Invariance of the parity conjecture for p-Selmer groups of elliptic curves in a D2pnD_{2p^n}-extension

In section 2, we show a $p$-parity result in a $D_{2p^{n}}$-extension of number fields $L/K$ ($p\geq 5$) for the twist $1\oplus \eta \oplus \tau$: W(E/K,1\oplus \eta \oplus \tau)=(-1)^{}, where $E$ is an elliptic curve over $K,$ $\eta$ and $\tau$ are respectively the quadratic character and an irreductible representation of degree 2 of $Gal(L/K)=D_{2p^{n}},$ and $X_{p}(E/L)$ is the $p$-Selmer group. The main novelty is that we use a congruence result between $$-factors (due to Deligne) for the determination of local root numbers in bad cases (places of additive reduction above 2 and 3). We also give applications to the $p$-parity conjecture (using the machinery of the Dokchitser brothers).Comment: 19 page

Power adjustment and scheduling in OFDMA femtocell networks

Densely-deployed femtocell networks are used to enhance wireless coverage in public spaces like office buildings, subways, and academic buildings. These networks can increase throughput for users, but edge users can suffer from co-channel interference, leading to service outages. This paper introduces a distributed algorithm for network configuration, called Radius Reduction and Scheduling (RRS), to improve the performance and fairness of the network. RRS determines cell sizes using a Voronoi-Laguerre framework, then schedules users using a scheduling algorithm that includes vacancy requests to increase fairness in dense femtocell networks. We prove that our algorithm always terminate in a finite time, producing a configuration that guarantees user or area coverage. Simulation results show a decrease in outage probability of up to 50%, as well as an increase in Jain's fairness index of almost 200%

On the vulnerabilities of voronoi-based approaches to mobile sensor deployment

Mobile sensor networks are the most promising solution to cover an Area of Interest (AoI) in safety critical scenarios. Mobile devices can coordinate with each other according to a distributed deployment algorithm, without resorting to human supervision for device positioning and network configuration. In this paper, we focus on the vulnerabilities of the deployment algorithms based on Voronoi diagrams to coordinate mobile sensors and guide their movements. We give a geometric characterization of possible attack configurations, proving that a simple attack consisting of a barrier of few compromised sensors can severely reduce network coverage. On the basis of the above characterization, we propose two new secure deployment algorithms, named SecureVor and Secure Swap Deployment (SSD). These algorithms allow a sensor to detect compromised nodes by analyzing their movements, under different and complementary operative settings. We show that the proposed algorithms are effective in defeating a barrier attack, and both have guaranteed termination. We perform extensive simulations to study the performance of the two algorithms and compare them with the original approach. Results show that SecureVor and SSD have better robustness and flexibility and excellent coverage capabilities and deployment time, even in the presence of an attac