Generalized Permutohedra from Probabilistic Graphical Models

A graphical model encodes conditional independence relations via the Markov properties. For an undirected graph these conditional independence relations can be represented by a simple polytope known as the graph associahedron, which can be constructed as a Minkowski sum of standard simplices. There is an analogous polytope for conditional independence relations coming from a regular Gaussian model, and it can be defined using multiinformation or relative entropy. For directed acyclic graphical models and also for mixed graphical models containing undirected, directed and bidirected edges, we give a construction of this polytope, up to equivalence of normal fans, as a Minkowski sum of matroid polytopes. Finally, we apply this geometric insight to construct a new ordering-based search algorithm for causal inference via directed acyclic graphical models.Comment: Appendix B is expanded. Final version to appear in SIAM J. Discrete Mat

Differentially Private Model Selection with Penalized and Constrained Likelihood

In statistical disclosure control, the goal of data analysis is twofold: The released information must provide accurate and useful statistics about the underlying population of interest, while minimizing the potential for an individual record to be identified. In recent years, the notion of differential privacy has received much attention in theoretical computer science, machine learning, and statistics. It provides a rigorous and strong notion of protection for individuals' sensitive information. A fundamental question is how to incorporate differential privacy into traditional statistical inference procedures. In this paper we study model selection in multivariate linear regression under the constraint of differential privacy. We show that model selection procedures based on penalized least squares or likelihood can be made differentially private by a combination of regularization and randomization, and propose two algorithms to do so. We show that our private procedures are consistent under essentially the same conditions as the corresponding non-private procedures. We also find that under differential privacy, the procedure becomes more sensitive to the tuning parameters. We illustrate and evaluate our method using simulation studies and two real data examples

Defect-induced perturbations of atomic monolayers on solid surfaces

We study long-range morphological changes in atomic monolayers on solid substrates induced by different types of defects; e.g., by monoatomic steps in the surface, or by the tip of an atomic force microscope (AFM), placed at some distance above the substrate. Representing the monolayer in terms of a suitably extended Frenkel-Kontorova-type model, we calculate the defect-induced density profiles for several possible geometries. In case of an AFM tip, we also determine the extra force exerted on the tip due to the tip-induced de-homogenization of the monolayer.Comment: 4 pages, 2 figure

On the driven Frenkel-Kontorova model: I. Uniform sliding states and dynamical domains of different particle densities

The dynamical behavior of a harmonic chain in a spatially periodic potential (Frenkel-Kontorova model, discrete sine-Gordon equation) under the influence of an external force and a velocity proportional damping is investigated. We do this at zero temperature for long chains in a regime where inertia and damping as well as the nearest-neighbor interaction and the potential are of the same order. There are two types of regular sliding states: Uniform sliding states, which are periodic solutions where all particles perform the same motion shifted in time, and nonuniform sliding states, which are quasi-periodic solutions where the system forms patterns of domains of different uniform sliding states. We discuss the properties of this kind of pattern formation and derive equations of motion for the slowly varying average particle density and velocity. To observe these dynamical domains we suggest experiments with a discrete ring of at least fifty Josephson junctions.Comment: Written in RevTeX, 9 figures in PostScrip

Making connections: technological interventions to support students in using, and tutors in creating, assessment feedback

This paper explores the potential of technology to enhance the assessment and feedback process for both staff and students. The ‘Making Connections’ project aimed to better understand the connections that students make between the feedback that they receive and future assignments, and explored whether technology can help them in this activity. The project interviewed 10 tutors and 20 students, using a semi-structured approach. Data were analysed using a thematic approach, and the findings have identified a number of areas in which improvements could be made to the assessment and feedback process through the use of technology. The findings of the study cover each stage of the assessment process from the perspective of both staff and students. The findings are discussed in the context of current literature, and special attention is given to projects from the UK higher education sector intended to address the same issues. Keywords: feed-forward; assessment; practices; technology; technology-enhanced learnin

The Cost-Effectiveness of Tuberculosis Preventive Therapy for HIV-Infected Individuals in Southern India: A Trial-Based Analysis

Regimens for isoniazid-based preventive therapy (IPT) for tuberculosis (TB) in HIV-infected individuals have not been widely adopted given concerns regarding efficacy, adherence and drug resistance. Further, the cost-effectiveness of IPT has not been studied in India.We used an HIV/TB model to project TB incidence, life expectancy, cost and incremental cost-effectiveness of six months of isoniazid plus ethambutol (6EH), thirty-six months of isoniazid (36H) and no IPT for HIV-infected patients in India. Model input parameters included a median CD4 count of 324 cells/mm(3), and a rate ratio of developing TB of 0.35 for 6EH and 0.22 for 36H at three years as compared to no IPT. Results of 6EH and 36H were also compared to six months of isoniazid (6H), three months of isoniazid plus rifampin (3RH) and three months of isoniazid plus rifapentine (3RPTH).Projected TB incidence decreased in the 6EH and 36H regimens by 51% and 62% respectively at three-year follow-up compared to no IPT. Without IPT, projected life expectancy was 136.1 months at a lifetime per person cost of $5,630. 6EH increased life expectancy by 0.8 months at an additional per person cost of$100 (incremental cost-effectiveness ratio (ICER) of $1,490/year of life saved (YLS)). 36H further increased life expectancy by 0.2 months with an additional per person cost of$55 (ICER of $3,120/YLS). The projected clinical impact of 6EH was comparable to 6H and 3RH; however when compared to these other options, 6EH was no longer cost-effective given the high cost of ethambutol. Results were sensitive to baseline CD4 count and adherence.Three, six and thirty-six-month regimens of isoniazid-based therapy are effective in preventing TB. Three months of isoniazid plus rifampin and six-months of isoniazid are similarly cost-effective in India, and should be considered part of HIV care

The cGMP-Dependent Protein Kinase II Is an Inhibitory Modulator of the Hyperpolarization-Activated HCN2 Channel

Opening of hyperpolarization-activated cyclic nucleotide-gated (HCN) channels is facilitated by direct binding of cyclic nucleotides to a cyclic nucleotide-binding domain (CNBD) in the C-terminus. Here, we show for the first time that in the HCN2 channel cGMP can also exert an inhibitory effect on gating via cGMP-dependent protein kinase II (cGKII)-mediated phosphorylation. Using coimmunoprecipitation and immunohistochemistry we demonstrate that cGKII and HCN2 interact and colocalize with each other upon heterologous expression as well as in native mouse brain. We identify the proximal C-terminus of HCN2 as binding region of cGKII and show that cGKII phosphorylates HCN2 at a specific serine residue (S641) in the C-terminal end of the CNBD. The cGKII shifts the voltage-dependence of HCN2 activation to 2–5 mV more negative voltages and, hence, counteracts the stimulatory effect of cGMP on gating. The inhibitory cGMP effect can be either abolished by mutation of the phosphorylation site in HCN2 or by impairing the catalytic domain of cGKII. By contrast, the inhibitory effect is preserved in a HCN2 mutant carrying a CNBD deficient for cGMP binding. Our data suggest that bidirectional regulation of HCN2 gating by cGMP contributes to cellular fine-tuning of HCN channel activity

Combined mutation screening of NKX2-5, GATA4, and TBX5 in congenital heart disease: multiple heterozygosity and novel mutations

Background: Variants of several genes encoding transcription modulators, signal transduction, and structural proteins are known to cause Mendelian congenital heart disease (CHD). NKX2-5 and GATA4 were the first CHD-causing genes identified by linkage analysis in large affected families. Mutations of TBX5 cause Holt–Oram syndrome, which includes CHD as a clinical feature. All three genes have a well-established role in cardiac development. Design: In order to investigate the possible role of multiple mutations in CHD, a combined mutation screening was performed in NKX2-5, GATA4, and TBX5 in the same patient cohort. Samples from a cohort of 331 CHD patients were analyzed by polymerase chain reaction, double high-performance liquid chromatography and sequencing in order to identify changes in the NKX2-5, GATA4, and TBX5 genes. Results: Two cases of multiple heterozygosity of putative disease-causing mutations were identified. One patient was found with a novel L122P NKX2-5 mutation in combination with the private A1443D mutation of MYH6. A patient heterozygote for a D425N GATA4 mutation carries also a private mutation of the MYH6 gene (V700M). Conclusions: In addition to reporting two novel mutations of NKX2-5 in CHD, we describe families where multiple individual mutations seem to have an additive effect over the pathogenesis of CHD. Our findings highlight the usefulness of multiple gene mutational analysis of large CHD cohorts

siRNA-Like Double-Stranded RNAs Are Specifically Protected Against Degradation in Human Cell Extract

RNA interference (RNAi) is a set of intracellular pathways in eukaryotes that controls both exogenous and endogenous gene expression. The power of RNAi to knock down (silence) any gene of interest by the introduction of synthetic small-interfering (si)RNAs has afforded powerful insight into biological function through reverse genetic approaches and has borne a new field of gene therapeutics. A number of questions are outstanding concerning the potency of siRNAs, necessitating an understanding of how short double-stranded RNAs are processed by the cell. Recent work suggests unmodified siRNAs are protected in the intracellular environment, although the mechanism of protection still remains unclear. We have developed a set of doubly-fluorophore labeled RNAs (more precisely, RNA/DNA chimeras) to probe in real-time the stability of siRNAs and related molecules by fluorescence resonance energy transfer (FRET). We find that these RNA probes are substrates for relevant cellular degradative processes, including the RNase H1 mediated degradation of an DNA/RNA hybrid and Dicer-mediated cleavage of a 24-nucleotide (per strand) double-stranded RNA. In addition, we find that 21- and 24-nucleotide double-stranded RNAs are relatively protected in human cytosolic cell extract, but less so in blood serum, whereas an 18-nucleotide double-stranded RNA is less protected in both fluids. These results suggest that RNAi effector RNAs are specifically protected in the cellular environment and may provide an explanation for recent results showing that unmodified siRNAs in cells persist intact for extended periods of time