Minimum cost of transport in human running is not ubiquitous

Purpose This study explores recent claims that humans exhibit a minimum cost of transport (CoTmin) for running which occurs at an intermediate speed, and assesses individual physiological, gait and training characteristics. Methods Twelve healthy participants with varying levels of fitness and running experience ran on a treadmill at six self-selected speeds in a discontinuous protocol over three sessions. Running speed (km[middle dot]hr-1), V[spacing dot above]O2 (mL[middle dot]kg-1[middle dot]km-1), CoT (kcal[middle dot]km-1), heart rate (beats[middle dot]min-1) and cadence (steps[middle dot]min-1) were continuously measured. V[spacing dot above]O2 max was measured on a fourth testing session. The occurrence of a CoTmin was investigated and its presence or absence examined with respect to fitness, gait and training characteristics. Results Five participants showed a clear CoTmin at an intermediate speed and a statistically significant (p < 0.05) quadratic CoT-speed function, while the other participants did not show such evidence. Participants were then categorized and compared with respect to the strength of evidence for a CoTmin (ClearCoTmin and NoCoTmin). The ClearCoTmin group displayed significantly higher correlation between speed and cadence; more endurance training and exercise sessions per week; than the NoCoTmin group; and a marginally non-significant but higher aerobic capacity. Some runners still showed a CoTmin at an intermediate speed even after subtraction of resting energy expenditure. Conclusion The findings confirm the existence of an optimal speed for human running, in some but not all participants. Those exhibiting a COTmin undertook a higher volume of running, ran with a cadence that was more consistently modulated with speed, and tended to be aerobically fitter. The ability to minimise the energetic cost of transport appears not to be ubiquitous feature of human running but may emerge in some individuals with extensive running experience.

Query cost estimation through remote system contention states analysis over the Internet

Query processing over the Internet involving autonomous data sources is a major task in data integration. It requires the estimated costs of possible queries in order to select the best one that has the minimum cost. In this context, the cost of a query is affected by three factors: network congestion, server contention state, and complexity of the query. In this paper, we study the effects of both the network congestion and server contention state on the cost of a query. We refer to these two factors together as system contention states. We present a new approach to determining the system contention states by clustering the costs of a sample query. For each system contention state, we construct two cost formulas for unary and join queries respectively using the multiple regression process. When a new query is submitted, its system contention state is estimated first using either the time slides method or the statistical method. The cost of the query is then calculated using the corresponding cost formulas. The estimated cost of the query is further adjusted to improve its accuracy. Our experiments show that our methods can produce quite accurate cost estimates of the submitted queries to remote data sources over the Internet.

Supply response and Cost of production of natural rubber- an econometric study

The study deals with the short and long term supply response of the natural rubber in India and to analyse the macro economic environment of NR industry and causative factors of the rubber price crash. It determines the minimum cost of production of natural rubber and to forecast the potential production of NR in India. There is positive response of short run and long run supply to prices. Since correlation analysis show close association between international and domestic price level, international price changes will have its domestic echo. Production and consumption will sustain its rising trend. This makes plans for increasing production estimates show that a mid way level i.e. the range between Rs.32-Rs.38 will give a fair enough profit to the grower in the present situation and provide for the viable sustenance of rubber cultivation. Identification of the SWOT of rubber cultivation would help in supporting rubber cultivation if remedial measures are undertaken with the true spirit. This would help Indian rubber to attain global competitiveness. Then the inflow of valuable foreign exchange will overcome the other economic drawbacks of rubber cultivation

Consideration of tip speed limitations in preliminary analysis of minimum COE wind turbines

A relation between Cost Of Energy, COE, maximum allowed tip speed, and rated wind speed, is obtained for wind turbines with a given goal rated power. The wind regime is characterised by the corresponding parameters of the probability density function of wind speed. The non-dimensional characteristics of the rotor: number of blades, the blade radial distributions of local solidity, twist angle, and airfoil type, play the role of parameters in the mentioned relation. The COE is estimated using a cost model commonly used by the designers. This cost model requires basic design data such as the rotor radius and the ratio between the hub height and the rotor radius. Certain design options, DO, related to the technology of the power plant, tower and blades are also required as inputs. The function obtained for the COE can be explored to �nd those values of rotor radius that give rise to minimum cost of energy for a given wind regime as the tip speed limitation changes. The analysis reveals that iso-COE lines evolve parallel to iso-radius lines for large values of limit tip speed but that this is not the case for small values of the tip speed limits. It is concluded that, as the tip speed limit decreases, the optimum decision for keeping minimum COE values can be: a) reducing the rotor radius for places with high weibull scale parameter or b) increasing the rotor radius for places with low weibull scale parameter

Effective web service discovery using a combination of a semantic model and a data mining technique

With the advent of Service Oriented Architecture, Web Services have gained tremendous popularity. Due to the availability of a large number of Web services, finding an appropriate Web service according to the requirement of the user is a challenge. This warrants the need to establish an effective and reliable process of Web service discovery. A considerable body of research has emerged to develop methods to improve the accuracy of Web service discovery to match the best service. The process of Web service discovery results in suggesting many individual services that partially fulfil the user’s interest. By considering the semantic relationships of words used in describing the services as well as the use of input and output parameters can lead to accurate Web service discovery. Appropriate linking of individual matched services should fully satisfy the requirements which the user is looking for. This research proposes to integrate a semantic model and a data mining technique to enhance the accuracy of Web service discovery. A novel three-phase Web service discovery methodology has been proposed. The first phase performs match-making to find semantically similar Web services for a user query. In order to perform semantic analysis on the content present in the Web service description language document, the support-based latent semantic kernel is constructed using an innovative concept of binning and merging on the large quantity of text documents covering diverse areas of domain of knowledge. The use of a generic latent semantic kernel constructed with a large number of terms helps to find the hidden meaning of the query terms which otherwise could not be found. Sometimes a single Web service is unable to fully satisfy the requirement of the user. In such cases, a composition of multiple inter-related Web services is presented to the user. The task of checking the possibility of linking multiple Web services is done in the second phase. Once the feasibility of linking Web services is checked, the objective is to provide the user with the best composition of Web services. In the link analysis phase, the Web services are modelled as nodes of a graph and an allpair shortest-path algorithm is applied to find the optimum path at the minimum cost for traversal. The third phase which is the system integration, integrates the results from the preceding two phases by using an original fusion algorithm in the fusion engine. Finally, the recommendation engine which is an integral part of the system integration phase makes the final recommendations including individual and composite Web services to the user. In order to evaluate the performance of the proposed method, extensive experimentation has been performed. Results of the proposed support-based semantic kernel method of Web service discovery are compared with the results of the standard keyword-based information-retrieval method and a clustering-based machine-learning method of Web service discovery. The proposed method outperforms both information-retrieval and machine-learning based methods. Experimental results and statistical analysis also show that the best Web services compositions are obtained by considering 10 to 15 Web services that are found in phase-I for linking. Empirical results also ascertain that the fusion engine boosts the accuracy of Web service discovery by combining the inputs from both the semantic analysis (phase-I) and the link analysis (phase-II) in a systematic fashion. Overall, the accuracy of Web service discovery with the proposed method shows a significant improvement over traditional discovery methods.

A new multilevel converter configuration for high power and high quality applications

The Queensland University of Technology (QUT) allows the presentation of theses for the Degree of Doctor of Philosophy in the format of published or submitted papers, where such papers have been published, accepted or submitted during the period of candidature. This thesis is composed of ten published /submitted papers and book chapters of which nine have been published and one is under review. This project is financially supported by an Australian Research Council (ARC) Discovery Grant with the aim of investigating multilevel topologies for high quality and high power applications, with specific emphasis on renewable energy systems. The rapid evolution of renewable energy within the last several years has resulted in the design of efficient power converters suitable for medium and high-power applications such as wind turbine and photovoltaic (PV) systems. Today, the industrial trend is moving away from heavy and bulky passive components to power converter systems that use more and more semiconductor elements controlled by powerful processor systems. However, it is hard to connect the traditional converters to the high and medium voltage grids, as a single power switch cannot stand at high voltage. For these reasons, a new family of multilevel inverters has appeared as a solution for working with higher voltage levels. Besides this important feature, multilevel converters have the capability to generate stepped waveforms. Consequently, in comparison with conventional two-level inverters, they present lower switching losses, lower voltage stress across loads, lower electromagnetic interference (EMI) and higher quality output waveforms. These properties enable the connection of renewable energy sources directly to the grid without using expensive, bulky, heavy line transformers. Additionally, they minimize the size of the passive filter and increase the durability of electrical devices. However, multilevel converters have only been utilised in very particular applications, mainly due to the structural limitations, high cost and complexity of the multilevel converter system and control. New developments in the fields of power semiconductor switches and processors will favor the multilevel converters for many other fields of application. The main application for the multilevel converter presented in this work is the front-end power converter in renewable energy systems. Diode-clamped and cascade converters are the most common type of multilevel converters widely used in different renewable energy system applications. However, some drawbacks – such as capacitor voltage imbalance, number of components, and complexity of the control system – still exist, and these are investigated in the framework of this thesis. Various simulations using software simulation tools are undertaken and are used to study different cases. The feasibility of the developments is underlined with a series of experimental results. This thesis is divided into two main sections. The first section focuses on solving the capacitor voltage imbalance for a wide range of applications, and on decreasing the complexity of the control strategy on the inverter side. The idea of using sharing switches at the output structure of the DC-DC front-end converters is proposed to balance the series DC link capacitors. A new family of multioutput DC-DC converters is proposed for renewable energy systems connected to the DC link voltage of diode-clamped converters. The main objective of this type of converter is the sharing of the total output voltage into several series voltage levels using sharing switches. This solves the problems associated with capacitor voltage imbalance in diode-clamped multilevel converters. These converters adjust the variable and unregulated DC voltage generated by renewable energy systems (such as PV) to the desirable series multiple voltage levels at the inverter DC side. A multi-output boost (MOB) converter, with one inductor and series output voltage, is presented. This converter is suitable for renewable energy systems based on diode-clamped converters because it boosts the low output voltage and provides the series capacitor at the output side. A simple control strategy using cross voltage control with internal current loop is presented to obtain the desired voltage levels at the output voltage. The proposed topology and control strategy are validated by simulation and hardware results. Using the idea of voltage sharing switches, the circuit structure of different topologies of multi-output DC-DC converters – or multi-output voltage sharing (MOVS) converters – have been proposed. In order to verify the feasibility of this topology and its application, steady state and dynamic analyses have been carried out. Simulation and experiments using the proposed control strategy have verified the mathematical analysis. The second part of this thesis addresses the second problem of multilevel converters: the need to improve their quality with minimum cost and complexity. This is related to utilising asymmetrical multilevel topologies instead of conventional multilevel converters; this can increase the quality of output waveforms with a minimum number of components. It also allows for a reduction in the cost and complexity of systems while maintaining the same output quality, or for an increase in the quality while maintaining the same cost and complexity. Therefore, the asymmetrical configuration for two common types of multilevel converters – diode-clamped and cascade converters – is investigated. Also, as well as addressing the maximisation of the output voltage resolution, some technical issues – such as adjacent switching vectors – should be taken into account in asymmetrical multilevel configurations to keep the total harmonic distortion (THD) and switching losses to a minimum. Thus, the asymmetrical diode-clamped converter is proposed. An appropriate asymmetrical DC link arrangement is presented for four-level diode-clamped converters by keeping adjacent switching vectors. In this way, five-level inverter performance is achieved for the same level of complexity of the four-level inverter. Dealing with the capacitor voltage imbalance problem in asymmetrical diodeclamped converters has inspired the proposal for two different DC-DC topologies with a suitable control strategy. A Triple-Output Boost (TOB) converter and a Boost 3-Output Voltage Sharing (Boost-3OVS) converter connected to the four-level diode-clamped converter are proposed to arrange the proposed asymmetrical DC link for the high modulation indices and unity power factor. Cascade converters have shown their abilities and strengths in medium and high power applications. Using asymmetrical H-bridge inverters, more voltage levels can be generated in output voltage with the same number of components as the symmetrical converters. The concept of cascading multilevel H-bridge cells is used to propose a fifteen-level cascade inverter using a four-level H-bridge symmetrical diode-clamped converter, cascaded with classical two-level Hbridge inverters. A DC voltage ratio of cells is presented to obtain maximum voltage levels on output voltage, with adjacent switching vectors between all possible voltage levels; this can minimize the switching losses. This structure can save five isolated DC sources and twelve switches in comparison to conventional cascade converters with series two-level H bridge inverters. To increase the quality in presented hybrid topology with minimum number of components, a new cascade inverter is verified by cascading an asymmetrical four-level H-bridge diode-clamped inverter. An inverter with nineteen-level performance was achieved. This synthesizes more voltage levels with lower voltage and current THD, rather than using a symmetrical diode-clamped inverter with the same configuration and equivalent number of power components. Two different predictive current control methods for the switching states selection are proposed to minimise either losses or THD of voltage in hybrid converters. High voltage spikes at switching time in experimental results and investigation of a diode-clamped inverter structure raised another problem associated with high-level high voltage multilevel converters. Power switching components with fast switching, combined with hard switched-converters, produce high di/dt during turn off time. Thus, stray inductance of interconnections becomes an important issue and raises overvoltage and EMI issues correlated to the number of components. Planar busbar is a good candidate to reduce interconnection inductance in high power inverters compared with cables. The effect of different transient current loops on busbar physical structure of the high-voltage highlevel diode-clamped converters is highlighted. Design considerations of proper planar busbar are also presented to optimise the overall design of diode-clamped converters.

Lifecycle optimization and tradeoff analysis among competing objectives for a road corridor

While the philosophical motivation behind Civil Infrastructure Management Systems is to achieve optimal level of service at a minimum cost, the allocation of scarce resources among competing alternatives is still a matter of debate. It appears to be widely accepted that results from tradeoff analysis can be measured by the degree of accomplishment of the objectives. Road management systems not only deal with different asset types but also with conflicting objectives. This paper presents a case study of lifecycle optimization with tradeoff analysis for a road corridor in New Brunswick. Objectives of the study included condition of bridge and roads and road safety. A road safety index was created based on potential for improvement. Road condition was based on roughness, rutting and cracking. Initial results show lack of sustainability in bridge performance. Therefore, bridges where broken by components: deck, superstructure and substructure. Visual inspections, in addition to construction age of each bridge, were combined to generate a surrogate apparent age. Two life cycle analysis were conducted; one aimed to minimize overall cost while achieving sustainable results and another one purely for optimization. -used to identify required levels of budget. Such analyses were used to identify the minimum required budget and to demonstrate that with the same amount of money it was possible to achieve better levels of performance. Dominance and performance driven criteria were combined to identify and select an optimal result. It was found that achievement of optimally sustained results is conditioned by the availability of treatments for all asset classes at across their life spans. For the case study a disaggregated bridge condition index was introduced to the original algorithm to attempt to achieve sustainability in all bridges components, however lack of early stage treatments for substructures produce declining trends for such a component.

Bayesian and Decision Tree Approaches for Pattern Recognition Including Feature Measurement Costs

The minimum cost classifier when general cost functionsare associated with the tasks of feature measurement and classification is formulated as a decision graph which does not reject class labels at intermediate stages. Noting its complexities, a heuristic procedure to simplify this scheme to a binary decision tree is presented. The optimizationof the binary tree in this context is carried out using ynamicprogramming. This technique is applied to the voiced-unvoiced-silence classification in speech processing.

A near Optimal Cane Rail Scheduler under Limited and Unlimited Capacity Constraints

Australia is the world’s third largest exporter of raw sugar after Brazil and Thailand, with around $2.0 billion in export earnings. Transport systems play a vital role in the raw sugar production process by transporting the sugarcane crop between farms and mills. In 2013, 87 per cent of sugarcane was transported to mills by cane railway. The total cost of sugarcane transport operations is very high. Over 35% of the total cost of sugarcane production in Australia is incurred in cane transport. A cane railway network mainly involves single track sections and multiple track sections used as passing loops or sidings. The cane railway system performs two main tasks: delivering empty bins from the mill to the sidings for filling by harvesters; and collecting the full bins of cane from the sidings and transporting them to the mill. A typical locomotive run involves an empty train (locomotive and empty bins) departing from the mill, traversing some track sections and delivering bins at specified sidings. The locomotive then, returns to the mill, traversing the same track sections in reverse order, collecting full bins along the way. In practice, a single track section can be occupied by only one train at a time, while more than one train can use a passing loop (parallel sections) at a time. The sugarcane transport system is a complex system that includes a large number of variables and elements. These elements work together to achieve the main system objectives of satisfying both mill and harvester requirements and improving the efficiency of the system in terms of low overall costs. These costs include delay, congestion, operating and maintenance costs. An effective cane rail scheduler will assist the traffic officers at the mill to keep a continuous supply of empty bins to harvesters and full bins to the mill with a minimum cost. This paper addresses the cane rail scheduling problem under rail siding capacity constraints where limited and unlimited siding capacities were investigated with different numbers of trains and different train speeds. The total operating time as a function of the number of trains, train shifts and a limited number of cane bins have been calculated for the different siding capacity constraints. A mathematical programming approach has been used to develop a new scheduler for the cane rail transport system under limited and unlimited constraints. The new scheduler aims to reduce the total costs associated with the cane rail transport system that are a function of the number of bins and total operating costs. The proposed metaheuristic techniques have been used to find near optimal solutions of the cane rail scheduling problem and provide different possible solutions to avoid being stuck in local optima. A numerical investigation and sensitivity analysis study is presented to demonstrate that high quality solutions for large scale cane rail scheduling problems are obtainable in a reasonable time. Keywords: Cane railway, mathematical programming, capacity, metaheuristics

Decision tree design and applications in speech processing

The design and operation of the minimum cost classifier, where the total cost is the sum of the measurement cost and the classification cost, is computationally complex. Noting the difficulties associated with this approach, decision tree design directly from a set of labelled samples is proposed in this paper. The feature space is first partitioned to transform the problem to one of discrete features. The resulting problem is solved by a dynamic programming algorithm over an explicitly ordered state space of all outcomes of all feature subsets. The solution procedure is very general and is applicable to any minimum cost pattern classification problem in which each feature has a finite number of outcomes. These techniques are applied to (i) voiced, unvoiced, and silence classification of speech, and (ii) spoken vowel recognition. The resulting decision trees are operationally very efficient and yield attractive classification accuracies.

Identification of prospective locations for generation expansion with least augmentation of network

With ever increasing demand for electric energy, additional generation and associated transmission facilities has to be planned and executed. In order to augment existing transmission facilities, proper planning and selective decisions are to be made whereas keeping in mind the interests of several parties who are directly or indirectly involved. Common trend is to plan optimal generation expansion over the planning period in order to meet the projected demand with minimum cost capacity addition along with a pre-specified reliability margin. Generation expansion at certain locations need new transmission network which involves serious problems such as getting right of way, environmental clearance etc. In this study, an approach to the citing of additional generation facilities in a given system with minimum or no expansion in the transmission facility is attempted using the network connectivity and the concept of electrical distance for projected load demand. The proposed approach is suitable for large interconnected systems with multiple utilities. Sample illustration on real life system is presented in order to show how this approach improves the overall performance on the operation of the system with specified performance parameters.

BELIEF PROPAGATION FOR OPTIMAL EDGE COVER IN THE RANDOM COMPLETE GRAPH

We apply the objective method of Aldous to the problem of finding the minimum-cost edge cover of the complete graph with random independent and identically distributed edge costs. The limit, as the number of vertices goes to infinity, of the expected minimum cost for this problem is known via a combinatorial approach of Hessler and Wastlund. We provide a proof of this result using the machinery of the objective method and local weak convergence, which was used to prove the (2) limit of the random assignment problem. A proof via the objective method is useful because it provides us with more information on the nature of the edge's incident on a typical root in the minimum-cost edge cover. We further show that a belief propagation algorithm converges asymptotically to the optimal solution. This can be applied in a computational linguistics problem of semantic projection. The belief propagation algorithm yields a near optimal solution with lesser complexity than the known best algorithms designed for optimality in worst-case settings.

Social optimum in social groups with give-and-take criterion

We consider a Social Group' of networked nodes, seeking a universe' of segments. Each node has a subset of the universe and access to an expensive resource for downloading data. Nodes can also acquire the universe by exchanging copies of segments among themselves, at low cost, using inter-node links. While exchanges over inter-node links ensure minimum cost, some nodes in the group try to exploit the system. We term such nodes as non-reciprocating nodes' and prohibit such behavior by proposing the give-and-take' criterion, where exchange is allowed if each node has segments unavailable with the other. Under this criterion, we consider the problem of maximizing the number of nodes with the universe at the end of local exchanges. First, we present a randomized algorithm that is shown to be optimal in the asymptotic regime. Then, we present greedy links algorithm, which performs well for most of the scenarios and yields an optimal result when the number of nodes is four. The polygon algorithm is proposed, which yields an optimal result when each of the nodes has a unique segment. After presenting some intuitive algorithms (e.g., greedy incremental algorithm and rarest first algorithm), we compare the performances of all proposed algorithms with the optimal. Copyright (c) 2015 John Wiley & Sons, Ltd.

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.