Pattern‐avoiding permutations and Brownian excursion part I: Shapes and fluctuations

Permutations that avoid given patterns are among the most classical objects in combinatorics and have strong connections to many fields of mathematics, computer science and biology. In this paper we study the scaling limits of a random permutation avoiding a pattern of length 3 and their relations to Brownian excursion. Exploring this connection to Brownian excursion allows us to strengthen the recent results of Madras and Pehlivan [25] and Miner and Pak [29] as well as to understand many of the interesting phenomena that had previously gone unexplained. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 50, 394–419, 2017     

ThrEEBoost: Thresholded Boosting for Variable Selection and Prediction via Estimating Equations

Most variable selection techniques for high-dimensional models are designed to be used in settings, where observations are independent and completely observed. At the same time, there is a rich literature on approaches to estimation of low-dimensional parameters in the presence of correlation, missingness, measurement error, selection bias, and other characteristics of real data. In this article, we present ThrEEBoost (Thresholded EEBoost), a general-purpose variable selection technique which can accommodate such problem characteristics by replacing the gradient of the loss by an estimating function. ThrEEBoost generalizes the previously proposed EEBoost algorithm (Wolfson 2011 Wolfson, J. (2011), “EEBoost: A General Method for Prediction and Variable Selection Based on Estimating Equations,” Journal of the American Statistical Association, 106, 296–305.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) by allowing the number of regression coefficients updated at each step to be controlled by a thresholding parameter. Different thresholding parameter values yield different variable selection paths, greatly diversifying the set of models that can be explored; the optimal degree of thresholding can be chosen by cross-validation. ThrEEBoost was evaluated using simulation studies to assess the effects of different threshold values on prediction error, sensitivity, specificity, and the number of iterations to identify minimum prediction error under both sparse and nonsparse true models with correlated continuous outcomes. We show that when the true model is sparse, ThrEEBoost achieves similar prediction error to EEBoost while requiring fewer iterations to locate the set of coefficients yielding the minimum error. When the true model is less sparse, ThrEEBoost has lower prediction error than EEBoost and also finds the point yielding the minimum error more quickly. The technique is illustrated by applying it to the problem of identifying predictors of weight change in a longitudinal nutrition study. Supplementary materials are available online.     

Programming With Models: Writing Statistical Algorithms for General Model Structures With NIMBLE

We describe NIMBLE, a system for programming statistical algorithms for general model structures within R. NIMBLE is designed to meet three challenges: flexible model specification, a language for programming algorithms that can use different models, and a balance between high-level programmability and execution efficiency. For model specification, NIMBLE extends the BUGS language and creates model objects, which can manipulate variables, calculate log probability values, generate simulations, and query the relationships among variables. For algorithm programming, NIMBLE provides functions that operate with model objects using two stages of evaluation. The first stage allows specialization of a function to a particular model and/or nodes, such as creating a Metropolis-Hastings sampler for a particular block of nodes. The second stage allows repeated execution of computations using the results of the first stage. To achieve efficient second-stage computation, NIMBLE compiles models and functions via C++, using the Eigen library for linear algebra, and provides the user with an interface to compiled objects. The NIMBLE language represents a compilable domain-specific language (DSL) embedded within R. This article provides an overview of the design and rationale for NIMBLE along with illustrative examples including importance sampling, Markov chain Monte Carlo (MCMC) and Monte Carlo expectation maximization (MCEM). Supplementary materials for this article are available online.     

An Organoruthenium Anticancer Agent Shows Unexpected Target Selectivity For Plectin

Organometallic metal(arene) anticancer agents require ligand exchange for their anticancer activity and this is generally believed to confer low selectivity for potential cellular targets. However, using an integrated proteomics-based target-response profiling approach as a potent hypothesis-generating procedure, we found an unexpected target selectivity of a ruthenium(arene) pyridinecarbothioamide (plecstatin) for plectin, a scaffold protein and cytolinker, which was validated in a plectin knock-out model in vitro. Plectin targeting shows potential as a strategy to inhibit tumor invasiveness as shown in cultured tumor spheroids while oral administration of plecstatin-1 to mice reduces tumor growth more efficiently in the invasive B16 melanoma than in the CT26 colon tumor model.     

Utilizing Paper-Based Devices for Antimicrobial-Resistant Bacteria Detection

Antimicrobial resistance (AMR), the ability of a bacterial species to resist the action of an antimicrobial drug, has been on the rise due to the widespread use of antimicrobial agents. Per the World Health Organization, AMR has an estimated annual cost of USD 34 billion in the US and is predicted to be the number one cause of death worldwide by 2050. One way AMR bacteria can spread, and by which individuals can contract AMR infections, is through contaminated water. Monitoring AMR bacteria in the environment currently requires that samples be transported to a central laboratory for slow and labor intensive tests. We have developed an inexpensive assay using paper-based analytical devices (PADs) that can test for the presence of β-lactamase-mediated resistance. To demonstrate viability, the PAD was used to detect β-lactam resistance in wastewater and sewage and identified resistance in individual bacterial species isolated from environmental water sources.     

Rethinking pedagogy for second-order differential equations: a simplified approach to understanding well-posed problems

Knowing an equation has a unique solution is important from both a modelling and theoretical point of view. For over 70 years, the approach to learning and teaching ‘well posedness’ of initial value problems (IVPs) for second- and higher-order ordinary differential equations has involved transforming the problem and its analysis to a first-order system of equations. We show that this excursion is unnecessary and present a direct approach regarding second- and higher-order problems that does not require an understanding of systems.     

On the set of elasticities in numerical monoids

In an atomic, cancellative, commutative monoid S, the elasticity of an element provides a coarse measure of its non-unique factorizations by comparing the largest and smallest values in its set of factorization lengths (called its length set). In this paper, we show that the set of length sets \({\mathcal {L}}(S)\) for any arithmetical numerical monoid S can be completely recovered from its set of elasticities R(S); therefore, R(S) is as strong a factorization invariant as \({\mathcal {L}}(S)\) in this setting. For general numerical monoids, we describe the set of elasticities as a specific collection of monotone increasing sequences with a common limit point of \(\max R(S)\).     

Inelastic constitutive equations for complex flows

A new class of inelastic constitutive equations is presented and discussed. In addition to the rate-of-strain tensor, the stress is assumed to depend also on the relative-rate-of-rotation tensor, a frame-indifferent quantity that brings information about the nature of the flow. The material functions predicted by these constitutive equations are given for simple shear and uniaxial extension. A special case of these equations takes the Newtonian form, except that the viscosity is a function of the invariants of both kinematic tensors on which the stress depends. This simple constitutive equation has potential applications in liquid flow process simulations, since it combines simplicity with the capability of responding independently to shear and extension, as real liquids seem to do. Finally, possible forms for the new viscosity function are discussed.     

Fluid dynamics of self-propelled microorganisms,from individuals to concentrated populations

Nearly close-packed populations of the swimming bacterium Bacillus subtilis form a collective phase, the “Zooming BioNematic” (ZBN). This state exhibits large-scale orientational coherence, analogous to the molecular alignment of nematic liquid crystals, coupled with remarkable spatial and temporal correlations of velocity and vorticity, as measured by both novel and standard applications of particle imaging velocimetry. The appearance of turbulent dynamics in a system which is nominally in the regime of Stokes flow can be understood by accounting for the local energy input by the swimmers, with a new dimensionless ratio analogous to the Reynolds number. The interaction between organisms and boundaries, and with one another, is modeled by application of the methods of regularized Stokeslets.