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 $n$ vertices in the plane, with traffic demand uniform over all source-destination pairs. Suppose the cost of a link of length $\ell$ and capacity $c$ scales as $\ell c^\beta$ for fixed $0<\beta<1$. Under appropriate standardization, the cost of the minimum cost Gilbert network grows essentially as $n^{\alpha(\beta)}$, where $\alpha(\beta) = 1 - \frac{\beta}{2}$ on $0 < \beta \leq {1/2}$ and $\alpha(\beta) = {1/2} + \frac{\beta}{2}$ on ${1/2} \leq \beta < 1$. 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 $1 + o(1)$ times average straight line length. The transition at $\beta = {1/2}$ 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 $s$ and the cost becomes $\ell c^\beta s^\gamma$.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 $\pi$ over a large set $\S$. This problem is solved using the {\em Markov chain Monte Carlo} method: a sparse, reversible Markov chain $P$ on $\S$ with stationary distribution $\pi$ is run to near equilibrium. The running time of this random walk algorithm, the so-called {\em mixing time} of $P$, is $O(\delta^{-1} \log 1/\pi_*)$ as shown by Aldous, where $\delta$ is the spectral gap of $P$ and $\pi_*$ is the minimum value of $\pi$. A natural question is whether a speedup of this classical method to $O(\sqrt{\delta^{-1}} \log 1/\pi_*)$, the diameter of the graph underlying $P$, 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 $\Z_n^d$ is $O(n d \log d)$, which is indeed $O(\sqrt{\delta^{-1}} \log 1/\pi_*)$ and is asymptotically no worse than the diameter of $\Z_n^d$ (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 $A, B$ merge stochastically at some rate $\lambda(A,B)$, 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 $\lambda$ 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 $\lambda(A,B) \equiv 1$. 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