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A deep learning-based Visual Inertial SLAM technique is proposed in this paper to ensure accurate autonomous localization of mobile robots in environments with dynamic objects. Addressing the limitations of real-time performance in deep learning algorithms and the poor robustness of pure visual geometry algorithms, this paper presents a deep learning-based Visual Inertial SLAM technique. Firstly, a non-blocking model is designed to extract semantic information from images. Then, a motion probability hierarchy model is proposed to obtain prior motion probabilities of feature points. For image frames without semantic information, a motion probability propagation model is designed to determine the prior motion probabilities of feature points. Furthermore, considering that the output of inertial measurements is unaffected by dynamic objects, this paper integrates inertial measurement information to improve the estimation accuracy of feature point motion probabilities. An adaptive threshold-based motion probability estimation method is proposed, and finally, the positioning accuracy is enhanced by eliminating feature points with excessively high motion probabilities. Experimental results demonstrate that the proposed algorithm achieves accurate localization in dynamic environments while maintaining real-time performance. [ABSTRACT FROM AUTHOR]

In this paper, we propose a Grid-based Non-uniform Probability Density Sampling Probabilistic Roadmap algorithm (GN-PRM) in response to the challenges of difficult sampling in narrow passages and low-probability map generation in traditional Probabilistic Roadmap algorithms (PRM). The improved algorithm incorporates grid-based processing for map segmentation, employing non-uniform probability density sampling based on the different attributes of each block to enhance sampling probability in narrow passages. Additionally, considering the computational cost and frequent ineffective searches in traditional PRM algorithms during pathfinding, this paper optimizes the time required for query route planning by altering connection strategies to improve the algorithm's runtime. Finally, the simulation results indicate that, with a reduction of over 50% in undirected line segments and a reduction of over 85% in runtime, the GN-PRM algorithm achieves a 100% success rate in complex planning scenarios with a sampling point value of K = 500. In comparison, the traditional PRM algorithm has a success rate of no more than 10%, with a sampling point value of K = 500. [ABSTRACT FROM AUTHOR]

We propose in this paper two heuristic strategies to solve the regenerator placement problem (RPP) in translucent networks under dynamic traffic. The heuristics are based on both the forecast of the offered load and estimates of blocking probabilities in the network nodes. The proposed heuristics are compared to other regenerator placement algorithms from the literature in two different topologies. The results show that one of the proposed algorithms outperforms, in the investigated scenarios, all other algorithms from the literature considered for comparison purposes in this paper, whereas the second proposed algorithm outperforms the algorithms from the literature only in some considered scenarios. [ABSTRACT FROM AUTHOR]

The binomial distribution is the probability distribution of the number of successes for a sequence of n independent trials with success probability p. Efficiently generating binomial random variates is important in many modeling and simulation applications, such as in medicine, risk management, and fraud and anomaly detection, among others. A variety of algorithms exist for generating binomial random variates. This paper concerns the algorithm chosen for ρ μ , an open source Java library for efficient randomization, which uses a hybrid of two existing binomial random variate algorithms: the BTPE Algorithm (Binomial, Triangle, Parallelogram, Exponential) and the inverse transform for cases that BTPE cannot handle. BTPE uses rejection sampling, and BTPE's authors originally provided an analytical formula for the expected number of iterations in terms of n and p. That expression is complicated to interpret in practical contexts. I explore BTPE by instrumenting ρ μ 's implementation to empirically analyze its acceptance/rejection behavior to gain further insights into its runtime performance. Although the number of iterations depends upon n and p, my experiments show that the average number of iterations is always under two, and that the average number of random uniform variates required to generate a single random binomial is under four (two per iteration). Thus, when analyzing the runtime of a simulation algorithm that includes steps generating random binomials, one can consider such steps to have a constant runtime. [ABSTRACT FROM AUTHOR]

Link prediction aims to identify unknown or missing connections in a network. The methods based on network structure similarity, known for their simplicity and effectiveness, have garnered widespread attention. A core metric in these methods is "proximity", which measures the similarity or linking probability between two nodes. These methods generally operate under the assumption that node pairs with higher proximity are more likely to form new connections. However, the accuracy of existing node proximity-based link prediction algorithms requires improvement. To address this, this paper introduces a Link Prediction Algorithm Based on Weighted Local and Global Closeness (LGC). This algorithm integrates the clustering coefficient to enhance prediction accuracy. A significant advantage of LGC is its dual consideration of a network's local and global features, allowing for a more precise assessment of node similarity. In experiments conducted on ten real-world datasets, the proposed LGC algorithm outperformed eight traditional link prediction methods, showing notable improvements in key evaluation metrics, namely precision and AUC. [ABSTRACT FROM AUTHOR]

This paper investigates the routing, modulation, and spectrum assignment (RMSA) problem for advance reservation (AR) requests in semi-filterless optical networks (semi-FONs). A link resource-aware (LRA) algorithm consisting of three parts is proposed. First, in the request scheduling phase, a request sorting strategy based on the flexible window size of the starting time is proposed. This strategy schedules AR requests based on the size of a flexible window with respect to the starting time. Next, in the routing phase, a link resource-aware strategy is proposed. This strategy evenly distributes the requests across the network resources, thereby avoiding request blocking due to excessive resource occupation on a single or few links. In the spectrum assignment phase, a frequency–time block-based metric is employed to measure the availability of each frequency–time block for AR requests. This metric is a sum of two factors: the distance to the block and spectrum boundaries, and the time interval between the request start time and the earliest start time. Our simulation results demonstrate that the proposed LRA algorithm has a lower blocking probability compared to the benchmark algorithms. [ABSTRACT FROM AUTHOR]

Simple Summary: Cancer is basically a tough condition on a patient's body where cell grows uncontrollably. Normal cells are affected, which destroys the health of the patient. The main problem in cancer is spreading from one part to another. Therefore, the mathematical modeling of cancerous tumors integrates to check overall stability. A novel approach is introduced such as Bernstein polynomial with combination of genetic algorithm, sliding mode controller, and synergetic control. The proposed solution has easily eliminated cancerous cells within five days using synergetic control. In addition, five cases are incorporated to evaluate error function. In addition, a brief comparative study is added to contrast the simulation results with theoretical modeling. Cancerous tumor cells divide uncontrollably, which results in either tumor or harm to the immune system of the body. Due to the destructive effects of chemotherapy, optimal medications are needed. Therefore, possible treatment methods should be controlled to maintain the constant/continuous dose for affecting the spreading of cancerous tumor cells. Rapid growth of cells is classified into primary and secondary types. In giving a proper response, the immune system plays an important role. This is considered a natural process while fighting against tumors. In recent days, achieving a better method to treat tumors is the prime focus of researchers. Mathematical modeling of tumors uses combined immune, vaccine, and chemotherapies to check performance stability. In this research paper, mathematical modeling is utilized with reference to cancerous tumor growth, the immune system, and normal cells, which are directly affected by the process of chemotherapy. This paper presents novel techniques, which include Bernstein polynomial (BSP) with genetic algorithm (GA), sliding mode controller (SMC), and synergetic control (SC), for giving a possible solution to the cancerous tumor cells (CCs) model. Through GA, random population is generated to evaluate fitness. SMC is used for the continuous exponential dose of chemotherapy to reduce CCs in about forty-five days. In addition, error function consists of five cases that include normal cells (NCs), immune cells (ICs), CCs, and chemotherapy. Furthermore, the drug control process is explained in all the cases. In simulation results, utilizing SC has completely eliminated CCs in nearly five days. The proposed approach reduces CCs as early as possible. [ABSTRACT FROM AUTHOR]

Effective personnel scheduling is crucial for organizations to match workload demands. However, staff scheduling is sometimes affected by unexpected events, such as the COVID-19 pandemic, that disrupt regular operations. Limiting the number of on-site staff in the workplace together with regular testing is an effective strategy to minimize the spread of infectious diseases like COVID-19 because they spread mostly through close contact with people. Therefore, choosing the best scheduling and testing plan that satisfies the goals of the organization and prevents the virus's spread is essential during disease outbreaks. In this paper, we formulate these challenges in the framework of two Mixed Integer Non-linear Programming (MINLP) models. The first model aims to derive optimal staff occupancy and testing strategies to minimize the risk of infection among employees, while the second is aimed only at optimal staff occupancy under a random testing strategy. To solve the problems expressed in the models, we propose a canonical genetic algorithm as well as two commercial solvers. Using both real and synthetic contact networks of employees, our results show that following the recommended occupancy and testing strategy reduces the risk of infection 25–60% under different scenarios. The minimum risk of infection can be achieved when the employees follow a planned testing strategy. Further, vaccination status and interaction rate of employees are important factors in developing scheduling strategies that minimize the risk of infection. [ABSTRACT FROM AUTHOR]

This paper generalizes the structural Markov properties for undirected decomposable graphs to arbitrary ones. This helps us to exploit the conditional independence properties of joint prior laws to analyze and compare multiple graphical structures, while being able to take advantage of the common conditional independence constraints. This work provides a theoretical support for full Bayesian posterior updating about the structure of a graph using data from a certain distribution. We further investigate the ratio of graph law so as to simplify the acceptance probability of the Metropolis–Hastings sampling algorithms. [ABSTRACT FROM AUTHOR]

With the increasing reliance on automated decision making, the issue of algorithmic fairness has gained increasing importance. In this paper, we propose a Generative Adversarial Network for tabular data generation. The model includes two phases of training. In the first phase, the model is trained to accurately generate synthetic data similar to the reference dataset. In the second phase we modify the value function to add fairness constraint, and continue training the network to generate data that is both accurate and fair. We test our results in both cases of unconstrained, and constrained fair data generation. We show that using a fairly simple architecture and applying quantile transformation of numerical attributes the model achieves promising performance. In the unconstrained case, i.e., when the model is only trained in the first phase and is only meant to generate accurate data following the same joint probability distribution of the real data, the results show that the model beats the state-of-the-art GANs proposed in the literature to produce synthetic tabular data. Furthermore, in the constrained case in which the first phase of training is followed by the second phase, we train the network and test it on four datasets studied in the fairness literature and compare our results with another state-of-the-art pre-processing method, and present the promising results that it achieves. Comparing to other studies utilizing GANs for fair data generation, our model is comparably more stable by using only one critic, and also by avoiding major problems of original GAN model, such as mode-dropping and non-convergence. [ABSTRACT FROM AUTHOR]

In recent movie recommendations, one of the most important issues is to predict the user's sequential behavior to be able to suggest the next movie to watch. However, capturing such sequential behavior is not easy because each user's short-term or long-term behavior must be taken into account. For this reason, many research results show that the performance of recommending a specific movie is not good in a sequential recommendation. In this paper, we propose a cluster-based method for classifying users with similar movie purchase patterns and a movie genre prediction algorithm rather than the movie itself considering their short-term and long-term behaviors. The movie genre prediction does not recommend a specific movie, but it predicts the genre for the next movie to watch in consideration of each user's preference for the movie genre based on the genre included in the movie. Using this, it will be possible to provide appropriate guidelines for recommending movies including the genres to users who tend to prefer a specific genre. In particular, in this study, users with similar genre preferences are organized into clusters to recommend genres. For clusters that do not have relatively specific tendencies, genre prediction is performed by appropriately trimming genres that are not necessary for recommendation in order to improve performance. We evaluate our method on well-known movie data sets and qualitatively determine that it captures personalized dynamics and is able to make meaningful recommendations. [ABSTRACT FROM AUTHOR]

In this paper, cluster analysis and the XGBoost method are used to analyze the related symptoms of various types of young hypertensive patients, and finally guide patients to target treatment. Hypertension is a chronic disease that is common worldwide. The incidence of it is increasing, and the age level of patients is decreasing year by year. Effective treatment of youth hypertension has become a problem in the world. In this paper, young hypertension patients are classified into two groups by cluster analysis; the proportion of different hypertension related symptoms in each group of patients is then counted; and after verifying the prediction accuracy of the XGBoost model with 10-fold cross-validation, the accuracy of clustering is calculated by the XGBoost method. The final result shows that there are significant differences in symptomatic entropy between patients with type II hypertension and those with type I hypertension. Patients with type II hypertension are more likely to have symptoms of ventricular hypertrophy and microalbuminuria. Through this analysis, patients can have preventive treatment according to their own situation, and this can reduce the burden of medical expenses and prevent major diseases. Applying the data analysis into the medical field has great practical significance. [ABSTRACT FROM AUTHOR]

Oblivious routing is a static algorithm for routing arbitrary user demands with the property that the competitive ratio, the proportion of the maximum congestion to the best possible congestion, is minimal. Oblivious routing turned out surprisingly efficient in this worst-case sense: in undirected graphs, we pay only a logarithmic performance penalty, and this penalty is usually smaller than 2 in directed graphs as well. However, compared to an optimal adaptive algorithm, which never causes congestion when subjected to a routable demand, oblivious routing surely has congestion. The open question is of how often is the network in a congested state. In this paper, we study two performance measures naturally arising in this context: the probability of congestion and the expected value of congestion. Our main result is the finding that, in certain directed graphs on n nodes, the probability of congestion approaches 1 in some undirected graphs, despite the competitive ratio being O (1) . [ABSTRACT FROM AUTHOR]

In order to provide the seamless navigation and positioning services for indoor environments, an indoor location based service (LBS) test bed is developed to integrate the indoor positioning system and the indoor three-dimensional (3D) geographic information system (GIS). A wireless sensor network (WSN) is used in the developed indoor positioning system. Considering the power consumption, in this paper the ZigBee radio is used as the wireless protocol, and the received signal strength (RSS) fingerprinting positioning method is applied as the primary indoor positioning algorithm. The matching processes of the user location include the nearest neighbor (NN) algorithm, the K-weighted nearest neighbors (KWNN) algorithm, and the probabilistic approach. To enhance the positioning accuracy for the dynamic user, the particle filter is used to improve the positioning performance. As part of this research, a 3D indoor GIS is developed to be used with the indoor positioning system. This involved using the computer-aided design (CAD) software and the virtual reality markup language (VRML) to implement a prototype indoor LBS test bed. Thus, a rapid and practical procedure for constructing a 3D indoor GIS is proposed, and this GIS is easy to update and maintenance for users. The building of the Department of Aeronautics and Astronautics at National Cheng Kung University in Taiwan is used as an example to assess the performance of various algorithms for the indoor positioning system. [ABSTRACT FROM AUTHOR]

The optimal fixed-point quantum search (OFPQS) algorithm [Phys. Rev. Lett. 113, 210501 (2014)] achieves both the fixed-point property and quadratic speedup over classical algorithms, which gives a sufficient condition on the number of iterations to ensure the success probability is no less than a given lower bound (denoted by 1 − δ 2 ). However, this condition is approximate and not exact. In this paper, we derive the sufficient and necessary condition on the number of feasible iterations, based on which the exact least number of iterations can be obtained. For example, when δ = 0. 8 , iterations can be saved by almost 25%. Moreover, to find a target item certainly, setting directly 1 − δ 2 = 100 % , the quadratic advantage of the OFPQS algorithm will be lost, then, applying the OFPQS algorithm with 1 − δ 2 < 100 % requires multiple executions, which leads to a natural problem of choosing the optimal parameter δ. For this, we analyze the extreme and minimum properties of the success probability and further analytically derive the optimal δ which minimizes the query complexity. Our study can be a guideline for both the theoretical and application research on the fixed-point quantum search algorithms. [ABSTRACT FROM AUTHOR]

In multi-target tracking, the key problem lies in estimating the number and states of individual targets, in which the challenge is the time-varying multi-target numbers and states. Recently, several multi-target tracking approaches, based on the sequential Monte Carlo probability hypothesis density (SMC-PHD) filter, have been presented to solve such a problem. However, most of these approaches select the transition density as the importance sampling (IS) function, which is inefficient in a nonlinear scenario. To enhance the performance of the conventional SMC-PHD filter, we propose in this paper two approaches using the cubature information filter (CIF) for multi-target tracking. More specifically, we first apply the posterior intensity as the IS function. Then, we propose to utilize the CIF algorithm with a gating method to calculate the IS function, namely CISMC-PHD approach. Meanwhile, a fast implementation of the CISMC-PHD approach is proposed, which clusters the particles into several groups according to the Gaussian mixture components. With the constructed components, the IS function is approximated instead of particles. As a result, the computational complexity of the CISMC-PHD approach can be significantly reduced. The simulation results demonstrate the effectiveness of our approaches. [ABSTRACT FROM AUTHOR]

Recently, developing efficient processing techniques in spatio-temporal databases has been a much discussed topic. Many applications, such as mobile information systems, traffic control system, and geographical information systems, can benefit from efficient processing of spatio-temporal queries. In this paper, we focus on processing an important type of spatio-temporal queries, the K-nearest neighbor (KNN) queries. Different from the previous research, the locations of objects are located by the sensors which are deployed in a grid-based manner. As the positioning technique used is not the GPS technique, but the sensor network technique, this results in a greater uncertainty regarding object location. With the uncertain location information of objects, we try to develop an efficient algorithm to process the KNN queries. Moreover, we design a probability model to quantify the possibility of each object being the query result. Finally, extensive experiments are conducted to demonstrate the efficiency of the proposed algorithms. [ABSTRACT FROM AUTHOR]

UAV trajectory planning is one of the research focuses in artificial intelligence and UAV technology. The asymmetric information, however, will lead to the uncertainty of the UAV trajectory planning; the probability theory as the most commonly used method to solve the trajectory planning problem in uncertain environment will lead to unrealistic conclusions under the condition of lacking samples, while the uncertainty theory based on uncertain measures is an efficient method to solve such problems. Firstly, the uncertainties in trajectory planning are sufficiently considered in this paper; the fuel consumption, concealment and threat degree with uncertain variables are taken as the objective functions; the constraints are analyzed according to the maneuverability; and the uncertain multi-objective trajectory planning (UMOTP) model is established. After that, this paper takes both the long-term benefits and its stability into account, and then, the expected-value and standard-deviation efficient trajectory model is established. What is more, this paper solves the Pareto front of the trajectory planning, satisfying various preferences, which avoids the defects of the trajectory obtained by traditional model only applicable to a certain specific situation. In order to obtain a better solution set, this paper proposes an improved backbones particle swarm optimization algorithm based on PSO and NSGA-II, which overcomes the shortcomings of the traditional algorithm such as premature convergence and poor robustness, and the efficiency of the algorithm is tested. Finally, the algorithm is applied to the UMOTP problem; then, the optimal trajectory set is obtained, and the effectiveness and reliability of the model is verified. [ABSTRACT FROM AUTHOR]

In a health management system, prognostics, which is an engineering discipline that predicts a system's future health, is an important aspect yet there is currently limited research in this field. In this paper, a hybrid approach for prognostics is proposed. The approach combines the least squares support vector regression (LSSVR) with the hidden Markov model (HMM). Features extracted from sensor signals are used to train HMMs, which represent different health levels. A LSSVR algorithm is used to predict the feature trends. The LSSVR training and prediction algorithms are modified by adding new data and deleting old data and the probabilities of the predicted features for each HMM are calculated based on forward or backward algorithms. Based on these probabilities, one can determine a system's future health state and estimate the remaining useful life (RUL). To evaluate the proposed approach, a test was carried out using bearing vibration signals. Simulation results show that the LSSVR/HMM approach can forecast faults long before they occur and can predict the RUL. Therefore, the LSSVR/HMM approach is very promising in the field of prognostics. [ABSTRACT FROM AUTHOR]

Kullback–Leibler divergence K L (p , q) is the standard measure of error when we have a true probability distribution p which is approximate with probability distribution q. Its efficient computation is essential in many tasks, as in approximate computation or as a measure of error when learning a probability. In high dimensional probabilities, as the ones associated with Bayesian networks, a direct computation can be unfeasible. This paper considers the case of efficiently computing the Kullback–Leibler divergence of two probability distributions, each one of them coming from a different Bayesian network, which might have different structures. The paper is based on an auxiliary deletion algorithm to compute the necessary marginal distributions, but using a cache of operations with potentials in order to reuse past computations whenever they are necessary. The algorithms are tested with Bayesian networks from the bnlearn repository. Computer code in Python is provided taking as basis pgmpy, a library for working with probabilistic graphical models. [ABSTRACT FROM AUTHOR]

The rise of machine learning-driven decision-making has sparked a growing emphasis on algorithmic fairness. Within the realm of clustering, the notion of balance is utilized as a criterion for attaining fairness, which characterizes a clustering mechanism as fair when the resulting clusters maintain a consistent proportion of observations representing individuals from distinct groups delineated by protected attributes. Building on this idea, the literature has rapidly incorporated a myriad of extensions, devising fair versions of the existing frequentist clustering algorithms, e.g., k-means, k-medioids, etc., that aim at minimizing specific loss functions. These approaches lack uncertainty quantification associated with the optimal clustering configuration and only provide clustering boundaries without quantifying the probabilities associated with each observation belonging to the different clusters. In this article, we intend to offer a novel probabilistic formulation of the fair clustering problem that facilitates valid uncertainty quantification even under mild model misspecifications, without incurring substantial computational overhead. Mixture model-based fair clustering frameworks facilitate automatic uncertainty quantification, but tend to showcase brittleness under model misspecification and involve significant computational challenges. To circumnavigate such issues, we propose a generalized Bayesian fair clustering framework that inherently enjoys decision-theoretic interpretation. Moreover, we devise efficient computational algorithms that crucially leverage techniques from the existing literature on optimal transport and clustering based on loss functions. The gain from the proposed technology is showcased via numerical experiments and real data examples. [ABSTRACT FROM AUTHOR]

Linear probing continues to be one of the best practical hashing algorithms due to its good average performance, efficiency, and simplicity of implementation. However, the worst-case performance of linear probing seems to degrade with high load factors due to a primary-clustering tendency of one collision to cause more nearby collisions. It is known that the maximum cluster size produced by linear probing, and hence the length of the longest probe sequence needed to insert or search for a key in a hash table of size n, is Ω (log n) , in probability. In this article, we introduce linear probing hashing schemes that employ two linear probe sequences to find empty cells for the keys. Our results show that two-way linear probing is a promising alternative to linear probing for hash tables. We show that two-way linear probing has an asymptotically almost surely O (log log n) maximum cluster size when the load factor is constant. Matching lower bounds on the maximum cluster size produced by any two-way linear probing algorithm are obtained as well. Our analysis is based on a novel approach that uses the multiple-choice paradigm and witness trees. [ABSTRACT FROM AUTHOR]

The retransmission threshold in wireless sensor networks is critical to the latency of data delivery in the networks. However, existing works on data transmission in sensor networks did not consider the optimization of the retransmission threshold, and they simply set the same retransmission threshold for all sensor nodes in advance. The method did not take link quality and delay requirement into account, which decreases the probability of a packet passing its delivery path within a given deadline. This paper investigates the problem of finding optimal retransmission thresholds for relay nodes along a delivery path in a sensor network. The object of optimizing retransmission thresholds is to maximize the summation of the probability of the packet being successfully delivered to the next relay node or destination node in time. A dynamic programming-based distributed algorithm for finding optimal retransmission thresholds for relay nodes along a delivery path in the sensor network is proposed. The time complexity is O(nΔ·max1≤i≤n{ui}), where ui is the given upper bound of the retransmission threshold of sensor node i in a given delivery path, n is the length of the delivery path and Δ is the given upper bound of the transmission delay of the delivery path. If Δ is greater than the polynomial, to reduce the time complexity, a linear programming-based (1 + pmin)-approximation algorithm is proposed. Furthermore, when the ranges of the upper and lower bounds of retransmission thresholds are big enough, a Lagrange multiplier-based distributedO(1)-approximation algorithm with time complexity O(1) is proposed. Experimental results show that the proposed algorithms have better performance. [ABSTRACT FROM AUTHOR]

Fault diagnosis in multistage manufacturing processes (MMPs) is a challenging task where most of the research presented in the literature considers a predefined inspection scheme to identify the sources of variation and make the process diagnosable. In this paper, a sequential inspection procedure to detect the process fault based on a sequential testing algorithm and a minimum monitoring system is proposed. After the monitoring system detects that the process is out of statistical control, the features to be inspected (end of line or in process measurements) are defined sequentially according to the expected information gain of each potential inspection measurement. A case study is analyzed to prove the benefits of this approach with respect to a predefined inspection scheme and a randomized sequential inspection considering both the use and non-use of fault probabilities from historical maintenance data. [ABSTRACT FROM AUTHOR]

In this paper, we study the problem of optimal routing for the pair of two-server heterogeneous queues operating in parallel and subsequent optimal allocation of customers between the servers in each queue. Heterogeneity implies different servers in terms of speed of service. An open-loop control assumes the static resource allocation when a router has no information about the state of the system. We discuss here the algorithm to calculate the optimal routing policy based on specially constructed Markov-modulated Poisson processes. As an alternative static policy, we consider an optimal Bernoulli splitting which prescribes the optimal allocation probabilities. Then, we show that the optimal allocation policy between the servers within each queue is of threshold type with threshold levels depending on the queue length and phase of an arrival process. This dependence can be neglected by using a heuristic threshold policy. A number of illustrative examples show interesting properties of the systems operating under the introduced policies and their performance characteristics. [ABSTRACT FROM AUTHOR]

Lattices used in cryptography are integer lattices. Defining and generating a "random integer lattice" are interesting topics. A generation algorithm for a random integer lattice can be used to serve as a random input of all the lattice algorithms. In this paper, we recall the definition of the random integer lattice given by G. Hu et al. and present an improved generation algorithm for it via the Hermite normal form. It can be proven that with probability ≥0.99, this algorithm outputs an n-dim random integer lattice within O (n 2) operations. [ABSTRACT FROM AUTHOR]

This paper employs Bayesian probability theory for analyzing data generated in femtosecond pump-probe photoelectron-photoion coincidence (PEPICO) experiments. These experiments allow investigating ultrafast dynamical processes in photoexcited molecules. Bayesian probability theory is consistently applied to data analysis problems occurring in these types of experiments such as background subtraction and false coincidences. We previously demonstrated that the Bayesian formalism has many advantages, amongst which are compensation of false coincidences, no overestimation of pump-only contributions, significantly increased signal-to-noise ratio, and applicability to any experimental situation and noise statistics. Most importantly, by accounting for false coincidences, our approach allows running experiments at higher ionization rates, resulting in an appreciable reduction of data acquisition times. In addition to our previous paper, we include fluctuating laser intensities, of which the straightforward implementation highlights yet another advantage of the Bayesian formalism. Our method is thoroughly scrutinized by challenging mock data, where we find a minor impact of laser fluctuations on false coincidences, yet a noteworthy influence on background subtraction. We apply our algorithm to data obtained in experiments and discuss the impact of laser fluctuations on the data analysis. [ABSTRACT FROM AUTHOR]

GDP is a classic indicator of the extent of national economic development. Research based on the World Trade Network has found that a country's GDP depends largely on the products it exports. In order to increase the competitiveness of a country and further increase its GDP, a crucial issue is finding the right direction to upgrade the industry so that the country can enhance its competitiveness. The proximity indicator measures the similarity between products and can be used to predict the probability that a country will develop a new industry. On the other hand, the Fitness–Complexity algorithm can help to find the important products and developing countries. In this paper, we find that the maximum of the proximity between a certain product and a country's existing products is highly correlated with the probability that the country exports this new product in the next year. In addition, we find that the more products that are related to a certain product, the higher probability of the emergence of the new product. Finally, we combine the proximity indicator and the Fitness–Complexity algorithm and then attempt to provide a recommendation list of new products that can help developing countries to upgrade their industry. A few examples are given in the end. [ABSTRACT FROM AUTHOR]

This paper proposes a hybrid classifier for polarimetric SAR images. The feature sets consist of span image, the H/A/α decomposition, and the GLCM-based texture features. Then, a probabilistic neural network (PNN) was adopted for classification, and a novel algorithm proposed to enhance its performance. Principle component analysis (PCA) was chosen to reduce feature dimensions, random division to reduce the number of neurons, and Brent's search (BS) to find the optimal bias values. The results on San Francisco and Flevoland sites are compared to that using a 3-layer BPNN to demonstrate the validity of our algorithm in terms of confusion matrix and overall accuracy. In addition, the importance of each improvement of the algorithm was proven. [ABSTRACT FROM AUTHOR]

The key to the study of node deployment in Wireless Sensor Networks (WSN) is to find the appropriate location of the WSN nodes and reduce the cost of network deployment while meeting the monitoring requirements in the covered area. This paper proposes a WSN node deployment algorithm based on real 3D terrain, which provides an effective solution to the surface-covering problem. First of all, actual geographic elevation data is adopted to conduct surface modeling. The model can vividly reflect the real terrain characteristics of the area to be deployed and make the deployment plan more visible and easy to adjust. Secondly, a probabilistic coverage model based on DEM (Digital Elevation Model) data is proposed. Based on the traditional spherical coverage model, the influence of signal attenuation and terrain occlusion on the coverage model is added to make the deployment model closer to reality. Finally, the Greedy algorithm based on grid scanning is used to deploy nodes. Simulation results show that the proposed algorithm can effectively improve the coverage rate, reduce the deployment cost, and reduce the time and space complexity in solving the WSN node deployment problem under the complex 3D land surface model, which verifies the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Simple Summary: Prediction of volume expected to be attained by a tumor of fourth grade malignancy becomes difficult when problem is subject to changes in time or when there exists heterogeneity among oncogenes for different subjects. The attempt here was to develop a time independent model which will only depend on some other radiomic properties of the tumor, also accommodating for the heterogeneity feature. Our model gives highly accurate results when we subject the initial volume of the tumor and eventually discover that the probability of no tumor cells remaining undetected is sufficiently high. Our model results are for glioblastoma tumor, but it can be applied on any other tumor volume prediction problem, and especially can be reliably adopted for tumors of high malignancy level. Predicting the eventual volume of tumor cells, that might proliferate from a given tumor, can help in cancer early detection and medical procedure planning to prevent their migration to other organs. In this work, a new statistical framework is proposed using Bayesian techniques for detecting the eventual volume of cells expected to proliferate from a glioblastoma (GBM) tumor. Specifically, the tumor region was first extracted using a parallel image segmentation algorithm. Once the tumor region was determined, we were interested in the number of cells that could proliferate from this tumor until its survival time. For this, we constructed the posterior distribution of the tumor cell numbers based on the proposed likelihood function and a certain prior volume. Furthermore, we extended the detection model and conducted a Bayesian regression analysis by incorporating radiomic features to discover those non-tumor cells that remained undetected. The main focus of the study was to develop a time-independent prediction model that could reliably predict the ultimate volume a malignant tumor of the fourth-grade severity could attain and which could also determine if the incorporation of the radiomic properties of the tumor enhanced the chances of no malignant cells remaining undetected. [ABSTRACT FROM AUTHOR]

Evidence theory (TE), based on imprecise probabilities, is often more appropriate than the classical theory of probability (PT) to apply in situations with inaccurate or incomplete information. The quantification of the information that a piece of evidence involves is a key issue in TE. Shannon's entropy is an excellent measure in the PT for such purposes, being easy to calculate and fulfilling a wide set of properties that make it axiomatically the best one in PT. In TE, a similar role is played by the maximum of entropy (ME), verifying a similar set of properties. The ME is the unique measure in TE that has such axiomatic behavior. The problem of the ME in TE is its complex computational calculus, which makes its use problematic in some situations. There exists only one algorithm for the calculus of the ME in TE with a high computational cost, and this problem has been the principal drawback found with this measure. In this work, a variation of the original algorithm is presented. It is shown that with this modification, a reduction in the necessary steps to attain the ME can be obtained because, in each step, the power set of possibilities is reduced with respect to the original algorithm, which is the key point of the complexity found. This solution can provide greater applicability of this measure. [ABSTRACT FROM AUTHOR]

The use of distributions to model and quantify risk is essential in risk assessment and management. In this study, the generalized unit half-logistic geometric (GUHLG) distribution is developed to model bounded insurance data on the unit interval. The corresponding probability density function plots indicate that the related distribution can handle data that exhibit left-skewed, right-skewed, symmetric, reversed-J, and bathtub shapes. The hazard rate function also suggests that the distribution can be applied to analyze data with bathtubs, N-shapes, and increasing failure rates. Subsequently, the inferential aspects of the proposed model are investigated. In particular, Monte Carlo simulation exercises are carried out to examine the performance of the estimation method by using an algorithm to generate random observations from the quantile function. The results of the simulation suggest that the considered estimation method is efficient. The univariate application of the distribution and the multivariate application of the associated regression using risk survey data reveal that the model provides a better fit than the other existing distributions and regression models. Under the multivariate application, we estimate the parameters of the regression model using both maximum likelihood and Bayesian estimations. The estimates of the parameters for the two methods are very close. Diagnostic plots of the Bayesian method using the trace, ergodic, and autocorrelation plots reveal that the chains converge to a stationary distribution. [ABSTRACT FROM AUTHOR]

Noise radars employ random waveforms in their transmission as compared to traditional radars. Considered as enhanced Low Probability of Intercept (LPI) radars, they are resilient to interference and jamming and less vulnerable to adversarial exploitation than conventional radars. At its simplest, using a random waveform such as bandpass Gaussian noise as a probing signal provides limited radar performance. After a concise review of a particular noise radar architecture and related correlation processing, this paper justifies the rationale for having synthetic (tailored) noise waveforms and proposes the Combined Spectral Shaping and Peak-to-Average Power Reduction (COSPAR) algorithm, which can be utilized for synthesizing noise-like sequences with a Taylor-shaped spectrum under correlation sidelobe level constraints and assigned Peak-to-Average-Power-Ratio (PAPR). Additionally, the Spectral Kurtosis measure is proposed to evaluate the LPI property of waveforms, and experimental results from field trials are reported. [ABSTRACT FROM AUTHOR]

In order to minimize the influence of decorrelation noise on multi-temporal interferometric synthetic aperture radar (MT-InSAR) applications, a series of phase reconstruction methods have been proposed in recent years. Unfortunately, current phase reconstruction methods generally exhibit a low computational efficiency due to their high non-linearity, in particular in the case that the dimension of a SAR stack is high. In this paper, a new approach is proposed to efficiently resolve phase reconstruction problems. This approach is inspired by the theory of probabilistic principle component analysis. A complex valued probability generative model is constructed to portray a phase reconstruction process. Moreover, in order to resolve such a model, a targeted algorithm based on the idea of expectation maximization is designed and implemented. For validation purposes, the proposed approach is compared to the traditional eigenvalue decomposition-based method by using simulated data and 101 real Sentinel-1A SAR images. The experimental results demonstrate that the proposed method can accelerate the phase reconstruction process drastically, in particular when a high-dimensional SAR stack is required to be processed. [ABSTRACT FROM AUTHOR]

In the present paper, a novel approach is introduced for the study, estimation and exact tracking of the finite precision error generated and accumulated during any number of multiplications. It is shown that, as a rule, this operation is very "toxic", in the sense that it may force the finite precision error accumulation to grow arbitrarily large, under specific conditions that are fully described here. First, an ensemble of definitions of general applicability is given for the rigorous determination of the number of erroneous digits accumulated in any quantity of an arbitrary algorithm. Next, the exact number of erroneous digits produced in a single multiplication is given as a function of the involved operands, together with formulae offering the corresponding probabilities. In case the statistical properties of these operands are known, exact evaluation of the aforementioned probabilities takes place. Subsequently, the statistical properties of the accumulated finite precision error during any number of successive multiplications are explicitly analyzed. A method for exact tracking of this accumulated error is presented, together with associated theorems. Moreover, numerous dedicated experiments are developed and the corresponding results that fully support the theoretical analysis are given. Eventually, a number of important, probable and possible applications is proposed, where all of them are based on the methodology and the results introduced in the present work. The proposed methodology is expandable, so as to tackle the round-off error analysis in all arithmetic operations. [ABSTRACT FROM AUTHOR]

In health sciences, identifying the leading causes that govern the behaviour of a response variable is a question of crucial interest. Formally, this can be formulated as a variable selection problem. In this paper, we introduce the basic concepts of the Bayesian approach for variable selection based on model choice, emphasizing the model space prior adoption and the algorithms for sampling from the model space and for posterior probabilities approximation; and show its application to two common problems in health sciences. The first concerns a problem in the field of genetics while the second is a longitudinal study in cardiology. In the context of these applications, considerations about control for multiplicity via the prior distribution over the model space, linear models in which the number of covariates exceed the sample size, variable selection with censored data, and computational aspects are discussed. The applications presented here also have an intrinsic statistical interest as the proposed models go beyond the standard general linear model. We believe this work will broaden the access of practitioners to Bayesian methods for variable selection. [ABSTRACT FROM AUTHOR]

In data clustering, the measured data are usually regarded as uncertain data. As a probability-based clustering technique, possible world can easily cluster the uncertain data. However, the method of possible world needs to satisfy two conditions: determine the data of different possible worlds and determine the corresponding probability of occurrence. The existing methods mostly make multiple measurements and treat each measurement as deterministic data of a possible world. In this paper, a possible world-based fusion estimation model is proposed, which changes the deterministic data into probability distribution according to the estimation algorithm, and the corresponding probability can be confirmed naturally. Further, in the clustering stage, the Kullback–Leibler divergence is introduced to describe the relationships of probability distributions among different possible worlds. Then, an application in wearable body networks (WBNs) is given, and some interesting conclusions are shown. Finally, simulations show better performance when the relationships between features in measured data are more complex. [ABSTRACT FROM AUTHOR]

Simple Summary: MR-Class is a deep learning-based MR image classification tool for brain images that facilitates and speeds up the initialization of big data MR-based studies by providing fast, robust and quality-assured imaging sequence classifications. Our studies observed up to 10% misclassification rates due to corrupt and misleading DICOM metadata. This highlights the need for a tool such as MR-Class to help with data curation. MR-Class can be integrated into workflows for DICOM inconsistency checks and flagging or completing missing DICOM metadata and thus contribute to the faster deployment of clinical artificial intelligence applications. Background: MR image classification in datasets collected from multiple sources is complicated by inconsistent and missing DICOM metadata. Therefore, we aimed to establish a method for the efficient automatic classification of MR brain sequences. Methods: Deep convolutional neural networks (DCNN) were trained as one-vs-all classifiers to differentiate between six classes: T1 weighted (w), contrast-enhanced T1w, T2w, T2w-FLAIR, ADC, and SWI. Each classifier yields a probability, allowing threshold-based and relative probability assignment while excluding images with low probability (label: unknown, open-set recognition problem). Data from three high-grade glioma (HGG) cohorts was assessed; C1 (320 patients, 20,101 MRI images) was used for training, while C2 (197, 11,333) and C3 (256, 3522) were for testing. Two raters manually checked images through an interactive labeling tool. Finally, MR-Class' added value was evaluated via radiomics model performance for progression-free survival (PFS) prediction in C2, utilizing the concordance index (C-I). Results: Approximately 10% of annotation errors were observed in each cohort between the DICOM series descriptions and the derived labels. MR-Class accuracy was 96.7% [95% Cl: 95.8, 97.3] for C2 and 94.4% [93.6, 96.1] for C3. A total of 620 images were misclassified; manual assessment of those frequently showed motion artifacts or alterations of anatomy by large tumors. Implementation of MR-Class increased the PFS model C-I by 14.6% on average, compared to a model trained without MR-Class. Conclusions: We provide a DCNN-based method for the sequence classification of brain MR images and demonstrate its usability in two independent HGG datasets. [ABSTRACT FROM AUTHOR]

We present REGA, a new adaptive-sampling-based algorithm for the control of finite-horizon Markov decision processes (MDPs) with very large state spaces and small action spaces. We apply a variant of the ϵ -greedy multiarmed bandit algorithm to each stage of the MDP in a recursive manner, thus computing an estimation of the "reward-to-go" value at each stage of the MDP. We provide a finite-time analysis of REGA. In particular, we provide a bound on the probability that the approximation error exceeds a given threshold, where the bound is given in terms of the number of samples collected at each stage of the MDP. We empirically compare REGA against another sampling-based algorithm called RASA by running simulations against the SysAdmin benchmark problem with 2 10 states. The results show that REGA and RASA achieved similar performance. Moreover, REGA and RASA empirically outperformed an implementation of the algorithm that uses the "original" ϵ -greedy algorithm that commonly appears in the literature. [ABSTRACT FROM AUTHOR]

As multimedia traffic has been increasing and is expected to grow more sharply, various technologies using caches have been attracting lots of attention. As one breakthrough technology to deal with the explosively growing traffic, exclusive OR (XOR)-based index coding has been widely investigated because it can greatly enhance the efficiency of network resource by reducing the number of transmissions. In this paper, we investigate how to apply XOR-based index coding to large-scaled practical streaming systems for video traffic that accounts for more than 70% of total Internet traffic. Contrary to most previous studies that have focused on theoretical analysis of optimal performance or development of optimal index coding schemes, our study proposes a new XOR coding-based video streaming (XC). We also propose a new grouping algorithm for creating XC groups while guaranteeing the complete backward compatibility of XC with existing streaming schemes such as unicast (UC), multicast (MC), and broadcast (BC). The performance of the proposed scheme is analyzed in two steps. First, the behavior of video contents in caches at clients is modeled as a Markov chain, and the steady-state probabilities and caching probabilities for each piece of video content are derived. Based on the probabilities, the performance of the proposed system is then analyzed in terms of the average number of connections that each client requires in order to receive one video content. Our numerical results show that the proposed video streaming scheme using XC can reduce the average number of transmissions by up to 18%, compared to the conventional scheme. [ABSTRACT FROM AUTHOR]

Probability of collision between non-cooperative space object (NCSO) and the reference spacecraft (RS) has been increased drastically over the past few decades. The traditional method is difficult to identify the maneuvering of non-cooperative space object. In the present paper, not only positions and velocities, but also accelerations of non-cooperative space object are estimated as parameters by the extended Kalman filtering based on setting up the state linear equation and measurement model of the non-cooperative space object. The algorithm for predicting collision probability is derived from position error ellipsoid, and the algorithm for determining maneuvering probability is derived from maneuvering acceleration and its error ellipsoid, which can be employed to identify whether the upcoming space object is being maneuvered. An epoch Earth-centered inertial (EECI) coordinate system is suggested to replace Earth-centered inertial (ECI) to simplify coordinate transformation. Finally, a set of simulations were conducted to validate the proposed algorithms with the simulated measurement data of the reference spacecraft space-borne millimeter-wave (MMW) radar. [ABSTRACT FROM AUTHOR]

About a decade ago, the PERTI algorithm was launched as a tool for a data-adaptive probability-based analysis of electrical resistivity tomography datasets. It proved to be an easy and versatile inversion method providing estimates of the resistivity values within a surveyed volume as weighted averages of the whole apparent resistivity dataset. In this paper, with the aim of improving the interpretative process, the PERTI method is extended by exploiting some peculiar aspects of the general theory of probability. Bernoulli's conceptual scheme is assumed to comply with any resistivity dataset, which allows a multiplicity of mutually independent subsets to be extracted and analysed singularly. A standard least squares procedure is at last adopted for the statistical determination of the model resistivity at each point of the surveyed volume as the slope of a linear equation that relates the multiplicity of the resistivity estimates from the extracted data subsets. A 2D synthetic test and a field apparent resistivity dataset collected for archaeological purposes are discussed using the new extended PERTI (E-PERTI) approach. The comparison with the results from the original PERTI shows that by the E-PERTI approach a significantly greater robustness against noise can be achieved, besides a general optimisation of the estimates of the most probable resistivity values. [ABSTRACT FROM AUTHOR]

An improved hybrid firefly algorithm with probability attraction model (IHFAPA) is proposed to solve the problems of low computational efficiency and low computational accuracy in solving complex optimization problems. First, the method of square-root sequence was used to generate the initial population, so that the initial population had better population diversity. Second, an adaptive probabilistic attraction model is proposed to attract fireflies according to the brightness level of fireflies, which can minimize the brightness comparison times of the algorithm and moderate the attraction times of the algorithm. Thirdly, a new location update method is proposed, which not only overcomes the deficiency in that the relative attraction of two fireflies is close to 0 when the distance is long but also overcomes the deficiency that the relative attraction of two fireflies is close to infinity when the distance is small. In addition, a combinatorial variational operator based on selection probability is proposed to improve the exploration and exploitation ability of the firefly algorithm (FA). Later, a similarity removal operation is added to maintain the diversity of the population. Finally, experiments using CEC 2017 constrained optimization problems and four practical problems in engineering show that IHFAPA can effectively improve the quality of solutions. [ABSTRACT FROM AUTHOR]

Recognizing the characteristics of a well-developed running style is a central issue in athletic sub-disciplines. The development of portable micro-electro-mechanical-system (MEMS) sensors within the last decades has made it possible to accurately quantify movements. This paper introduces an analysis method, based on limit-cycle attractors, to identify subjects by their specific running style. The movement data of 30 athletes were collected over 20 min. in three running sessions to create an individual gaitprint. A recognition algorithm was applied to identify each single individual as compared to other participants. The analyses resulted in a detection rate of 99% with a false identification probability of 0.28%, which demonstrates a very sensitive method for the recognition of athletes based solely on their running style. Further, it can be seen that these differentiations can be described as individual modifications of a general running pattern inherent in all participants. These findings open new perspectives for the assessment of running style, motion in general, and a person's identification, in, for example, the growing e-sports movement. [ABSTRACT FROM AUTHOR]

Digital flicker detection devices need to store a large amount of evaluation data during measurement process, which leads to high requirements for hardware resources and algorithm execution efficiency. In this paper, a digital flicker detection method based on probability resampling is studied. In particular, before statistical evaluation, probability resampling is applied to screen the instantaneous flicker visual sensitivity data to compress redundant data. Additionally, the effectiveness of the method was numerically simulated and experimentally tested. The results show that the proposed method can accurately measure the voltage flicker value and can effectively compress the redundant evaluation data to be evaluated and has significant advantages in releasing hardware storage space, in improving algorithm execution efficiency and real-time performance, and in reducing processor workload. This method provides an engineering application reference for designing digital flicker detectors, especially for the software upgrade of traditional power quality testing equipment. [ABSTRACT FROM AUTHOR]

In this paper, we prove recursive formulas for ultimate time survival probability when three random claims X , Y , Z in the discrete time risk model occur in a special way. Namely, we suppose that claim X occurs at each moment of time t ∈ { 1 , 2 , ... } , claim Y additionally occurs at even moments of time t ∈ { 2 , 4 , ... } and claim Z additionally occurs at every moment of time, which is a multiple of three t ∈ { 3 , 6 , ... } . Under such assumptions, the model that is obtained is called the three-risk discrete time model. Such a model is a particular case of a nonhomogeneous risk renewal model. The sequence of claims has the form { X , X + Y , X + Z , X + Y , X , X + Y + Z , ... } . Using the recursive formulas, algorithms were developed to calculate the exact values of survival probabilities for the three-risk discrete time model. The running of algorithms is illustrated via numerical examples. [ABSTRACT FROM AUTHOR]

The Jensen–Shannon divergence is a renown bounded symmetrization of the Kullback–Leibler divergence which does not require probability densities to have matching supports. In this paper, we introduce a vector-skew generalization of the scalar α -Jensen–Bregman divergences and derive thereof the vector-skew α -Jensen–Shannon divergences. We prove that the vector-skew α -Jensen–Shannon divergences are f-divergences and study the properties of these novel divergences. Finally, we report an iterative algorithm to numerically compute the Jensen–Shannon-type centroids for a set of probability densities belonging to a mixture family: This includes the case of the Jensen–Shannon centroid of a set of categorical distributions or normalized histograms. [ABSTRACT FROM AUTHOR]

For the linear model Y = X b + e r r o r , where the number of regressors (p) exceeds the number of observations (n), the Elastic Net (EN) was proposed, in 2005, to estimate b. The EN uses both the Lasso, proposed in 1996, and ordinary Ridge Regression (RR), proposed in 1970, to estimate b. However, when p > n , using only RR to estimate b has not been considered in the literature thus far. Because RR is based on the least-squares framework, only using RR to estimate b is computationally much simpler than using the EN. We propose a generalized ridge regression (GRR) algorithm, a superior alternative to the EN, for estimating b as follows: partition X from left to right so that every partition, but the last one, has 3 observations per regressor; for each partition, we estimate Y with the regressors in that partition using ordinary RR; retain the regressors with statistically significant t -ratios and the corresponding RR tuning parameter k , by partition; use the retained regressors and k values to re-estimate Y by GRR across all partitions, which yields b. Algorithmic efficacy is compared using 4 metrics by simulation, because the algorithm is mathematically intractable. Three metrics, with their probabilities of RR's superiority over EN in parentheses, are: the proportion of true regressors discovered (99%); the squared distance, from the true coefficients, of the significant coefficients (86%); and the squared distance, from the true coefficients, of estimated coefficients that are both significant and true (74%). The fourth metric is the probability that none of the regressors discovered are true, which for RR and EN is 4% and 25%, respectively. This indicates the additional advantage RR has over the EN in terms of discovering causal regressors. [ABSTRACT FROM AUTHOR]

We consider the problem of learning a Bayesian network structure given n examples and the prior probability based on maximizing the posterior probability. We propose an algorithm that runs in O(n log n) time and that addresses continuous variables and discrete variables without assuming any class of distribution. We prove that the decision is strongly consistent, i.e., correct with probability one as n → ∞. To date, consistency has only been obtained for discrete variables for this class of problem, and many authors have attempted to prove consistency when continuous variables are present. Furthermore, we prove that the "log n" term that appears in the penalty term of the description length can be replaced by 2(1+ϵ) log log n to obtain strong consistency, where ϵ > 0 is arbitrary, which implies that the Hannan-Quinn proposition holds. [ABSTRACT FROM AUTHOR]