Outage Constraint Robust Cooperative Beamforming and Jamming Design for Secure AF Relay Networks

This paper investigates a joint robust scheme in a secrecy relay network where distributed relays perform cooperative beamforming and a friendly jammer transmits jamming signal to enhance the information security. Specifically, we consider the outage constraint secrecy rate maximization design with imperfect channel state information. Through semidefinite relaxation and one-dimensional search, we propose a two-layer optimization method to solve the nonconvex problem. In addition, the Bernstein-type inequality and large deviation inequality are utilized to convert the probabilistic constraint. Simulation results demonstrate the performance of the proposed design.

ANALISIS EKSPLORATIF TERHADAP PEMIKIRAN YŪSUF AL-QARḌĀWĪ TENTANG KESETARAAN DAN KEADILAN GENDER SEBAGAI BAGIAN MAQᾹṢID AL-QUR’ᾹN

<p class="Iabstrak">Gender justice and gender equality are complex topics and drew the attention of many people. A number of Muslim jurists have studied it from various perspectives in order to understand and find a fair solution to the problem. However, most of them are rare to study it from the lens of <em>maqāṣid al-Qur’ān</em>, the purpose of al-Qur’an was revealed to the earth. Incorporating gender justice and gender equality in <em>maqāṣid al-Qur’ān</em> is considered urgent with the intent that people will really pay attention, watch, and put male and female proportionally. This paper focuses on analyzing Yūsuf al-Qarḍāwī's thought about gender equality and justice as part of <em>maqāṣid al-Qur’ān</em>. This article includes library research, whose datas are sourced from the literature. The results of this study revealed that men and women have equal rights in every aspect of life; education; economics, social, political, and law. They are also given equal rights in participating to be public leaders. Besides that, they have equal rights in selecting their belief (religion) based on their strong desire and their own belief and they have rights to get heritance as well as having rights to the goods they have. On the contrary, any kinds of discriminations, subordination, stereotyping, violence, and all forms of deviation inequality of gender bias, contradict and contrasted with <em>maqāṣid al-Qur’ān</em>.</p>

Inference on Causal and Structural Parameters using Many Moment Inequalities

This article considers the problem of testing many moment inequalities where the number of moment inequalities, denoted by $p$, is possibly much larger than the sample size $n$. There is a variety of economic applications where solving this problem allows to carry out inference on causal and structural parameters; a notable example is the market structure model of Ciliberto and Tamer (2009) where $p=2^{m+1}$ with $m$ being the number of firms that could possibly enter the market. We consider the test statistic given by the maximum of $p$ Studentized (or $t$-type) inequality-specific statistics, and analyse various ways to compute critical values for the test statistic. Specifically, we consider critical values based upon (1) the union bound combined with a moderate deviation inequality for self-normalized sums, (2) the multiplier and empirical bootstraps, and (3) two-step and three-step variants of (1) and (2) by incorporating the selection of uninformative inequalities that are far from being binding and a novel selection of weakly informative inequalities that are potentially binding but do not provide first-order information. We prove validity of these methods, showing that under mild conditions, they lead to tests with the error in size decreasing polynomially in $n$ while allowing for $p$ being much larger than $n$; indeed $p$ can be of order $\exp (n^{c})$ for some $c > 0$. Importantly, all these results hold without any restriction on the correlation structure between $p$ Studentized statistics, and also hold uniformly with respect to suitably large classes of underlying distributions. Moreover, in the online supplement, we show validity of a test based on the block multiplier bootstrap in the case of dependent data under some general mixing conditions.

A deviation bound for α-dependent sequences with applications to intermittent maps

We prove a deviation bound for the maximum of partial sums of functions of [Formula: see text]-dependent sequences as defined in [2]. As a consequence, we extend the Rosenthal inequality of Rio [16] for [Formula: see text]-mixing sequences in the sense of Rosenblatt [18] to the larger class of [Formula: see text]-dependent sequences. Starting from the deviation inequality, we obtain upper bounds for large deviations and Hölderian invariance principle for the Donsker line. We illustrate our results through the example of intermittent maps of the interval, which are not [Formula: see text]-mixing in the sense of Rosenblatt.

Large Deviations for the Graph Distance in Supercritical Continuum Percolation

Denote the Palm measure of a homogeneous Poisson process Hλ with two points 0 and x by P0,x. We prove that there exists a constant μ ≥ 1 such that P0,x(D(0, x) / μ||x||2 ∉ (1 − ε, 1 + ε) | 0, x ∈ C∞) exponentially decreases when ||x||2 tends to ∞, where D(0, x) is the graph distance between 0 and x in the infinite component C∞ of the random geometric graph G(Hλ; 1). We derive a large deviation inequality for an asymptotic shape result. Our results have applications in many fields and especially in wireless sensor networks.

Large Deviations for the Graph Distance in Supercritical Continuum Percolation

Denote the Palm measure of a homogeneous Poisson process H λ with two points 0 and x by P0,x . We prove that there exists a constant μ ≥ 1 such that P0,x (D(0, x) / μ||x||2 ∉ (1 − ε, 1 + ε) | 0, x ∈ C ∞) exponentially decreases when ||x||2 tends to ∞, where D(0, x) is the graph distance between 0 and x in the infinite component C ∞ of the random geometric graph G(H λ; 1). We derive a large deviation inequality for an asymptotic shape result. Our results have applications in many fields and especially in wireless sensor networks.