equilibria of two sided matching games with common preferences problems of matching have long been studied in the operations research literature assignment problem secretary problem stable marriage problem all of these consider a centralized mechanism whereby a single decision maker chooses a complete matching which optimizes some criterion this paper analyzes a more realistic scenario in which members of the two groups buyers sellers employers workers males females randomly meet each other in pairs interviews dates over time and form couples if there is mutual agreement to do so we assume members of each group have common preferences over members of the other group generalizing an earlier model of alpern and reyniers alpern s reyniers d j 2005 strategic mating with common preferences j theor biol 237 337 354 we assume that one group called males is r times larger than the other r 1 thus all females but only 1 r of the males end up matched unmatched males have negative utility c we analyze equilibria of this matching game depending on the parameters r and c in a region of r c space with multiple equilibria we compare these and analyze their efficiency in several respects this analysis should prove useful for designers of matching mechanisms who have some control over the sex ratio e g by capping numbers of males at a singles event or by having ladies free nights or the nonmating cost c e g tax benefits to married couples

the expansion of functions under transformation and its application to optimization abstract this paper proposes the expansion of functions under transformation which represents infinite kinds of extensions of taylor s expansion based on this duffin s condensation formula is developed as a condensation formula of high order furthermore a theorem of efficiently solving mathematical programming by using the expansion of functions is proposed according to the condensation formula of high order two kinds of second order primal algorithms are proposed for solving generalized geometric programming with rapid and stable convergence which could be applied to a wide range of structural optimization problems finally an efficient fully stressed design method under the function transformation is proposed using these expansions of functions

monte carlo computation of cluster free energies in the ising model a test for the validity of the capillarity approximation a new monte carlo technique is proposed to compute directly the free energy difference fn 1 fn of two clusters with size n 1 and n the algorithm is applied to the two dimensional square ising model with nearest neighbour interactions results are given for 1 9 but for smaller cluster sizes the obtained energies are larger than predicted by the capillarity model the deviation exhibits no systematic size dependence but a strong temperature dependence the existence of a size independent term in fn is confirmed by the values of the internal energy un obtained as a by product of the calculation

rendezvous search on the labeled line the rendezvous search problem is the problem of finding optimal search strategies for two people who are placed randomly on a known search region and want to meet each other in minimal expected time we focus on initial location distributions that are centrally symmetric and nonincreasing as one moves away from the center including the discretized and or truncated gaussian densities when the search region is a discrete or a continuous interval and the interval is labeled so that the searchers know their own location at all times we prove that the optimal strategy for both searchers is to go directly to the center and wait there the same result also holds for rendezvous search on the infinite line

rendezvous search on the line with indistinguishable players alpern introduced a problem in which two players are placed on the real line at a distance drawn from a bounded distribution f known to both they can move at maximum velocity one and wish to meet as soon as possible neither knows the direction of the other nor do they have a common notion of a positive direction on the line it is required to find the symmetric rendezvous value r s f which is the minimum expected meeting time achievable by players using the same mixed strategy this corresponds to the case where the players are indistinguishable they both take directions from a controller who does not know their names in this paper we give a mixed strategy which has an expected meeting time of 1 78d mu 2 where d is the maximum of f and mu its mean this leads to an upper bound r s f le 1 78d mu 2 on the symmetric rendezvous value which is better than the upper bound r s f le 2d mu 2 obtained by alpern

a new hybrid method for solving global optimization problem abstract in this paper we present a new hybrid method called the sasp method the purpose of this method is the hybridization of the simulated annealing sa with the descent method where we estimate the gradient using simultaneous perturbation firstly the new hybrid method finds a local minimum using the descent method then sa is executed in order to escape from the currently discovered local minimum to a better one from which the descent method restarts a new local search and so on until convergence the new hybrid method can be widely applied to a class of global optimization problems for continuous functions with constraints experiments on 30 benchmark functions including high dimensional functions show that the new method is able to find near optimal solutions efficiently in addition its performance as a viable optimization method is demonstrated by comparing it with other existing algorithms numerical results improve the robustness and efficiency of the method presented

asynchronous deterministic rendezvous in graphs two mobile agents robots having distinct labels and located in nodes of an unknown anonymous connected graph have to meet we consider the asynchronous version of this well studied rendezvous problem and we seek fast deterministic algorithms for it since in the asynchronous setting meeting at a node which is normally required in rendezvous is in general impossible we relax the demand by allowing meeting of the agents inside an edge as well the measure of performance of a rendezvous algorithm is its cost for a given initial location of agents in a graph this is the number of edge traversals of both agents until rendezvous is achieved if agents are initially situated at a distance d in an infinite line we show a rendezvous algorithm with cost o d lmin 2 when d is known and o d lmax 3 if d is unknown where lmin and lmax are the lengths of the shorter and longer label of the agents respectively these results still hold for the case of the ring of unknown size but then we also give an optimal algorithm of cost o n lmin if the size n of the ring is known and of cost o n lmax if it is unknown for arbitrary graphs we show that rendezvous is feasible if an upper bound on the size of the graph is known and we give an optimal algorithm of cost o d lmin if the topology of the graph and the initial positions are known to agents

a nonisolated optimal solution for special reverse convex programming problems in this paper an efficient algorithm is proposed for globally solving special reverse convex programming problems with more than one reverse convex constraints the proposed algorithm provides a nonisolated global optimal solution which is also stable under small perturbations of the constraints and it turns out that such an optimal solution is adequately guaranteed to be feasible and to be close to the actual optimal solution convergence of the algorithm is shown and the numerical experiment is given to illustrate the feasibility of the presented algorithm

searching for an agent who may or may not want to be found there is an extensive theory regarding optimal continuous path search for a mobile or immobile target the traditional theory assumes that the target is one of three types i an object with a known distribution of paths ii a mobile or immobile hider who wants to avoid or delay capture or iii a rendezvouser who wants to find the searcher this paper introduces a new type of search problem by assuming that aims of the target are not known to the searcher the target may be either a type iii cooperator with a known cooperation probabilityc or a type ii evader this formulation models search problems like that for a lost teenager who may be a runaway or a lost intelligence agent who may be a defector in any given search context it produces a continuum of search problems g c 0 c 1 linking a zero sum searchgame withc 0 to a rendezvous problem withc 1 these models thus provide a theoretical bridge between two previously distinct parts of search theory namely searchgames and rendezvous search

on the multichannel rendezvous problem fundamental limits optimal hopping sequences and bounded time to rendezvous one of the fundamental problems in a cognitive radio network known as the multichannel rendezvous problem is for two secondary users to find a common channel that is not blocked by primary users the basic idea for solving such a problem in most works in the literature is for the two users to select their own channel hopping sequences and then rendezvous when they both hop to a common unblocked channel at the same time in this paper we focus on the fundamental limits of the multichannel rendezvous problem and formulate such a problem as a constrained optimization problem where the selection of the random hopping sequences of the two secondary users must satisfy certain constraints we derive various lower bounds for the expected respectively maximum time to rendezvous under certain constraints for some of these lower bounds we are also able to construct optimal channel hopping sequences that achieve the lower bounds inspired by the constructions of quorum systems and relative difference sets our constructions of the channel hopping sequences are based on the mathematical theories of finite projective planes orthogonal latin squares and sawtooth sequences the use of such theories in the constructions of channel hopping sequences appear to be new and better than other existing schemes in terms of minimizing the expected respectively maximum time to rendezvous

the ising model below tc calculation of nonuniversal amplitudes using a primitive droplet model using recent exact results for the surface free energies of ising droplets on a square lattice and applying a primitive droplet theory due to langer 1967 the author obtains an expression for the principal nonuniversal amplitude appearing in the imaginary part of the analytic continuation of the free energy across the coexistence line for the square lattice ising model below tc the significance of this calculation is the known dependence on this amplitude of the large order terms in the expansion of the physical free energy in powers of h thus allowing a direct numerical comparison with existing series data to be made after carrying out a simple renormalisation of the droplet volume term the author finds excellent numerical agreement

rendezvous on the line when the players initial distance is given by an unknown probability distribution two players a and b are randomly placed on a line the distribution of the distance between them is unknown except that the expected initial distance of the two players does not exceed some constant mu the players can move with maximal velocity 1 and would like to meet one another as soon as possible most of the paper deals with the asymmetric rendezvous in which each player can use a different trajectory we find rendezvous trajectories which are efficient against all probability distributions in the above class it turns out that our trajectories do not depend on the value of mu we also obtain the minimax trajectory of player a if player b just waits for him this trajectory oscillates with a geometrically increasing amplitude it guarantees an expected meeting time not exceeding 6 8 mu we show that if player b also moves then the expected meeting time can be reduced to 5 7 mu the expected meeting time can be further reduced if the players use mixed strategies we show that if player b rests then the optimal strategy of player a is a mixture of geometric trajectories it guarantees an expected meeting time not exceeding 4 6 mu this value can be reduced even more below 4 42 mu if player b also moves according to a correlated mixed strategy we also obtain a bound for the expected meeting time of the corresponding symmetric rendezvous problem

comparison of monte carlo results for the 3d ising interface tension and interface energy with extrapolated series expansions abstract we compare monte carlo results for the interface tension and interface energy of the 3 dimensional ising model with pade and inhomogeneous differential approximants of the low temperature series that was recently extended by arisue to 17th order in u exp 4 the series is expected to suffer from the roughening singularity at u 0 196 the comparison with the monte carlo data shows that the pade and inhomogeneous differential approximants fail to improve the truncated series result of the interface tension and the interface energy in the region around the roughening transition the monte carlo data show that the specific heat displays a peak in the smooth phase neither the truncated series nor the pade approximants find this peak we also compared monte carlo data for the energy of the asos model with the corresponding low temperatures series that we extended to order u12

numerical tests of nucleation theories for the ising models the classical nucleation theory cnt is tested systematically by computer simulations of the two dimensional 2d and three dimensional 3d ising models with a glauber type spin flip dynamics while previous studies suggested potential problems with cnt our numerical results show that the fundamental assumption of cnt is correct in particular the becker doring theory accurately predicts the nucleation rate if the correct droplet free energy function is provided as input this validates the coarse graining of the system into a one dimensional markov chain with the largest droplet size as the reaction coordinate furthermore in the 2d ising model the droplet free energy predicted by cnt matches numerical results very well after a logarithmic correction term from langer s field theory and a constant correction term are added but significant discrepancies are found between the numerical results and existing theories on the magnitude of the logarithmic correction term in the 3d ising model our analysis underscores the importance of correctly accounting for the temperature dependence of surface energy when comparing numerical results and nucleation theories

a new rectangle branch and pruning approach for generalized geometric programming generalized geometric programming ggp problem occurs frequently in engineering design and management in this paper a branch and pruning global optimization algorithm is proposed for ggp by utilizing some transformations a linear relaxation of the problem ggp is obtained based on the linear lower bound functions of objective and constraint functions inside some hyperrectangle region then a new pruning technique is given to accelerate the convergence of the given algorithm and this pruning technique offers the possibility to cut away a large part of the current investigated region in which there no exist global optimum solution the proposed algorithm which connects branch and bound method with the pruning technique successfully is convergent to the global minimum according to the successive refinement of the linear relaxation of feasible region of the objective function and the solutions of a series of linear relaxation problems and finally numerical experiment is given to illustrate the feasibility and efficiency of the proposed algorithm

rendezvous in higher dimensions two players are placed on the integer lattice z n consisting of points in n dimensional space with all coordinates integers so that their vector difference is of length 2 and parallel to one of the axes their aim is to move to an adjacent node in each period so that they meet occupy same node in least expected time r left n right called the rendezvous value we assume they have no common notion of directions or orientations i e no common notion of clockwise we extend the known result r left 1 right 3 25 of alpern and gal to obtain r left 2 right 197 32 allowbreak 6 allowbreak16 and the bounds 2n leq r left n right leq left 32n 3 12n 2 2n 3 right 12n 2 for n 2 we characterize the set of all optimal strategies and show that none of them simultaneously maximizes the probability of meeting by time t for all t this behavior differs from that found by anderson and fekete and the authors for the related problem where the players are initially placed at diagonals of one of the squares of the lattice z 2

on generalized geometric programming problems with non positive variables generalized geometric programming ggp problems occur frequently in engineering design and management some exponential based decomposition methods have been developed for solving global optimization of ggp problems however the use of logarithmic exponential transformations restricts these methods to handle the problems with strictly positive variables this paper proposes a technique for treating non positive variables with integer powers in ggp problems by means of variable transformation the ggp problem with non positive variables can be equivalently solved with another one having positive variables in addition we present some computationally efficient convexification rules for signomial terms to enhance the efficiency of the optimization approach numerical examples are presented to demonstrate the usefulness of the proposed method in ggp problems with non positive variables

a global optimization algorithm using linear relaxation various local optimization approaches have been developed for solving the non convex quadratically constrained quadratic programs qp but up to now less work has been devoted to solving global optimization of qp problem due to the inherent difficulty this paper considers the global minimum of qp that arise in various practice problems by utilizing the inherent property of the quadratic function an approximations a linear relaxation of qp is then obtained thus initial qp is reduced to a sequence of linear programming problems through the successive refinement of a linear relaxation of feasible region of the objective function the proposed algorithm is convergent to the global minimum of qp by means of the subsequent solutions of a series of linear programming problems test results indicate that the proposed algorithm is extremely robust and can be used successfully to solve the global minimum of qp on a microcomputer

collapse transition and asymptotic scaling behavior of lattice animals low temperature expansion a low temperature expansion for the free energy density of lattice animals is derived analysis of the series yields a collapse transition temperature oftc 0 54 in close agreement with previous estimates it is demonstrated that p k the number ofp particle p bond animals obeys the asymptotic scaling law log p k pg k p o p the low temperature series and numerical data are used to estimate the scaling function

accelerating method of global optimization for signomial geometric programming abstract signomial geometric programming sgp has been an interesting problem for many authors recently many methods have been provided for finding locally optimal solutions of sgp but little progress has been made for global optimization of sgp in this paper we propose a new accelerating method for global optimization algorithm of sgp using a suitable deleting technique this technique offers a possibility to cut away a large part of the currently investigated region in which the globally optimal solution of sgp does not exist and can be seen as an accelerating device for global optimization algorithm of sgp problem compared with the method of shen and zhang global optimization of signomial geometric programming using linear relaxation appl math comput 150 2004 99 114 numerical results show that the computational efficiency is improved obviously by using this new technique in the number of iterations the required saving list length and the execution time of the algorithm

global optimization for sum of generalized fractional functions this paper considers the solution of generalized fractional programming gfp problem which contains various variants such as a sum or product of a finite number of ratios of linear functions polynomial fractional programming generalized geometric programming etc over a polytope for such problems we present an efficient unified method in this method by utilizing a transformation and a two part linearization method a sequence of linear programming relaxations of the initial nonconvex programming problem are derived which are embedded in a branch and bound algorithm numerical results are given to show the feasibility and effectiveness of the proposed algorithm

minimax rendezvous on the line suppose that n players are placed randomly on the real line at consecutive integers and faced in random directions each player has maximum speed one cannot see the others and doesn t know his relative position what is the minimum time m n required to ensure that all the players can meet together at a single point regardless of their initial placement we prove that m 2 3 m 3 4 and m n is asymptotic to n 2 we also consider a variant of the problem which requires players who meet to stick together and find in this case that three players require 5 time units to ensure a meeting this paper is thus a minimax version of the rendezvous search problem which has hitherto been studied only in terms of minimizing the expected meeting time

the rendezvous search problem the author considers the problem faced by two people who are placed randomly in a known search region and move about at unit speed to find each other in the least expected time this time is called the rendezvous value of the region it is shown how symmetries in the search region may hinder the process by preventing coordination based on concepts such as north or clockwise a general formulation of the rendezvous search problem is given for a compact metric space endowed with a group of isometrics which represents the spatial uncertainties of the players these concepts are illustrated by considering upper bounds for various rendezvous values for the circle and an arbitrary metric network the discrete rendezvous problem on a cycle graph for players restricted to symmetric markovian strategies is then solved finally the author considers the problem faced by two people on an infinite line who each know the distribution of the distance but not the direction to each other

the princess and monster game on an interval a minimizing searcher s and a maximizing hider h move at unit speed on a closed interval until the first capture or payoff time t min t s t h t that they meet this zero sum princess and monster game or less colorfully search game with mobile hider was proposed by rufus isaacs for general networks q while the existence and finiteness of the value v v q has been established for such games only the circle network has been solved value and optimal mixed strategies it seems that the interval network q 1 1 had not been studied because it was assumed to be trivial with value 3 2 and obvious searcher mixed strategy going equiprobably from one end to the other we establish that this game is in fact nontrivial by showing that v 3 2 using a combination of continuous and discrete mixed strategies for both players we show that 15 11 leq v leq 13 9 the full solution of this very simple game is still open and appears difficult though many properties of the optimal strategies are derived here

find and fetch search on a tree we introduce a new type of search game called the find and fetch game f q o the hider simply picks any point h in the network q the searcher starts at time zero at a given point o of q moving at unit speed until he reaches h finds the hider then he returns at a given speed along the shortest path back to o arriving at time r the payoff this models the problem faced in many types of search including search and rescue problems and foraging problems of animals where food must be found and returned to the lair when q is a binary tree we derive optimal probabilities for the searcher to branch at the nodes these probabilities give a positive bias towards searching longer branches first we show that the minimax value of the return time r the game value of f q o is d where is the total length of q and d is the mean distance from the root o to the leaves terminal nodes of q where the mean is taken with respect to what is known as the equal branch density distribution as goes to infinity our problem reduces to the search game model where the payoff is simply the time to reach the hider and our results tend to those obtained by gal gal s 1979 search games with mobile and immobile hider siam j control optim 17 1 99 122 and anderson and gal anderson e j s gal 1990 search in a maze probab engrg inform sci 4 3 311 318 for that model we also apply our return time formula d to determine the ideal location for the root lair or rescue center o assuming it can be moved in the traditional find only model the location of o does not matter

a global optimization using linear relaxation for generalized geometric programming many local optimal solution methods have been developed for solving generalized geometric programming ggp but up to now less work has been devoted to solving global optimization of ggp problem due to the inherent difficulty this paper considers the global minimum of ggp problems by utilizing an exponential variable transformation and the inherent property of the exponential function and some other techniques the initial nonlinear and nonconvex ggp problem is reduced to a sequence of linear programming problems the proposed algorithm is proven that it is convergent to the global minimum through the solutions of a series of linear programming problems test results indicate that the proposed algorithm is extremely robust and can be used successfully to solve the global minimum of ggp on a microcomputer

rendezvous search on the interval and the circle two people are placed randomly and independently on a street of unit length they attempt to find each other in the shortest possible expected time we solve this problem assuming each searcher knows where he or she is on the street for monotonic density functions for the initial placement this includes the uniform pdf as a special case this gives an example of a rendezvous search problem where there is no advantage in being allowed to use asymmetric strategies we also solve some corresponding problems for the circle when asymmetric strategies are permitted one of these shows that it can sometimes be optimal for one player to wait for the other to find him

rendezvous on a planar lattice we analyze the optimal behavior of two players who are lost on a planar surface and who want to meet each other in least expected time they each know the initial distribution of the other s location but have no common labeling of points and so cannot simply go to a location agreed to in advance they have no compasses so do not even have a common notion of north for simplicity we restrict their motions to the integer lattice z2 graph paper and their motions to horizontal and vertical directions as in the original work of anderson and fekete 2001

rendezvous search on the line with distinguishable players two players are placed on the real line at a distance d with a distribution f known to both neither knows the direction of the other nor do they have a common notion of a positive direction on the line we seek the least expected rendezvous time r r left f right in which they can meet given maximum speeds of one we consider the cases where f is a bounded point discrete or finite mean distribution we obtain upper bounds or exact values for r and in one case an optimality condition for search strategies a connection with beck s linear search problem is established

range division and contraction algorithm for a class of global optimization problems abstract this article presents a range division and contraction algorithm for a class of global optimization problems in the algorithm the original problem is first converted into an equivalent monotonic optimization problem whose objective function is just a simple univariate by exploiting the particularity of this monotonicity the variable bound in a particular node is then tightened and the bounds on the constraints are calculated to remove the region which doesn t contain optimal solutions the proposed method can reach an approximate solution within an acceptable error in which such solution is adequately guaranteed to be feasible and to be close to the actual global optimal solution several numerical examples are given to illustrate the feasibility and efficiency of the present algorithm

hide and seek games on a network using combinatorial search paths this paper introduces a new search paradigm to hide and seek games on networks the hider locates at any point on any arc the searcher adopts a combinatorial path when searching the network a sequence of arcs each adjacent to the last and traced out at unit speed in previous literature the searcher was allowed simple motion any unit speed path including ones that turn around inside an arc the new approach more closely models real problems such as search for improvised explosive devices using vehicles that can only turn around at particular locations on a road the search game is zero sum with the time taken to find the hider as the payoff using a lemma giving an upper bound for the expected search time on a semi eulerian network we solve the search game on a network q3 consisting of two nodes connected by three arcs of arbitrary lengths when two q3 networks with unit length arcs are linked by two small central arcs incident at the start node one of these arcs must be traversed at least th

global optimization for sum of geometric fractional functions this paper presents an efficient branch and bound algorithm for globally solving sum of geometric fractional functions under geometric constraints which arise in various practical problems by using an equivalent transformation and a new linear relaxation technique a linear relaxation programming problem of the equivalent problem is obtained the proposed algorithm is convergent to the global optimal solution by means of the subsequent solutions of a series of linear programming problems numerical results are reported to show the feasibility of our algorithm

a common notion of clockwise can help in planar rendezvous two players are lost in a grid of city streets and wish to meet as soon as possible knowing only the distribution of the other s initial location two nodes away in one of the four compass directions how do they move from intersection to intersection between nodes of the lattice z2 to achieve this we assume that they do not have common compass directions to coordinate on but that they can use their common notion of clockwise we show that the latter realistic assumption can aid them in expediting their meeting relative to a previous rendezvous problem which did not allow this we also solve the easier streets and avenues version of the problem in which the players can distinguish between the axes between streets and avenues we discover several new phenomenae which have not been seen before in planar rendezvous

rendezvous evasion search in two boxes an agent who may or may not want to be found is located in one of two boxes at time 0 suppose that he is in box b with probability p he wishes to be found in which case he has been asked to stay in box b with probability 1 p he tries to evade the searcher in which case he may move between boxes a and b the searcher looks into one of the boxes at times 1 2 3 between each search the agent may change boxes if he wants the searcher is trying to minimise the expected time to discovery the agent is trying to minimise this time if he wants to be found but trying to maximise it otherwise this paper finds a solution to this game in a sense defined in the paper associated strategies for the searcher and each type of agent and a continuous value function v p giving the expected time for the agent to be discovered the solution method which is to solve an associated zero sum game would apply generally to this type of game of incomplete information

global optimization of generalized linear fractional programming with nonlinear constraints this paper presents a branch and bound algorithm for globally solving a wide class of generalized linear fractional programming problems glfp this class includes such problems as minimizing a sum or error for product of a finite number of ratios of linear functions linear multiplicative programming polynomial programming etc over nonconvex feasible region first a problem q is derived which is equivalent to problem glfp in the algorithm lower bounds are derived by solving a sequence of linear relaxation programming problems which is based on the construction of the linear lower bounding functions for the objective function and constraint functions of problem q over the feasible region convergent property of the presented algorithm is proved and numerical results are given to show the feasibility of the proposed algorithm

rendezvous search on the line we present two new results for the asymmetric rendezvous problem on the line we first show that it is never optimal for one player to be stationary during the entire search period in the two player rendezvous then we consider the meeting time of n players in the worst case and show that it has an asymptotic behavior of n 2 o log n

a new bound and reduce approach of nonconvex quadratic programming problems abstract for the nonconvex quadratic programming problem a new linear programming relaxation bound and reduce algorithm is proposed and its convergence is proved in this algorithm a new hyper rectangle partition technique and a new linear programming relaxation tactics are used at the same time the hyper rectangular reduction method is used to raise its convergent speed the numerical results demonstrate the effectiveness and feasibility of the proposed algorithm

asymmetric rendezvous on the line is a double linear search problem we apply a new method of analysis to the asymmetric rendezvous search problem on the line arspl this problem previously studied in a paper of alpern and gal 1995 asks how two blind speed one players placed a distance d apart on the line can find each other in minimum expected time the distance d is drawn from a known cumulative probability distribution g and the players are faced in random directions we show that the arspl is strategically equivalent to a new problem we call the double linear search problem dlsp where an object is placed equiprobably on one of two lines and equiprobably at positions d a searcher is placed at the origin of each of these lines the two searchers move with a combined speed of one to minimize the expected time before one of them finds the object using results from a concurrent paper of the first author and j v howard 1998 we solve the dlsp and hence the arspl for the case where g is convex on its support and show that the solution is that conjectured in a paper of baston and gal 1998

optimal trade off between speed and acuity when searching for a small object a searcher seeks to find a stationary hider located at some point h not necessarily a node on a given network q the searcher can move along the network from a given starting point at unit speed but to actually find the hider she must pass it while moving at a fixed slower speed which may depend on the arc in this bimodal search game the payoff is the first time the searcher passes the hider while moving at her slow speed this game models the search for a small or well hidden object e g a contact lens improvised explosive device predator search for camouflaged prey we define a bimodal chinese postman tour as a tour of minimum time i which traverses every point of every arc at least once in the slow mode for trees and weakly eulerian networks networks containing a number of disjoint eulerian cycles connected in a tree like fashion the value of the bimodal search game is i 2 for trees the optimal hider strategy has full support on the network this differs from traditional search games where it is optimal for him to hide only at leaf nodes we then consider the notion of a lucky searcher who can also detect the hider with a positive probability q even when passing him at her fast speed this paper has particular importance for demining problems

validity of classical nucleation theory for ising models while the classical nucleation theory cnt is widely used to predict the rate of first order phase transitions its validity has been questioned due to discrepancies with experiments we systematically test the individual components of cnt by computer simulations of the ising models and confirm its fundamental assumptions under a wide range of conditions h 0 01 text char21 0 13j t 0 44 text char21 0 84 t c in two dimensions and h 0 30 text char21 0 60j t 0 48 text char21 0 62 t c in three dimensions first cnt accurately predicts the nucleation rate if the correct droplet free energy is provided furthermore theoretical prediction of droplet free energy matches numerical results very well in the two dimensional 2d ising model if appropriate correction terms are added this establishes the 2d ising model as an important reference point where existing theories can predict nucleation rate accurately with no adjustable parameters

mining coal or finding terrorists the expanding search paradigm we show how to optimize the search for a hidden object terrorist or simply hider located at a point h according to a known or unknown distribution v on a rooted network q we modify the traditional pathwise search approach to a more general notion of expanding search when the hider is restricted to the nodes of q an expanding search s consists of an ordering a1 a2 of the arcs of a spanning subtree such that the root node is in a1 and every arc ai is adjacent to a previous arc aj j i if ak contains h the search time t is a1 ak5 where is length measure on q for more general distributions v an expanding search s is described by the nested family of connected sets s4t5 that specify the area of q that has been covered by time t s 0 is the root s t t and t min t h 2 s t for a known hider distribution v on a tree q the expected time minimizing strategy sn begins with the rooted subtree q maximizing the density v q q for arbitrary networks we use this criterion on all spanning subtrees the search sn can be interpreted as the optimal method of mining known coal seams when the time to move miners or machines is negligible compared to digging time when the hider distribution is unknown we consider the zero sum search game where the hider picks h the searcher s and the payoff is t for trees q the value is v q d 2 where d is a mean distance from root to leaf nodes if q is 2 arc connected v q 2 applications and interpretations of the expanding search paradigm are given particularly to multiple agent search

global optimization of signomial geometric programming using linear relaxation various local optimization approaches have been developed for solving signomial geometric programming sgp problems but up to now less work has been devoted to solving global optimization of sgp due to the inherent difficulty this paper considers the global minimum of sgp that arise in various practice problems by utilizing an exponential variable transformation and tangential hypersurfaces and convex envelop approximations a linear relaxation of sgp is then obtained thus initial nonconvex nonlinear problem sgp is reduced to a sequence of linear programming problems through the successive refinement of a linear relaxation of feasible region of the objective function the proposed algorithm is convergent to the global minimum of sgp by means of the subsequent solutions of a series of linear programming problems test results indicate that the proposed algorithm is extremely robust and can be used successfully to solve global minimum of sgp on a microcomputer