Which-path problem for one and two particles with two degrees of freedom and a relation between transverse spatial structure and group velocity of light

Quantum mechanics, optics and indeed any wave theory exhibits the phenomenon of interference. In this thesis we present two problems investigating interference due to indistinguishable alternatives and a mostly unrelated investigation into the free space propagation speed of light pulses in particular spatial modes. In chapter 1 we introduce the basic properties of the electromagnetic field needed for the subsequent chapters. In chapter 2 we review the properties of interference using the beam splitter and the Mach-Zehnder interferometer. In particular we review what happens when one of the paths of the interferometer is marked in some way so that the particle having traversed it contains information as to which path it went down (to be followed up in chapter 3) and we review Hong-Ou-Mandel interference at a beam splitter (to be followed up in chapter 5). In chapter 3 we present the first of the interference problems. This consists of a nested Mach-Zehnder interferometer in which each of the free space propagation segments are weakly marked by mirrors vibrating at different frequencies [1]. The original experiment drew the conclusions that the photons followed disconnected paths. We partition the description of the light in the interferometer according to the number of paths it contains which-way information about and reinterpret the results reported in [1] in terms of the interference of paths spatially connected from source to detector. In chapter 4 we briefly review optical angular momentum, entanglement and spontaneous parametric down conversion. These concepts feed into chapter 5 in which we present the second of the interference problems namely Hong-Ou-Mandel interference with particles possessing two degrees of freedom. We analyse the problem in terms of exchange symmetry for both boson and fermion pairs and show that the particle statistics at a beam splitter can be controlled for suitably chosen states. We propose an experimental test of these ideas using orbital angular momentum entangled photons. In chapter 6 we look at the effect that the transverse spatial structure of the mode that a pulse of light is excited in has on its group velocity. We show that the resulting group velocity is slower than the speed of light in vacuum for plane waves and that this reduction in the group velocity is related to the spread in the wave vectors required to create the transverse spatial structure. We present experimental results of the measurement of this slowing down using Hong-Ou-Mandel interference.

Assessing the ex ante economic impacts of transportation infrastructure policies in Brazil

This paper uses a fully operational inter-regional computable general equilibrium (CGE) model implemented for the Brazilian economy, based on previous work by Haddad and Hewings, in order to assess the likely economic effects of road transportation policy changes in Brazil. Among the features embedded in this framework, modelling of external scale economies and transportation costs provides an innovative way of dealing explicitly with theoretical issues related to integrated regional systems. The model is calibrated for 109 regions. The explicit modelling of transportation costs built into the inter-regional CGE model, based on origin-destination flows, which takes into account the spatial structure of the Brazilian economy, creates the capability of integrating the inter-regional CGE model with a geo-coded transportation network model enhancing the potential of the framework in understanding the role of infrastructure on regional development. The transportation model used is the so-called Highway Development and Management, developed by the World Bank, implemented using the software TransCAD. Further extensions of the current model specification for integrating other features of transport planning in a continental industrialising country like Brazil are discussed, with the goal of building a bridge between conventional transport planning practices and the innovative use of CGE models. In order to illustrate the analytical power of the integrated system, the authors present a set of simulations, which evaluate the ex ante economic impacts of physical/qualitative changes in the Brazilian road network (for example, a highway improvement), in accordance with recent policy developments in Brazil. Rather than providing a critical evaluation of this debate, they intend to emphasise the likely structural impacts of such policies. They expect that the results will reinforce the need to better specifying spatial interactions in inter-regional CGE models.

A theory of rational spatial agglomerations

We model the behavior of rational forward-looking agents in a spatial economy. The economic geography structure is built on Fujita et al. (1999)'s racetrack economy. Workers choose optimally what to consume at each period, as well as which spatial itinerary to follow in the geographical space. The spatial extent of the resulting agglomerations increases with the taste for variety and the expenditure share on manufactured goods, and decreases with transport costs. Because forward-looking agents anticipate the future formation of agglomerations, they are more responsive to spatial utility differentials than myopic agents. As a consequence, the emerging agglomerations are larger under perfect foresight spatial adjustments than under myopic ones.

Pollinator community responses to the spatial population structure of wild plants: A pan-European approach

Land-use changes can alter the spatial population structure of plant species, which may in turn affect the attractiveness of flower aggregations to different groups of pollinators at different spatial scales. To assess how pollinators respond to spatial heterogeneity of plant distributions and whether honeybees affect visitation by other pollinators we used an extensive data set comprising ten plant species and their flower visitors from five European countries. In particular we tested the hypothesis that the composition of the flower visitor community in terms of visitation frequencies by different pollinator groups were affected by the spatial plant population structure, viz. area and density measures, at a within-population (‘patch’) and among-population (‘population’) scale. We found that patch area and population density were the spatial variables that best explained the variation in visitation frequencies within the pollinator community. Honeybees had higher visitation frequencies in larger patches, while bumblebees and hoverflies had higher visitation frequencies in sparser populations. Solitary bees had higher visitation frequencies in sparser populations and smaller patches. We also tested the hypothesis that honeybees affect the composition of the pollinator community by altering the visitation frequencies of other groups of pollinators. There was a positive relationship between visitation frequencies of honeybees and bumblebees, while the relationship with hoverflies and solitary bees varied (positive, negative and no relationship) depending on the plant species under study. The overall conclusion is that the spatial structure of plant populations affects different groups of pollinators in contrasting ways at both the local (‘patch’) and the larger (‘population’) scales and, that honeybees affect the flower visitation by other pollinator groups in various ways, depending on the plant species under study. These contrasting responses emphasize the need to investigate the entire pollinator community when the effects of landscape change on plant–pollinator interactions are studied.

Designing a sampling scheme to reveal correlations between weeds and soil properties at multiple spatial scales

Weeds tend to aggregate in patches within fields and there is evidence that this is partly owing to variation in soil properties. Because the processes driving soil heterogeneity operate at different scales, the strength of the relationships between soil properties and weed density would also be expected to be scale-dependent. Quantifying these effects of scale on weed patch dynamics is essential to guide the design of discrete sampling protocols for mapping weed distribution. We have developed a general method that uses novel within-field nested sampling and residual maximum likelihood (REML) estimation to explore scale-dependent relationships between weeds and soil properties. We have validated the method using a case study of Alopecurus myosuroides in winter wheat. Using REML, we partitioned the variance and covariance into scale-specific components and estimated the correlations between the weed counts and soil properties at each scale. We used variograms to quantify the spatial structure in the data and to map variables by kriging. Our methodology successfully captured the effect of scale on a number of edaphic drivers of weed patchiness. The overall Pearson correlations between A. myosuroides and soil organic matter and clay content were weak and masked the stronger correlations at >50 m. Knowing how the variance was partitioned across the spatial scales we optimized the sampling design to focus sampling effort at those scales that contributed most to the total variance. The methods have the potential to guide patch spraying of weeds by identifying areas of the field that are vulnerable to weed establishment.

Competition may explain the fine-scale spatial patterns and genetic structure of two co-occurring plant congeners

1. The spatial distribution of individual plants within a population and the population’s genetic structure are determined by several factors, like dispersal, reproduction mode or biotic interactions. The role of interspecific interactions in shaping the spatial genetic structure of plant populations remains largely unknown. 2. Species with a common evolutionary history are known to interact more closely with each other than unrelated species due to the greater number of traits they share. We hypothesize that plant interactions may shape the fine genetic structure of closely related congeners. 3. We used spatial statistics (georeferenced design) and molecular techniques (ISSR markers) to understand how two closely related congeners, Thymus vulgaris (widespread species) and T. loscosii (narrow endemic) interact at the local scale. Specific cover, number of individuals of both study species and several community attributes were measured in a 10 × 10 m plot. 4. Both species showed similar levels of genetic variation, but differed in their spatial genetic structure. Thymus vulgaris showed spatial aggregation but no spatial genetic structure, while T. loscosii showed spatial genetic structure (positive genetic autocorrelation) at short distances. The spatial pattern of T. vulgaris’ cover showed significant dissociation with that of T. loscosii. The same was true between the spatial patterns of the cover of T. vulgaris and the abundance of T. loscosii and between the abundance of each species. Most importantly, we found a correlation between the genetic structure of T. loscosii and the abundance of T. vulgaris: T. loscosii plants were genetically more similar when they were surrounded by a similar number of T. vulgaris plants. 5. Synthesis. Our results reveal spatially complex genetic structures of both congeners at small spatial scales. The negative association among the spatial patterns of the two species and the genetic structure found for T. loscosii in relation to the abundance of T. vulgaris indicate that competition between the two species may account for the presence of adapted ecotypes of T. loscosii to the abundance of a competing congeneric species. This suggests that the presence and abundance of close congeners can influence the genetic spatial structure of plant species at fine scales.

Measurement of genetic structure within populations using Moran's spatial autocorrelation statistics.

Spatial structure of genetic variation within populations, an important interacting influence on evolutionary and ecological processes, can be analyzed in detail by using spatial autocorrelation statistics. This paper characterizes the statistical properties of spatial autocorrelation statistics in this context and develops estimators of gene dispersal based on data on standing patterns of genetic variation. Large numbers of Monte Carlo simulations and a wide variety of sampling strategies are utilized. The results show that spatial autocorrelation statistics are highly predictable and informative. Thus, strong hypothesis tests for neutral theory can be formulated. Most strikingly, robust estimators of gene dispersal can be obtained with practical sample sizes. Details about optimal sampling strategies are also described.

Spatial structures of manufacturing clusters in Cambodia, Lao People's Democratic Republic, and Thailand

Examining the spatial structure of clusters is essential for deriving regional development policy implications. In this study, we identify the manufacturing clusters in Cambodia, the Lao People's Democratic Republic, and Thailand, using two indices—global extent (GE) and local density (LD)—as proposed by Mori and Smith (2013). We also analyze four different combinations of these indices to highlight the spatial structures of industrial agglomerations. Since industrial clusters often spread over administrative boundaries, the GE and LD indices—along with cluster mapping—display how the detected clusters fit into specific spatial structures.

The spatial dimension of cycle logistics

US Cycle logistics is emerging as a promising alternative in urban freight transport. Compared to fossil fuelled vans, the use of cycles for delivering goods within urban areas offers advantages in terms of environmental friendliness, economic efficiency, flexibility, and liveability of urban neighbourhood. At the same time, cycle logistics has to face limits in terms of weight and volume of goods that can be delivered, distances that can be covered, and spatial urban structures that can be served. This latter issue has till now received less attention in the scientific literature: it is generally recognized that cycle logistics performs at its best in inner urban areas, but no systematic study has been realized to identify specific spatial requisites for the effectiveness of cycle logistics. This paper provides a brief review of the main issues that emerge from the literature over cycle logistics, and contributes to stimulate the debate over the spatial dimension of cycle logistics: it presents a classification of cycle logistics schemes, on the basis of their integration with other urban logistic facilities and of the spatial structure of delivery operations. A three-level classification is proposed, depending on the type of goods consolidation: only distribution without consolidation, consolidation in a fixed urban consolidation centre, or consolidation in a mobile depot; for each level, operational examples and case studies are provided. This systematizing typology could support both public and private operators in decisions about the organization of cycle logistics facilities, such as the location of urban consolidation centres or the composition of cycle fleets.

Marine protected areas for spatially structured exploited stocks

Many harvested marine and terrestrial populations have segments of their range protected in areas free from exploitation. Reasons for areas being protected from harvesting include conservation, tourism, research, protection of breeding grounds, stock recovery, harvest regulation, or habitat that is uneconomical to exploit. In this paper we consider the problem of optimally exploiting a single species local population that is connected by dispersing larvae to an unharvested local population. We define a spatially-explicit population dynamics model and apply dynamic optimization techniques to determine policies for harvesting the exploited patch. We then consider how reservation affects yield and spawning stock abundance when compared to policies that have not recognised the spatial structure of the metapopulation. Comparisons of harvest strategies between an exploited metapopulation with and without a harvest refuge are also made. Results show that in a 2 local population metapopulation with unidirectional larval transfer, the optimal exploitation of the harvested population should be conducted as if it were independent of the reserved population. Numerical examples suggest that relative source populations should be exploited if the objective is to maximise spawning stock abundance within a harvested metapopulation that includes a protected local population. However, this strategy can markedly reduce yield over a sink harvested reserve system and may require strict regulation for conservation goals to be realised. If exchange rates are high, results indicate that spawning stock abundance can be less in a reserve system than in a fully exploited metapopulation. In order to maximise economic gain in the reserve system, results indicate that relative sink populations should be harvested. Depending on transfer levels, loss in harvest through reservation can be minimal, and is likely to be compensated by the potential environmental and economic benefits of the reserve.

Cold-water coral communities in the Azores : diversity, habitat and conservation

Tese de Doutoramento, Ciências do Mar (especialidade em Ecologia Marinha), 11 de Setembro de 2015, Universidade dos Açores.

The spatial effect of intra-metropolitan agglomeration economies

This study deals with the role of spatial accessibility to agglomeration economies in the change in spatial structure of industrial employment for the case of the Barcelona Metropolitan Region of Barcelona (BMR). Using the growth in gross density of municipal employment between 1986 and 1996 for seven manufacturing industries as an indicator of changes in the spatial structure of employment, an exploration is made of the spatial impact of agglomeration economies operating on a local scale the municipality and three areas 5, 8 and 12 kilometres away surrounding the municipality itself - , agglomeration economies emerging from CBD and the main specialised subcentres in the region, and the network economies associated with the total jobs in the region, access to which depends on the distance from the main transport infrastructures

Stochastic stability and the evolution of coordination in spatially structured populations.

Animals can often coordinate their actions to achieve mutually beneficial outcomes. However, this can result in a social dilemma when uncertainty about the behavior of partners creates multiple fitness peaks. Strategies that minimize risk ("risk dominant") instead of maximizing reward ("payoff dominant") are favored in economic models when individuals learn behaviors that increase their payoffs. Specifically, such strategies are shown to be "stochastically stable" (a refinement of evolutionary stability). Here, we extend the notion of stochastic stability to biological models of continuous phenotypes at a mutation-selection-drift balance. This allows us to make a unique prediction for long-term evolution in games with multiple equilibria. We show how genetic relatedness due to limited dispersal and scaled to account for local competition can crucially affect the stochastically-stable outcome of coordination games. We find that positive relatedness (weak local competition) increases the chance the payoff dominant strategy is stochastically stable, even when it is not risk dominant. Conversely, negative relatedness (strong local competition) increases the chance that strategies evolve that are neither payoff nor risk dominant. Extending our results to large multiplayer coordination games we find that negative relatedness can create competition so extreme that the game effectively changes to a hawk-dove game and a stochastically stable polymorphism between the alternative strategies evolves. These results demonstrate the usefulness of stochastic stability in characterizing long-term evolution of continuous phenotypes: the outcomes of multiplayer games can be reduced to the generic equilibria of two-player games and the effect of spatial structure can be analyzed readily.