How to run a campaign: Optimal control of SIS and SIR information epidemics

Information spreading in a population can be modeled as an epidemic. Campaigners (e.g., election campaign managers, companies marketing products or movies) are interested in spreading a message by a given deadline, using limited resources. In this paper, we formulate the above situation as an optimal control problem and the solution (using Pontryagin's Maximum Principle) prescribes an optimal resource allocation over the time of the campaign. We consider two different scenarios-in the first, the campaigner can adjust a direct control (over time) which allows her to recruit individuals from the population (at some cost) to act as spreaders for the Susceptible-Infected-Susceptible (SIS) epidemic model. In the second case, we allow the campaigner to adjust the effective spreading rate by incentivizing the infected in the Susceptible-Infected-Recovered (SIR) model, in addition to the direct recruitment. We consider time varying information spreading rate in our formulation to model the changing interest level of individuals in the campaign, as the deadline is reached. In both the cases, we show the existence of a solution and its uniqueness for sufficiently small campaign deadlines. For the fixed spreading rate, we show the effectiveness of the optimal control strategy against the constant control strategy, a heuristic control strategy and no control. We show the sensitivity of the optimal control to the spreading rate profile when it is time varying. (C) 2014 Elsevier Inc. All rights reserved.

Optimization of bus allocation to depots by minimizing dead kilometers

In metropolitan cities, public transportation service plays a vital role in mobility of people, and it has to introduce new routes more frequently due to the fast development of the city in terms of population growth and city size. Whenever there is introduction of new route or increase in frequency of buses, the nonrevenue kilometers covered by the buses increases as depot and route starting/ending points are at different places. This non-revenue kilometers or dead kilometers depends on the distance between depot and route starting point/ending point. The dead kilometers not only results in revenue loss but also results in an increase in the operating cost because of the extra kilometers covered by buses. Reduction of dead kilometers is necessary for the economic growth of the public transportation system. Therefore, in this study, the attention is focused on minimizing dead kilometers by optimizing allocation of buses to depots depending upon the shortest distance between depot and route starting/ending points. We consider also depot capacity and time period of operation during allocation of buses to ensure parking safety and proper maintenance of buses. Mathematical model is developed considering the aforementioned parameters, which is a mixed integer program, and applied to Bangalore Metropolitan Transport Corporation (BMTC) routes operating presently in order to obtain optimal bus allocation to depots. Database for dead kilometers of depots in BMTC for all the schedules are generated using the Form-4 (trip sheet) of each schedule to analyze depot-wise and division-wise dead kilometers. This study also suggests alternative locations where depots can be located to reduce dead kilometers. Copyright (C) 2015 John Wiley & Sons, Ltd.

Outage exponents of block-fading channels with power allocation

Power allocation is studied for fixed-rate transmission over block-fading channels with arbitrary continuous fading distributions and perfect transmitter and receiver channel state information. Both short- and long-term power constraints for arbitrary input distributions are considered. Optimal power allocation schemes are shown to be direct applications of previous results in the literature. It is shown that the short- and long-term outage exponents for arbitrary input distributions are related through a simple formula. The formula is useful to predict when the delay-limited capacity is positive. Furthermore, this characterization is useful for the design of efficient coding schemes for this relevant channel model. © 2010 IEEE.

How optimal life history changes with the community size-spectrum

This paper derives optimal life histories for fishes or other animals in relation to the size spectrum of the ecological community in which they are both predators and prey. Assuming log-linear size-spectra and well known scaling laws for feeding and mortality, we first construct the energetics of the individual. From these we find, using dynamic programming, the optimal allocation of energy between growth and reproduction as well as the trade-off between offspring size and numbers. Optimal strategies were found to be strongly dependent on size spectrum slope. For steep size spectra (numbers declining rapidly with size), determinate growth was optimal and allocation to somatic growth increased rapidly with increasing slope. However, restricting reproduction to a fixed mating season changed optimal allocations to give indeterminate growth approximating a von Bertalanffy trajectory. The optimal offspring size was as small as possible given other restrictions such as newborn starvation mortality. For shallow size spectra, finite optimal maturity size required a decline in fitness for large size or age. All the results are compared with observed size spectra of fish communities to show their consistency and relevance.

Capacity and resource allocation of cooperative MIMO in ad hoc networks

Cooperative MIMO (Multiple Input–Multiple Output) allows multiple nodes share their antennas to emulate antenna arrays and transmit or receive cooperatively. It has the ability to increase the capacity for future wireless communication systems and it is particularly suited for ad hoc networks. In this study, based on the transmission procedure of a typical cooperative MIMO system, we first analyze the capacity of single-hop cooperative MIMO systems, and then we derive the optimal resource allocation strategy to maximize the end-to-end capacity in multi-hop cooperative MIMO systems. The study shows three implications. First, only when the intra-cluster channel is better than the inter-cluster channel, cooperative MIMO results in a capacity increment. Second, for a given scenario there is an optimal number of cooperative nodes. For instance, in our study an optimal deployment of three cooperative nodes achieve a capacity increment of 2 bps/Hz when compared with direct transmission. Third, an optimal resource allocation strategy plays a significant role in maximizing end-to-end capacity in multi-hop cooperative MIMO systems. Numerical results show that when optimal resource allocation is applied we achieve more than 20% end-to-end capacity increment in average when compared with an equal resource allocation strategy.

Power Allocation Strategies across N Orthogonal Channels at Both Source and Relay

A wireless relay network with one source, one relay and one destination is considered, where nodes communicate via N orthogonal channels. We develop optimal power allocation strategies at both the source and relay for maximizing the overall source-destination capacity under individual power constraints at the source and relay. Some properties of the optimal solution are studied. © 2012 IEEE.

Power allocation strategies across N orthogonal channels for single-relay networks at both source and relay

We consider a wireless relay network with one source, one relay and one destination, where communications between nodes are preformed over N orthogonal channels. This, for example, is the case when orthogonal frequency division multiplexing is employed for data communications. Since the power available at the source and relay is limited, we study optimal power allocation strategies at the source and relay in order to maximize the overall source-destination capacity. Depending on the availability of the channel state information at both the source and relay or only at the relay, power allocation is performed at both the source and relay or only at the relay. Considering different setups for the problem, various optimization problems are formulated and solved. Some properties of the optimal solution are also proved.

Optimal Time Series Momentum

We develop a continuous-time asset price model to capture the timeseries momentum documented recently. The underlying stochastic delay differentialsystem facilitates the analysis of effects of different time horizons used bymomentum trading. By studying an optimal asset allocation problem, we find thatthe performance of time series momentum strategy can be significantly improvedby combining with market fundamentals and timing opportunity with respect tomarket trend and volatility. Furthermore, the results also hold for different timehorizons, the out-of-sample tests and with short-sale constraints. The outperformanceof the optimal strategy is immune to market states, investor sentiment andmarket volatility.

Long-Term Economic Model for Allocation of FACTS Devices in Restructured Power System Integrated Wind Generation

This study proposes an approach to optimally allocate multiple types of flexible AC transmission system (FACTS) devices in market-based power systems with wind generation. The main objective is to maximise profit by minimising device investment cost, and the system's operating cost considering both normal conditions and possible contingencies. The proposed method accurately evaluates the long-term costs and benefits gained by FACTS devices (FDs) installation to solve a large-scale optimisation problem. The objective implies maximising social welfare as well as minimising compensations paid for generation re-scheduling and load shedding. Many technical operation constraints and uncertainties are included in problem formulation. The overall problem is solved using both particle swarm optimisations for attaining optimal FDs allocation as main problem and optimal power flow as sub-optimisation problem. The effectiveness of the proposed approach is demonstrated on modified IEEE 14-bus test system and IEEE 118-bus test system.

An heuristic approach for optimal location of gas supply units in transportation system

The best places to locate the Gas Supply Units (GSUs) on a natural gas systems and their optimal allocation to loads are the key factors to organize an efficient upstream gas infrastructure. The number of GSUs and their optimal location in a gas network is a decision problem that can be formulated as a linear programming problem. Our emphasis is on the formulation and use of a suitable location model, reflecting real-world operations and constraints of a natural gas system. This paper presents a heuristic model, based on lagrangean approach, developed for finding the optimal GSUs location on a natural gas network, minimizing expenses and maximizing throughput and security of supply.The location model is applied to the Iberian high pressure natural gas network, a system modelised with 65 demand nodes. These nodes are linked by physical and virtual pipelines – road trucks with gas in liquefied form. The location model result shows the best places to locate, with the optimal demand allocation and the most economical gas transport mode: by pipeline or by road truck.

Optimal methodology for renewable energy dispatching in islanded operation

The management of energy resources for islanded operation is of crucial importance for the successful use of renewable energy sources. A Virtual Power Producer (VPP) can optimally operate the resources taking into account the maintenance, operation and load control considering all the involved cost. This paper presents the methodology approach to formulate and solve the problem of determining the optimal resource allocation applied to a real case study in Budapest Tech’s. The problem is formulated as a mixed-integer linear programming model (MILP) and solved by a deterministic optimization technique CPLEX-based implemented in General Algebraic Modeling Systems (GAMS). The problem has also been solved by Evolutionary Particle Swarm Optimization (EPSO). The obtained results are presented and compared.

Optimal management of natural resources. Accounting for heterogeneity

Dynamic optimization methods have become increasingly important over the last years in economics. Within the dynamic optimization techniques employed, optimal control has emerged as the most powerful tool for the theoretical economic analysis. However, there is the need to advance further and take account that many dynamic economic processes are, in addition, dependent on some other parameter different than time. One can think of relaxing the assumption of a representative (homogeneous) agent in macro- and micro-economic applications allowing for heterogeneity among the agents. For instance, the optimal adaptation and diffusion of a new technology over time, may depend on the age of the person that adopted the new technology. Therefore, the economic models must take account of heterogeneity conditions within the dynamic framework. This thesis intends to accomplish two goals. The first goal is to analyze and revise existing environmental policies that focus on defining the optimal management of natural resources over time, by taking account of the heterogeneity of environmental conditions. Thus, the thesis makes a policy orientated contribution in the field of environmental policy by defining the necessary changes to transform an environmental policy based on the assumption of homogeneity into an environmental policy which takes account of heterogeneity. As a result the newly defined environmental policy will be more efficient and likely also politically more acceptable since it is tailored more specifically to the heterogeneous environmental conditions. Additionally to its policy orientated contribution, this thesis aims making a methodological contribution by applying a new optimization technique for solving problems where the control variables depend on two or more arguments --- the so-called two-stage solution approach ---, and by applying a numerical method --- the Escalator Boxcar Train Method --- for solving distributed optimal control problems, i.e., problems where the state variables, in addition to the control variables, depend on two or more arguments. Chapter 2 presents a theoretical framework to determine optimal resource allocation over time for the production of a good by heterogeneous producers, who generate a stock externalit and derives government policies to modify the behavior of competitive producers in order to achieve optimality. Chapter 3 illustrates the method in a more specific context, and integrates the aspects of quality and time, presenting a theoretical model that allows to determine the socially optimal outcome over time and space for the problem of waterlogging in irrigated agricultural production. Chapter 4 of this thesis concentrates on forestry resources and analyses the optimal selective-logging regime of a size-distributed forest.

Power allocation strategies for distributed space-time codes in two-way relay networks

We study a two-way relay network (TWRN), where distributed space-time codes are constructed across multiple relay terminals in an amplify-and-forward mode. Each relay transmits a scaled linear combination of its received symbols and their conjugates,with the scaling factor chosen based on automatic gain control. We consider equal power allocation (EPA) across the relays, as well as the optimal power allocation (OPA) strategy given access to instantaneous channel state information (CSI). For EPA, we derive an upper bound on the pairwise-error-probability (PEP), from which we prove that full diversity is achieved in TWRNs. This result is in contrast to one-way relay networks, in which case a maximum diversity order of only unity can be obtained. When instantaneous CSI is available at the relays, we show that the OPA which minimizes the conditional PEP of the worse link can be cast as a generalized linear fractional program, which can be solved efficiently using the Dinkelback-type procedure.We also prove that, if the sum-power of the relay terminals is constrained, then the OPA will activate at most two relays.

Risk allocation in public-private partnership projects : an innovative model with an intelligent approach

Both the increasing private participation in public projects and the critical importance of appropriate risk allocation to the success of Public-private partnership (PPP) projects justify specific research on how to establish effective risk allocation strategies in PPP projects. Partner’s risk management capability is currently the main concern to risk allocation in PPP projects. Following the transaction cost economics, it is argued that factors such as partner’s commitment and risk management structure should be considered simultaneously in order to develop effective risk allocation strategies. Based on the holistic capability-commitment governance-driven view, this paper proposed a model for generating an optimal risk allocation strategy in PPP projects. The model is demonstrated and described. An artificial intelligent technique integrated with fuzzy logic for model testing and validation is then introduced and justified. The innovative model is expected to provide a logical and complete understanding of the risk allocation strategy selection process, and to provide stakeholders with a richer framework than previously existing ones to guide their decision-making on risk allocation strategies.

Interjurisdictional allocation of multinational banking income : aligning taxation principles with economic activity

This thesis argues that one type of multinational entity – the multinational bank – poses particularly significant challenges to the international tax regime in terms of its current profit allocation rules. Multinational banks are a unique subset of multinational entities, and as a consequence of their unique traits, the traditional international tax regime foes not yield an optimal interjurisdictional allocation of taxing rights. The opportunity for tax minimisation, achievable because of the unique traits, and realised through exploitation of the traditional source and transfer pricing regime, results in a jurisdictional distribution of taxing rights which does not reflect economic reality. There are two distinct ways in which the traditional international tax regime fails to reflect economic activity. The first way that economic activity may not be reflected in the distribution of the taxing rights to income from multinational banking is through the application of traditional source rules. The traditional sources rules allocate income where transactions are completed rather than where the intermediation services are arranged. As a result of their unique commercial role as financial intermediaries, by separating intermediary economic activity from legal transactions with third parties, multinational banks may distort the true location of the activity giving rise to income. The second way in which the traditional tax regime may fail to reflect economic activity is through the traditional transfer pricing regime requiring related or internal transaction to be undertaken at an arm’s length price. The arm’s length pricing requirement is theoretically deficient in its failure to recognise the highly integrated nature of multinational banking. In practice, the arm’s length pricing requirement is also difficult, if not impossible, to apply to multinational banks because of the requirement of comparability. The difficulties associated with the current model have resulted in a subtle move by multinational banks towards global formulary apportionment. This thesis concludes that, for the international taxation of multinational banks, the current source regime should be replaced with a system that allocates profits for tax purposes on the basis of income source, with source determined using a unitary taxation or global formulary apportionment system. It is argued that global formulary apportionment is a theoretically superior model that provides both jurisdiction to tax and allocated profits on the basis of the economic activity that generates the income.