Spanning trees short or small

We study the problem of finding small trees. Classical network design problems are considered with the additional constraint that only a specified number $k$ of nodes are required to be connected in the solution. A prototypical example is the $k$MST problem in which we require a tree of minimum weight spanning at least $k$ nodes in an edge-weighted graph. We show that the $k$MST problem is NP-hard even for points in the Euclidean plane. We provide approximation algorithms with performance ratio $2\sqrt{k}$ for the general edge-weighted case and $O(k^{1/4})$ for the case of points in the plane. Polynomial-time exact solutions are also presented for the class of decomposable graphs which includes trees, series-parallel graphs, and bounded bandwidth graphs, and for points on the boundary of a convex region in the Euclidean plane. We also investigate the problem of finding short trees, and more generally, that of finding networks with minimum diameter. A simple technique is used to provide a polynomial-time solution for finding $k$-trees of minimum diameter. We identify easy and hard problems arising in finding short networks using a framework due to T. C. Hu.Comment: 27 page

Bicriteria Network Design Problems

We study a general class of bicriteria network design problems. A generic problem in this class is as follows: Given an undirected graph and two minimization objectives (under different cost functions), with a budget specified on the first, find a <subgraph \from a given subgraph-class that minimizes the second objective subject to the budget on the first. We consider three different criteria - the total edge cost, the diameter and the maximum degree of the network. Here, we present the first polynomial-time approximation algorithms for a large class of bicriteria network design problems for the above mentioned criteria. The following general types of results are presented. First, we develop a framework for bicriteria problems and their approximations. Second, when the two criteria are the same %(note that the cost functions continue to be different) we present a ``black box'' parametric search technique. This black box takes in as input an (approximation) algorithm for the unicriterion situation and generates an approximation algorithm for the bicriteria case with only a constant factor loss in the performance guarantee. Third, when the two criteria are the diameter and the total edge costs we use a cluster-based approach to devise a approximation algorithms --- the solutions output violate both the criteria by a logarithmic factor. Finally, for the class of treewidth-bounded graphs, we provide pseudopolynomial-time algorithms for a number of bicriteria problems using dynamic programming. We show how these pseudopolynomial-time algorithms can be converted to fully polynomial-time approximation schemes using a scaling technique.Comment: 24 pages 1 figur

Robustness against parametric noise of non ideal holonomic gates

Holonomic gates for quantum computation are commonly considered to be robust against certain kinds of parametric noise, the very motivation of this robustness being the geometric character of the transformation achieved in the adiabatic limit. On the other hand, the effects of decoherence are expected to become more and more relevant when the adiabatic limit is approached. Starting from the system described by Florio et al. [Phys. Rev. A 73, 022327 (2006)], here we discuss the behavior of non ideal holonomic gates at finite operational time, i.e., far before the adiabatic limit is reached. We have considered several models of parametric noise and studied the robustness of finite time gates. The obtained results suggest that the finite time gates present some effects of cancellation of the perturbations introduced by the noise which mimic the geometrical cancellation effect of standard holonomic gates. Nevertheless, a careful analysis of the results leads to the conclusion that these effects are related to a dynamical instead of geometrical feature.Comment: 8 pages, 8 figures, several changes made, accepted for publication on Phys. Rev.

Particle current in symmetric exclusion process with time-dependent hopping rates

In a recent study, (Jain et al 2007 Phys. Rev. Lett. 99 190601), a symmetric exclusion process with time-dependent hopping rates was introduced. Using simulations and a perturbation theory, it was shown that if the hopping rates at two neighboring sites of a closed ring vary periodically in time and have a relative phase difference, there is a net DC current which decreases inversely with the system size. In this work, we simplify and generalize our earlier treatment. We study a model where hopping rates at all sites vary periodically in time, and show that for certain choices of relative phases, a DC current of order unity can be obtained. Our results are obtained using a perturbation theory in the amplitude of the time-dependent part of the hopping rate. We also present results obtained in a sudden approximation that assumes large modulation frequency.Comment: 17 pages, 2 figure

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

Norepinephrine directly activates adult hippocampal precursors via beta(3)-adrenergic receptors

Adult hippocampal neurogenesis is a critical form of cellular plasticity that is greatly influenced by neural activity. Among the neurotransmitters that are widely implicated in regulating this process are serotonin and norepinephrine, levels of which are modulated by stress, depression and clinical antidepressants. However, studies to date have failed to address a direct role for either neurotransmitter in regulating hippocampal precursor activity. Here we show that norepinephrine but not serotonin directly activates self-renewing and multipotent neural precursors, including stem cells, from the hippocampus of adult mice. Mechanistically, we provide evidence that beta(3)-adrenergic receptors, which are preferentially expressed on a Hes5-expressing precursor population in the subgranular zone (SGZ), mediate this norepinephrine-dependent activation. Moreover, intrahippocampal injection of a selective beta(3)-adrenergic receptor agonist in vivo increases the number of proliferating cells in the SGZ. Similarly, systemic injection of the beta-adrenergic receptor agonist isoproterenol not only results in enhancement of proliferation in the SGZ but also leads to an increase in the percentage of nestin/glial fibrillary acidic protein double-positive neural precursors in vivo. Finally, using a novel ex vivo "slice-sphere" assay that maintains an intact neurogenic niche, we demonstrate that antidepressants that selectively block the reuptake of norepinephrine, but not serotonin, robustly increase hippocampal precursor activity via beta-adrenergic receptors. These findings suggest that the activation of neurogenic precursors and stem cells via beta(3)-adrenergic receptors could be a potent mechanism to increase neuronal production, providing a putative target for the development of novel antidepressants

Periodically specified satisfiability problems with applications: An alternative to domino problems

We characterize the complexities of several basic generalized CNF satisfiability problems SAT(S), when instances are specified using various kinds of 1- and 2-dimensional periodic specifications. We outline how this characterization can be used to prove a number of new hardness results for the complexity classes DSPACE(n), NSPACE(n), DEXPTIME, NEXPTIME, EXPSPACE etc. The hardness results presented significantly extend the known hardness results for periodically specified problems. Several advantages axe outlined of the use of periodically specified satisfiability problems over the use of domino problems in proving both hardness and easiness results. As one corollary, we show that a number of basic NP-hard problems become EXPSPACE hard when inputs axe represented using 1-dimensional infinite periodic wide specifications. This answers a long standing open question posed by Orlin