Plan dachi obrazovannoĭ iz Kolfondov chasti Nº 387 i NºNº 389, 390, 392 i 466, Odesskŏi gubernii Khersoskogo okruga, Snigirskogo raĭona i Nº398 Khersonskogo raĭna razverstannoi na optimalʻnye uchastki

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Optimal popular matchings

In this paper we consider the problem of computing an “optimal” popular matching. We assume that our input instance View the MathML source admits a popular matching and here we are asked to return not any popular matching but an optimal popular matching, where the definition of optimality is given as a part of the problem statement; for instance, optimality could be fairness in which case we are required to return a fair popular matching. We show an O(n2+m) algorithm for this problem, assuming that the preference lists are strict, where m is the number of edges in G and n is the number of applicants.

Optimal maintenance and replacement via a semi-Markov decision model

Optimal bang-coast maintenance policies for a machine, subject to failure, are considered. The approach utilizes a semi-Markov model for the system. A simplified model for modifying the probability of machine failure with maintenance is employed. A numerical example is presented to illustrate the procedure and results.

Measuring cost and affordability of healthy and less healthy diet globally

The INFORMAS food prices module proposes a step-wise framework to measure the cost and affordability of population diets. The price differential and the tax component of healthy and less healthy foods, food groups, meals and diets will be benchmarked and monitored over time. Results can be used to model or assess the impact of fiscal policies, such as ‘fat taxes’ or subsidies. Key methodological challenges include: defining healthy and less healthy foods, meals, diets and commonly consumed items; including costs of alcohol, takeaways, convenience foods and time; selecting the price metric; sampling frameworks; and standardizing collection and analysis protocols. The minimal approach uses three complementary methods to measure the price differential between pairs of healthy and less healthy foods. Specific challenges include choosing policy relevant pairs and defining an anchor for the lists. The expanded approach measures the cost of a healthy diet compared to the current (less healthy) diet for a reference household. It requires dietary principles to guide the development of the healthy diet pricing instrument and sufficient information about the population’s current intake to inform the current (less healthy) diet tool. The optimal approach includes measures of affordability and requires a standardised measure of household income that can be used for different countries. The feasibility of implementing the protocol in different countries is being tested in New Zealand, Australia and Fiji. The impact of different decision points to address challenges will be investigated in a systematic manner. We will present early insights and results from this work.

Optimal adaptive sequential spatial sampling of soil using pair-copulas

A spatial sampling design that uses pair-copulas is presented that aims to reduce prediction uncertainty by selecting additional sampling locations based on both the spatial configuration of existing locations and the values of the observations at those locations. The novelty of the approach arises in the use of pair-copulas to estimate uncertainty at unsampled locations. Spatial pair-copulas are able to more accurately capture spatial dependence compared to other types of spatial copula models. Additionally, unlike traditional kriging variance, uncertainty estimates from the pair-copula account for influence from measurement values and not just the configuration of observations. This feature is beneficial, for example, for more accurate identification of soil contamination zones where high contamination measurements are located near measurements of varying contamination. The proposed design methodology is applied to a soil contamination example from the Swiss Jura region. A partial redesign of the original sampling configuration demonstrates the potential of the proposed methodology.

Constrained linear filter and its relation to singular optimal control

This paper presents an analysis of an optimal linear filter in the presence of constraints on the moan squared values of the estimates from the viewpoint of singular optimal control. The singular arc has been shown to satisfy the generalized Legcndrc-Clebseh condition and Jacobson's condition. Both the cases of white measurement noise and coloured measurement noise are considered. The constrained estimate is shown to be a linear transformation of the unconstrained Kalman estimate.

Optimal maintenance policy for equipment subject to random deterioration and random failure A modern control theory approach.

The stochastic version of Pontryagin's maximum principle is applied to determine an optimal maintenance policy of equipment subject to random deterioration. The deterioration of the equipment with age is modelled as a random process. Next the model is generalized to include random catastrophic failure of the equipment. The optimal maintenance policy is derived for two special probability distributions of time to failure of the equipment, namely, exponential and Weibull distributions Both the salvage value and deterioration rate of the equipment are treated as state variables and the maintenance as a control variable. The result is illustrated by an example

An Optimal Mechanism for Sponsored Search Auctions on the Web and Comparison With Other Mechanisms

In this paper, we first describe a framework to model the sponsored search auction on the web as a mechanism design problem. Using this framework, we describe two well-known mechanisms for sponsored search auction-Generalized Second Price (GSP) and Vickrey-Clarke-Groves (VCG). We then derive a new mechanism for sponsored search auction which we call optimal (OPT) mechanism. The OPT mechanism maximizes the search engine's expected revenue, while achieving Bayesian incentive compatibility and individual rationality of the advertisers. We then undertake a detailed comparative study of the mechanisms GSP, VCG, and OPT. We compute and compare the expected revenue earned by the search engine under the three mechanisms when the advertisers are symmetric and some special conditions are satisfied. We also compare the three mechanisms in terms of incentive compatibility, individual rationality, and computational complexity. Note to Practitioners-The advertiser-supported web site is one of the successful business models in the emerging web landscape. When an Internet user enters a keyword (i.e., a search phrase) into a search engine, the user gets back a page with results, containing the links most relevant to the query and also sponsored links, (also called paid advertisement links). When a sponsored link is clicked, the user is directed to the corresponding advertiser's web page. The advertiser pays the search engine in some appropriate manner for sending the user to its web page. Against every search performed by any user on any keyword, the search engine faces the problem of matching a set of advertisers to the sponsored slots. In addition, the search engine also needs to decide on a price to be charged to each advertiser. Due to increasing demands for Internet advertising space, most search engines currently use auction mechanisms for this purpose. These are called sponsored search auctions. A significant percentage of the revenue of Internet giants such as Google, Yahoo!, MSN, etc., comes from sponsored search auctions. In this paper, we study two auction mechanisms, GSP and VCG, which are quite popular in the sponsored auction context, and pursue the objective of designing a mechanism that is superior to these two mechanisms. In particular, we propose a new mechanism which we call the OPT mechanism. This mechanism maximizes the search engine's expected revenue subject to achieving Bayesian incentive compatibility and individual rationality. Bayesian incentive compatibility guarantees that it is optimal for each advertiser to bid his/her true value provided that all other agents also bid their respective true values. Individual rationality ensures that the agents participate voluntarily in the auction since they are assured of gaining a non-negative payoff by doing so.

A Modified Dubins Method for Optimal Path Planning of a Miniature Air Vehicle Converging to a Straight Line Path

This paper presents a Dubins model based strategy to determine the optimal path of a Miniature Air Vehicle (MAV), constrained by a bounded turning rate, that would enable it to fly along a given straight line, starting from an arbitrary initial position and orientation. The method is then extended to meet the same objective in the presence of wind which has a magnitude comparable to the speed of the MAV. We use a modification of the Dubins' path method to obtain the complete optimal solution to this problem in all its generality.

Determination of optimal trajectory under design constraints for a satellite launch vehicle

An optimal pitch steering programme of a solid-fuel satellite launch vehicle to maximize either (1) the injection velocity at a given altitude, or (2) the size of circular orbit, for a given payload is presented. The two-dimensional model includes the rotation of atmosphere with the Earth, the vehicle's lift and drag, variation of thrust with time and altitude, inverse-square gravitational field, and the specified initial vertical take-off. The inequality constraints on the aerodynamic load, control force, and turning rates are also imposed. Using the properties of the central force motion the terminal constraint conditions at coast apogee are transferred to the penultimate stage burnout. Such a transformation converts a time-free problem into a time-fixed one, reduces the number of terminal constraints, improves accuracy, besides demanding less computer memory and time. The adjoint equations are developed in a compact matrix form. The problem is solved on an IBM 360/44 computer using a steepest ascent algorithm. An illustrative analysis of a typical launch vehicle establishes the speed of convergence, and accuracy and applicability of the algorithm.

Optimal iterative schemes for computing the Moore-Penrose matrix inverse

Among the iterative schemes for computing the Moore — Penrose inverse of a woll-conditioned matrix, only those which have an order of convergence three or two are computationally efficient. A Fortran programme for these schemes is provided.

Influence of adhesive non-linearities on the performance and optimal length of adhesive bonded joints

An analytical study for the static strength of adhesive lap joints is presented. The earlier solutions of Volkersen [i], DeBruyne[2] and others were limited to linear adhesives. The influence of adhesive non-linearity was first considered by Grimes' et al[3] and Dickson et al [4]. Recently Hart-Smith[5] successfully introduced elastic-plastic behaviour of the adhesive. In the present study the problem is formulated for general non-linear adhesive behaviour and an efficient numerical algorithm is written for the solution. Bilinear and trilinear models for the nonlinearity yield closed form analytical solutions.

A model for determining the optimal project life span and concession period of BOT projects

The concession agreement is the core feature of BOT projects, with the concession period being the most essential feature in determining the time span of the various rights, obligations and responsibilities of the government and concessionaire. Concession period design is therefore crucial for financial viability and determining the benefit/cost allocation between the host government and the concessionaire. However, while the concession period and project life span are essentially interdependent, most methods to date consider their determination as contiguous events that are determined exogenously. Moreover, these methods seldom consider the, often uncertain, social benefits and costs involved that are critical in defining, pricing and distributing benefits and costs between the various parties and evaluating potentially distributable cash flows. In this paper, we present the results of the first stage of a research project aimed at determining the optimal build-operate-transfer (BOT) project life span and concession period endogenously and interdependently by maximizing the combined benefits of stakeholders. Based on the estimation of the economic and social development involved, a negotiation space of the concession period interval is obtained, with its lower boundary creating the desired financial return for the private investors and its upper boundary ensuring the economic feasibility of the host government as well as the maximized welfare within the project life. The outcome of the new quantitative model is considered as a suitable basis for future field trials prior to implementation. The structure and details of the model are provided in the paper with Hong Kong tunnel project as a case study to demonstrate its detailed application. The basic contributions of the paper to the theory of construction procurement are that the project life span and concession period are determined jointly and the social benefits taken into account in the examination of project financial benefits. In practical terms, the model goes beyond the current practice of linear-process thinking and should enable engineering consultants to provide project information more rationally and accurately to BOT project bidders and increase the government's prospects of successfully entering into a contract with a concessionaire. This is expected to generate more negotiation space for the government and concessionaire in determining the major socioeconomic features of individual BOT contracts when negotiating the concession period. As a result, the use of the model should increase the total benefit to both parties.

Trajectory sensitivity modification in optimal linear systems

A new procedure for reducing trajectory sensitivity for the optimal linear regulator is described. The design is achieved without increase in the order of optimization and without the feedback of trajectory sensitivity. The procedure is also used in the input signal design problem for linear system identification by interpreting it as increasing trajectory sensitivity with respect to parameters to be estimated.

A closed-form optimal tuning of mass dampers for one degree-of-freedom systems under rotating unbalance forcing

This paper is focused on the study of a vibrating system forced by a rotating unbalance and coupled to a tuned mass damper (TMD). The analysis of the dynamic response of the entire system is used to define the parameters of such device in order to achieve optimal damping properties. The inertial forcing due to the rotating unbalance depends quadratically on the forcing frequency and it leads to optimal tuning parameters that differ from classical values obtained for pure harmonic forcing. Analytical results demonstrate that frequency and damping ratios, as a function of the mass parameter, should be higher than classical optimal parameters. The analytical study is carried out for the undamped primary system, and numerically investigated for the damped primary system. We show that, for practical applications, proper TMD tuning allows to achieve a reduction in the steady-state response of about 20% with respect to the response achieved with a classically tuned damper. Copyright © 2015 by ASME.