Monomial Dynamical Systems of Dimension One over Finite Fields

In this paper we study the monomial dynamical systems of dimension one over finite fields from the viewpoints of arithmetic and graph theory. We give formulas for the number of periodic points with period r and cycles with length r. Then we compute the natural distributions of periodic points and cycles. We also define and compute the Dirichlet distributions of periodic points and cycles. Especially, we associate the monomial dynamical systems with function fields to compute distributions.Comment: Accepted by Acta Arithmetica. (SCI

Beyond Massive-MIMO: The Potential of Positioning with Large Intelligent Surfaces

We consider the potential for positioning with a system where antenna arrays are deployed as a large intelligent surface (LIS), which is a newly proposed concept beyond massive-MIMO where future man-made structures are electronically active with integrated electronics and wireless communication making the entire environment \lq\lq{}intelligent\rq\rq{}. In a first step, we derive Fisher-information and Cram\'{e}r-Rao lower bounds (CRLBs) in closed-form for positioning a terminal located perpendicular to the center of the LIS, whose location we refer to as being on the central perpendicular line (CPL) of the LIS. For a terminal that is not on the CPL, closed-form expressions of the Fisher-information and CRLB seem out of reach, and we alternatively find approximations of them which are shown to be accurate. Under mild conditions, we show that the CRLB for all three Cartesian dimensions ($x$, $y$ and $z$) decreases quadratically in the surface-area of the LIS, except for a terminal exactly on the CPL where the CRLB for the $z$-dimension (distance from the LIS) decreases linearly in the same. In a second step, we analyze the CRLB for positioning when there is an unknown phase $\varphi$ presented in the analog circuits of the LIS. We then show that the CRLBs are dramatically increased for all three dimensions but decrease in the third-order of the surface-area. Moreover, with an infinitely large LIS the CRLB for the $z$-dimension with an unknown $\varphi$ is 6 dB higher than the case without phase uncertainty, and the CRLB for estimating $\varphi$ converges to a constant that is independent of the wavelength $\lambda$. At last, we extensively discuss the impact of centralized and distributed deployments of LIS, and show that a distributed deployment of LIS can enlarge the coverage for terminal-positioning and improve the overall positioning performance.Comment: Submitted to IEEE Trans. on Signal Processing on Apr. 2017; 30 pages; 13 figure

Beyond Massive-MIMO: The Potential of Data-Transmission with Large Intelligent Surfaces

In this paper, we consider the potential of data-transmission in a system with a massive number of radiating and sensing elements, thought of as a contiguous surface of electromagnetically active material. We refer to this as a large intelligent surface (LIS). The "LIS" is a newly proposed concept, which conceptually goes beyond contemporary massive MIMO technology, that arises from our vision of a future where man-made structures are electronically active with integrated electronics and wireless communication making the entire environment "intelligent". We consider capacities of single-antenna autonomous terminals communicating to the LIS where the entire surface is used as a receiving antenna array. Under the condition that the surface-area is sufficiently large, the received signal after a matched-filtering (MF) operation can be closely approximated by a sinc-function-like intersymbol interference (ISI) channel. We analyze the capacity per square meter (m^2) deployed surface, \hat{C}, that is achievable for a fixed transmit power per volume-unit, \hat{P}. Moreover, we also show that the number of independent signal dimensions per m deployed surface is 2/\lambda for one-dimensional terminal-deployment, and \pi/\lambda^2 per m^2 for two and three dimensional terminal-deployments. Lastly, we consider implementations of the LIS in the form of a grid of conventional antenna elements and show that, the sampling lattice that minimizes the surface-area of the LIS and simultaneously obtains one signal space dimension for every spent antenna is the hexagonal lattice. We extensively discuss the design of the state-of-the-art low-complexity channel shortening (CS) demodulator for data-transmission with the LIS.Comment: Submitted to IEEE Trans. on Signal Process., 30 pages, 12 figure

Being Negative but Constructively: Lessons Learnt from Creating Better Visual Question Answering Datasets

Visual question answering (Visual QA) has attracted a lot of attention lately, seen essentially as a form of (visual) Turing test that artificial intelligence should strive to achieve. In this paper, we study a crucial component of this task: how can we design good datasets for the task? We focus on the design of multiple-choice based datasets where the learner has to select the right answer from a set of candidate ones including the target (\ie the correct one) and the decoys (\ie the incorrect ones). Through careful analysis of the results attained by state-of-the-art learning models and human annotators on existing datasets, we show that the design of the decoy answers has a significant impact on how and what the learning models learn from the datasets. In particular, the resulting learner can ignore the visual information, the question, or both while still doing well on the task. Inspired by this, we propose automatic procedures to remedy such design deficiencies. We apply the procedures to re-construct decoy answers for two popular Visual QA datasets as well as to create a new Visual QA dataset from the Visual Genome project, resulting in the largest dataset for this task. Extensive empirical studies show that the design deficiencies have been alleviated in the remedied datasets and the performance on them is likely a more faithful indicator of the difference among learning models. The datasets are released and publicly available via http://www.teds.usc.edu/website_vqa/.Comment: Accepted for Oral Presentation at NAACL-HLT 201