Tile Number and Space-Efficient Knot Mosaics

In this paper we introduce the concept of a space-efficient knot mosaic. That is, we seek to determine how to create knot mosaics using the least number of non-blank tiles necessary to depict the knot. This least number is called the tile number of the knot. We determine strict bounds for the tile number of a knot in terms of the mosaic number of the knot. In particular, if $t$ is the tile number of a prime knot with mosaic number $m$, then $5m-8 \leq t \leq m^2-4$ if $m$ is even and $5m-8 \leq t \leq m^2-8$ if $m$ is odd. We also determine the tile number of several knots and provide space-efficient knot mosaics for each of them.Comment: The original version of this article was split into two articles during refereein

Giving Up the Ghost: Death in the Depression

The preceding section is the human evidence behind this paper: what did the Great Depression feel like? What was it like to live in a Hooverville? To travel across the country in a rundown Jalopy? To Jump freight trains and live in box cars? To go on relief? What impact did the depression have on the national and individual psyche? Many authors have dealt with these questions, so why do it again? First, this thesis represents a attempt to draw together all the information for myself. Second, it is also an endeavor to find what people considered then (and perhaps still do) most important in their lives. Third, it may lead to a deeper understanding of what sort of society entered the depression and how the depression changed it. The first thing to be discussed is the economics of the depression. Most importantly, Just what is a depression? No one seems to know. Economists have agreed on a definition for the term recession, but have not reached a consensus on the term depression. Five different handbooks of economics give five different definitions of the word ranging from a severe slowdown in the economy, to a long lasting recession in economic activity . Perhaps the best way to define a depression is to list its characteristics. Generally, business activity is far below normal, there is great pessimism among business and consumers alike, there is a sharp curtailment of production, little capital investment, contraction of credit, falling prices, mass unemployment, and a high rate of business failures

Giving Up the Ghost: Death in the Depression

The preceding section is the human evidence behind this paper: what did the Great Depression feel like? What was it like to live in a Hooverville? To travel across the country in a rundown Jalopy? To Jump freight trains and live in box cars? To go on relief? What impact did the depression have on the national and individual psyche? Many authors have dealt with these questions, so why do it again? First, this thesis represents a attempt to draw together all the information for myself. Second, it is also an endeavor to find what people considered then (and perhaps still do) most important in their lives. Third, it may lead to a deeper understanding of what sort of society entered the depression and how the depression changed it. The first thing to be discussed is the economics of the depression. Most importantly, Just what is a depression? No one seems to know. Economists have agreed on a definition for the term recession, but have not reached a consensus on the term depression. Five different handbooks of economics give five different definitions of the word ranging from a severe slowdown in the economy, to a long lasting recession in economic activity . Perhaps the best way to define a depression is to list its characteristics. Generally, business activity is far below normal, there is great pessimism among business and consumers alike, there is a sharp curtailment of production, little capital investment, contraction of credit, falling prices, mass unemployment, and a high rate of business failures

Modelling aggregation on the large scale and regularity on the small scale in spatial point pattern datasets

We consider a dependent thinning of a regular point process with the aim of obtaining aggregation on the large scale and regularity on the small scale in the resulting target point process of retained points. Various parametric models for the underlying processes are suggested and the properties of the target point process are studied. Simulation and inference procedures are discussed when a realization of the target point process is observed, depending on whether the thinned points are observed or not. The paper extends previous work by Dietrich Stoyan on interrupted point processes

Dynamic Spatial Autoregressive Models with Autoregressive and Heteroskedastic Disturbances

We propose a new class of models specifically tailored for spatio-temporal data analysis. To this end, we generalize the spatial autoregressive model with autoregressive and heteroskedastic disturbances, i.e. SARAR(1,1), by exploiting the recent advancements in Score Driven (SD) models typically used in time series econometrics. In particular, we allow for time-varying spatial autoregressive coefficients as well as time-varying regressor coefficients and cross-sectional standard deviations. We report an extensive Monte Carlo simulation study in order to investigate the finite sample properties of the Maximum Likelihood estimator for the new class of models as well as its flexibility in explaining several dynamic spatial dependence processes. The new proposed class of models are found to be economically preferred by rational investors through an application in portfolio optimization.Comment: 33 pages, 5 figure

Classic and spatial shift-share analysis of state-level employment change in Brazil

This paper combines classic and spatial shift-share decompositions of 1981 to 2006 employment change across the 27 states of Brazil. The classic shift-share method shows higher employment growth rates for underdeveloped regions that are due to an advantageous industry-mix and also due to additional job creation, commonly referred to as the competitive effect. Alternative decompositions proposed in the literature do not change this broad conclusion. Further examination employing exploratory spatial data analysis (ESDA) shows spatial correlation of both the industry-mix and the competitive effects. Considering that until the 1960s economic activities were more concentrated in southern regions of Brazil than they are nowadays, these results support beta convergence theories but also find evidence of agglomeration effects. Additionally, a very simple spatial decomposition is proposed that accounts for the spatially-weighted growth of surrounding states. Favourable growth in northern and centre-western states is basically associated with those states’ strengths in potential spatial spillover effect and in spatial competitive effect

Geographic Coincidence of Increased Malaria Transmission Hazard and Vulnerability Occurring at the Periphery of two Tanzanian Villages.

The goal of malaria elimination necessitates an improved understanding of any fine-scale geographic variations in transmission risk so that complementary vector control tools can be integrated into current vector control programmes as supplementary measures that are spatially targeted to maximize impact upon residual transmission. This study examines the distribution of host-seeking malaria vectors at households within two villages in rural Tanzania. Host-seeking mosquitoes were sampled from 72 randomly selected households in two villages on a monthly basis throughout 2008 using CDC light-traps placed beside occupied nets. Spatial autocorrelation in the dataset was examined using the Moran's I statistic and the location of any clusters was identified using the Getis-Ord Gi* statistic. Statistical associations between the household characteristics and clusters of mosquitoes were assessed using a generalized linear model for each species. For both Anopheles gambiae sensu lato and Anopheles funestus, the density of host-seeking females was spatially autocorrelated, or clustered. For both species, houses with low densities were clustered in the semi-urban village centre while houses with high densities were clustered in the periphery of the villages. Clusters of houses with low or high densities of An. gambiae s.l. were influenced by the number of residents in nearby houses. The occurrence of high-density clusters of An. gambiae s.l. was associated with lower elevations while An. funestus was also associated with higher elevations. Distance from the village centre was also positively correlated with the number of household occupants and having houses constructed with open eaves. The results of the current study highlight that complementary vector control tools could be most effectively targeted to the periphery of villages where the households potentially have a higher hazard (mosquito densities) and vulnerability (open eaves and larger households) to malaria infection

Southeastern Pacific humpback whales (Megaptera novaeangliae) and their breeding grounds : distribution and habitat preference of singers and social groups off the coast of Ecuador

The study was supported by a Rufford Small Grant, ECG. is currently funded by a Royal Society Newton International Fellowship; part of this work was completed while ECG was funded by a National Research Council (National Academy of Sciences) Postdoctoral Fellowship at the National Marine Mammal Laboratory, AFSC, NMFS, NOAA.Understanding the distribution, habitat preference and social structure of highly migratory species at important life history stages (e.g., breeding and calving) is essential for conservation efforts. We investigated the spatial distribution and habitat preference of humpback whale social groups and singers, in relation to depth categories (50 m) and substrate type (muddy and mixed) on a coastal southeastern Pacific breeding ground. One hundred and forty-three acoustic stations and 304 visual sightings were made at the breeding ground off the coast of Esmeraldas, Ecuador. Spatial autocorrelation analysis suggested singers were not randomly distributed, and Neu’s method and Monte Carlo simulations indicated that singers frequented depths of <20 m and mixed substrate. Singletons, and groups with a calf displayed a preference for shallower waters (0–20 m), while pairs and groups with a calf primarily inhabited mixed bottom substrates. In contrast, competitive groups showed no clear habitat preference and exhibited social segregation from other whales. Understanding the habitat preference and distribution of humpback whales on breeding and calving grounds vulnerable to anthropogenic disturbance provides important baseline information that should be incorporated into conservation efforts at a regional scale.PostprintPeer reviewe