Capacity expansion under a service-level constraint for uncertain demand with lead times

For a service provider facing stochastic demand growth, expansion lead times and economies of scale complicate the expansion timing and sizing decisions. We formulate a model to minimize the infinite horizon expected discounted expansion cost under a service-level constraint. The service level is defined as the proportion of demand over an expansion cycle that is satisfied by available capacity. For demand that follows a geometric Brownian motion process, we impose a stationary policy under which expansions are triggered by a fixed ratio of demand to the capacity position, i.e., the capacity that will be available when any current expansion project is completed, and each expansion increases capacity by the same proportion. The risk of capacity shortage during a cycle is estimated analytically using the value of an up-and-out partial barrier call option. A cutting plane procedure identifies the optimal values of the two expansion policy parameters simultaneously. Numerical instances illustrate that if demand grows slowly with low volatility and the expansion lead times are short, then it is optimal to delay the start of expansion beyond when demand exceeds the capacity position. Delays in initiating expansions are coupled with larger expansion sizes

Stochastic pump of interacting particles

We consider the overdamped motion of Brownian particles, interacting via particle exclusion, in an external potential that varies with time and space. We show that periodic potentials that maintain specific position-dependent phase relations generate time-averaged directed current of particles. We obtain analytic results for a lattice version of the model using a recently developed perturbative approach. Many interesting features like particle-hole symmetry, current reversal with changing density, and system-size dependence of current are obtained. We propose possible experiments to test our predictions.Comment: 4 pages, 2 figure

Gauge theory of Faddeev-Skyrme functionals

We study geometric variational problems for a class of nonlinear sigma-models in quantum field theory. Mathematically, one needs to minimize an energy functional on homotopy classes of maps from closed 3-manifolds into compact homogeneous spaces G/H. The minimizers are known as Hopfions and exhibit localized knot-like structure. Our main results include proving existence of Hopfions as finite energy Sobolev maps in each (generalized) homotopy class when the target space is a symmetric space. For more general spaces we obtain a weaker result on existence of minimizers in each 2-homotopy class. Our approach is based on representing maps into G/H by equivalence classes of flat connections. The equivalence is given by gauge symmetry on pullbacks of G-->G/H bundles. We work out a gauge calculus for connections under this symmetry, and use it to eliminate non-compactness from the minimization problem by fixing the gauge.Comment: 34 pages, no figure

Patterns in abundance and diversity of faecally dispersed parasites of tiger in Tadoba National Park, central India

BACKGROUND: Importance of parasites in ecological and evolutionary interactions is being increasingly recognized. However, ecological data on parasites of important host species is still scanty. We analyze the patterns seen in the faecal parasites of tigers in the Tadoba National Park, India, and speculate on the factors and processes shaping the parasite community and the possible implications for tiger ecology. RESULTS: The prevalence and intensities were high and the parasite community was dominated by indirect life cycle parasites. Across all genera of parasites variance scaled with the square of the mean and there was a significant positive correlation between prevalence and abundance. There was no significant association between different types of parasites. CONCLUSIONS: The 70 samples analyzed formed 14 distinct clusters. If we assume each of the clusters to represent individual tigers that were sampled repeatedly and that resident tigers are more likely to be sampled repeatedly, the presumed transient tigers had significantly greater parasite loads than the presumed resident ones

Knowledge, attitudes and breast-feeding practices of postnatal mothers in Central India

Background: Breast feeding is vital for the health of baby & mother. It is of advantage to baby, mother, family, society and nation. Present study was carried out to evaluate knowledge, attitude and breast feeding practices of postnatal women.Methods: This cross-sectional study was carried out at immunization centre. 208 postnatal women were interviewed.Results: Out of 208 postnatal women, 148 women (71.15%) had delivery by caesarean section while 60 women (28.84%) had vaginal delivery. 118 women (56.73%) started breast feeding the baby within 2 hours of delivery, 52 women (25%) started breast feeding the baby after 24 hours of delivery, 26 women (12.5%) started breast feeding the baby after 2-6 hours of delivery while 12 women (5.76%) started breast feeding the baby after 6-24 hours of delivery. 174 women (83.65%) were giving exclusive breast feeding to their babies, 32 women (15.38%) were giving mixed feeding to their babies due to failure to thrive because of inadequate breast secretions. 28 (13.46%) preferred to give formula feeds while 7 (3.36%) preferred to give cow’s milk when needed. 180 (86.53%) intend or started weaning after 6 months while 28 women (13.46%) started weaning to their babies due to failure of baby to thrive or inadequate lactation.Conclusions: Awareness of breast feeding was good. Majority preferred exclusive breast feeding. Still, antenatal counseling about breast feeding can be further of advantage

Level-treewidth property, exact algorithms and approximation schemes

Informally, a class of graphs Q is said to have the level-treewidth property (LT-property) if for every G {element_of} Q there is a layout (breadth first ordering) L{sub G} such that the subgraph induced by the vertices in k-consecutive levels in the layout have treewidth O(f (k)), for some function f. We show that several important and well known classes of graphs including planar and bounded genus graphs, (r, s)-civilized graphs, etc, satisfy the LT-property. Building on the recent work, we present two general types of results for the class of graphs obeying the LT-property. (1) All problems in the classes MPSAT, TMAX and TMIN have polynomial time approximation schemes. (2) The problems considered in Eppstein have efficient polynomial time algorithms. These results can be extended to obtain polynomial time approximation algorithms and approximation schemes for a number of PSPACE-hard combinatorial problems specified using different kinds of succinct specifications studied in. Many of the results can also be extended to {delta}-near genus and {delta}-near civilized graphs, for any fixed {delta}. Our results significantly extend the work in and affirmatively answer recent open questions

Complexity and efficient approximability of two dimensional periodically specified problems

The authors consider the two dimensional periodic specifications: a method to specify succinctly objects with highly regular repetitive structure. These specifications arise naturally when processing engineering designs including VLSI designs. These specifications can specify objects whose sizes are exponentially larger than the sizes of the specification themselves. Consequently solving a periodically specified problem by explicitly expanding the instance is prohibitively expensive in terms of computational resources. This leads one to investigate the complexity and efficient approximability of solving graph theoretic and combinatorial problems when instances are specified using two dimensional periodic specifications. They prove the following results: (1) several classical NP-hard optimization problems become NEXPTIME-hard, when instances are specified using two dimensional periodic specifications; (2) in contrast, several of these NEXPTIME-hard problems have polynomial time approximation algorithms with guaranteed worst case performance