On the longest length of consecutive integers

Choose m numbers from the set {1, 2, …, n} at random without replacement. In this paper we first establish the limiting distribution of the longest length of consecutive integers and then apply the result to test randomness of selecting numbers without replacement.     

Outlier-aware cooperative spectrum sensing in cognitive radio networks

This paper considers the problem of cooperative spectrum sensing in cognitive radio networks (CRN). Communication in CRNs may be disrupted due to the presence of malicious secondary users (SU) or channel impairments such as shadowing. This paper proposes a spatio-frequency framework that can detect and track malicious users and anomalous measurements in CRNs. The joint problem of spectrum sensing and malicious user identification is posed as an optimization problem that aims to exploit the sparsity inherent to both, spectrum occupancy and malicious user occurrence. Proposed scheme obtains improved performance by utilizing node location information, and can handle missing or inaccurate location information, and noisy SU reports. A distributed block-coordinate descent-based algorithm is proposed that is shown to outperform the state-of-the-art PCA-based approach, and is flexible enough to defeat a variety of attacks encountered in SU networks. An online algorithm, that can handle incorporate multiple SU readings sequentially and adapt to time-varying channels, primary user, and malicious user activity, is also proposed and shown to be consistent. Simulation results demonstrate the efficacy of the proposed algorithms.     

Detecting and interpreting clusters of economic activity in rural areas using scan statistic and LISA under a unified framework

The primary aim of this paper is to expose the use and the value of spatial statistical analysis in business and especially in designing economic policies in rural areas. Specifically, we aim to present under a unified framework, the use of both point and area‐based methods, in order to analyze in‐depth economic data, as well as, to drive conclusions through interpreting the analysis results. The motivating problem is related to the establishment of women‐run enterprises in a rural area of Greece. Moreover, in this article, the spatial scan statistic is successfully applied to the spatial economic data at hand, in order to detect possible clusters of small women‐run enterprises in a rural mountainous and disadvantaged region of Greece. Then, it is combined with Geographical Information System based on Local Indicator of Spatial Autocorrelation scan statistic for further exploring and interpreting the spatial patterns. The rejection of the random establishment of women‐run enterprises and the interpretation of the clustering patterns are deemed necessary, in order to assist government in designing policies for rural development. Copyright © 2014 John Wiley & Sons, Ltd.     

Recursive methods for a multi-dimensional risk process with common shocks

In this paper, a multi-dimensional risk model with common shocks is studied. Using a simple probabilistic approach via observing the risk processes at claim instants, recursive integral formulas are developed for the survival probabilities as well as for a class of Gerber-Shiu expected discounted penalty functions that include the surplus levels at ruin. Under the assumption of exponential or mixed Erlang claims, the recursive integrals can be simplified to give recursive sums which are computationally more tractable. Numerical examples including an optimal capital allocation problem are also given towards the end.     

A minimal pair of -degrees

We construct a minimal pair of -degrees. We do this by showing the existence of an unbounded nondecreasing function which forces -triviality in the sense that is -trivial if and only if for all , .

     

Weak quasi‐randomness for uniform hypergraphs

We study quasi‐random properties of k‐uniform hypergraphs. Our central notion is uniform edge distribution with respect to large vertex sets. We will find several equivalent characterisations of this property and our work can be viewed as an extension of the well known Chung‐Graham‐Wilson theorem for quasi‐random graphs. Moreover, let K_k be the complete graph on k vertices and M(k) the line graph of the graph of the k‐dimensional hypercube. We will show that the pair of graphs (K_k,M(k)) has the property that if the number of copies of both K_k and M(k) in another graph G are as expected in the random graph of density d, then G is quasi‐random (in the sense of the Chung‐Graham‐Wilson theorem) with density close to d. © 2011 Wiley Periodicals, Inc. Random Struct. Alg., 2011     

A Langevin approach to the Log–Gauss–Pareto composite statistical structure

The distribution of wealth in human populations displays a Log–Gauss–Pareto composite statistical structure: its density is Log–Gauss in its central body, and follows power-law decay in its tails. This composite statistical structure is further observed in other complex systems, and on a logarithmic scale it displays a Gauss-Exponential structure: its density is Gauss in its central body, and follows exponential decay in its tails. In this paper we establish an equilibrium Langevin explanation for this statistical phenomenon, and show that: (i) the stationary distributions of Langevin dynamics with sigmoidal force functions display a Gauss-Exponential composite statistical structure; (ii) the stationary distributions of geometric Langevin dynamics with sigmoidal force functions display a Log–Gauss–Pareto composite statistical structure. This equilibrium Langevin explanation is universal — as it is invariant with respect to the specific details of the sigmoidal force functions applied, and as it is invariant with respect to the specific statistics of the underlying noise.     

Security Analysis of Sending or Not-Sending Twin-Field Quantum Key Distribution with Weak Randomness

Sending-or-not sending twin-field quantum key distribution (SNS TF-QKD) has the advantage of tolerating large amounts of misalignment errors, and its key rate can exceed the linear bound of repeaterless quantum key distribution. However, the weak randomness in a practical QKD system may lower the secret key rate and limit its achievable communication distance, thus compromising its performance. In this paper, we analyze the effects of the weak randomness on the SNS TF-QKD. The numerical simulation shows that SNS TF-QKD can still have an excellent performance under the weak random condition: the secret key rate can exceed the PLOB boundary and achieve long transmission distances. Furthermore, our simulation results also show that SNS TF-QKD is more robust to the weak randomness loopholes than the BB84 protocol and the measurement-device-independent QKD (MDI-QKD). Our results emphasize that keeping the randomness of the states is significant to the protection of state preparation devices.     

Enhancing Chaos Complexity of a Plasma Model through Power Input with Desirable Random Features

The present work introduces an analysis framework to comprehend the dynamics of a 3D plasma model, which has been proposed to describe the pellet injection in tokamaks. The analysis of the system reveals the existence of a complex transition from transient chaos to steady periodic behavior. Additionally, without adding any kind of forcing term or controllers, we demonstrate that the system can be changed to become a multi-stable model by injecting more power input. In this regard, we observe that increasing the power input can fluctuate the numerical solution of the system from coexisting symmetric chaotic attractors to the coexistence of infinitely many quasi-periodic attractors. Besides that, complexity analyses based on Sample entropy are conducted, and they show that boosting power input spreads the trajectory to occupy a larger range in the phase space, thus enhancing the time series to be more complex and random. Therefore, our analysis could be important to further understand the dynamics of such models, and it can demonstrate the possibility of applying this system for generating pseudorandom sequences.