Quadri-tilings of the plane

We introduce {\em quadri-tilings} and show that they are in bijection with dimer models on a {\em family} of graphs $\{R^*\}$ arising from rhombus tilings. Using two height functions, we interpret a sub-family of all quadri-tilings, called {\em triangular quadri-tilings}, as an interface model in dimension 2+2. Assigning "critical" weights to edges of $R^*$, we prove an explicit expression, only depending on the local geometry of the graph $R^*$, for the minimal free energy per fundamental domain Gibbs measure; this solves a conjecture of \cite{Kenyon1}. We also show that when edges of $R^*$ are asymptotically far apart, the probability of their occurrence only depends on this set of edges. Finally, we give an expression for a Gibbs measure on the set of {\em all} triangular quadri-tilings whose marginals are the above Gibbs measures, and conjecture it to be that of minimal free energy per fundamental domain.Comment: Revised version, minor changes. 30 pages, 13 figure

Tighter Relations Between Sensitivity and Other Complexity Measures

Sensitivity conjecture is a longstanding and fundamental open problem in the area of complexity measures of Boolean functions and decision tree complexity. The conjecture postulates that the maximum sensitivity of a Boolean function is polynomially related to other major complexity measures. Despite much attention to the problem and major advances in analysis of Boolean functions in the past decade, the problem remains wide open with no positive result toward the conjecture since the work of Kenyon and Kutin from 2004. In this work, we present new upper bounds for various complexity measures in terms of sensitivity improving the bounds provided by Kenyon and Kutin. Specifically, we show that deg(f)^{1-o(1)}=O(2^{s(f)}) and C(f) < 2^{s(f)-1} s(f); these in turn imply various corollaries regarding the relation between sensitivity and other complexity measures, such as block sensitivity, via known results. The gap between sensitivity and other complexity measures remains exponential but these results are the first improvement for this difficult problem that has been achieved in a decade.Comment: This is the merged form of arXiv submission 1306.4466 with another work. Appeared in ICALP 2014, 14 page

The risks of concurrent treatment with tenofovir and aminoglycosides in patients with HIV-associated tuberculosis

The South African public sector antiretroviral treatment (ART) guidelines have recently been changed to include tenofovir in the first-line regimen.1 Injectable drugs from the aminoglycoside class are part of the intensive phase of regimen 2 tuberculosis (TB) treatment and the multidrug-resistant (MDR) TB treatment regimen in the South African TB programme. We wish to draw the attention of clinicians managing patients with HIVassociated TB to the potential dangers of concurrent administration of these drugs. We present two illustrative cases

Uncovering Cryptic Parasitoid Diversity in Horismenus (Chalcidoidea, Eulophidae)

The file attached is the Published/publisher’s pdf version of the article.© 2015 Kenyon et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited

Collisional Cascades in Planetesimal Disks II. Embedded Planets

We use a multiannulus planetesimal accretion code to investigate the growth of icy planets in the outer regions of a planetesimal disk. In a quiescent minimum mass solar nebula, icy planets grow to sizes of 1000--3000 km on a timescale t = 15-20 Myr (a/30 AU)^3 where a is the distance from the central star. Planets form faster in more massive nebulae. Newly-formed planets stir up leftover planetesimals along their orbits and produce a collisional cascade where icy planetesimals are slowly ground to dust. The dusty debris of planet formation has physical characteristics similar to those observed in beta Pic, HR 4796A, and other debris disks. We derive dust masses for small particles, 1 mm and smaller, and large particles, 1 mm and larger, as a function of the initial conditions in the planetesimal disk. The dust luminosities derived from these masses are similar to those observed in Vega, HR 4796A, and other debris disks. The calculations produce bright rings and dark gaps. Bright rings occur where 1000 km and larger planets have recently formed. Dark gaps are regions where planets have cleared out dust or shadows where planets have yet to form.Comment: to be published in the Astronomical Journal, January 2004; 7 pages of text; 17 figures at http://cfa-www.harvard.edu/~kenyon/pf/emb-planet-figures.pdf; 2 animations at http://cfa-www.harvard.edu/~kenyon/pf/emb-planet-movies.htm

Formation of Kuiper Belt Binaries by Gravitational Collapse

A large fraction of 100-km-class low-inclination objects in the classical Kuiper Belt (KB) are binaries with comparable mass and wide separation of components. A favored model for their formation was capture during the coagulation growth of bodies in the early KB. Instead, recent studies suggested that large objects can rapidly form in the protoplanetary disks when swarms of locally concentrated solids collapse under their own gravity. Here we examine the possibility that KB binaries formed during gravitational collapse when the excess of angular momentum prevented the agglomeration of available mass into a solitary object. We find that this new mechanism provides a robust path toward the formation of KB binaries with observed properties, and can explain wide systems such as 2001 QW322 and multiples such as (47171) 1999 TC36. Notably, the gravitational collapse is capable of producing 100% binary fraction for a wide range of the swarm's initial angular momentum values. The binary components have similar masses (80% have the secondary-over-primary radius ratio >0.7) and their separation ranges from ~1,000 to ~100,000 km. The binary orbits have eccentricities from e=0 to ~1, with the majority having e<0.6. The binary orbit inclinations with respect to the initial angular momentum of the swarm range from i=0 to ~90 deg, with most cases having i<50 deg. Our binary formation mechanism implies that the primary and secondary components in each binary pair should have identical bulk composition, which is consistent with the current photometric data. We discuss the applicability of our results to the Pluto-Charon, Orcus-Vanth, (617) Patroclus-Menoetius and (90) Antiope binary systems.Comment: Astronomical Journal, in pres

The TAOS Project: Upper Bounds on the Population of Small KBOs and Tests of Models of Formation and Evolution of the Outer Solar System

We have analyzed the first 3.75 years of data from TAOS, the Taiwanese American Occultation Survey. TAOS monitors bright stars to search for occultations by Kuiper Belt Objects (KBOs). This dataset comprises 5e5 star-hours of multi-telescope photometric data taken at 4 or 5 Hz. No events consistent with KBO occultations were found in this dataset. We compute the number of events expected for the Kuiper Belt formation and evolution models of Pan & Sari (2005), Kenyon & Bromley (2004), Benavidez & Campo Bagatin (2009), and Fraser (2009). A comparison with the upper limits we derive from our data constrains the parameter space of these models. This is the first detailed comparison of models of the KBO size distribution with data from an occultation survey. Our results suggest that the KBO population is comprised of objects with low internal strength and that planetary migration played a role in the shaping of the size distribution.Comment: 18 pages, 16 figures, Aj submitte

Migration intensity has no effect on peak HIV prevalence: An ecological study

Background: Correctly identifying the determinants of generalized HIV epidemics is crucial to bringing down ongoing high HIV incidence in these countries. High rates of migration are believed to be an important determinant of HIV prevalence. This study has two aims. Firstly, it evaluates the ecological association between levels of internal and international migration and national peak HIV prevalence using thirteen variables from a variety of sources to capture various aspects of internal and international migration intensity. Secondly, it examines the relationship between circular migration and HIV at an individual and population-level in South Africa.Methods: Linear regression was used to analyze the association between the various measures of migration intensity and peak national HIV prevalence for 141 countries and HIV prevalence by province and ethnic group in South Africa.Results: No evidence of a positive ecological association between national migration intensity and HIV prevalence was found. This remained the case when the analyses were limited to the countries of sub-Saharan Africa. On the whole, countries with generalized HIV epidemics had lower rates of internal and external migration. Likewise, no association was found between migration and HIV positivity at an individual or group-level in South Africa.Conclusion: These results do not support the thesis that migration measured at the country level plays a significant role in determining peak HIV prevalence