computing invariants of semi log canonical surfaces we describe some general methods to compute fundamental groups co homology and irregularity of semi log canonical surfaces as an application we show that there are exactly two irregular gorenstein stable surfaces with k 2 1 which have chi x 0 and mathrm pic 0 x mathbb c but different homotopy type

note an improved conditional monte carlo technique for the stochastic shortest path problem this paper describes a simulation procedure for estimating the distribution function of the shortest path length in a network with random arc lengths the method extends the concept of conditional monte carlo utilizing special properties of the uniformly directed cutsets and the unique arcs the objective here is to reduce the sampling effort and utilize known probability information to derive multivariate integrals of lower dimension the experimental results show that the proposed method is substantially cost effective and performs better than traditional monte carlo and conditional methods

estimating network characteristics in stochastic activity networks this paper describes a monte carlo method based on the theory of quasirandom points for estimating the distribution functions and means of network completion time and shortest path time in a stochastic activity network in particular the method leads to estimators whose absolute errors converge as log kn k where k denotes the number of replications collected in the experiment and n is the number of dimensions for sampling this rate compares favorably with the standard error of estimate o1 k1 2 which obtains for experiments that use random sampling moreover since quasirandom points are nonrandom the upper bound log kn k is deterministic in contrast to the random sampling rate o1 k1 2 which is probabilistic the paper demonstrates how the use of a cutset of the network reduces n in the bound when estimating the distribution functions two examples illustrate the benefits and costs of using quasirandom points

binary operations and canonical forms for factorial and related models abstract binary operations on commutative jordan algebras are used to extend the grouping of treatments in blocks and the taking of fractional replicates to models where factors have arbitrary number of levels up to now these techniques had been restricted to models whose factors have a prime or a power of a prime number of levels moreover the binary operations will enable the use of simple models as building blocks for more complex designs

stochastic shortest path problems with piecewise linear concave utility functions this paper considers a stochastic shortest path problem where the arc lengths are independent random variables following a normal distribution in this problem the optimal path is one that maximizes the expected utility with the utility function being piecewise linear and concave such a utility function can be used to approximate nonlinear utility functions that capture risk averse behaviour for a wide class of problems the principal contribution of this paper is the development of exact algorithms to solve large problem instances two algorithms are developed and incorporated in labelling procedures computational testing is done to evaluate the performance of the algorithms overall both algorithms are very effective in solving large problems quickly the relative performance of the two algorithms is found to depend on the curvature of the piecewise linear utility function

risk taking in stochastic pert networks abstract this paper studies a pert problem which incorporates project managers risk taking behavior in stochastic environments in this stochastic pert network which we refer to as riskpert activity durations are nonnegative random variables and a project manager uses a disutility function to evaluate each path and chooses that path which maximizes his expected disutility as an optimal or critical path this path as opposed to the classical critical path is used as a basis to analyze the pert network and to estimate the probability of completion time the general riskpert is difficult to solve however special cases when activity durations are statistically independent and disutility functions are linear exponential quadratic or linear exponential are solvable exactly the illustrative examples demonstrate that riskpert captures managers risk taking behavior and provides results that are more realistic than those of the classical pert models furthermore this paper extends some of the riskpert models to include multi dimensional pert networks

lattices of jordan algebras commutative jordan algebras play a central part in orthogonal models the generations of these algebras is studied and applied in deriving lattices of such algebras these lattices constitute the natural framework for deriving new orthogonal models through factor aggregation and disaggregation

jordan algebras and bayesian quadratic estimation of variance components the authors consider a linear model ey x cov y v where v is a quadratic subspace a jordan algebra using this property it is shown how multiplication computation of g inverses determination of a neutral element can be done more efficiently in v finally this technique is applied to obtain formulae for locally optimal estimators and bayesian estimators

bounding the project completion time distribution in pert networks we consider the pert model of a project composed of activities whose durations are random variables with known distributions for the situations in which the activity durations are completely independent we present a new method for obtaining a probability distribution function that bounds the exact probability distribution of the project completion time from below the bounding distribution can be used to obtain an upper bound on the mean completion time of the project we also prove and illustrate that this bounding distribution is better tighter than any of the existing lower bounds implying that the corresponding upper bound on the mean completion time is tighter than any of the existing upper bounds

exact algorithms for the stochastic shortest path problem with a decreasing deadline utility function in this paper the stochastic shortest path problem of determining a path that maximizes the expected utility is considered the nature of the utility function used to evaluate paths is of a decreasing deadline type the principal contribution of this paper is the development of exact algorithms that use two types of pruning techniques that are incorporated in labeling procedures one type of pruning makes use of the concept of local preference relations while the other type makes use of relaxations specifically two algorithms are developed each containing the same preference relation but two different relaxations our extensive computational testing indicate that both these algorithms are able to solve even large size problems quickly more importantly even for large problems both the algorithms solved them by enumerating a very small percentage of all paths

dynamic journeying under uncertainty abstract we introduce a journey planning problem in multi modal transportation networks under uncertainty the goal is to find a journey possibly involving transfers between different transport services from a given origin to a given destination within a specified time horizon due to uncertainty in travel times the arrival times of transport services at public transport stops are modeled as random variables if a transfer between two services is rendered unsuccessful the commuter has to reconsider the remaining path to the destination the problem is modeled as a markov decision process in which states are defined as paths in the transport network the main contribution is a backward induction method that generates an optimal policy for traversing the public transport network in terms of maximizing the probability of reaching the destination in time by assuming history independence and independence of successful transfers between services we obtain approximate methods for the same problem analysis and numerical experiments suggest that while solving the path dependent model requires the enumeration of all paths from the origin to the destination the proposed approximations may be useful for practical purposes due to their computational simplicity in addition to on time arrival probability we show how travel and overdue costs can be taken into account making the model applicable to freight transportation problems

a probabilistic model for minmax regret in combinatorial optimization in this paper we propose a new probabilistic model for minimizing the anticipated regret in combinatorial optimization problems with distributional uncertainty in the objective coefficients the interval uncertainty representation of data is supplemented with information on the marginal distributions as a decision criterion we minimize the worst case conditional value at risk of regret the proposed model includes the interval data minmax regret model as a special case for the class of combinatorial optimization problems with a compact convex hull representation a polynomial sized mixed integer linear program is formulated when a the range and mean are known and b the range mean and mean absolute deviation are known and a mixed integer second order cone program is formulated when c the range mean and standard deviation are known for the subset selection problem of choosing k elements of maximum total weight out of a set of n elements the probabilistic regret model is shown to be solvable in polynomial time in the instances a and b above this extends the current known polynomial complexity result for minmax regret subset selection with range information only

pluricanonical maps of stable log surfaces abstract stable surfaces and their log analogues are the type of varieties naturally occurring as boundary points in moduli spaces we extend classical results of kodaira and bombieri to this more general setting if x is a stable log surface with reduced boundary possibly empty and i is its global index then 4 i k x is base point free and 8 i k x is very ample these bounds can be improved under further assumptions on the singularities or invariants for example 5 k x is very ample if x has semi canonical singularities

arc reduction and path preference in stochastic acyclic networks the paper presents a heuristic for determining the path that maximizes the expected utility of a stochastic acyclic network the focus is on shortest route problems where a general nonlinear utility function is used to measure outcomes for such problems enumerating all feasible paths is the only way to guarantee that the global optimum has been found alternatively we develop a reduction algorithm based on stochastic dominance to speed up the computations monte carlo simulation is used to evaluate the approach in all 70 test problems comprising 20 to 60 nodes are randomly generated and analyzed the results indicate that the heuristic produces significant computational saving as the size of the network grows and that the quality of the reduced network solutions are better than those obtained from the original formulation

technical note a note on the stochastic shortest route problem an optimality index for choosing the shortest route in an acyclic stochastic network has recently been proposed the present note identifies certain anomalies in using that index and proposes another optimality index the results of using these indices are compared in a simple example

least squares approximation to the distribution of project completion times with gaussian uncertainty this paper is motivated by the following question how to construct good approximation for the distribution of the solution value to linear optimization problem when the random objective coefficients follow a multivariate normal distribution using stein s identity we show that the least squares normal approximation of the random optimal value can be computed by estimating the persistency values of the corresponding optimization problem we further extend our method to construct a least squares quadratic estimator to improve the accuracy of the approximation in particular to capture the skewness of the objective computational studies show that the new approach provides more accurate estimates of the distributions of project completion times compared to existing methods

binary operations on jordan algebras and orthogonal normal models jordan algebras are used to present normal orthogonal models in a canonical form binary operations are defined on these algebras which enable us to build complex models based on simpler ones properties of these operations and their relation with balanced models are studied the canonical model formulation is interesting because it leads to complete sufficient statistics these statistics are then used to obtain estimators in order to test hypothesis on the model parameters