but their effectiveness has also been challenged. We ran two experiments on researchers with expertise in statistical analysis to compare several alternative representations of confidence intervals and used Bayesian multilevel models to estimate the effects of the representation styles on differences in researchers’ subjective confidence in the results. We also asked the respondents’ opinions and preferences in representation styles. Our results suggest that adding visual information to classic CI representation can decrease the tendency towards dichotomous interpretations – measured as the ‘cliff effect’: the sudden drop in confidence around $p$ p -value 0.05 – compared with classic CI visualization and textual representation of the CI with $p$ p -values. All data and analyses are publicly available at https://github.com/helske/statvis. [ABSTRACT FROM AUTHOR]

In the group testing problem we aim to identify a small number of infected individuals within a large population. We avail ourselves to a procedure that can test a group of multiple individuals, with the test result coming out positive iff at least one individual in the group is infected. With all tests conducted in parallel, what is the least number of tests required to identify the status of all individuals? In a recent test design [Aldridge et al. 2016] the individuals are assigned to test groups randomly with replacement, with every individual joining an almost equal number of groups. We pinpoint the sharp threshold for the number of tests required in this randomised design so that it is information-theoretically possible to infer the infection status of every individual. Moreover, we analyse two efficient inference algorithms. These results settle conjectures from [Aldridge et al. 2014, Johnson et al. 2019]. [ABSTRACT FROM AUTHOR]

To reopen the economy safely during the COVID-19 pandemic, governments need the capability to proactively identify new and often asymptomatic infections, as well as contact tracing. Policymakers and public health professionals need a sampling-testing method that can achieve broad population coverage without overwhelming medical workers. We observe that COVID-19 high-risk groups are located in the hubs and cliques of our geo-social network, formed by the close encounters of people during daily life. These individuals are the de facto “canary in a coal mine”. We propose that nations offer free and anonymous testing service to them. With open-source computer algorithms and datasets, only a small fraction of the population selected for COVID-19 testing can cover the majority of high-exposure-risk individuals. A 0.3% sampled testing for a megacity covers 3/4 of its entire population. A 3% sampled testing for a rural town covers 3/4 of its entire population. With government oversight and public consent, this approach can serve each province/state or city/township for decentralized daily testing planning. However, to protect privacy, we recommend constructing the geo-social network of anonymized cellphones, not named individuals. This infrastructure should be dismantled once the pandemic is largely over. This can be achieved by policymakers, health workers, and engineers together in solidarity. [ABSTRACT FROM AUTHOR]

Testing is one of the most important parts of the software process, which aims at detecting software faults/bugs and thus guarantees the quality of the final product. Its expense is nearly half of the total cost of software development [7], [9]. Most of the current approaches to software testing are manual, but it has been recently suggested [1] that automated testing should be done to save human resources and budget, as well as to produce high-quality software. [ABSTRACT FROM PUBLISHER]