6,318 research outputs found
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 of nodes are required to be connected in the solution. A
prototypical example is the MST problem in which we require a tree of
minimum weight spanning at least nodes in an edge-weighted graph. We show
that the MST problem is NP-hard even for points in the Euclidean plane. We
provide approximation algorithms with performance ratio for the
general edge-weighted case and 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 -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
Clinical submission of supernumerary head of adducter brevis muscle
Adductor brevis is an important member of the adductor family occupying the medial compartment of the thigh executing the function of adduction and medial rotation. Deviations from normal anatomy are unusual and rarely reported. A survey of anatomical archives revealed occasional mention of additional bellies of adductor brevis muscle. The present study reports a double belly of adductor brevis muscle (AB) found during a cadaveric dissection class for medical students. The left sided AB displayed two bellies disposed in the same plane. This case report attempts to present the clinical applications of supernumerary bellies of this important adductor muscle of the thigh. It is feasible to categorize these muscular variations upon specialized radiological procedures such as CT and MRI scans only if the radiologist possesses satisfactory understanding of variant anatomy of this region. It is thereafter inferred that upon recognition these muscles present a fair chance of being of utilitised in reconstructions. A biomechanical overview of the present anomaly is also attempte
Origin of charge density wave formation in insulators from a high resolution photoemission study of BaIrO3
We investigate the origin of charge density wave (CDW) formation in
insulators by studying BaIrO3 using high resolution (1.4 meV) photoemission
spectroscopy. The spectra reveal the existence of localized density of states
at the Fermi level in the vicinity of room temperature. These localized states
are found to vanish as the temperature is lowered thereby, opening a soft gap
at the Fermi level, as a consequence of CDW transition. In addition, the energy
dependence of the spectral density of states reveals the importance of magnetic
interactions, rather than well-known Coulomb repulsion effect, in determining
the electronic structure thereby implying a close relationship between
ferromagnetism and CDW observed in this compound. Also, Ba core level spectra
surprisingly exhibit an unusual behavior prior to CDW transition.Comment: 4 pages, 4 figures. To appear in Physical Review Letter
Some Elementary Inequalities Between Mean and Standard Deviation
Some inequalities for the mean and standard deviation of continuous probability distributions are presented here in this paper and their geometrical significance has also been discussed. It has been shown that the inequalities obtained in this paper are better than the inequalities discussed by J. Muilwijk[6]
Solution of Space-Time Fractional Schrödinger Equation Occurring in Quantum Mechanics
Dedicated to Professor A.M. Mathai on the occasion of his 75-th birthday. Mathematics Subject Classi¯cation 2010: 26A33, 44A10, 33C60, 35J10.The object of this article is to present the computational solution of one-dimensional space-time fractional Schrödinger equation occurring in quantum mechanics. The method followed in deriving the solution is that of joint Laplace and Fourier transforms. The solution is derived in a closed and computational form in terms of the H-function. It provides an elegant extension of a result given earlier by Debnath, and by Saxena et al. The main result is obtained in the form of Theorem 1. Three special cases of this theorem are given as corollaries. Computational representation of the fundamental solution of the proposed equation is also investigated
On associating Fast Radio Bursts with afterglows
A radio source that faded over six days, with a redshift of
host, has been identified by Keane et al. (2016) as the transient afterglow to
a fast radio burst (FRB 150418). We report follow-up radio and optical
observations of the afterglow candidate and find a source that is consistent
with an active galactic nucleus. If the afterglow candidate is nonetheless a
prototypical FRB afterglow, existing slow-transient surveys limit the fraction
of FRBs that produce afterglows to 0.25 for afterglows with fractional
variation, , and 0.07 for , at 95%
confidence. In anticipation of a barrage of bursts expected from future FRB
surveys, we provide a simple framework for statistical association of FRBs with
afterglows. Our framework properly accounts for statistical uncertainties, and
ensures consistency with limits set by slow-transient surveys.Comment: Accepted version (ApJL
- …