The complexity of resolving conflicts on MAC

We consider the fundamental problem of multiple stations competing to transmit on a multiple access channel (MAC). We are given $n$ stations out of which at most $d$ are active and intend to transmit a message to other stations using MAC. All stations are assumed to be synchronized according to a time clock. If $l$ stations node transmit in the same round, then the MAC provides the feedback whether $l=0$, $l=2$ (collision occurred) or $l=1$. When $l=1$, then a single station is indeed able to successfully transmit a message, which is received by all other nodes. For the above problem the active stations have to schedule their transmissions so that they can singly, transmit their messages on MAC, based only on the feedback received from the MAC in previous round. For the above problem it was shown in [Greenberg, Winograd, {\em A Lower bound on the Time Needed in the Worst Case to Resolve Conflicts Deterministically in Multiple Access Channels}, Journal of ACM 1985] that every deterministic adaptive algorithm should take $\Omega(d (\lg n)/(\lg d))$ rounds in the worst case. The fastest known deterministic adaptive algorithm requires $O(d \lg n)$ rounds. The gap between the upper and lower bound is $O(\lg d)$ round. It is substantial for most values of $d$: When $d =$ constant and $d \in O(n^{\epsilon})$ (for any constant $\epsilon \leq 1$, the lower bound is respectively $O(\lg n)$ and O(n), which is trivial in both cases. Nevertheless, the above lower bound is interesting indeed when $d \in$ poly($\lg n$). In this work, we present a novel counting argument to prove a tight lower bound of $\Omega(d \lg n)$ rounds for all deterministic, adaptive algorithms, closing this long standing open question.}Comment: Xerox internal report 27th July; 7 page

Faster Gossiping in Bidirectional Radio Networks with Large Labels

We consider unknown ad-hoc radio networks, when the underlying network is bidirectional and nodes can have polynomially large labels. For this model, we present a deterministic protocol for gossiping which takes $O(n \lg^2 n \lg \lg n)$ rounds. This improves upon the previous best result for deterministic gossiping for this model by [Gasienec, Potapov, Pagourtizis, Deterministic Gossiping in Radio Networks with Large labels, ESA (2002)], who present a protocol of round complexity $O(n \lg^3 n \lg \lg n)$ for this problem. This resolves open problem posed in [Gasienec, Efficient gossiping in radio networks, SIROCCO (2009)], who cite bridging gap between lower and upper bounds for this problem as an important objective. We emphasize that a salient feature of our protocol is its simplicity, especially with respect to the previous best known protocol for this problem

Empirical analysis of spatial location of activity: a proposal of using spatial association statistics

Based on the initial paper of Krugman (1991), several works have analysed the consequences of the integration process on the activity location. In this sense, Puga (1996) and Puga and Venables (1996) among others, have derived an inverse U-shape relationship between integration and agglomeration. In order to check this hypothesis, it is habitual to compute some of the traditional concentration indexes. However, this kind of indexes considers each region as an isolated economy, discarding links with others. Taking into account these ideas, this paper proposes the use of some spatial association tests in order to shed light on the consequences of an integration process, overcoming the limitations shown by other indexes of concentration. First, we discuss, from a theoretical point of view, the utility of these spatial econometric tools to get the goal of the paper. So, we analyse the behaviour of the spatial correlograms (global spatial autocorrelation tests for different orders of contiguity) and the local spatial association tests for some theoretical spatial distributions of the product (even distribution, core- periphery scheme, monocentral distribution with and without hierarchical distribution around the centre, etc). Then, we derive different temporal evolutions both of these correlograms and the local statistics related to possible scenarios after the integration (more concentration, more random distribution, etc). Second, we apply this analysis to the European Union case. In this sense, we compare the evolution shown by the GDP pc among the European regions during the period 1975-1992 with the theoretical distributions defined in the first part of the paper in order to know the trend of the spatial distribution of the activity after the deepening in the integration process. Keywords: Spatial association test, spatial econometrics, integration process

Achieving Dilution without Knowledge of Coordinates in the SINR Model

Considerable literature has been developed for various fundamental distributed problems in the SINR (Signal-to-Interference-plus-Noise-Ratio) model for radio transmission. A setting typically studied is when all nodes transmit a signal of the same strength, and each device only has access to knowledge about the total number of nodes in the network $n$, the range from which each node's label is taken $[1,\dots,N]$, and the label of the device itself. In addition, an assumption is made that each node also knows its coordinates in the Euclidean plane. In this paper, we create a technique which allows algorithm designers to remove that last assumption. The assumption about the unavailability of the knowledge of the physical coordinates of the nodes truly captures the `ad-hoc' nature of wireless networks. Previous work in this area uses a flavor of a technique called dilution, in which nodes transmit in a (predetermined) round-robin fashion, and are able to reach all their neighbors. However, without knowing the physical coordinates, it's not possible to know the coordinates of their containing (pivotal) grid box and seemingly not possible to use dilution (to coordinate their transmissions). We propose a new technique to achieve dilution without using the knowledge of physical coordinates. This technique exploits the understanding that the transmitting nodes lie in 2-D space, segmented by an appropriate pivotal grid, without explicitly referring to the actual physical coordinates of these nodes. Using this technique, it is possible for every weak device to successfully transmit its message to all of its neighbors in $\Theta(\lg N)$ rounds, as long as the density of transmitting nodes in any physical grid box is bounded by a known constant. This technique, we feel, is an important generic tool for devising practical protocols when physical coordinates of the nodes are not known.Comment: 10 page

Is the influence of quality of life on urban growth non-stationary in space? A case study of Barcelona

There are several determinants that influence household location decisions. More concretely, recent economic literature assigns an increasingly important role to the variables governing quality of life. Nevertheless, the spatial stationarity of the parameters is implicitly assumed in most studies. Here we analyse the role of quality of life in urban economics and test for the spatial stationarity of the relationship between city growth and quality of life.quality of life, urban economics, geographically weighted regressions

Influence of Price Formation in Indian Gold Market

The paper inspects the general productivity of Gold Exchange Traded Funds (ETF) against spot gold and gold prospects in Indian situation utilizing a progression of regular and limit cointegration insights. The outcomes uncover that gold ETFs and spot gold just as gold ETFs and gold prospects combine over the long haul. Likewise, developments in spot costs and prospects costs are found to lead those in ETF costs, in this manner, giving a degree to executing beneficial exchanging methodologies ETFs. The examination further investigates the plausible reasons that may represent the relative wastefulness saw in ETF costs. Gold ETFs and gold fates speak to two such sections that empower speculators to gain presentation to the value development of gold in a way like that of stocks exchanged at the trade. With various portions of the market following a similar resource class, the present examination endeavors to research the general proficiency of one market over the other for example between spot cost of physical gold and gold ETFs just as between gold ETFs and gold fates in Indian setting which records for perhaps the biggest buyer of the metal on the planet. Utilizing different econometric strategies, for example, cointegration, Vector Error Correction Model (VECM), Gregory-Hansen (1996) insights and Toda-Yamamoto trial of causality, the outcomes uncover that gold ETFs, when contrasted with their spot and prospects partners, are generally wasteful. ETF costs are found to slack both the spot just as prospects costs. Restricted cooperation, constrained mindfulness, illiquidity, and nonappearance of edge exchanging are observed to be the prime reasons clarifying the general wastefulness of gold ETFs. The examination likewise accommodates the alert that should be practiced while deciphering the outcomes for straight cointegration which may neglect to distinguish the presence of a long run connection between the factors within the sight of auxiliary brake characteristic in the information arrangement