The size function of quadratic extensions of complex quadratic fields

The function $h^0$ for a number field is an analogue of the dimension of the Riemann-Roch spaces of divisors on an algebraic curve. In this paper, we prove the conjecture of van der Geer and Schoof about the maximality of $h^0$ at the trivial Arakelov divisor for quadratic extensions of complex quadratic fields

Computing dimensions of spaces of Arakelov divisors of number fields

The function $h^0$ for a number field is analogous to the dimension of the Riemann-Roch spaces at divisors on an algebraic curve. We provide a method to compute this function for number fields with unit group of rank at most 2, even with large discriminant. This method is based on using LLL-reduced bases, the "jump algorithm" and Poisson summation formula

Reduced ideals from the reduction algorithm

The reduction algorithm is used to compute reduced ideals of a number field. However, there are reduced ideals that can never be obtained from this algorithm. In this paper, we will show that these ideals have inverses of larger norms among reduced ones. Especially, we represent a sufficient and necessary condition for reduced ideals of real quadratic fields to be obtained from the reduction algorithm

RF Wireless Power Transfer: Regreening Future Networks

Green radio communication is an emerging topic since the overall footprint of information and communication technology (ICT) services is predicted to triple between 2007 and 2020. Given this research line, energy harvesting (EH) and wireless power transfer (WPT) networks can be evaluated as promising approaches. In this paper, an overview of recent trends for future green networks on the platforms of EH and WPT is provided. By rethinking the application of radio frequency (RF)-WPT, a new concept, namely green RF-WTP, is introduced. Accordingly, opening challenges and promising combinations among current technologies, such as small-cell, millimeter (mm)-wave, and Internet of Things (IoT) networks, are discussed in details to seek solutions for the question with how to re-green the future networks?Comment: 6 pages, 5 figure

XACs-DyPol: Towards an XACML-based Access Control Model for Dynamic Security Policy

Authorization and access control play an essential role in protecting sensitive information from malicious users. The system is based on security policies to determine if an access request is allowed. However, of late, the growing popularity of big data has created a new challenge which the security policy management is facing with such as dynamic and update policies in run time. Applications of dynamic policies have brought many benefits to modern domains. To the best of our knowledge, there are no previous studies focusing on solving authorization problems in the dynamic policy environments. In this article, we focus on analyzing and classifying when an update policy occurs, and provide a pragmatic solution for such dynamic policies. The contribution of this work is twofold: a novel solution for managing the policy changes even when the access request has been granted, and an XACML-based implementation to empirically evaluate the proposed solution. The experimental results show the comparison between the newly introduced XACs-DyPol framework with Balana (an open source framework supporting XACML 3.0). The datasets are XACML 3.0-based policies, including three samples of real-world policy sets. According to the comparison results, our XACs-DyPol framework performs better than Balana in terms of all updates in dynamic security policy cases. Specially, our proposed solution outperforms by an order of magnitude when the policy structure includes complex policy sets, policies, and rules or some complicated comparison expression which contains higher than function and less than function.Comment: 12 page

Downlink Power Optimization for Heterogeneous Networks with Time Reversal-based Transmission under Backhaul Limitation

In this paper, we investigate an application of two different beamforming techniques and propose a novel downlink power minimization scheme for a two-tier heterogeneous network (HetNet) model. In this context, we employ time reversal (TR) technique to a femtocell base station (FBS) whereas we assume that a macrocell base station (MBS) uses a zero-forcing-based algorithm and the communication channels are subject to frequency selective fading. Additionally, HetNet's backhaul connection is unable to support a sufficient throughput for signaling information exchange between two tiers. Given the considered HetNet model, a downlink power minimization scheme is proposed, and closed-form expressions concerning the optimal solution are provided, taking this constraint into account. Furthermore, considering imperfect channel estimation at TR-employed femtocell, a worst-case robust power minimization problem is formulated. By devising TR worst-case analysis, this robust problem is transformed into an equivalent formulation that is tractable to solve. The results presented in our paper show that the TR technique outperforms the zero-forcing one in the perspective of beamforming methods for femtocell working environments. Finally, we validate the proposed power loading strategy for both cases of perfect and imperfect channel estimations.Comment: 15 pages, 8 figure

Boundary regularity of the solution to the Complex Monge-Amp\`{e}re equation on pseudoconvex domains of infinite type

Let $\Omega$ be a bounded, pseudoconvex domain of $\mathbb C^n$ satisfying the "$f$-Property". The $f$-Property is a consequence of the geometric "type" of the boundary; it holds for all pseudoconvex domains of finite type but may also occur for many relevant classes of domains of infinite type. In this paper, we prove the existence, uniqueness and "weak" H\"older-regularity up to the boundary of the solution to the Dirichlet problem for the complex Monge-Amp\`{e}re equation $$\begin{cases} \det\left[\dfrac{\partial^2(u)}{\partial z_i\partial\bar z_j}\right]=h\ge 0 & \text{in}\quad\Omega,\\ u=\phi & \text{on} \quad b\Omega. \end{cases}$$Comment: 15 page

On the volume and the number of lattice of some semialgebraic sets

Let $f = (f_1,\ldots,f_m) : \R^n \longrightarrow \R^m$ be a polynomial map; $G^f(r) = \{x\in\R^n : |f_i(x)| \leq r,\ i =1,\ldots, m\}$. We show that if $f$ satisfies the Mikhailov - Gindikin condition then \begin{itemize} \item[(i)] $\text{Volume}\ G^f(r) \asymp r^\theta (\ln r)^k$ \item[(ii)] $\text{Card}\left(G^f(r) \cap \overset{o}{\ \Z^n}\right) \asymp r^{\theta'}(\ln r)^{k'}$, as $r\to \infty$, \end{itemize} where the exponents $\theta,\ k,\ \theta',\ k'$are determined explicitly in terms of the Newton polyhedra of$f$. \\ \indent Moreover, the polynomial maps satisfy the Mikhailov - Gindikin condition form an open subset of the set of polynomial maps having the same Newton polyhedron

An explicit estimate on multiplicity truncation in the second main theorem for holomorphic curves encountering hypersurfaces in general position in projective space

Yan and Chen proved a weak Cartan-type second main theorem for holomorphic curves meeting hypersurfaces in projective space that included truncated counting functions. Here we give an explicit estimate for the level of truncation

ICE: A General and Validated Energy Complexity Model for Multithreaded Algorithms

Like time complexity models that have significantly contributed to the analysis and development of fast algorithms, energy complexity models for parallel algorithms are desired as crucial means to develop energy efficient algorithms for ubiquitous multicore platforms. Ideal energy complexity models should be validated on real multicore platforms and applicable to a wide range of parallel algorithms. However, existing energy complexity models for parallel algorithms are either theoretical without model validation or algorithm-specific without ability to analyze energy complexity for a wide-range of parallel algorithms. This paper presents a new general validated energy complexity model for parallel (multithreaded) algorithms. The new model abstracts away possible multicore platforms by their static and dynamic energy of computational operations and data access, and derives the energy complexity of a given algorithm from its work, span and I/O complexity. The new model is validated by different sparse matrix vector multiplication (SpMV) algorithms and dense matrix multiplication (matmul) algorithms running on high performance computing (HPC) platforms (e.g., Intel Xeon and Xeon Phi). The new energy complexity model is able to characterize and compare the energy consumption of SpMV and matmul kernels according to three aspects: different algorithms, different input matrix types and different platforms. The prediction of the new model regarding which algorithm consumes more energy with different inputs on different platforms, is confirmed by the experimental results. In order to improve the usability and accuracy of the new model for a wide range of platforms, the platform parameters of ICE model are provided for eleven platforms including HPC, accelerator and embedded platforms.Comment: 23 pages, 8 figures, 33 reference