Maximum Number of Minimum Dominating and Minimum Total Dominating Sets

Given a connected graph with domination (or total domination) number \gamma>=2, we ask for the maximum number m_\gamma and m_{\gamma,T} of dominating and total dominating sets of size \gamma. An exact answer is provided for \gamma=2and lower bounds are given for \gamma>=3.Comment: 6 page

General Bounds on the Downhill Domination Number in Graphs.

A path π = (v1, v2,...vk+1) in a graph G = (V,E) is a downhill path if for every i, 1 \u3c i \u3c k, deg(vi) \u3e deg(vi+1), where deg(vi) denotes the degree of vertex vi ∊ V. The downhill domination number equals the minimum cardinality of a set S ⊂ V having the property that every vertex v ∊ V lies on a downhill path originating from some vertex in S. We investigate downhill domination numbers of graphs and give upper bounds. In particular, we show that the downhill domination number of a graph is at most half its order, and that the downhill domination number of a tree is at most one third its order. We characterize the graphs obtaining each of these bounds

Demarcating the Granular Frontier:planetary urbanization without an inside

In its age of global crisis, sand has acquired a conspicuous profile as an urban resource and undercover vector of statecraft. Amidst mounting reports of the disastrous effects of sand mining stoked by intense cycles of urbanization and territorial expansion across the world, it is critical to understand the formation of sand’s granular frontiers, and how their differentiated expression through the global sand crisis demands a reconsideration of the theoretical frontiers of urbanization, territory, and global trade. Building on conceptualisations of sand’s granular geographies and its “geologising” of urban political ecology, this paper seeks to demarcate the theoretical and empirical terrain of sand’s granular frontiers, and how they problematize contemporary debates around urbanization’s “planetary” scope and its extractive underbelly. By reconnecting the frontiers of sand extraction and urbanization, this article theorizes the enclosure of geomorphology and where sand’s satiation of urban and state development is leading. In examining how sand’s simultaneous exclusion from formal processes of valuation and regulation structures urbanization in unpredictable ways, it seeks to provide an account of planetary urbanization without an inside

All Lines Flow In:excavating the geophilosophical relations of Singapore’s infrastructure through SEA STATE

Infrastructure has proven a polyvalent concept in human geography and anthropology for exploring the intersection of the social and technical. However, the ?below? of infrastructure, the infra, has remained underexamined in its relationship to the state, territory and the earth. This article proposes that infrastructure is better understood as a geophilosophical relation that renders a set of relations a subsurface for the propagation of another: it designates a socio-natural ground for political-economic figuration. It outlines the geophilosophical relations of infrastructure through thinking with the project SEA STATE by Singaporean artist Charles Lim, a series of artworks which document Singapore?s infrastructural underside, which Lim terms the sea-state, and provides a conceptual elaboration of SEA STATE?s aesthetic figures. In positing the continuity of figures across the sea-state?s varied infrastructures, SEA STATE exposes the colonial trajectory of its infrastructural systems, the contingencies it churns up as it endeavours to maintain its place in the world market, and the fundamental inversion of figure and ground the sea-state has effectuated. This inversion is all the more evident when we consider the expansive land reclamation projects of modern Singapore, wherein its territory has become infrastructure for bespoke logistical and petrochemical concerns, and will continue until the end of the century under the auspices of mitigating sea level rise. As the geological imaginary of the Anthropocene begins to seep into infrastructural anxieties of maintenance, breakdown and inundation, with governments and policymakers demanding that nature itself become infrastructure, it is critical to trace the longue durée of these infrastructural formations, how their continuities are remade and reiterated by the demands of subsequent historical-geographical junctures, and how the designation of figure and ground can ultimately result in the figure becoming the condition of possibility for its ground, requiring its continual reproduction

Sharp Concentration of Hitting Size for Random Set Systems

Consider the random set system of {1,2,...,n}, where each subset in the power set is chosen independently with probability p. A set H is said to be a hitting set if it intersects each chosen set. The second moment method is used to exhibit the sharp concentration of the minimal size of H for a variety of values of p.Comment: 11 page

Individual Based Model to Simulate the Evolution of Insecticide Resistance

Insecticides play a critical role in agricultural productivity. However, insecticides impose selective pressures on insect populations, so the Darwinian principles of natural selection predict that resistance to the insecticide is likely to form in the insect populations. Insecticide resistance, in turn, severely reduces the utility of the insecticides being used. Thus there is a strong economic incentive to reduce the rate of resistance evolution. Moreover, resistance evolution represents an example of evolution under novel selective pressures, so its study contributes to the fundamental understanding of evolutionary theory. Insecticide resistance often represents a complex interplay of multiple fitness trade-offs for individual insects. Resistant individuals tend to suffer significant decreases in fitness when no insecticide is present, resulting in non-resistant individuals having the tendency to outcompete resistant ones in areas with no insecticide. In the use of standard modeling practices, difficulties arise when trying to incorporate these complexities in a fashion which facilitates the simulation of the model and analyzing the results. Individual based models (IBMs) are one approach to overcoming these difficulties by leveraging modern computational techniques and modern computer power. In an IBM each member of the population is simulated to follow a set of stochastic rules, which includes rules about the behaviors and interactions of individuals. We propose to apply an IBM approach to modeling the evolution of insecticide resistance in an insect species population. The fall armyworm is an economically damaging pest which has recently become invasive in Africa, India, and China. A common type of insecticide used control fall armyworms is Bacillus thuringiensis (Bt). We hypothesize that individuals that are resistant to Bt grow at slower rates than their counterparts. This creates a strong fitness disadvantage when Bt is not present because the fall armyworms are cannibalistic, where smaller individuals have a large disadvantage. Thus we use our IBM to explore the nature of the fitness trade-offs between resistance and growth rate in order to understand how it could be exploited to lessen the rate of resistance evolution in the species. Adviser: Richard Rebarber and Brigitte Tenhumber

Financial signal processing: a self calibrating model

Previous work on multifactor term structure models has proposed that the short rate process is a function of some unobserved diffusion process. We consider a model in which the short rate process is a function of a Markov chain which represents the 'state of the world'. This enables us to obtain explicit expressions for the prices of zero-coupon bonds and other securities. Discretizing our model allows the use of signal processing techniques from Hidden Markov Models. This means we can estimate not only the unobserved Markov chain but also the parameters of the model, so the model is self-calibrating. The estimation procedure is tested on a selection of U.S. Treasury bills and bonds.Bonds