multimodality image registration by maximization of mutual information a new approach to the problem of multimodality medical image registration is proposed using a basic concept from information theory mutual information mi or relative entropy as a new matching criterion the method presented in this paper applies mi to measure the statistical dependence or information redundancy between the image intensities of corresponding voxels in both images which is assumed to be maximal if the images are geometrically aligned maximization of mi is a very general and powerful criterion because no assumptions are made regarding the nature of this dependence and no limiting constraints are imposed on the image content of the modalities involved the accuracy of the mi criterion is validated for rigid body registration of computed tomography ct magnetic resonance mr and photon emission tomography pet images by comparison with the stereotactic registration solution while robustness is evaluated with respect to implementation issues such as interpolation and optimization and image content including partial overlap and image degradation our results demonstrate that subvoxel accuracy with respect to the stereotactic reference solution can be achieved completely automatically and without any prior segmentation feature extraction or other preprocessing steps which makes this method very well suited for clinical applications

an exposition of the ahp in reply to the paper remarks on the analytic hierarchy process it is a fact that people make decisions and have been making decisions for a very long time contrary to what some of us who are interested in decision making may like to believe most people do not take seriously the existence of theories which purport to set their thinking and feeling right they claim to know their own value system and what they want they may wonder how anyone else can know well enough to tell them how best to organize their thinking in order to make better choices yet research has shown that complex decisions are beyond the capacity of the brain to synthesize intuitively and efficiently since decision making is a natural characteristic of people how do we describe what they do so that an ordinary mortal can understand what we are saying we do not wish to legislate the method with which people should make decisions but only to describe it even when it is prescribed by some method in the process we may learn things that can help people make better decisions how the analytic hierarchy process ahp forman et al harker 1986 harker and vargas 1987 saaty 1986 1988a b saaty and vargas 1987 xu 1988 golden et al 1989 saaty and alexander 1989 is a theory of measurement when applied in decision making it assists one to describe the general decision operation by decomposing a complex problem into a multi level hierarchic structure of objectives criteria subcriteria and alternatives the ahp provides a fundamental scale of relative magnitudes expressed in dominance units to represent judgments in the form of paired comparisons a ratio scale of relative magnitudes expressed in priority units is then derived from each set of comparisons an overall rcatio scale of priorities is then synthesized to obtain a ranking of the alternatives from its axioms to its procedures the ahp has turned out to be historically and theoretically a different and independent theory of decision making from utility theory much as a dialogue evolved in mathematics around the consistency of different geometries and around absolute and relative space and time in physics both to dispel absolute notions those who believe that only utility theory can tell us the absolute truth about man s decision making might take a close look at the ahp it has found varied and serious applications it also has a particular way of generating ratio scales and dealing with inconsistency in judgment that have contributed to its effectiveness in resource allocation and in the setting of priorities by a group of decision makers utility theory is a normative process the ahp as a descriptive theory encompasses procedures leading to outcomes as would be ranked by a normative theory but it must go beyond to deal with outcomes not accounted for by the demanding assumptions of a normative theory we must briefly describe the ahp to enable the reader to see that a practicable theory based on ratio scales need not dilute itself to satisfy expectations of people who derive their understanding from a theory based on interval scales this is particularly true if the rival theory in aspiring for generality also makes unrealistic assumptions for example about the transitivity and consistency of preferences and the difficult use of lotteries

stereo without epipolar lines a maximum flow formulation this paper describes a new algorithm for solving the stereo correspondence problem with a global 2 d optimization by transforming it into a maximum flow problem in a graph this transformation effectively removes explicit use of epipolar geometry thus allowing direct use of multiple cameras with arbitrary geometries the maximum flow solved both efficiently and globally yields a minimum cut that corresponds to a disparity surface for the whole image at once this global and efficient approach to stereo analysis allows the reconstruction to proceed in an arbitrary volume of space and provides a more accurate and coherent depth map than the traditional stereo algorithms in particular smoothness is applied uniformly instead of only along epipolar lines while the global optimality of the depth surface is guaranteed results show improved depth estimation as well as better handling of depth discontinuities while the worst case running time is o n 1 5 d 1 5 log nd the observed average running time is o n 1 2 d 1 3 for an image size of n pixels and depth resolution d

ranking with partial information a method and an application a method is presented for ranking multiattributed alternatives using a weighted additive evaluation function with partial information about the weighting scaling constants the method is applied to evaluate materials for use in nuclear waste containment the paper derives conditions to determine whether a pair of alternatives can be ranked given the partial information about weighting constants and presents an algorithm that partially rank orders the complete set of alternatives based on the pairwise ranking information

asynchronous iterative water filling for gaussian frequency selective interference channels this paper considers the maximization of information rates for the gaussian frequency selective interference channel subject to power and spectral mask constraints on each link to derive decentralized solutions that do not require any cooperation among the users the optimization problem is formulated as a static noncooperative game of complete information to achieve the so called nash equilibria of the game we propose a new distributed algorithm called asynchronous iterative water filling algorithm in this algorithm the users update their power spectral density psd in a completely distributed and asynchronous way some users may update their power allocation more frequently than others and they may even use outdated measurements of the received interference the proposed algorithm represents a unified framework that encompasses and generalizes all known iterative water filling algorithms e g sequential and simultaneous versions the main result of the paper consists of a unified set of conditions that guarantee the global converge of the proposed algorithm to the unique nash equilibrium of the game

preference assessment by imprecise ratio statements the pairs method developed in this paper introduces imprecise preference statements into value trees the assessment of attribute weights in pairs extends the well known smart technique so that in addition to exact statements the decision maker can enter interval judgments which indicate ranges for the relative importance of the attributes the interval judgments and the possibly range valued information about the outcomes of the alternatives are processed with linear programming into value intervals and dominance relations as the decision maker refines the description of his preferences either by entering new statements or by tightening his earlier judgments these results become more detailed and convey more information about which alternatives are preferred throughout the interactive refinement process pairs supports the decision maker by deriving and displaying the consequences of his earlier judgments

a fuzzy extension of saaty s priority theory we present a fuzzy method for choosing among a number of alternatives under conflicting decision criteria a fuzzy version of saaty s pairwise comparison method 1980 extended by de graan 1980 and lootsma 1981 each ratio expressing the relative significance of a pair of factors is displayed in a matrix from which suitable weights can be extracted since these ratios are essentially fuzzy they express the opinion of a decision maker on the importance of a pair of factors we have adapted the above mentioned method in such a way that decision makers are asked to express their opinions in fuzzy numbers with triangular membership functions we apply the method at two distinct levels first to find fuzzy weights for the decision criteria and second to find fuzzy weights for the alternatives under each of the decision criteria by a suitable combination of these results we obtain fuzzy scores for the alternatives as well as their sensitivities using these fuzzy scores the decision makers should be able to make a choice for one of the alternatives

on the variational equilibrium as a refinement of the generalized nash equilibrium we are concerned with a class of games in which the players strategy sets are coupled by a shared constraint a widely employed solution concept for such generalized nash games is the generalized nash equilibrium gne the variational equilibrium ve facchinei kanzow 2007 is a specific kind of gne characterized by the solution of the variational inequality formed from the common constraint and the mapping of the gradients of player objectives our contribution is a theory that provides sufficient conditions for ensuring that the existence of a gne implies the existence of a ve in such an instance the ve is said to be a refinement of the gne for certain games these conditions are shown to be necessary this theory rests on a result showing the equality of the brouwer degree of two suitably defined functions whose zeros are the gne and ve respectively this theory has a natural extension to the primal dual space of strategies and lagrange multipliers corresponding to the shared constraint our results unify some known results pertaining to such equilibria and provide mathematical substantiation for ideas that were known to be appealing to economic intuition

asymmetric variational inequality problems over product sets applications and iterative methods in this paper we i describe how several equilibrium problems can be uniformly modelled by a finite dimensional asymmetric variational inequality defined over a cartesian product of sets and ii investigate the local and global convergence of various iterative methods for solving such a variational inequality problem because of the special cartesian product structure these iterative methods decompose the original variational inequality problem into a sequence of simpler variational inequality subproblems in lower dimensions the resulting decomposition schemes often have a natural interpretation as some adjustment processes

further developments and tests of a progressive algorithm for multiple criteria decision making p korhonen h moskowitz and j wallenius 1986 developed a progressive algorithm and the supporting theory for modeling and solving multiple criteria decision problems with discrete alternatives a special feature of the algorithm is that it relaxes the usual assumption of a fixed set of available decision alternatives and complete knowledge of a decision maker s dm s preference structure or value function the algorithm is based on progressively sampling the decision space obtaining preference information from the dm determining the likelihood of finding possibly surely better alternatives and based on this information continuing the search or terminating it by making the final choice we describe a computerized implementation and extensive computational tests of the algorithm as well as some of our experiences in applying and field testing it in practice we also consider several improvements and developments of the algorithm to further facilitate its use in practice

hammer hierarchical attribute matching mechanism for elastic registration a new approach is presented for elastic registration of medical images and is applied to magnetic resonance images of the brain experimental results demonstrate very high accuracy in superposition of images from different subjects there are two major novelties in the proposed algorithm first it uses an attribute vector i e a set of geometric moment invariants gmis that are defined on each voxel in an image and are calculated from the tissue maps to reflect the underlying anatomy at different scales the attribute vector if rich enough can distinguish between different parts of an image which helps establish anatomical correspondences in the deformation procedure it also helps reduce local minima by reducing ambiguity in potential matches this is a fundamental deviation of our method referred to as the hierarchical attribute matching mechanism for elastic registration hammer from other volumetric deformation methods which are typically based on maximizing image similarity second in order to avoid being trapped by local minima i e suboptimal poor matches hammer uses a successive approximation of the energy function being optimized by lower dimensional smooth energy functions which are constructed to have significantly fewer local minima this is achieved by hierarchically selecting the driving features that have distinct attribute vectors thus drastically reducing ambiguity in finding correspondence a number of experiments demonstrate that the proposed algorithm results in accurate superposition of image data from individuals with significant anatomical differences

a generalized iterative water filling algorithm for distributed power control in the presence of a jammer consider a scenario in which k users and a jammer share a common spectrum of n orthogonal tones both the users and the jammer have limited power budgets the goal of each user is to allocate its power across the n tones in such a way that maximizes the total sum rate that he she can achieve while treating the interference of other users and the jammer s signal as additive gaussian noise the jammer on the other hand wishes to allocate its power in such a way that minimizes the utility of the whole system that being the total sum of the rates communicated over the network for this noncooperative game we propose a generalized version of the existing iterative water filling algorithm whereby the users and the jammer update their power allocations in a greedy manner we study the existence of a nash equilibrium of this noncooperative game as well as conditions under which the generalized iterative water filling algorithm converges to a nash equilibrium of the game the conditions that we derive in this paper depend only on the system parameters and hence can be checked a priori simulations show that when the convergence conditions are violated the presence of a jammer can cause the otherwise convergent iterative water filling algorithm to oscillate

minimizing nonsubmodular functions with graph cuts a review optimization techniques based on graph cuts have become a standard tool for many vision applications these techniques allow to minimize efficiently certain energy functions corresponding to pairwise markov random fields mrfs currently there is an accepted view within the computer vision community that graph cuts can only be used for optimizing a limited class of mrf energies e g submodular functions in this survey we review some results that show that graph cuts can be applied to a much larger class of energy functions in particular nonsubmodular functions while these results are well known in the optimization community to our knowledge they were not used in the context of computer vision and mrf optimization we demonstrate the relevance of these results to vision on the problem of binary texture restoration

joint sensing and power allocation in nonconvex cognitive radio games quasi nash equilibria in this paper we propose a novel class of nash problems for cognitive radio cr networks composed of multiple primary users pus and secondary users sus wherein each su player competes against the others to maximize his own opportunistic throughput by choosing jointly the sensing duration the detection thresholds and the vector power allocation over a multichannel link in addition to power budget constraints several deterministic or probabilistic interference constraints can be accommodated in the proposed general formulation such as constraints on the maximum individual aggregate probabilistic interference tolerable from the pus to keep the optimization as decentralized as possible global interference constraints when present are imposed via pricing the prices are thus additional variables to be optimized the resulting players optimization problems are nonconvex and there are price clearance conditions associated with the nonconvex global interference constraints to be satisfied by the equilibria of the game which make the analysis of the proposed game a challenging task none of classical results in the game theory literature can be successfully applied to deal with the nonconvexity of the game we introduce a relaxed equilibrium concept the quasi nash equilibrium qne and study its main properties performance and connection with local nash equilibria quite interestingly the proposed game theoretical formulations yield a considerable performance improvement with respect to current centralized and decentralized designs of cr systems which validates the concept of qne

remarks on the analytic hierarchy process the analytic hierarchy process ahp is flawed as a procedure for ranking alternatives in that the rankings produced by this procedure are arbitrary this paper provides a brief review of several areas of operational difficulty with the ahp and then focuses on the arbitrary rankings that occur when the principle of hierarchic composition is assumed this principle requires that the weights on the higher levels of a hierarchy can be determined independently of the weights on the lower levels virtually all of the published examples of the use of the ahp to evaluate alternatives relative to a set of criteria have assumed this principle the key to correcting this flaw is the synthesis of the ahp with the concepts of multiattribute utility theory

distributed power allocation with rate constraints in gaussian parallel interference channels this paper considers the minimization of transmit power in gaussian parallel interference channels subject to a rate constraint for each user to derive decentralized solutions that do not require any cooperation among the users we formulate this power control problem as a generalized nash equilibrium ne game we obtain sufficient conditions that guarantee the existence and nonemptiness of the solution set to our problem then to compute the solutions of the game we propose two distributed algorithms based on the single user water filling solution the sequential and the simultaneous iterative water filling algorithms wherein the users update their own strategies sequentially and simultaneously respectively we derive a unified set of sufficient conditions that guarantee the uniqueness of the solution and global convergence of both algorithms our results are applicable to all practical distributed multipoint to multipoint interference systems either wired or wireless where a quality of service in qos terms of information rate must be guaranteed for each link

dual methods for nonconvex spectrum optimization of multicarrier systems the design and optimization of multicarrier communications systems often involve a maximization of the total throughput subject to system resource constraints the optimization problem is numerically difficult to solve when the problem does not have a convexity structure this paper makes progress toward solving optimization problems of this type by showing that under a certain condition called the time sharing condition the duality gap of the optimization problem is always zero regardless of the convexity of the objective function further we show that the time sharing condition is satisfied for practical multiuser spectrum optimization problems in multicarrier systems in the limit as the number of carriers goes to infinity this result leads to efficient numerical algorithms that solve the nonconvex problem in the dual domain we show that the recently proposed optimal spectrum balancing algorithm for digital subscriber lines can be interpreted as a dual algorithm this new interpretation gives rise to more efficient dual update methods it also suggests ways in which the dual objective may be evaluated approximately further improving the numerical efficiency of the algorithm we propose a low complexity iterative spectrum balancing algorithm based on these ideas and show that the new algorithm achieves near optimal performance in many practical situations

distributed computation of equilibria in misspecified convex stochastic nash games the distributed computation of nash equilibria is assuming growing relevance in engineering where such problems emerge in the context of distributed control accordingly we present schemes for computing equilibria of two classes of static stochastic convex games complicated by a parametric misspecification a natural concern in the control of large scale networked engineered system in both schemes players learn the equilibrium strategy while resolving the misspecification 1 monotone stochastic nash games we present a set of coupled stochastic approximation schemes distributed across agents in which the first scheme updates each agent s strategy via a projected stochastic gradient step whereas the second scheme updates every agent s belief regarding its misspecified parameter using an independently specified learning problem we proceed to show that the produced sequences converge in an almost sure sense to the true equilibrium strategy and the true parameter respectively surprisingly convergence in the equilibrium strategy achieves the optimal rate of convergence in a mean squared sense with a quantifiable degradation in the rate constant 2 stochastic nash cournot games with unobservable aggregate output we refine 1 to a cournot setting where we assume that the tuple of strategies is unobservable while payoff functions and strategy sets are public knowledge through a common knowledge assumption by utilizing observations of noise corrupted prices iterative fixed point schemes are developed allowing for simultaneously learning the equilibrium strategies and the misspecified parameter in an almost sure sense

extended methods for identifying dominance and potential optimality in multi criteria analysis with imprecise information abstract many of the recent prescriptive approaches to multi attribute decision analysis have dealt with situations in which trade off weights are known imprecisely while marginal values are known exactly a way to handle such problems is to utilize a linear programming technique from which non dominated and or potentially optimal score vectors can be obtained in some attributes however it is not easy for decision makers to provide the marginal value functions that are explicit and exact the purpose of this paper is to address problems such that the both attribute weights and marginal values are known imprecisely we then assume without loss of generality that these imprecise information on both weights and values are in the form of inequalities and or equalities such as rankings and bounds the first formulations for checking dominance and potential optimality become non linear programming problems hard to be solved generally we thus present how these non linear problems are reduced to linear programming equivalents

a novel learning based dissimilarity metric for rigid and non rigid medical image registration by using bhattacharyya distances image registration is one of the major technologies of the medical image processing and analysis according to the nature of the transformation image registration can be categorized into two main classes rigid registration and non rigid registration in this paper a novel learning based dissimilarity metric and its approximation are proposed and respectively adopted to the rigid and non rigid registration of medical images this novel metric utilizes bhattacharyya distances to measure the dissimilarity of the testing image pairs by incorporating the expected intensity distributions which is learnt from the registered training image pairs in order to test the robustness and accuracy of the proposed metric in the multi modal rigid registration one thousand eight hundred randomized ctt1 registrations were performed and evaluated by the retrospective image registration evaluation rire project for the non rigid registration the approximation of the proposed dissimilarity metric is adopted with the markov random field mrf modeled non rigid registration approach non rigid registration experiments of 2d synthetic images with artificial deformation fields and 3d images from the simulated brain database were performed and evaluated respectively in this paper the experimental results of both rigid and non rigid medical image registrations demonstrated that the proposed dissimilarity metric outperforms the state of the art approach mutual information and the close related approach kullbackleibler distances highlightswe propose a novel learning based dissimilarity metric for both rigid and non rigid medical image registrations the novel dissimilarity metric is based on the bhattacharyya distance a lot of experiments were done to evaluate our method in term of accuracy and robustness we compared the proposed method with state of the art methods of both rigid and non rigid image registration our method is more robust against different challenging cases with consistently higher accuracy

existence of generalized equilibria we consider the problem of the existence of equilibria generalized equilibria and 8xed points of a correspondence f de8ned on a compact subset m of rn with values in rn when the set m is neither assumed to be convex nor smooth 1 the general framework of the article is the following let f be a correspondence from m to rn that is a map from m to the set of all the subsets of rn the correspondence f is said to be upper semicontinuous u s c if the set x m f x v is open in m for every open set v rn let n be a normal cone correspondence i e at this stage n is a correspondence from m to rn such that for every x m n x

preference programming through approximate ratio comparisons abstract in the context of hierarchical weighting this paper operationalizes interval judgments which allow the decision maker to enter ambiguous preference statements by indicating the relative importance of factors as intervals of values on a ratio scale through such judgments the decision maker can capture the subjective uncertainty in his preferences and thus avoid the often cumbersome elicitation of exact ratio estimates after each new statement the interval judgments are synthesized into dominance relations on the alternatives by solving a series of linear programming problems this leads to an interactive process of preference programming which provides more detailed results as the decision maker gradually enters a more specific preference description moreover the overall effort of preference elicitation is smaller than in the analytic hierarchy process because the most preferred alternative can usually be identified before all possible comparisons between pairs of factors have been completed

on the solution of affine generalized nash equilibrium problems with shared constraints by lemke s method affine generalized nash equilibrium problems agneps represent a class of non cooperative games in which players solve convex quadratic programs with a set of linear constraints that couple the players variables the generalized nash equilibria gne associated with such games are given by solutions to a linear complementarity problem lcp this paper treats a large subclass of agneps wherein the coupled constraints are shared by i e common to the players specifically we present several avenues for computing structurally different gne based on varying consistency requirements on the lagrange multipliers associated with the shared constraints traditionally variational equilibria ve have been amongst the more well studied gne and are characterized by a requirement that the shared constraint multipliers be identical across players we present and analyze a modification to lemke s method that allows us to compute gne that are not necessarily ve if successful the modified method computes a partial variational equilibrium characterized by the property that some shared constraints are imposed to have common multipliers across the players while other are not so imposed trajectories arising from regularizing the lcp formulations of agneps are shown to converge to a particular type of gne more general than rosen s normalized equilibrium that in turn includes a variational equilibrium as a special case a third avenue for constructing alternate gne arises from employing a novel constraint reformulation and parameterization technique the associated parametric solution method is capable of identifying continuous manifolds of equilibria numerical results suggest that the modified lemke s method is more robust than the standard version of the method and entails only a modest increase in computational effort on the problems tested finally we show that the conditions for applying the modified lemke s scheme are readily satisfied in a breadth of application problems drawn from communication networks environmental pollution games and power markets

fast approximate energy minimization via graph cuts many tasks in computer vision involve assigning a label such as disparity to every pixel a common constraint is that the labels should vary smoothly almost everywhere while preserving sharp discontinuities that may exist e g at object boundaries these tasks are naturally stated in terms of energy minimization the authors consider a wide class of energies with various smoothness constraints global minimization of these energy functions is np hard even in the simplest discontinuity preserving case therefore our focus is on efficient approximation algorithms we present two algorithms based on graph cuts that efficiently find a local minimum with respect to two types of large moves namely expansion moves and swap moves these moves can simultaneously change the labels of arbitrarily large sets of pixels in contrast many standard algorithms including simulated annealing use small moves where only one pixel changes its label at a time our expansion algorithm finds a labeling within a known factor of the global minimum while our swap algorithm handles more general energy functions both of these algorithms allow important cases of discontinuity preserving energies we experimentally demonstrate the effectiveness of our approach for image restoration stereo and motion on real data with ground truth we achieve 98 percent accuracy

distributed algorithms for aggregative games on graphs we consider a class of nash games termed as aggregative games being played over a networked system in an aggregative game a player s objective is a function of the aggregate of all the players decisions every player maintains an estimate of this aggregate and the players exchange this information with their local neighbors over a connected network we study distributed synchronous and asynchronous algorithms for information exchange and equilibrium computation over such a network under standard conditions we establish the almost sure convergence of the obtained sequences to the equilibrium point we also consider extensions of our schemes to aggregative games where the players objectives are coupled through a more general form of aggregate function finally we present numerical results that demonstrate the performance of the proposed schemes

variational convergence of bifunctions motivating applications it is shown that a number of variational and equilibrium problems can be cast as finding the maxinf points or minsup points of bivariate functions for short bifunctions these problems include linear and nonlinear complementarity problems fixed points variational inequalities inclusions noncooperative games and walras and nash equilibrium problems one appeals to the theory of lopsided convergence for bifunctions to derive stability results for each one of these problems

local indices for degenerate variational inequalities we provide an index formula for solutions of variational inequality problems defined by a continuously differentiable function f over a convex set m represented by a finite number of inequality constraints our index formula can be applied when the solutions are nonsingular and possibly degenerate as long as they also satisfy the injective normal map inm property which is implied by strong stability we show that when the inm property holds the degeneracy in a solution can be removed by perturbing the function f slightly i e the index of a degenerate solution is equal to the index of a nondegenerate solution of a slightly perturbed variational inequality problem we further show that our definition of the index is equivalent to the topological index of the normal map at the zero corresponding to the solution as an application of our index formula we provide a global index theorem for variational inequalities which holds even when the solutions are degenerate

optimal linear precoding strategies for wideband noncooperative systems based on game theory part i nash equilibria in this two part paper we propose a decentralized strategy based on a game theoretic formulation to find out the optimal precoding multiplexing matrices for a multipoint to multipoint communication system composed of a set of wideband links sharing the same physical resources i e time and bandwidth we assume as optimality criterion the achievement of a nash equilibrium and consider two alternative optimization problems 1 the competitive maximization of mutual information on each link given constraints on the transmit power and on the spectral mask imposed by the radio spectrum regulatory bodies and 2 the competitive maximization of the transmission rate using finite order constellations under the same constraints as above plus a constraint on the average error probability in this first part of the paper we start by showing that the solution set of both noncooperative games is always nonempty and contains only pure strategies then we prove that the optimal precoding multiplexing scheme for both games leads to a channel diagonalizing structure so that both matrix valued problems can be recast in a simpler unified vector power control game with no performance penalty thus we study this simpler game and derive sufficient conditions ensuring the uniqueness of the nash equilibrium interestingly although derived under stronger constraints incorporating for example spectral mask constraints our uniqueness conditions have broader validity than previously known conditions finally we assess the goodness of the proposed decentralized strategy by comparing its performance with the performance of a pareto optimal centralized scheme to reach the nash equilibria of the game in part ii we propose alternative distributed algorithms along with their convergence conditions

decision analysis with incomplete utility and probability information an approach to the solution of decision analysis problems under uncertainty with imprecise and incomplete information is presented the methodology is designed for cases in which payoffs conditional on the state of nature are known precisely but only limited or imprecise probability and utility information is available regarding a decision maker s beliefs and tastes a decision maker provides conditional payoffs optionally bounds on state probabilities bounds on the certainty equivalent for a simple lottery any known relationships between probabilities of states of nature and a series of strict preferences between pairs of vectors of conditional payoffs we assume an exponential utility function with unknown parameter the method proceeds by sequentially eliciting preferences new bounds on probabilities and or the certainty equivalent and new relationships among probabilities until the problem is solved the methodology is demonstrated through a two state and a three state example which illust

spatial oligopolistic equilibria with arbitrage shared resources and price function conjectures this paper considers equilibria among multiple firms that are competing non cooperatively against each other to sell electric power and buy resources needed to produce that power examples of such resources include fuels power plant sites and emissions allowances the electric power market is a spatial market on a network in which flows are constrained by kirchhoff s current and voltage laws arbitragers in the power market erase spatial price differences that are non cost based power producers can compete in power markets a la cournot game in quantities or in a generalization of the cournot game termed the conjectured supply function game in which they anticipate that rivals will respond to price changes in input markets producers either compete a la bertrand price taking behavior or they can conjecture that price will increase with consumption of the resource the simultaneous competition in power and input markets presents opportunities for strategic price behavior that cannot be analyzed using models of power markets alone depending on whether the producers treat the arbitrager endogenously or exogenously we derive two mixed nonlinear complementarity formulations of the oligopolistic problem we establish the existence and uniqueness of solutions as well as connections among the solutions to the model formulations a numerical example is provided for illustrative purposes

mrf based deformable registration and ventilation estimation of lung ct deformable image registration is an important tool in medical image analysis in the case of lung computed tomography ct registration there are three major challenges large motion of small features sliding motions between organs and changing image contrast due to compression recently markov random field mrf based discrete optimization strategies have been proposed to overcome problems involved with continuous optimization for registration in particular its susceptibility to local minima however to date the simplifications made to obtain tractable computational complexity reduced the registration accuracy we address these challenges and preserve the potentially higher quality of discrete approaches with three novel contributions first we use an image derived minimum spanning tree as a simplified graph structure which copes well with the complex sliding motion and allows us to find the global optimum very efficiently second a stochastic sampling approach for the similarity cost between images is introduced within a symmetric diffeomorphic b spline transformation model with diffusion regularization the complexity is reduced by orders of magnitude and enables the minimization of much larger label spaces in addition to the geometric transform labels hyper labels are introduced which represent local intensity variations in this task and allow for the direct estimation of lung ventilation we validate the improvements in accuracy and performance on exhale inhale ct volume pairs using a large number of expert landmarks

nash cournot equilibria in electric power markets with piecewise linear demand functions and joint constraints most previous nash cournot models of competition among electricity generators have assumed smooth demand price functions facilitating computation and proofs of existence and uniqueness however nonsmooth demand functions are an important feature of real power markets due for example to price caps and generator recognition of transmission constraints that limit exports a more general model of nash cournot competition on networks is proposed that accounts for these features by including 1 concave piecewise linear demand curves and 2 joint constraints that include variables from other generating companies within the profit maximization problems for individual generators the piecewise demand curves imply in general a nonmonotone multivalued variational inequality problem thus for instance imposition of a price cap can destroy the uniqueness properties found in previous models so that distinct solutions can yield different sets of profits for market participants the joint constraints turn the equilibrium problem into a quasi variational inequality which also can yield multiple solutions the formulation poses computational challenges that can cause lemke s algorithm to fail a restricted formulation is proposed that can be solved by that algorithm

nonconvex games with side constraints this paper develops an optimization based theory for the existence and uniqueness of equilibria of a noncooperative game wherein the selfish players optimization problems are nonconvex and there are side constraints and an associated price clearance to be satisfied by the equilibria a new concept of equilibrium for such a nonconvex game which we term a quasi nash equilibrium qne is introduced as a solution of the variational inequality vi obtained by aggregating the first order optimality conditions of the players problems while retaining the convex constraints if any in the defining set of the vi under a second order sufficiency condition from nonlinear programming a qne becomes a local nash equilibrium of the game uniqueness of a qne is established using a degree theoretic proof under a key boundedness property of the karush kuhn tucker multipliers of the nonconvex constraints and the positive definiteness of the hessians of the players lagrangian functions we establish the single valuedness of the players best response maps from which the existence of a nash equilibrium ne of the nonconvex game follows we also present a distributed algorithm for computing an ne of such a game and provide a matrix theoretic condition for the convergence of the algorithm an application is presented that pertains to a special multi leader follower game wherein the nonconvexity is due to the followers equilibrium conditions in the leaders optimization problems another application to a cognitive radio paradigm in a signal processing game is described in detail in g scutari and j s pang ieee trans inform theory submitted j s pang and g scutari joint ieee trans signal process submitted

non rigid image registration of brain magnetic resonance images using graph cuts we present a graph cuts based method for non rigid medical image registration on brain magnetic resonance images in this paper the non rigid medical image registration problem is reformulated as a discrete labeling problem based on a voxel to voxel intensity similarity measure each voxel in the source image is assigned a displacement label which represents a displacement vector indicating which position in the floating image it is spatially corresponding to in the proposed method a smoothness constraint based on the first derivative is used to penalize sharp changes in the adjacent displacement labels across voxels the image registration problem is therefore modeled by two energy terms based on intensity similarity and smoothness of the displacement field these energy terms are submodular and can be optimized by using the graph cuts method via email protected expansions which is a powerful combinatorial optimization tool and capable of yielding either a global minimum or a local minimum in a strong sense using the realistic brain phantoms obtained from the simulated brain database we compare the registration results of the proposed method with two state of the art medical image registration approaches free form deformation based method and demons method in addition the registration results are also compared with that of the linear programming based image registration method it is found that the proposed method is more robust against different challenging non rigid registration cases with consistently higher registration accuracy than those three methods and gives realistic recovered deformation fields

multiple criteria robust interactive decision analysis mcrid for optimizing public policies abstract important public policy decisions are often very complex involving many factors large uncertainties and multiple conflicting objectives decision analysis which is a formal framework for dealing with such issues has been applied to a variety of public sector problems over the last two decades a limitation of using decision analysis is the often onerous assessment burden it places on the decision maker dm we have developed a novel interactive procedure and decision support system dss for performing decision analysis on the personal computer called robust interactive decision analysis rid which avoids the difficult problems of precisely assessing a dm s utility and state probability functions associated with traditional decision treee analysis the rid method permits a dm to voluntarily and interactively express strong viz sure binary preferences for actions partial decision functions and full decision functions and only imprecise probability and utility function assessments the inputs are used with various dominance operators via a mathematical programming framework to prune the state probability utility and decision space until there is convergence on a relatively small subset of efficient strategies or an optimal choice strategy conceptually the operation of the rid method can be regarded as a state pruning system and its computer implementation as a dss in this paper we extended the rid concept and dss to deal with multiple criteria decisions obviating the need to precisely and completely assess attribute weights tradeoffs consequences and or value utility functions the approach which we call multiple criteria robust interactive decision analysis mcrid is developed illustrated and shown to be effective in eliminating many inefficient alternatives however since the aggregate utility of each alternative is interval valued it then becomes difficult to intuitively choose an optimal alternative from among the remaining efficient ones since the intervals are not defined by any specific probability distributions we have tentatively shown that aggregate utility intervals ultimately converge toward a normal density function and can be so approximated with relatively few attributes hence stochastic dominance is employed to further filter out alternatives an interactive goal programming gp technique is then developed to assist the dm in choosing an optimal alternative

real and complex monotone communication games noncooperative game theoretic tools have been increasingly used to study many important resource allocation problems in communications networking smart grids and portfolio optimization in this paper we consider a general class of convex nash equilibrium problems neps where each player aims at solving an arbitrary smooth convex optimization problem differently from most of current works we do not assume any specific structure for the players problems and we allow the optimization variables of the players to be matrices in the complex domain our main contribution is the design of a novel class of distributed asynchronous best response algorithms suitable for solving the proposed neps even in the presence of multiple solutions the new methods whose convergence analysis is based on variational inequality vi techniques can select among all the equilibria of a game those that optimize a given performance criterion at the cost of limited signaling among the players this is a major departure from existing best response algorithms whose convergence conditions imply the uniqueness of the ne some of our results hinge on the use of vi problems directly in the complex domain the study of these new kind of vis also represents a noteworthy innovative contribution we then apply the developed methods to solve some new generalizations of single input single output siso and multiple input multiple output mimo games in cognitive radio systems showing a considerable performance improvement over classical pure noncooperative schemes

partial information dominance and potential optimality in multiattribute utility theory when a multiattribute utility function is only partially specified by prior preference statements what can be said about the relative desirability of actual alternatives this question is addressed for the cases of additively separable cardinal utility with unknown scaling constants multiplicatively separable cardinal utility with unknown scaling constants and additively separable ordinal utility we review previous approaches and treat issues of consistency is the prior information consistent dominance does the prior preference information imply that one outcome is preferred to another and potential optimality are there utility functions of the given form consistent with prior preference information under which a particular outcome is preference optimal in the additive cases a key relationship between dominance and potential optimality may be derived the paper concludes by presenting an example application to a well known nuclear siting study

preference modelling by estimating local utility functions for multiobjective optimization abstract this paper is intended to design goal programming models for capturing the decision maker s dm s preference information and for supporting the search for the best compromise solutions in multiobjective optimization at first a linear goal programming model is built to estimate piecewise linear local utility functions based on pairwise comparisons of efficient solutions as well as objectives the interactive step trade off method istm is employed to generate a typical subset of efficient solutions of a multiobjective problem another general goal programming model is then constructed to embed the estimated utility functions in the original multiobjective problem for utility optimization using ordinary nonlinear programming algorithms this technique consisting of the istm method and the newly investigated search process facilitates the identification and elimination of possible inconsistent information which may exist in the dm s preferences it also provides various ways to carry out post optimality analysis to test the robustness of the obtained best solutions a modified nonlinear multiobjective management problem is taken as example to demonstrate the technique

three modeling paradigms in mathematical programming celebrating the sixtieth anniversary since the zeroth international symposium on mathematical programming was held in 1949 this paper discusses several promising paradigms in mathematical programming that have gained momentum in recent years but have yet to reach the main stream of the field these are competition dynamics and hierarchy the discussion emphasizes the interplay between these paradigms and their connections with existing subfields including disjunctive equilibrium and nonlinear programming and variational inequalities we will describe the modeling approaches mathematical formulations and recent results of these paradigms and sketch some open mathematical and computational challenges arising from the resulting optimization and equilibrium problems our goal is to elucidate the need for a systematic study of these problems and to inspire new research in the field

design of cognitive radio systems under temperature interference constraints a variational inequality approach the concept of cognitive radio cr has recently received great attention from the research community as a promising paradigm to achieve efficient use of the frequency resource by allowing the coexistence of licensed primary and unlicensed secondary users in the same bandwidth in this paper we propose a novel nash equilibrium ne problem to model concurrent communications of cognitive secondary users who compete against each other to maximize their information rate the formulation contains constraints on the transmit power and possibly spectral masks as well as aggregate interference tolerable at the primary users receivers the coupling among the strategies of the players due to the interference constraints presents a new challenge for the analysis of this class of nash games that cannot be addressed using the game theoretical models proposed in the literature for this purpose we need the framework given by the more advanced theory of finite dimensional variational inequalities vi this provides us with all the mathematical tools necessary to analyze the proposed ne problem e g existence and uniqueness of the solution and to devise alternative distributed algorithms along with their convergence properties

joint sensing and power allocation in nonconvex cognitive radio games nash equilibria and distributed algorithms in this paper we propose a novel class of nash problems for cognitive radio cr networks modeled as gaussian frequency selective interference channels wherein each secondary user su competes against the others to maximize his own opportunistic throughput by choosing jointly the sensing duration the detection thresholds and the vector power allocation the proposed general formulation allows us to accommodate several transmit power and deterministic probabilistic interference constraints such as constraints on the maximum individual and or aggregate probabilistic interference tolerable at the primary receivers to keep the optimization as decentralized as possible global coupling interference constraints are imposed by penalizing each su with a set of time varying prices based upon his contribution to the total interference the prices are thus additional variable to optimize the resulting players optimization problems are nonconvex moreover there are possibly price clearing conditions associated with the global constraints to be satisfied by the solution all this makes the analysis of the proposed games a challenging task none of classical results in the game theory literature can be successfully applied the main contribution of this paper is to develop a novel optimization based theory for studying the proposed nonconvex games we provide a comprehensive analysis of the existence and uniqueness of a standard nash equilibrium devise alternative best response based algorithms and establish their convergence some of the proposed algorithms are totally distributed and asynchronous whereas some others require limited signaling among the sus in the form of consensus algorithms in favor of better performance overall they are thus applicable to a variety of cr scenarios either cooperative or noncooperative which allows the sus to explore the existing tradeoff between signaling and performance

optimal wideband spectrum sensing framework for cognitive radio systems an optimal wideband spectrum sensing framework which identifies secondary transmission opportunities over multiple nonoverlapping narrowband channels is presented the framework which is referred to as multiband sensing time adaptive joint detection improves the overall secondary user performance while protecting the primary network and keeping the harmful interference below a desired low level considering a periodic sensing scheme the detection problem is formulated as a joint optimization problem to maximize the aggregate achievable secondary throughput capacity given a bound on the aggregate interference imposed on the primary network it is demonstrated that the problem can be solved by convex optimization if certain practical constraints are applied simulation results attest that the proposed wideband spectrum sensing framework achieves superior performance compared to contemporary frameworks an efficient iterative algorithm which solves the optimization problem with much lower complexity compared to other numerical methods is presented it is established that the iteration complexity and the complexity per iteration of the proposed algorithm increases linearly as the number of optimization variables i e the number of narrowband channels increases the algorithm is evaluated via simulation and is shown to obtain the optimal solution very quickly and efficiently