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In this paper, we will give two proofs of the Cluckers-Veys conjecture on exponential sums for the case of polynomials in $\mathbb{Z}[x_{1},\ldots,x_{n}]$ having log-canonical thresholds at most one half. In particular, these results imply Igusa's conjecture and Denef-Sperber's conjecture under the same restriction on the log-canonical threshold.

In this paper, we conceive an advanced neutral host micro operator (NH-{\mu}O) network approach providing venues with services tailored to their specialized/specific requirements and/or local context related services that the mobile network operators (MNOs) are poorly-suited to providing it, as well as mobile broadband experience to the users from MNOs in a venue where only a single infrastructure is mandated under shared spectrum access framework. A radio access network slicing concept is conceived to support and optimize both the slice instance (SI) use cases independently and efficiently by running all network implementations in parallel, simultaneously on a common physical network infrastructure. We devise a common shared architecture for the NH-{\mu}O small cell base stations and dynamic spectrum assignment control unit, and their required functionalities supporting coexistence of different SIs as well as multiple MNOs in shared spectrum access communications. We devise both inter-SI and intra- SI dynamic spectrum allocation policies considering time-varying requirements of different SIs. The policies are capable of taking care of application level priority, -i.e., mixture of guaranteed quality of service and best-effort service users served by each SI while ensuring a healthy competition. Our proposed framework serves two-fold advantages, such as it gives the venue owner its own managed wireless networks tailored to its very specific requirements, and it also brings out cost savings and coverage extension for MNOs and efficiency of resources that arise from sharing wireless networks, and delivering the network capacity into high density venues.

We address in this paper the problem of modifying both profits and costs of a fractional knapsack problem optimally such that a prespecified solution becomes an optimal solution with prespect to new parameters. This problem is called the inverse fractional knapsack problem. Concerning the $l_1$-norm, we first prove that the problem is NP-hard. The problem can be however solved in quadratic time if we only modify profit parameters. Additionally, we develop a quadratic-time algorithm that solves the inverse fractional knapsack problem under $l_\infty$-norm., Comment: 11 pages

This paper considers a multicell downlink channel in which multiple base stations (BSs) cooperatively serve users by jointly precoding shared data transported from a central processor over limited-capacity backhaul links. We jointly design the beamformers and BS-user link selection so as to maximize the sum rate subject to user-specific signal-to-interference-noise (SINR) requirements, per-BS backhaul capacity and per-BS power constraints. As existing solutions for the considered problem are suboptimal and their optimality remains unknown due to the lack of globally optimal solutions, we characterized this gap by proposing a globally optimal algorithm for the problem of interest. Specifically, the proposed method is customized from a generic framework of a branch and bound algorithm applied to discrete monotonic optimization. We show that the proposed algorithm converges after a finite number of iterations, and can serve as a benchmark for existing suboptimal solutions and those that will be developed for similar contexts in the future. In this regard, we numerically compare the proposed optimal solution to a current state-of-the-art, which show that this suboptimal method only attains 70% to 90% of the optimal performance., Comment: 5 pages, 2 figures; Accepted for publication, ICASSP 2017

This paper considers a downlink transmission of cloud radio access network (C-RAN) in which precoded baseband signals at a common baseband unit are compressed before being forwarded to radio units (RUs) through limited fronthaul capacity links. We investigate the joint design of precoding, multivariate compression and RU-user selection which maximizes the energy efficiency of downlink C-RAN networks. The considered problem is inherently a rank-constrained mixed Boolean nonconvex program for which a globally optimal solution is difficult and computationally expensive to find. In order to derive practically appealing solutions, we invoke some useful relaxation and transformation techniques to arrive at a more tractable (but still nonconvex) continuous program. To solve the relaxation problem, we propose an iterative procedure based on DC algorithms which is provably convergent. Numerical results demonstrate the superior of the proposed solution in terms of achievable energy efficiency compared to existing schemes., Comment: 6 pages, 3 figures, accepted to IEEE ICC 2017 - Signal Processing for Communications Symposium

Small cells deployment is one of the most significant long-term strategic policies of the mobile network operators. In heterogeneous networks (HetNets), small cells serve as offloading spots in the radio access network to offload macro users (MUs) and their associated traffic from congested macrocells. In this paper, we perform analytical analysis and investigate how the radio propagation effects such as multipath and shadowing and small cell base station density affect MUs' offloading to small cell network (SCN). In particular, we exploit composite fading channels in our evaluation when an MU is offloaded to SCN with varying small and macro cell densities in the stochastic HetNets framework. We derive the expressions for outage probability (equivalently success probability) of the MU in macro network and SCN for two different cases, viz.: i) Nakagami-lognormal channel fading; ii) time-shared (combined) shadowed/unshadowed channel fading. We propose efficient approximations for the probability density functions of the channel fading (power) for the above-mentioned fading distributions that do not have closed-form expressions employing Gauss-Hermite integration and finite exponential series, respectively. Finally, the outage probability performance of MU with and without offloading options/services is analyzed for various settings of fading channels.

Poincar\'e series of $p$-adic, definable equivalence relations have been studied in various cases since Igusa's and Denef's work related to counting solutions of polynomial equations modulo $p^n$ for prime $p$. General semi-algebraic equivalence relations on local fields have been studied uniformly in $p$ recently in \cite{16}. Here we generalize the rationality result of \cite{16} to the analytic case, unifomly in $p$, building further on the appendix of \cite{16} and on \cite{13b}, \cite{03}. In particular, the results hold for large positive characteristic local fields. We also introduce rational motivic constructible functions and their motivic integrals, as a tool to prove our main results.

We show there are intermediate $P$-minimal structures between the semi-algebraic and sub-analytic languages which do not have definable Skolem functions. As a consequence, by a result of Mourgues, this shows there are $P$-minimal structures which do not admit classical cell decomposition., Comment: 9 pages, (added missing grant acknowledgement)

We concern the problem of modifying the edge lengths of a tree in minimum total cost so that the prespecified $p$ vertices become the $p$-maxian with respect to the new edge lengths. This problem is called the inverse $p$-maxian problem on trees. \textbf{Gassner} proposed efficient combinatorial alogrithm to solve the the inverse 1-maxian problem on trees in 2008. For the problem with $p \geq 2$, we claim that the problem can be reduced to finitely many inverse $2$-maxian problem. We then develop algorithms to solve the inverse $2$-maxian problem for various objective functions. The problem under $l_1$-norm can be formulated as a linear program and thus can be solved in polynomial time. Particularly, if the underlying tree is a star, then the problem can be solved in linear time. We also devised $O(n\log n)$ algorithms to solve the problems under Chebyshev norm and bottleneck Hamming distance, where $n$ is the number of vertices of the tree. Finally, the problem under weighted sum Hamming distance is $NP$-hard., Comment: 9 pages