Simulation of the supply capability of sheep on the Mitchell grass downs of north west Queensland

Sheep in western Queensland have been predominantly reared for wool. When wool prices became depressed interest in the sheep meat industry, increased. For north west Queensland producers, opportunities may exist to participate in live sheep and meat export to Asia. A simulation model was developed to determine whether this sheep producing area has the capability to provide sufficient numbers of sheep under variable climatic conditions while sustaining the land resources. Maximum capacity for sustainability of resources (as described by stock numbers) was derived from an in-depth study of the agricultural and pastoral potential of Queensland. Decades of sheep production and climatic data spanning differing seasonal conditions were collated for analysis. A ruminant biology model adapted from Grazplan was used to simulate pregnancy rate. Empirical equations predict mortalities, marking rates, and weight characteristics of sheep of various ages from simple climatic measures, stocking rate and reproductive status. The initial age structure of flocks was determined by running the model for several years with historical climatic conditions. Drought management strategies such as selling a proportion of wethers progressively down to two-tooth and oldest ewes were incorporated. Management decisions such as time of joining, age at which ewes were cast-for-age, wether turn-off age and turning-off rate of lambs vary with geographical area and can be specified at run time. The model is run for sequences of climatic conditions generated stochastically from distributions based on historical climatic data correlated in some instances. The model highlights the difficulties of sustaining a consistent supply of sheep under variable climatic conditions.

Inconsistencies in and the inadequacies of the family counselling and FDR confidentiality and admissibility provisions: The need for reform

In this article the author discusses issues arising from counselling and family dispute resolution (FDR) in relation to confidentiality and admissibility, such as whether an admission of abuse to a child, or a threat to harm the other parent, can be disclosed by the counsellor or family dispute resolution practitioner (FDRP) and used in court proceedings. It is found that the admissibility provisions in the Family Law Act 1975 (Cth) are far more narrowly defined than the confidentiality requirements and have been interpreted strictly by the courts. There are competing policy considerations: the strict “traditionalist” approach, that people can have absolute faith in the integrity of counsellors and mediators and in the confidential nature of the process, must be balanced against a more “protectionist” stance, being the individual rights of victims to have all relevant information placed before the court and to be protected from violence and abuse. It is suggested that legislative reform is required to ensure that courts balance these considerations appropriately and don’t compromise the safety of victims of abuse and family violence.

Analysis of laminated shells of revolution with laminated stiffeners using a doubly curved quadrilateral finite element

A finite element analysis of laminated shells of revolution reinforced with laminated stifieners is described here-in. A doubly curved quadrilateral laminated anisotropic shell of revolution finite element of 48 d.o.f. is used in conjunction with two stiffener elements of 16 d.o.f. namely: (i) A laminated anisotropic parallel circle stiffener element (PCSE); (ii) A laminated anisotropic meridional stiffener element (MSE). These stifiener elements are formulated under line member assumptions as degenerate cases of the quadrilateral shell element to achieve compatibility all along the shell-stifiener junction lines. The solutions to the problem of a stiffened cantilever cylindrical shell are used to check the correctness of the present program while it's capability is shown through the prediction of the behavior of an eccentrically stiffened laminated hyperboloidal shell.

Rearing strategies of young dairy calves in relation to production, behaviour and welfare

Vasikoiden kasvatus yksilökarsinoissa, imemismahdollisuuden puute maitojuoton yhteydessä sekä pienet juomamäärät ovat tekijöitä, jotka mahdollisesti voivat vähentää vasikoiden hyvinvointia. Vasikoiden kasvatukseen etsitäänkin uusia tapoja, joissa eläinten käyttäytymistarpeet ja hyvinvointi otetaan entistä paremmin huomioon. Tässä väitöskirjassa vasikoiden kasvatusta on tarkasteltu sekä tuotannon että vasikoiden käyttäytymisen ja hyvinvoinnin kannalta. Väitöskirja koostuu kolmesta kokeesta, joista ensimmäisessä tutkittiin vasikoiden kasvatusta ryhmäkarsinoissa ulkona tai sisällä ja vasikoiden kasvatusta sisällä ryhmä- tai yksilökarsinoissa. Toisessa kokeessa vasikoiden annettiin imeä emiään rajoitetusti lypsyn jälkeen viiden tai kahdeksan viikon ajan ja kolmannessa selvitettiin vasikoiden veden juontia, kun vasikat saivat juomarehua vapaasti. Lisäksi kokeiden yhdistetystä aineistosta analysoitiin eri rehujen syöntimäärien suhdetta sekä rehujen vaikutusta kasvuun ennen ja jälkeen maidosta vieroituksen. Tutkimuksessa todettiin, että vasikoita voi ryhmässä kasvattaa kylmissä ja vaihtelevissa sääoloissa ulkona, kunhan ne hoidetaan ja ruokitaan erittäin huolellisesti. Kylmällä ilmalla vasikat saattavat kuitenkin syödä väkirehua vähemmän varsinkin, jos ruokailupaikka on ulkona ja makuualue sisällä. Ryhmässä kasvaneet vasikat aloittivat sekä kuivien rehujen syönnin että märehtimisen nuorempina kuin yksilökarsinassa kasvaneet. Ryhmissä esiintyvää käyttäytymisongelmaa, toisten vasikoiden imemistä, voidaan vähentää hoito- ja ruokintamenetelmillä. Annettaessa vasikoiden imeä emiään rajoitetusti lypsyn jälkeen vasikat oppivat imemään emiään hyvin nopeasti. Lypsytyö vaikeutui muutamien lehmien kohdalla, sillä ne pidättivät maitoa lypsettäessä. Saadessaan imeä rajoitetusti vasikat imivät suurehkoja maitomääriä kerrallaan. Vieroittaminen suurilta maitomääriltä viiden viikon iässä oli kuitenkin liian aikaista, koska vasikat eivät vielä syöneet riittävästi kuivia rehuja. Vieroitus emästä niin viiden kuin kahdeksankin viikon iässä aiheutti vasikoissa levottomuutta ja ääntelyn lisääntymistä. Saadessaan hapatettua juomarehua vapaasti vasikat joivat keskimäärin vain vähän vettä, olipa vesilähteenä avoin ämpäri tai vesinippa. Vasikoiden välillä oli suurta vaihtelua veden juontimäärissä. Viikkoa ennen maidosta vieroitusta vasikat joivat 0-3 l vettä päivässä. Vasikat joivat nipasta kerrallaan vähemmän vettä kuin ämpäristä, ja käyttivät enemmän aikaa päivässä veden juomiseen kuin vesiämpäristä juoneet vasikat. Suurin osa vasikoista joi vettä juomanipoista erikoisella tavalla esimerkiksi painamalla nippaa otsalla ja juomalla tippuvaa vettä. Vesinipat voivat olla siis vasikoille joko vaikeita tai epämukavia käyttää. Vasikoiden juoman maitomäärän lisääntyessä kasvu lisääntyy selvästi. Runsas maidon juominen vähentää kuitenkin kuivien rehujen syöntiä ja vieroitusvaiheessa kasvu voi hidastua. Vasikat olisikin tärkeää vieroittaa vähitellen, ettei muutoksia kasvuun tulisi. Syönti- ja kasvutulokset eivät aina anna oikeaa kuvaa kasvatusmenetelmien eroista eläinten hyvinvoinnin kannalta. Käyttäytyminen on herkkä hyvinvoinnin mittari ja se tulisikin aina huomioida eri kasvatusmenetelmiä arvioitaessa. .

Information, risk and trust in the food chain : Ex-ante valuation of consumer willingness to pay for beef quality information using the contingent valuation method

The safety of food has become an increasingly interesting issue to consumers and the media. It has also become a source of concern, as the amount of information on the risks related to food safety continues to expand. Today, risk and safety are permanent elements within the concept of food quality. Safety, in particular, is the attribute that consumers find very difficult to assess. The literature in this study consists of three main themes: traceability; consumer behaviour related to both quality and safety issues and perception of risk; and valuation methods. The empirical scope of the study was restricted to beef, because the beef labelling system enables reliable tracing of the origin of beef, as well as attributes related to safety, environmental friendliness and animal welfare. The purpose of this study was to examine what kind of information flows are required to ensure quality and safety in the food chain for beef, and who should produce that information. Studying the willingness to pay of consumers makes it possible to determine whether the consumers consider the quantity of information available on the safety and quality of beef sufficient. One of the main findings of this study was that the majority of Finnish consumers (73%) regard increased quality information as beneficial. These benefits were assessed using the contingent valuation method. The results showed that those who were willing to pay for increased information on the quality and safety of beef would accept an average price increase of 24% per kilogram. The results showed that certain risk factors impact consumer willingness to pay. If the respondents considered genetic modification of food or foodborne zoonotic diseases as harmful or extremely harmful risk factors in food, they were more likely to be willing to pay for quality information. The results produced by the models thus confirmed the premise that certain food-related risks affect willingness to pay for beef quality information. The results also showed that safety-related quality cues are significant to the consumers. In the first place, the consumers would like to receive information on the control of zoonotic diseases that are contagious to humans. Similarly, other process-control related information ranked high among the top responses. Information on any potential genetic modification was also considered important, even though genetic modification was not regarded as a high risk factor.

Rwanda Crisis and Genocide in Case Law of Rwanda Tribunal

After the Second World War the public was shocked to learn about the horrors perpetrated. As a response to the Holocaust, the newly established United Nations adopted the Genocide Convention of 1948 to prevent future genocides and to punish the perpetrators. The Convention remained, however, almost dead letter until the present day. In 1994, the long-lasted tension between the major groups of Hutu and Tutsi in Rwanda erupted in mass scale violence towards the Tutsi ethnic group. The purpose was to eradicate the Tutsi population of Rwanda. The international community did not halt the genocide. It stood by idle, failing to follow the swearing-in of the past. The United Nations established the International Criminal Tribunal for Rwanda (the ICTR) to bring to justice persons responsible for the genocide. Ever since its creation the ICTR has delivered a wealth of judgements elucidating the legal ingredients of the crime of genocide. The case law on determining the membership of national, ethnic, racial or religious groups has gradually shifted from the objective to subjective position. The membership of a group is seen as a subjective rather than objective concept. However, a totally subjective approach is not accepted. Therefore, it is necessary to determine some objective existence of a group. The provision on the underlying offences is not so difficult to interpret compared to the corresponding one on the protected groups and the mental element of genocide. The case law examined, e.g., whether there is any difference between the words killing and meurtre, the nature of mental harm caused by the perpetrator and sexual violence in the conflict. The mental element of genocide or dolus specialis of genocide is not thoroughly examined in the case law of the ICTR. In this regard, reference in made, in addition, to the case law of the other ad hoc Tribunal. The ICTR has made a significant contribution to the law of genocide and international criminal justice in general. The corpus of procedural and substantive law constitutes a basis for subsequent trials in international and hybrid tribunals. For national jurisdictions the jurisprudence on substantive law is useful while prosecuting international crimes.

Functional transfer of Salmonella pathogenicity island 2 to Salmonella bongori and Escherichia coli.

The type III secretion system (T3SS) encoded by the Salmonella pathogenicity island 2 (SPI2) has a central role in systemic infections by Salmonella enterica and for the intracellular phenotype. Intracellular S. enterica uses the SPI2-encoded T3SS to translocate a set of effector proteins into the host cell, which modify host cell functions, enabling intracellular survival and replication of the bacteria. We sought to determine whether specific functions of the SPI2-encoded T3SS can be transferred to heterologous hosts Salmonella bongori and Escherichia coli Mutaflor, species that lack the SPI2 locus and loci encoding effector proteins. The SPI2 virulence locus was cloned and functionally expressed in S. bongori and E. coli. Here, we demonstrate that S. bongori harboring the SPI2 locus is capable of secretion of SPI2 substrate proteins under culture conditions, as well as of translocation of effector proteins under intracellular conditions. An SPI2-mediated cellular phenotype was induced by S. bongori harboring the SPI2 if the sifA locus was cotransferred. An interference with the host cell microtubule cytoskeleton, a novel SPI2-dependent phenotype, was observed in epithelial cells infected with S. bongori harboring SPI2 without additional effector genes. S. bongori harboring SPI2 showed increased intracellular persistence in a cell culture model, but SPI2 transfer was not sufficient to confer to S. bongori systemic pathogenicity in a murine model. Transfer of SPI2 to heterologous hosts offers a new tool for the study of SPI2 functions and the phenotypes of individual effectors.

On the maximal rate of non-square STBCs from complex orthogonal designs

A Linear Processing Complex Orthogonal Design (LPCOD) is a p x n matrix epsilon, (p >= n) in k complex indeterminates x(1), x(2),..., x(k) such that (i) the entries of epsilon are complex linear combinations of 0, +/- x(i), i = 1,..., k and their conjugates, (ii) epsilon(H)epsilon = D, where epsilon(H) is the Hermitian (conjugate transpose) of epsilon and D is a diagonal matrix with the (i, i)-th diagonal element of the form l(1)((i))vertical bar x(1)vertical bar(2) + l(2)((i))vertical bar x(2)vertical bar(2)+...+ l(k)((i))vertical bar x(k)vertical bar(2) where l(j)((i)), i = 1, 2,..., n, j = 1, 2,...,k are strictly positive real numbers and the condition l(1)((i)) = l(2)((i)) = ... = l(k)((i)), called the equal-weights condition, holds for all values of i. For square designs it is known. that whenever a LPCOD exists without the equal-weights condition satisfied then there exists another LPCOD with identical parameters with l(1)((i)) = l(2)((i)) = ... = l(k)((i)) = 1. This implies that the maximum possible rate for square LPCODs without the equal-weights condition is the same as that or square LPCODs with equal-weights condition. In this paper, this result is extended to a subclass of non-square LPCODs. It is shown that, a set of sufficient conditions is identified such that whenever a non-square (p > n) LPCOD satisfies these sufficient conditions and do not satisfy the equal-weights condition, then there exists another LPCOD with the same parameters n, k and p in the same complex indeterminates with l(1)((i)) = l(2)((i)) = ... = l(k)((i)) = 1.

STBC's from representation of extended Clifford Algebras

A set of sufficient conditions to construct lambda-real symbol Maximum Likelihood (ML) decodable STBCs have recently been provided by Karmakar et al. STBCs satisfying these sufficient conditions were named as Clifford Unitary Weight (CUW) codes. In this paper, the maximal rate (as measured in complex symbols per channel use) of CUW codes for lambda = 2(a), a is an element of N is obtained using tools from representation theory. Two algebraic constructions of codes achieving this maximal rate are also provided. One of the constructions is obtained using linear representation of finite groups whereas the other construction is based on the concept of right module algebra over non-commutative rings. To the knowledge of the authors, this is the first paper in which matrices over non-commutative rings is used to construct STBCs. An algebraic explanation is provided for the 'ABBA' construction first proposed by Tirkkonen et al and the tensor product construction proposed by Karmakar et al. Furthermore, it is established that the 4 transmit antenna STBC originally proposed by Tirkkonen et al based on the ABBA construction is actually a single complex symbol ML decodable code if the design variables are permuted and signal sets of appropriate dimensions are chosen.

Effect of GPS on understanding relationship between mobile map and environment : A field experiment

Objectives: GPS technology enables the visualisation of a map reader s location on a mobile map. Earlier research on the cognitive aspects of map reading identified that searching for map-environment points is an essential element for the process of determining one s location on a mobile map. Map-environment points refer to objects that are visualized on the map and are recognizable in the environment. However, because the GPS usually adds only one point to the map that has a relation to the environment, it does not provide a sufficient amount of information for self-location. The aim of the present thesis was to assess the effect of GPS on the cognitive processes involved in determining one s location on a map. Methods: The effect of GPS on self-location was studied in a field experiment. The subjects were shown a target on a mobile map, and they were asked to point in the direction of the target. In order for the map reader to be able to deduce the direction of the target, he/she has to locate himself/herself on the map. During the pointing tasks, the subjects were asked to think aloud. The data from the experiment were used to analyze the effect of the GPS on the time needed to perform the task. The subjects verbal data was used to assess the effect of the GPS on the number of landmark concepts mentioned during a task (landmark concepts are words referring to objects that can be recognized both on the map and in the environment). Results and conclusions: The results from the experiment indicate that the GPS reduces the time needed to locate oneself on a map. The analysis of the verbal data revealed that the GPS reduces the number of landmark concepts in the protocols. The findings suggest that the GPS guides the subject s search for the map-environment points and narrows the area on the map that must be searched for self-location.

Autoimmune Regulator (AIRE) in the Maintenance of Immunological Tolerance

Autoimmune regulator (AIRE) is the gene mutated in the human polyglandular autoimmune disease called Autoimmune polyendocrinopathy, candidiasis, and ectodermal dystrophy (APECED) that belongs to the Finnish disease heritage. Murine Aire has been shown to be important in the generation of the T cell central tolerance in the thymus by promoting the expression of ectopic tissue-specific antigens in the thymic medulla. Aire is also involved in the thymus tissue organization during organogenesis. In addition to the thymus, AIRE/Aire is expressed in the secondary lymphoid organs. Accordingly, a role for AIRE/Aire in the maintenance of peripheral tolerance has been suggested. Peripheral tolerance involves mechanisms that suppress immune responses in secondary lymphoid organs. Regulatory T cells (Tregs) are an important suppressive T cell population mediating the peripheral tolerance. Tregs are generated in the thymus but also in the peripheral immune system T cells can acquire the Treg-phenotype. The aim of this study was to characterize Tregs in APECED patients and in the APECED mouse model (Aire-deficient mice). In the mouse model, it was possible to separate Aire expression in the thymus and in the secondary lymphoid organs. The relative importance of thymic and peripheral Aire expression in the maintenance of immunological tolerance was studied in an experimental model that was strongly biased towards autoimmunity, i.e. lymphopenia-induced proliferation (LIP) of lymphocytes. This experimental model was also utilised to study the behaviour of T cells with dual-specific T cell receptors (TCR) during the proliferation. The Treg phenotype was studied by flow cytometry and relative gene expression with real-time polymerase chain reaction. TCR repertoires of the Tregs isolated from APECED patients and healthy controls were also compared. The dual-specific TCRs were studied with the TCR repertoire analysis that was followed with sequencing of the chosen TCR genes in order to estimate changes in the dual-specific TCR diversity. The Treg function was tested with an in vitro suppression assay. The APECED patients had normal numbers of Tregs but the phenotype and suppressive functions of the Tregs were impaired. In order to separate Aire functions in the thymus from its yet unknown role in the secondary lymphoid organs, the phenomenon of LIP was utilised. In this setting, the lymphocytes that are adoptively transferred to a lymphopenic recipient proliferate to stimuli from self-originating antigens. This proliferation can result in autoimmunity if peripheral tolerance is not fully functional. When lymphocytes that had matured without Aire in the thymus were transferred to lymphopenic Aire-sufficient recipients, no clinical autoimmunity followed. The Aire-deficient donor-originating lymphocytes hyperproliferated, and other signs of immune dysregulation were also found in the recipients. Overt autoimmunity, however, was prevented by the Aire-deficient donor-originating Tregs that hyperproliferated in the recipients. Aire-deficient lymphopenic mice were used to study whether peripheral loss of Aire had an impact on the maintenance of peripheral tolerance. When normal lymphocytes were transferred to these Aire-deficient lymphopenic recipients, the majority of recipients developed a clinically symptomatic colitis. The colitis was confirmed also by histological analysis of the colon tissue sections. In the Aire-deficient lymphopenic recipients Tregs were proliferating significantly less than in the control group s recipients that had normal Aire expression in their secondary lymphoid organs. This study shows that Aire is not only important in the central tolerance but is also has a significant role in the maintenance of the peripheral tolerance both in mice and men. Aire expressed in the secondary lymphoid organs is involved in the functions of Tregs during an immune response. This peripheral expression appears to be relatively more important in some situations since only those lymphopenic recipients that had lost peripheral expression of Aire developed a symptomatic autoimmune disease. This AIRE-related Treg defect could be clinically important in understanding the pathogenesis of APECED.

Finite Element Analysis of Deformed Legs of Offshore Platform Structures

The element stiffness matrix of the equivalent beam or pipe element of the deformed leg of the platform is derived by the finite element method. The stresses and displacements of some damaged components are calculated, and the numeri-cal solutions agree well with those obtained by the fine mesh finite element method. Finally, as an application of this method, the stresses of some platform structures are calculated and analyzed.

The ecological basis of fishery yield of the Puerto Rico-Virgin Islands Insular Shelf: 1987 Assessment

A literature review was conducted to locate information on the flow of energy from primary producers to the fishery stocks of the Puerto Rican-Virgin Islands insular shelf. This report uses site-specific information to describe the major ecological subsystems, or habitats, of the region, to identify the more common species and the subsystems in which they occur, to quantify productivity and biomass, and to outline trophic relationships. Discussions on each topic and subsystem vary in substance and detail, being limited by the availability and accessibility of information. (PDF contains 189 pages) Seven distinct subsystems are described: mangrove estuary, seagrass bed, coral reef, algal plain, sand/mud bottom, shelf break, and overlying pelagic. Over 50 tables provide lists of species found in each habitat on various surveys dating back to 1956. Estimates of density, relative abundance, and productivity are provided when possible. We evaluated whether sufficient information exists to support an analysis of the energy basis of fishery production in the area, beginning with the design and development of an ecosystem model. Data needs in three categories - species lists, biomass, and trophic relations - were examined for each subsystem and for each of three species groups - primary producers, invertebrates, and fish. We concluded that adequate data, sufficient for modeling purposes, are available in 16 (25%) of 64 categories; limited data, those requiring greater extrapolation, are available in 35 (55%) categories; and no data are available in 13 (20%) categories. The best-studied subsystems are seagrass beds and coral reefs, with at least limited data in all categories. Invertebrates, the intermediate link in the food web between primary producers and fishes, are the least quantified group in the region. Primary production and fishes, however, are relatively well-studied, providing sufficient data to support an ecosystem-level analysis and to initiate a modeling effort.

Role of G protein coupled inwardly rectifier K+ channels (GIRK) on the neurobiology depression

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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.