Marine spatial planning approaches at the state level: Similarities and differences between MSP efforts across the country

Competing uses, sensitive and valuable marine resources, and overlapping jurisdictions complicate management decision making in the marine environment. States are developing marine spatial planning capacity to help make better decisions, particularly as demand for ocean space and resources is growing because of emerging human uses (renewable energy, aquaculture) and traditional human uses (commercial fishing, commerce). This paper offers perspectives on marine spatial planning efforts being carried out in four states across the US, and demonstrates similarities and differences between them. The approach to marine spatial planning in each state is discussed with specific attention given to issues such as what is driving the effort, data availability, maturity of the effort, and level of resources devoted to it. Highlighting the similarities and differences illustrates state and region specific challenges and the approaches being used to meet them. (PDF contains 4 pages)

Coastal plant growth and CO2 enrichment: Can the productivity of black needle rush keep pace with sea level rise?

The rate of sea level change has varied considerably over geological time, with rapid increases (0.25 cm yr-1) at the end of the last ice age to more modest increases over the last 4,000 years (0.04 cm yr-1; Hendry 1993). Due to anthropogenic contributions to climate change, however, the rate of sea level rise is expected to increase between 0.10 and 0.25 cm year-1 for many coastal areas (Warrick et al. 1996). Notwithstanding, it has been predicted that over the next 100 years, sea levels along the northeastern coast of North Carolina may increase by an astonishing 0.8 m (0.8 cm yr-1); through a combination of sea-level rise and coastal subsidence (Titus and Richman 2001; Parham et al. 2006). As North Carolina ranks third in the United States with land at or just above sea level, any additional sea rise may promote further deterioration of vital coastal wetland systems. (PDF contains 4 pages)

Mathematical study of complex networks : brain, internet, and power grid

The dissertation is concerned with the mathematical study of various network problems. First, three real-world networks are considered: (i) the human brain network (ii) communication networks, (iii) electric power networks. Although these networks perform very different tasks, they share similar mathematical foundations. The high-level goal is to analyze and/or synthesis each of these systems from a “control and optimization” point of view. After studying these three real-world networks, two abstract network problems are also explored, which are motivated by power systems. The first one is “flow optimization over a flow network” and the second one is “nonlinear optimization over a generalized weighted graph”. The results derived in this dissertation are summarized below.

Brain Networks: Neuroimaging data reveals the coordinated activity of spatially distinct brain regions, which may be represented mathematically as a network of nodes (brain regions) and links (interdependencies). To obtain the brain connectivity network, the graphs associated with the correlation matrix and the inverse covariance matrix—describing marginal and conditional dependencies between brain regions—have been proposed in the literature. A question arises as to whether any of these graphs provides useful information about the brain connectivity. Due to the electrical properties of the brain, this problem will be investigated in the context of electrical circuits. First, we consider an electric circuit model and show that the inverse covariance matrix of the node voltages reveals the topology of the circuit. Second, we study the problem of finding the topology of the circuit based on only measurement. In this case, by assuming that the circuit is hidden inside a black box and only the nodal signals are available for measurement, the aim is to find the topology of the circuit when a limited number of samples are available. For this purpose, we deploy the graphical lasso technique to estimate a sparse inverse covariance matrix. It is shown that the graphical lasso may find most of the circuit topology if the exact covariance matrix is well-conditioned. However, it may fail to work well when this matrix is ill-conditioned. To deal with ill-conditioned matrices, we propose a small modification to the graphical lasso algorithm and demonstrate its performance. Finally, the technique developed in this work will be applied to the resting-state fMRI data of a number of healthy subjects.

Communication Networks: Congestion control techniques aim to adjust the transmission rates of competing users in the Internet in such a way that the network resources are shared efficiently. Despite the progress in the analysis and synthesis of the Internet congestion control, almost all existing fluid models of congestion control assume that every link in the path of a flow observes the original source rate. To address this issue, a more accurate model is derived in this work for the behavior of the network under an arbitrary congestion controller, which takes into account of the effect of buffering (queueing) on data flows. Using this model, it is proved that the well-known Internet congestion control algorithms may no longer be stable for the common pricing schemes, unless a sufficient condition is satisfied. It is also shown that these algorithms are guaranteed to be stable if a new pricing mechanism is used.

Electrical Power Networks: Optimal power flow (OPF) has been one of the most studied problems for power systems since its introduction by Carpentier in 1962. This problem is concerned with finding an optimal operating point of a power network minimizing the total power generation cost subject to network and physical constraints. It is well known that OPF is computationally hard to solve due to the nonlinear interrelation among the optimization variables. The objective is to identify a large class of networks over which every OPF problem can be solved in polynomial time. To this end, a convex relaxation is proposed, which solves the OPF problem exactly for every radial network and every meshed network with a sufficient number of phase shifters, provided power over-delivery is allowed. The concept of “power over-delivery” is equivalent to relaxing the power balance equations to inequality constraints.

Flow Networks: In this part of the dissertation, the minimum-cost flow problem over an arbitrary flow network is considered. In this problem, each node is associated with some possibly unknown injection, each line has two unknown flows at its ends related to each other via a nonlinear function, and all injections and flows need to satisfy certain box constraints. This problem, named generalized network flow (GNF), is highly non-convex due to its nonlinear equality constraints. Under the assumption of monotonicity and convexity of the flow and cost functions, a convex relaxation is proposed, which always finds the optimal injections. A primary application of this work is in the OPF problem. The results of this work on GNF prove that the relaxation on power balance equations (i.e., load over-delivery) is not needed in practice under a very mild angle assumption.

Generalized Weighted Graphs: Motivated by power optimizations, this part aims to find a global optimization technique for a nonlinear optimization defined over a generalized weighted graph. Every edge of this type of graph is associated with a weight set corresponding to the known parameters of the optimization (e.g., the coefficients). The motivation behind this problem is to investigate how the (hidden) structure of a given real/complex valued optimization makes the problem easy to solve, and indeed the generalized weighted graph is introduced to capture the structure of an optimization. Various sufficient conditions are derived, which relate the polynomial-time solvability of different classes of optimization problems to weak properties of the generalized weighted graph such as its topology and the sign definiteness of its weight sets. As an application, it is proved that a broad class of real and complex optimizations over power networks are polynomial-time solvable due to the passivity of transmission lines and transformers.

Quantum error correction with biased noise

Quantum computing offers powerful new techniques for speeding up the calculation of many classically intractable problems. Quantum algorithms can allow for the efficient simulation of physical systems, with applications to basic research, chemical modeling, and drug discovery; other algorithms have important implications for cryptography and internet security.

At the same time, building a quantum computer is a daunting task, requiring the coherent manipulation of systems with many quantum degrees of freedom while preventing environmental noise from interacting too strongly with the system. Fortunately, we know that, under reasonable assumptions, we can use the techniques of quantum error correction and fault tolerance to achieve an arbitrary reduction in the noise level.

In this thesis, we look at how additional information about the structure of noise, or "noise bias," can improve or alter the performance of techniques in quantum error correction and fault tolerance. In Chapter 2, we explore the possibility of designing certain quantum gates to be extremely robust with respect to errors in their operation. This naturally leads to structured noise where certain gates can be implemented in a protected manner, allowing the user to focus their protection on the noisier unprotected operations.

In Chapter 3, we examine how to tailor error-correcting codes and fault-tolerant quantum circuits in the presence of dephasing biased noise, where dephasing errors are far more common than bit-flip errors. By using an appropriately asymmetric code, we demonstrate the ability to improve the amount of error reduction and decrease the physical resources required for error correction.

In Chapter 4, we analyze a variety of protocols for distilling magic states, which enable universal quantum computation, in the presence of faulty Clifford operations. Here again there is a hierarchy of noise levels, with a fixed error rate for faulty gates, and a second rate for errors in the distilled states which decreases as the states are distilled to better quality. The interplay of of these different rates sets limits on the achievable distillation and how quickly states converge to that limit.

Phase-dependent properties for absorption and dispersion in a closed equispaced three-level ladder system

It is shown that in a closed equispaced three-level ladder system, by controlling the relative phase of two applied coherent fields, the conversion from absorption with inversion to lasing without inversion (LWI) can be realized; a large index of the refraction with zero absorption can be gotten; considerable increasing of the spectrum region and value of the LWI gain can be achieved. Our study also reveals that the incoherent pumping will produce a remarkable effect oil the phase-dependent properties of the system. Modifying value of the incoherent pumping can change the property of the system from absorption to amplification and enhance significantly LWI gain. If the incoherent pumping is absent, we cannot get any gain for any value of the relative phase. (c) 2007 Elsevier GmbH. All rights reserved.

Poverty alleviation among fishermen within the floodplains of Kaduna River: implication for introducing commercial fish farming at village level in Doko local government area of Niger State, Nigeria

A diagnostic survey was conducted among the fishermen in six selected villages in Doko Local Government Area of Niger State. One hundred and fifty fishermen were randomly selected and interviewed to find out whether or not they had interest in commercial fish farming aimed at improving their livelihood. The dwindling fish catches in the natural flood plain ponds and Ex-bow Lakes continue to have a serious negative effect on the socio-economic well being of the village communities in question. A break on natural regular annual flooding of the plains had resulted into very low natural fish recruitment. Data analysis using simple descriptive statistics revealed that land tenure system, educational status, inadequate infrastructural facilities, religious taboos, existing fish species among others were found to be favourable indices for commercial fish farming. However, serious conflicts among the fishermen concerning the ownership status of these natural fish ponds are found to be major obstacles to commercial fish farming despite that the traditional ownership of the ponds were vested in the lands of individuals and village communities. Extensive fish farming and small-scale fish farming in the ponds and Ex-bow Lake with improved management practices are considered to be profitable venture. Despite the fact that fish seeds supply and extension effort are still inadequate, the fish farmers have indicated willingness to adopt commercial fish farming in the Ex-bow Lakes and flood plains in order to restore abundant fish production thereby providing for their food security and also increasing the daily income

Phase control of switching from positive to negative index material in a four-level atomic system

Electric and magnetic responses of the medium to the probe field are analysed in a four-level loop atomic system by taking into account the relative phase of the applied fields. An interesting phenomenon is found: under suitable conditions, a change of the refractive index from positive to negative can occur by modulating the relative phase of the applied fields. Then the medium can be switched from a positive index material to a negative index material in our scheme. In addition, a negative index material can be realized in different frequency regions by adjusting the relative phase. It may give us a convenient way to obtain the desired material with positive or negative index.

Sideband manipulation of population inversion in a three-level Λ atomic system

Sideband manipulation of population inversion in a three-level A atomic configuration is investigated theoretically. Compared with the case of a nearly monochromatic field, a population inversion between an excited state and a ground state has been found in a wide sideband intensity range by increasing the difference in frequency between three components. Furthermore, the population inversion can be controlled by the sum of the relative phases of the sideband components of the trichromatic pump field with respective to the phase of the central component. Changing the sum phase from 0 to pi, the population inversion between the excited state and the ground state can increase within nearly half of the sideband intensity range. At the same time, the sideband intensity range that corresponds to the system exhibiting inversion rho(00) > rho 11 also becomes wider evidently.

An arithmetical theorem for partially ordered sets

The simplest multiplicative systems in which arithmetical ideas can be defined are semigroups. For such systems irreducible (prime) elements can be introduced and conditions under which the fundamental theorem of arithmetic holds have been investigated (Clifford (3)). After identifying associates, the elements of the semigroup form a partially ordered set with respect to the ordinary division relation. This suggests the possibility of an analogous arithmetical result for abstract partially ordered sets. Although nothing corresponding to product exists in a partially ordered set, there is a notion similar to g.c.d. This is the meet operation, defined as greatest lower bound. Thus irreducible elements, namely those elements not expressible as meets of proper divisors can be introduced. The assumption of the ascending chain condition then implies that each element is representable as a reduced meet of irreducibles. The central problem of this thesis is to determine conditions on the structure of the partially ordered set in order that each element have a unique such representation.

Part I contains preliminary results and introduces the principal tools of the investigation. In the second part, basic properties of the lattice of ideals and the connection between its structure and the irreducible decompositions of elements are developed. The proofs of these results are identical with the corresponding ones for the lattice case (Dilworth (2)). The last part contains those results whose proofs are peculiar to partially ordered sets and also contains the proof of the main theorem.

Spatiotemporal evolution and multiple self-focusing of ultrashort pulses in a resonant two-level medium

The spatiotemporal evolutions of ultrashort pulses in two dimensions are investigated numerically by solving the coupled Maxwell-Bloch equations without invoking the slowly varying envelope approximation and rotating-wave approximation. For an on-axis 2n pi sech pulse, local delay makes the temporal split 2 pi sech pulses crescent-shaped in the transverse distribution. Due to the transverse effect, the temporal split 2 pi sech pulses become unstable and experience reshaping during the propagation process. Then, interference occurs between the successive crescent-shaped pulses and multiple self-focusing can form.

Trichromatic manipulation of Kerr nonlinearity in a three-level lambda atomic system

Trichromatic manipulation of Kerr nonlinearity in a three-level A atomic configuration is investigated theoretically. It is shown that for a weak monochromatic probe field, the enhanced Kerr nonlinearity can be achieved in multiple separate transparent windows due to interference effect of multiple two-photon Raman channels. Furthermore, the property of Kerr nonlinearity can be controlled by the sum of the relative phases of the sideband components of the trichromatic pump field compared to the central component.

Atom localization in a four-level alkaline earth atomic system

We propose an atom localization scheme for a four-level alkaline earth atom via a classical standing-wave field, and give the analytical expressions of the localization peak positions as well as the widths versus the parameters of the optical fields. We show that the probability of finding the atom at a particular position can be increased from 1/4 to 1/3 or 1/2 by adjusting the detuning of the probe field and the Rabi frequencies of the optical fields. Furthermore, the localization precision can be dramatically enhanced by increasing the intensity of the standing-wave field or decreasing the detuning of the probe field. The analytical results are quite accordant to the numerical solutions.

Effect of vacuum-induced coherence on lasing without inversion in an equispaced three-level ladder system

The effects of vacuum-induced coherence (VIC) on the properties of the absorption and gain of the probe field in an equispaced three-level ladder atomic system are investigated. It is found that lasing without inversion (LWI) is remarkably enhanced due to the effect of VIC in the case of the small incoherent pump rate.

Propagation of an arbitrary elliptically polarized few-cycle ultrashort laser pulse in resonant two-level quantum systems

We investigate the propagation of an arbitrary elliptically polarized few-cycle ultrashort laser pulse in resonant two-level quantum systems using an iterative predictor-corrector finite-difference time-domain method. It is shown that when the initial effective area is equal to 2 pi, the effective area will remain invariant during the course of propagation, and a complete Rabi oscillation can be achieved. However, for an elliptically polarized few-cycle ultrashort laser pulse, polarization conversion can occur. Eventually, the laser pulse will evolve into two separate circularly polarized laser pulses with opposite helicities.

Propagation of a few-cycle laser pulse in a V-type three-level system

Propagation of a few-cycle laser pulse in a V-type three-level system (fine structure levels of rubidium) is investigated numerically. The full three-level Maxwell-Bloch equations without the rotating wave approximation and the standing slowly varying envelope approximation are solved by using a finite-difference time-domain method. It is shown that, when the usual unequal oscillator strengths are considered, self-induced transparency cannot be recovered and higher spectral components can be produced even for small-area pulses. (c) 2005 Pleiades Publishing, Inc.