Typical dynamics of plane rational maps with equal degrees

Let $f:\mathbb{CP}^2\dashrightarrow\mathbb{CP^2}$ be a rational map with algebraic and topological degrees both equal to $d\geq 2$. Little is known in general about the ergodic properties of such maps. We show here, however, that for an open set of automorphisms $T:\mathbb{CP}^2\to\mathbb{CP}^2$, the perturbed map $T\circ f$ admits exactly two ergodic measures of maximal entropy $\log d$, one of saddle and one of repelling type. Neither measure is supported in an algebraic curve, and $T\circ f$ is `fully two dimensional' in the sense that it does not preserve any singular holomorphic foliation. Absence of an invariant foliation extends to all $T$ outside a countable union of algebraic subsets. Finally, we illustrate all of our results in a more concrete particular instance connected with a two dimensional version of the well-known quadratic Chebyshev map.Comment: Many small changes in accord with referee comments and suggestion

Fundamentals of Inter-cell Overhead Signaling in Heterogeneous Cellular Networks

Heterogeneous base stations (e.g. picocells, microcells, femtocells and distributed antennas) will become increasingly essential for cellular network capacity and coverage. Up until now, little basic research has been done on the fundamentals of managing so much infrastructure -- much of it unplanned -- together with the carefully planned macro-cellular network. Inter-cell coordination is in principle an effective way of ensuring different infrastructure components behave in a way that increases, rather than decreases, the key quality of service (QoS) metrics. The success of such coordination depends heavily on how the overhead is shared, and the rate and delay of the overhead sharing. We develop a novel framework to quantify overhead signaling for inter-cell coordination, which is usually ignored in traditional 1-tier networks, and assumes even more importance in multi-tier heterogeneous cellular networks (HCNs). We derive the overhead quality contour for general K-tier HCNs -- the achievable set of overhead packet rate, size, delay and outage probability -- in closed-form expressions or computable integrals under general assumptions on overhead arrivals and different overhead signaling methods (backhaul and/or wireless). The overhead quality contour is further simplified for two widely used models of overhead arrivals: Poisson and deterministic arrival process. This framework can be used in the design and evaluation of any inter-cell coordination scheme. It also provides design insights on backhaul and wireless overhead channels to handle specific overhead signaling requirements.Comment: 21 pages, 9 figure

Open, Closed, and Shared Access Femtocells in the Downlink

A fundamental choice in femtocell deployments is the set of users which are allowed to access each femtocell. Closed access restricts the set to specifically registered users, while open access allows any mobile subscriber to use any femtocell. Which one is preferable depends strongly on the distance between the macrocell base station (MBS) and femtocell. The main results of the paper are lemmas which provide expressions for the SINR distribution for various zones within a cell as a function of this MBS-femto distance. The average sum throughput (or any other SINR-based metric) of home users and cellular users under open and closed access can be readily determined from these expressions. We show that unlike in the uplink, the interests of home and cellular users are in conflict, with home users preferring closed access and cellular users preferring open access. The conflict is most pronounced for femtocells near the cell edge, when there are many cellular users and fewer femtocells. To mitigate this conflict, we propose a middle way which we term shared access in which femtocells allocate an adjustable number of time-slots between home and cellular users such that a specified minimum rate for each can be achieved. The optimal such sharing fraction is derived. Analysis shows that shared access achieves at least the overall throughput of open access while also satisfying rate requirements, while closed access fails for cellular users and open access fails for the home user.Comment: 26 pages, 8 figures, Submitted to IEEE Transactions on Wireless Communication

Keyword Search on RDF Graphs - A Query Graph Assembly Approach

Keyword search provides ordinary users an easy-to-use interface for querying RDF data. Given the input keywords, in this paper, we study how to assemble a query graph that is to represent user's query intention accurately and efficiently. Based on the input keywords, we first obtain the elementary query graph building blocks, such as entity/class vertices and predicate edges. Then, we formally define the query graph assembly (QGA) problem. Unfortunately, we prove theoretically that QGA is a NP-complete problem. In order to solve that, we design some heuristic lower bounds and propose a bipartite graph matching-based best-first search algorithm. The algorithm's time complexity is $O(k^{2l} \cdot l^{3l})$, where $l$ is the number of the keywords and $k$ is a tunable parameter, i.e., the maximum number of candidate entity/class vertices and predicate edges allowed to match each keyword. Although QGA is intractable, both $l$ and $k$ are small in practice. Furthermore, the algorithm's time complexity does not depend on the RDF graph size, which guarantees the good scalability of our system in large RDF graphs. Experiments on DBpedia and Freebase confirm the superiority of our system on both effectiveness and efficiency

Non-long terminal repeat (non-LTR) retrotransposons: mechanisms, recent developments, and unanswered questions

Non-long terminal repeat (non-LTR) retrotransposons are present in most eukaryotic genomes. In some species, such as humans, these elements are the most abundant genome sequence and continue to replicate to this day, creating a source of endogenous mutations and potential genotoxic stress. This review will provide a general outline of the replicative cycle of non-LTR retrotransposons. Recent findings regarding the host regulation of non-LTR retrotransposons will be summarized. Finally, future directions of interest will be discussed

Physical Model of the Immune Response of Bacteria Against Bacteriophage Through the Adaptive CRISPR-Cas Immune System

Bacteria and archaea have evolved an adaptive, heritable immune system that recognizes and protects against viruses or plasmids. This system, known as the CRISPR-Cas system, allows the host to recognize and incorporate short foreign DNA or RNA sequences, called `spacers' into its CRISPR system. Spacers in the CRISPR system provide a record of the history of bacteria and phage coevolution. We use a physical model to study the dynamics of this coevolution as it evolves stochastically over time. We focus on the impact of mutation and recombination on bacteria and phage evolution and evasion. We discuss the effect of different spacer deletion mechanisms on the coevolutionary dynamics. We make predictions about bacteria and phage population growth, spacer diversity within the CRISPR locus, and spacer protection against the phage population.Comment: 37 pages, 13 figure

An examination of the processes by which construal level affects the implicit evaluation of goal relevant stimuli.

Previous research has found that construal level—how abstractly or concretely people represent events—can impact implicit evaluations. Abstract high-level construal (vs. concrete low-level construal) promotes evaluative responses consistent with global (strongly held, long-term) rather than local (short-term, situational) goals. It remains unclear by what cognitive process(es) this occurs. In this paper, we examine two possibilities. High-level construal might enhance the unintended influence of activated evaluative associations or facilitate the detection and implementation of intentional responses. To examine these possibilities, the current study applies a multinomial processing tree model to data from Fujita and Han (2009). Results suggest that high-level construal facilitates goal-consistent evaluations by increasing both the unintentional influence of activated goal-consistent positive associations and the intentional detection of and implementation of accurate responding to goal-relevant stimuli. These findings extend our understanding of how construal level promotes goal consistent evaluations

AUTONOMOUS ROBOT FOR COLLECTING TENNIS BALL

The objective of the project is to provide a means to save tennis players' energy and time in collecting tennis ball, which in this project is achieved by building an autonomous machine that collects tennis balls by sweeping around on the tennis court itself. This report starts with a brief introduction and the objective of the project is mentioned, followed by a literature review section, which tells different types of tennis ball collectors and different means of building a tennis ball collector prototype

Learning in Parallel

In this paper, we extend Valiant's sequential model of concept learning from examples [Valiant 1984] and introduce models for the e cient learning of concept classes from examples in parallel. We say that a concept class is NC-learnable if it can be learned in polylog time with a polynomial number of processors. We show that several concept classes which are polynomial-time learnable are NC-learnable in constant time. Some other classes can be shown to be NC-learnable in logarithmic time, but not in constant time. Our main result shows that other classes, such as s-fold unions of geometrical objects in Euclidean space, which are polynomial-time learnable by a greedy set cover technique, are NC-learnable using a non-greedy technique. We also show that (unless P RNC) several polynomial-time learnable concept classes related to linear programming are not NC-learnable. Equivalence of various parallel learning models and issues of fault-tolerance are also discussed

Nearly Optimal Vector Quantization via Linear Programming

(c) 1992 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.We present new vector quantization algorithms based on the theory devel- oped in [LiV]. The new approach is to formulate a vector quantization problem as a 0-1 integer linear program. We rst solve its relaxed linear program by linear programming techniques. Then we transform the linear program solu- tion into a provably good solution for the vector quantization problem. These methods lead to the rst known polynomial-time full-search vector quanti- zation codebook design algorithm and tree pruning algorithm with provable worst-case performance guarantees. We also introduce the notion of pseudo- random pruned tree-structured vector quantizers. Initial experimental results on image compression are very encouraging