Do dentists prescribe narcotics excessively?

Journal ArticleDealing with pain is an inevitable sequela to dental treatment. Although several drug regimens primarily involving narcotics have been used in the past, availability of nonsteroidal anti-inflammatory drugs (NSAIDs) has increased recently. A study was conducted to analyze dental prescribing patterns for analgesics. Data analysis of a survey of 130 dentists revealed that respondents still rely on narcotic analgesics for pain relief and generally exceed needed potency and quantities in their prescribing habits. Dentists are treating rather than preventing pain, and NSAIDs are underused

Guide to oral health for non-dental health providers

ManuscriptOral health and disease topics are not given significant coverage in the non-dental health professional curriculum. Yet all care providers can and should contribute to enhancing oral health. This guide provides information on the ways in which practitioners can incorporate oral health care and disease prevention as part of standard patient care. Topics include oral disease managment and prevention, oral examination, oral health, and referral of patients to oral health practitioners

Scaling and Universality in Continuous Length Combinatorial Optimization

We consider combinatorial optimization problems defined over random ensembles, and study how solution cost increases when the optimal solution undergoes a small perturbation delta. For the minimum spanning tree, the increase in cost scales as delta^2; for the mean-field and Euclidean minimum matching and traveling salesman problems in dimension d>=2, the increase scales as delta^3; this is observed in Monte Carlo simulations in d=2,3,4 and in theoretical analysis of a mean-field model. We speculate that the scaling exponent could serve to classify combinatorial optimization problems into a small number of distinct categories, similar to universality classes in statistical physics.Comment: 5 pages; 3 figure

Multiclass Hammersley-Aldous-Diaconis process and multiclass-customer queues

In the Hammersley-Aldous-Diaconis process infinitely many particles sit in R and at most one particle is allowed at each position. A particle at x$ whose nearest neighbor to the right is at y, jumps at rate y-x to a position uniformly distributed in the interval (x,y). The basic coupling between trajectories with different initial configuration induces a process with different classes of particles. We show that the invariant measures for the two-class process can be obtained as follows. First, a stationary M/M/1 queue is constructed as a function of two homogeneous Poisson processes, the arrivals with rate \lambda and the (attempted) services with rate \rho>\lambda. Then put the first class particles at the instants of departures (effective services) and second class particles at the instants of unused services. The procedure is generalized for the n-class case by using n-1 queues in tandem with n-1 priority-types of customers. A multi-line process is introduced; it consists of a coupling (different from Liggett's basic coupling), having as invariant measure the product of Poisson processes. The definition of the multi-line process involves the dual points of the space-time Poisson process used in the graphical construction of the system. The coupled process is a transformation of the multi-line process and its invariant measure the transformation described above of the product measure.Comment: 21 pages, 6 figure

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

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

Exact calculations of first-passage quantities on recursive networks

We present general methods to exactly calculate mean-first passage quantities on self-similar networks defined recursively. In particular, we calculate the mean first-passage time and the splitting probabilities associated to a source and one or several targets; averaged quantities over a given set of sources (e.g., same-connectivity nodes) are also derived. The exact estimate of such quantities highlights the dependency of first-passage processes with respect to the source-target distance, which has recently revealed to be a key parameter to characterize transport in complex media. We explicitly perform calculations for different classes of recursive networks (finitely ramified fractals, scale-free (trans)fractals, non-fractals, mixtures between fractals and non-fractals, non-decimable hierarchical graphs) of arbitrary size. Our approach unifies and significantly extends the available results in the field.Comment: 16 pages, 10 figure

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

Mean-field methods in evolutionary duplication-innovation-loss models for the genome-level repertoire of protein domains

We present a combined mean-field and simulation approach to different models describing the dynamics of classes formed by elements that can appear, disappear or copy themselves. These models, related to a paradigm duplication-innovation model known as Chinese Restaurant Process, are devised to reproduce the scaling behavior observed in the genome-wide repertoire of protein domains of all known species. In view of these data, we discuss the qualitative and quantitative differences of the alternative model formulations, focusing in particular on the roles of element loss and of the specificity of empirical domain classes.Comment: 10 Figures, 2 Table