Chains of Non-regular de Branges Spaces

We consider canonical systems with singular left endpoints, and discuss the concept of a scalar spectral measure and the corresponding generalized Fourier transform associated with a canonical system with a singular left endpoint. We use the framework of de Branges’ theory of Hilbert spaces of entire functions to study the correspondence between chains of non-regular de Branges spaces, canonical systems with singular left endpoints, and spectral measures.

We find sufficient integrability conditions on a Hamiltonian H which ensure the existence of a chain of de Branges functions in the first generalized Pólya class with Hamiltonian H. This result generalizes de Branges’ Theorem 41, which showed the sufficiency of stronger integrability conditions on H for the existence of a chain in the Pólya class. We show the conditions that de Branges came up with are also necessary. In the case of Krein’s strings, namely when the Hamiltonian is diagonal, we show our proposed conditions are also necessary.

We also investigate the asymptotic conditions on chains of de Branges functions as t approaches its left endpoint. We show there is a one-to-one correspondence between chains of de Branges functions satisfying certain asymptotic conditions and chains in the Pólya class. In the case of Krein’s strings, we also establish the one-to-one correspondence between chains satisfying certain asymptotic conditions and chains in the generalized Pólya class.

Force chains, friction, and flow: Behavior of granular media across length scales

We study the behavior of granular materials at three length scales. At the smallest length scale, the grain-scale, we study inter-particle forces and "force chains". Inter-particle forces are the natural building blocks of constitutive laws for granular materials. Force chains are a key signature of the heterogeneity of granular systems. Despite their fundamental importance for calibrating grain-scale numerical models and elucidating constitutive laws, inter-particle forces have not been fully quantified in natural granular materials. We present a numerical force inference technique for determining inter-particle forces from experimental data and apply the technique to two-dimensional and three-dimensional systems under quasi-static and dynamic load. These experiments validate the technique and provide insight into the quasi-static and dynamic behavior of granular materials.

At a larger length scale, the mesoscale, we study the emergent frictional behavior of a collection of grains. Properties of granular materials at this intermediate scale are crucial inputs for macro-scale continuum models. We derive friction laws for granular materials at the mesoscale by applying averaging techniques to grain-scale quantities. These laws portray the nature of steady-state frictional strength as a competition between steady-state dilation and grain-scale dissipation rates. The laws also directly link the rate of dilation to the non-steady-state frictional strength.

At the macro-scale, we investigate continuum modeling techniques capable of simulating the distinct solid-like, liquid-like, and gas-like behaviors exhibited by granular materials in a single computational domain. We propose a Smoothed Particle Hydrodynamics (SPH) approach for granular materials with a viscoplastic constitutive law. The constitutive law uses a rate-dependent and dilation-dependent friction law. We provide a theoretical basis for a dilation-dependent friction law using similar analysis to that performed at the mesoscale. We provide several qualitative and quantitative validations of the technique and discuss ongoing work aiming to couple the granular flow with gas and fluid flows.

Stationary absolute distributions for chains of infinite order

Let {Ƶ_n}^∞_{n = -∞} be a stochastic process with state space S₁ = {0, 1, …, D – 1}. Such a process is called a chain of infinite order. The transitions of the chain are described by the functions

Q_i(i⁽⁰⁾) = Ƥ(Ƶ_n = i | Ƶ_{n - 1} = i ⁽⁰⁾₁, Ƶ_{n - 2} = i ⁽⁰⁾₂, …) (i ɛ S₁), where i⁽⁰⁾ = (i⁽⁰⁾₁, i⁽⁰⁾₂, …) ranges over infinite sequences from S₁. If i⁽ⁿ⁾ = (i⁽ⁿ⁾₁, i⁽ⁿ⁾₂, …) for n = 1, 2,…, then i⁽ⁿ⁾ → i⁽⁰⁾ means that for each k, i⁽ⁿ⁾_k = i⁽⁰⁾_k for all n sufficiently large.

Given functions Q_i(i⁽⁰⁾) such that

(i) 0 ≤ Q_i(i⁽⁰) ≤ ξ ˂ 1

(ii)D – 1/Ʃ/i = 0 Q_i(i⁽⁰⁾) Ξ 1

(iii) Q_i(i⁽ⁿ⁾) → Q_i(i⁽⁰⁾) whenever i⁽ⁿ⁾ → i⁽⁰⁾,

we prove the existence of a stationary chain of infinite order {Ƶ_n} whose transitions are given by

Ƥ (Ƶ_n = i | Ƶ_{n - 1}, Ƶ_{n - 2}, …) = Q_i(Ƶ_{n - 1}, Ƶ_{n - 2}, …)

With probability 1. The method also yields stationary chains {Ƶ_n} for which (iii) does not hold but whose transition probabilities are, in a sense, “locally Markovian.” These and similar results extend a paper by T.E. Harris [Pac. J. Math., 5 (1955), 707-724].

Included is a new proof of the existence and uniqueness of a stationary absolute distribution for an Nth order Markov chain in which all transitions are possible. This proof allows us to achieve our main results without the use of limit theorem techniques.

Impacts of climate change and variability on fish value chains in Uganda

This study examines the vulnerability of fish pr oduction in Uganda, particularly as it r elates to the predicted impacts from climate change, using the concept of the value chain. The value chain approach has been recommended as a useful tool to study specific challenges facing a sector resulting from various drivers of change, including climate. Critically, such analyses can reveal context-specific response strategies to enhance a sector (Jacinto and Pomer oy 2010). The specific purpose of the study was to identify curr ent and potential impacts of climate change and corresponding adaptation strategies in fish value chains. The study builds upon information fr om earlier value chain analyses on fisheries and aquaculture production in Uganda to provide a more in-depth understanding of issues facing the fish industry, in particular, those to be incorporated in the CGIAR Resear ch Program Livestock and Fish.

Uganda aquaculture value chains: strategic planning mission: summary report

This report presents the findings and recommendations of a strategic planning mission to reevaluate the feasibility of WorldFish implementing a fish value chain research program in Uganda under the CGIAR Research Program on Livestock and Fish (L&F). The over-arching goal of L&F is to increase productivity of small-scale livestock and fish systems so as to increase availability and affordability of meat, milk and fish for poor consumers and, in doing so, to reduce poverty through greater participation by the poor along animal source food value chains. This will be achieved by making a small number of carefully selected animal source food value chains function better, for example by identifying and addressing key constraints and opportunities (from production to consumption), improving institutional arrangements and capacities, and supporting the establishment of enabling pro-poor policy and institutional environments.

Uganda aquaculture value chains: strategic planning mission report

This report presents the findings and recommendations of a strategic planning mission to reevaluate the feasibility of WorldFish implementing a fish value chain research program in Uganda under the CGIAR Research Program on Livestock and Fish (L&F). The over-arching goal of L&F is to increase productivity of small-scale livestock and fish systems so as to increase availability and affordability of meat, milk and fish for poor consumers and, in doing so, to reduce poverty through greater participation by the poor along animal source food value chains. This will be achieved by making a small number of carefully selected animal source food value chains function better, for example by identifying and addressing key constraints and opportunities (from production to consumption), improving institutional arrangements and capacities, and supporting the establishment of enabling pro-poor policy and institutional environments.

The design, construction, operation, and maintenance of the Replicated Modular Estuarine Mesocosm

Perhaps the most difficult job of the ecotoxicologist is extrapolating data calculated from laboratory experiments with high precision and accuracy into the real world of highly-dynamics aquatic environments. The establishment of baseline laboratory toxicity testing data for individual compounds and ecologically important and field studies serve as a precursor to ecosystem level studies needed for ecological risk assessment. The first stage in the field portion of risk assessment is the determination of actual environmental concentrations of the contaminant being studied and matching those concentrations with laboratory toxicity tests. Risk estimates can be produced via risk quotients that would determine the probability that adverse effects may occur. In this first stage of risk assessment, environmental realism is often not achieved. This is due, in part, to the fact that single-species laboratory toxicity tests, while highly controlled, do not account for the complex interactions (Chemical, physical, and biological) that take place in the natural environment. By controlling as many variables in the laboratory as possible, an experiment can be produced in such a fashion that real effects from a compound can be determined for a particular test organism. This type of approach obviously makes comparison with real world data most difficult. Conversely, field oriented studies fall short in the interpretation of ecological risk assessment because of low statistical power, lack of adequate replicaiton, and the enormous amount of time and money needed to perform such studies. Unlike a controlled laboratory bioassay, many other stressors other than the chemical compound in question affect organisms in the environment. These stressors range from natural occurrences (such as changes in temperature, salinity, and community interactions) to other confounding anthropogenic inputs. Therefore, an improved aquatic toxicity test that will enhance environmental realism and increase the accuracy of future ecotoxicological risk assessments is needed.

Global commodity chains and the development of poor fisherfolk in Uganda

The Ugandan fishery, heavily influenced by the emergence of global markets, is extremely dynamic. In recent years a major export trade, principally in Nile perch fillets from Lake Victoria, has expanded markedly. The growth of this factory based processing industry has had a marked impact on the pre-existing artisanal fishery, which has become increasingly dependent on supplying the export market instead of its traditional local small-scale markets. The industrial fishery developed as a response to the liberalisation of the management of the Ugandan economy and the consequent opening up of the export markets in North America and Europe. The emergence of the export industry has resulted in the creation of a dual structure in the fisheries sector, with the Nile perch catching and processing chain operating to European standards, whilst the artisanal sub-sector still utilises traditional methods. This dual structure is a potential source of disadvantage to the artisanal fishery which has command over fewer financial assets than the export fishery.