934 research outputs found
The Synthesis of Potential Antitumor Compounds
The antitumor activity found in such ring systems as the purine, pyrazolo [3,4-d] pyrimidine, and the 8-azapurine prompted the preparation of the imidazo [4,5-d] pyridazine ring system. Castle and Seese were one of the first to study this ring system. 4-Aminoimidazo[4,5-d]pyridazine possessed some anitumor activity. This antitumor activity suggested the preparation of the 4,7-disubstituted-aminoimidazo{4,5-d]pyridazines reported here. The antileukemic activity reported for 6-purinethiol led to the synthesis of several 4- and/or 7-mono-and disubstitutedthioimidazo[4,5-d]pyridazines
Ground States for Exponential Random Graphs
We propose a perturbative method to estimate the normalization constant in
exponential random graph models as the weighting parameters approach infinity.
As an application, we give evidence of discontinuity in natural parametrization
along the critical directions of the edge-triangle model.Comment: 12 pages, 3 figures, 1 tabl
Noon report data uncertainty
Noon report data is a low resolution dataset (sampling frequency of approximately 24 hours) from which it is possible to extract the principal variables required to define the ship’s performance in terms of fuel consumption. There are increasing economic and environmental incentives for ship owners and operators to develop tools to optimise operational decisions with the aim of reducing fuel consumption and/or maximising profit. Further, a ships current performance needs to be measured in order for fuel savings from technological interventions to be assessed. These tools and measurements may be based on models developed from historical trends that are extracted from noon reports; however there is inherent uncertainty in this dataset. As a prerequisite the uncertainty must be quantified to understand fully the potential and limitations of predictive models from which operational tools may be designed and of statistical models from which technological interventions are assessed. This paper initially presents a method for quantifying the uncertainty in reported fuel consumption using between two months and one year’s worth of data from 89 ships. The subsequently calculated confidence is then compared to the uncertainty in the data acquired from an on board continuous monitoring system
South African congenital disorders data, 2006 - 2014
Background. The National Department of Health in South Africa (SA) routinely collects congenital disorder (CD) data for its national CD surveillance system. The current system has been implemented since 2006, but no reports on the data collected, methodology, achievements or challenges have been published to date.Objectives. To ascertain the effectiveness of the current national CD surveillance system and its implementation.Method. A descriptive, retrospective study using an audit of the current database was undertaken to evaluate the number of notifications received, types of CDs reported and the quality of reporting across SA for data received from 2006 to 2014.Results. A total of 14 571 notifications were received, including 13 252 CDs and 1 319 zero notifications, across all nine provinces. Commonly reported CDs included Down syndrome, cleft lip and palate, talipes equinovarus, neural tube defects and albinism.Conclusions. The major challenges identified included erratic compliance by health facilities and a lack of healthcare providers trained in human genetics related to CDs. This has led to misdiagnosed and undiagnosed CDs, collectively resulting in under-reporting of cases by >98% during the review period. Owing to limited human and financial resources, it is recommended that the surveillance system be modified into an electronic format. This should be piloted alongside relevant training in specific sentinel sites, to improve data coverage and quality for further evaluation
Multicritical continuous random trees
We introduce generalizations of Aldous' Brownian Continuous Random Tree as
scaling limits for multicritical models of discrete trees. These discrete
models involve trees with fine-tuned vertex-dependent weights ensuring a k-th
root singularity in their generating function. The scaling limit involves
continuous trees with branching points of order up to k+1. We derive explicit
integral representations for the average profile of this k-th order
multicritical continuous random tree, as well as for its history distributions
measuring multi-point correlations. The latter distributions involve
non-positive universal weights at the branching points together with fractional
derivative couplings. We prove universality by rederiving the same results
within a purely continuous axiomatic approach based on the resolution of a set
of consistency relations for the multi-point correlations. The average profile
is shown to obey a fractional differential equation whose solution involves
hypergeometric functions and matches the integral formula of the discrete
approach.Comment: 34 pages, 12 figures, uses lanlmac, hyperbasics, eps
Optimal spatial transportation networks where link-costs are sublinear in link-capacity
Consider designing a transportation network on vertices in the plane,
with traffic demand uniform over all source-destination pairs. Suppose the cost
of a link of length and capacity scales as for fixed
. Under appropriate standardization, the cost of the minimum cost
Gilbert network grows essentially as , where on and on . This quantity is an upper bound in
the worst case (of vertex positions), and a lower bound under mild regularity
assumptions. Essentially the same bounds hold if we constrain the network to be
efficient in the sense that average route-length is only times
average straight line length. The transition at corresponds to
the dominant cost contribution changing from short links to long links. The
upper bounds arise in the following type of hierarchical networks, which are
therefore optimal in an order of magnitude sense. On the large scale, use a
sparse Poisson line process to provide long-range links. On the medium scale,
use hierachical routing on the square lattice. On the small scale, link
vertices directly to medium-grid points. We discuss one of many possible
variant models, in which links also have a designed maximum speed and the
cost becomes .Comment: 13 page
Quantum speedup of classical mixing processes
Most approximation algorithms for #P-complete problems (e.g., evaluating the
permanent of a matrix or the volume of a polytope) work by reduction to the
problem of approximate sampling from a distribution over a large set
. This problem is solved using the {\em Markov chain Monte Carlo} method: a
sparse, reversible Markov chain on with stationary distribution
is run to near equilibrium. The running time of this random walk algorithm, the
so-called {\em mixing time} of , is as shown
by Aldous, where is the spectral gap of and is the minimum
value of . A natural question is whether a speedup of this classical
method to , the diameter of the graph
underlying , is possible using {\em quantum walks}.
We provide evidence for this possibility using quantum walks that {\em
decohere} under repeated randomized measurements. We show: (a) decoherent
quantum walks always mix, just like their classical counterparts, (b) the
mixing time is a robust quantity, essentially invariant under any smooth form
of decoherence, and (c) the mixing time of the decoherent quantum walk on a
periodic lattice is , which is indeed
and is asymptotically no worse than the
diameter of (the obvious lower bound) up to at most a logarithmic
factor.Comment: 13 pages; v2 revised several part
Empires and Percolation: Stochastic Merging of Adjacent Regions
We introduce a stochastic model in which adjacent planar regions merge
stochastically at some rate , and observe analogies with the
well-studied topics of mean-field coagulation and of bond percolation. Do
infinite regions appear in finite time? We give a simple condition on
for this {\em hegemony} property to hold, and another simple condition for it
to not hold, but there is a large gap between these conditions, which includes
the case . For this case, a non-rigorous analytic
argument and simulations suggest hegemony.Comment: 13 page
Dynamic critical exponents of Swendsen-Wang and Wolff algorithms by nonequilibrium relaxation
With a nonequilibrium relaxation method, we calculate the dynamic critical
exponent z of the two-dimensional Ising model for the Swendsen-Wang and Wolff
algorithms. We examine dynamic relaxation processes following a quench from a
disordered or an ordered initial state to the critical temperature T_c, and
measure the exponential relaxation time of the system energy. For the
Swendsen-Wang algorithm with an ordered or a disordered initial state, and for
the Wolff algorithm with an ordered initial state, the exponential relaxation
time fits well to a logarithmic size dependence up to a lattice size L=8192.
For the Wolff algorithm with a disordered initial state, we obtain an effective
dynamic exponent z_exp=1.19(2) up to L=2048. For comparison, we also compute
the effective dynamic exponents through the integrated correlation times. In
addition, an exact result of the Swendsen-Wang dynamic spectrum of a
one-dimension Ising chain is derived.Comment: 13 pages, 6 figure
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