Computing the period of an Ehrhart quasi-polynomial

If P is a rational polytope in R^d, then i_P(t):=#(tP\cap Z^d) is a quasi-polynomial in t, called the Ehrhart quasi-polynomial of P. A period of i_P(t) is D(P), the smallest positive integer D such that D*P has integral vertices. Often, D(P) is the minimum period of i_P(t), but, in several interesting examples, the minimum period is smaller. We prove that, for fixed d, there is a polynomial time algorithm which, given a rational polytope P in R^d and an integer n, decides whether n is a period of i_P(t). In particular, there is a polynomial time algorithm to decide whether i_P(t) is a polynomial. We conjecture that, for fixed d, there is a polynomial time algorithm to compute the minimum period of i_P(t). The tools we use are rational generating functions.Comment: 15 page

Neighborhood complexes and generating functions for affine semigroups

Given a_1,a_2,...,a_n in Z^d, we examine the set, G, of all non-negative integer combinations of these a_i. In particular, we examine the generating function f(z)=\sum_{b\in G} z^b. We prove that one can write this generating function as a rational function using the neighborhood complex (sometimes called the complex of maximal lattice-free bodies or the Scarf complex) on a particular lattice in Z^n. In the generic case, this follows from algebraic results of D. Bayer and B. Sturmfels. Here we prove it geometrically in all cases, and we examine a generalization involving the neighborhood complex on an arbitrary lattice

Neighborhood Complexes and Generating Functions for Affine Semigroups

Given a_{1}; a_{2},...a_{n} in Z^{d}, we examine the set, G, of all nonnegative integer combinations of these ai. In particular, we examine the generating function f(z) = Sum_{b in G}z^{b}. We prove that one can write this generating function as a rational function using the neighborhood complex (sometimes called the complex of maximal lattice-free bodies or the Scarf complex) on a particular lattice in Z^{n}. In the generic case, this follows from algebraic results of D. Bayer and B. Sturmfels. Here we prove it geometrically in all cases, and we examine a generalization involving the neighborhood complex on an arbitrary lattice.Integer programming, Complex of maximal lattice free bodies, Generating functions

Parametric inference of recombination in HIV genomes

Recombination is an important event in the evolution of HIV. It affects the global spread of the pandemic as well as evolutionary escape from host immune response and from drug therapy within single patients. Comprehensive computational methods are needed for detecting recombinant sequences in large databases, and for inferring the parental sequences. We present a hidden Markov model to annotate a query sequence as a recombinant of a given set of aligned sequences. Parametric inference is used to determine all optimal annotations for all parameters of the model. We show that the inferred annotations recover most features of established hand-curated annotations. Thus, parametric analysis of the hidden Markov model is feasible for HIV full-length genomes, and it improves the detection and annotation of recombinant forms. All computational results, reference alignments, and C++ source code are available at http://bio.math.berkeley.edu/recombination/.Comment: 20 pages, 5 figure

Neighborhood Complexes and Generating Functions

Given a 1 , a 2 ,…, a n in Z d , we examine the set, G , of all nonnegative integer combinations of these a i . In particular, we examine the generating function f ( z ) = Sum {b in G} z b . We prove that one can write this generating function as a rational function using the neighborhood complex (sometimes called the complex of maximal lattice-free bodies or the Scarf complex) on a particular lattice in Z n . In the generic case, this follows from algebraic results of D . Bayer and B. Sturmfels. Here we prove it geometrically in all cases, and we examine a generalization involving the neighborhood complex on an arbitrary lattice

The Prelude to and Aftermath of the Giant Flare of 2004 December 27: Persistent and Pulsed X-ray Properties of SGR 1806-20 from 1993 to 2005

On 2004 December 27, a highly-energetic giant flare was recorded from the magnetar candidate SGR 1806-20. In the months preceding this flare, the persistent X-ray emission from this object began to undergo significant changes. Here, we report on the evolution of key spectral and temporal parameters prior to and following this giant flare. Using the Rossi X-ray Timing Explorer, we track the pulse frequency of SGR 1806-20 and find that the spin-down rate of this SGR varied erratically in the months before and after the flare. Contrary to the giant flare in SGR 1900+14, we find no evidence for a discrete jump in spin frequency at the time of the December 27th flare (|dnu/nu| < 5 X 10^-6). In the months surrounding the flare, we find a strong correlation between pulsed flux and torque consistent with the model for magnetar magnetosphere electrodynamics proposed by Thompson, Lyutikov & Kulkarni (2002). As with the flare in SGR 1900+14, the pulse morphology of SGR 1806-20 changes drastically following the flare. Using the Chandra X-ray Observatory and other publicly available imaging X-ray detector observations, we construct a spectral history of SGR 1806-20 from 1993 to 2005. The usual magnetar persistent emission spectral model of a power-law plus a blackbody provides an excellent fit to the data. We confirm the earlier finding by Mereghetti et al. (2005) of increasing spectral hardness of SGR 1806-20 between 1993 and 2004. Contrary to the direct correlation between torque and spectral hardness proposed by Mereghetti et al., we find evidence for a sudden torque change that triggered a gradual hardening of the energy spectrum on a timescale of years. Interestingly, the spectral hardness, spin-down rate, pulsed, and phase-averaged of SGR 1806-20 all peak months before the flare epoch.Comment: 37 pages, 8 figures, 8 tables. Accepted for publication in ApJ. To appear in the Oct 20 2006 editio

Creating the capacity for innovation : U.S. Army 1945-1960

This dissertation argues that in the years immediately following the Second World War, the United States Army created a set of intellectual, organizational, and ultimately institutional processes, which are essential to military innovation. Prior to the Second World War, innovation in the army had remained isolated, ad hoc, and difficult to harness towards a common goal. That changed substantively in the period after the war. Unlike most studies of military innovation, this work does not follow the efforts of a single genius but rather three interrelated activities that when fully developed provide the institutional foundations for an ability to change. First, the army adopted the field of operations research as an essential element of military analysis and decision-making. Second, the army created a set of activities known collectively as 'combat developments', where new ideas moved through a deliberate process of deliberation, analyses, testing, and prototyping in order to deliver a new military capability to the field. Finally, this dissertation describes the modernization of officer education and the change in doctrine development from a focus on near-term doctrine for a mobilizing force to forward-looking doctrine appropriate to a standing force in a time of technological change. Most historians have judged the army of early Cold War to be an innovative failure with a readiness crisis at the beginning of the Korean War, a spectacular failure with its Pentomic concept, and its supposed inability to anticipate and prepare for large-scale counterinsurgencies in the 1960s. However, as this dissertation demonstrates, it was during this same period that more fundamental changes occurred that set the pattern for how the institution would change over the course of the remainder of the century

Identifying High and Low Walkable Neighbourhoods Using Multi-disciplinary Walkability Criteria

Neighbourhood features contributing to the walkability (pedestrian friendliness) of a neighbourhood are diverse and depend on both its physical and social attributes. Earlier work in the Cleaner, Greener, Leaner (CGL) Study identified differences in opinion between professional stakeholder groups (planners, designers, engineers, public representatives, and public health and advocacy professionals) on what constitutes a walkable environment [1]. This diversity has implications for neighbourhood design and planning policy. The findings of a multi-disciplinary focus group study were used to generate a list of walkability criteria to select areas for a population study. In this study twenty areas were shortlisted and grouped under four categories: high walkable deprived, high walkable not deprived, low walkable deprived and low walkable not deprived. This paper presents the process undertaken to identify the study sites. International walkability research has favoured macro-scale objective geographic information systems (GIS) information to identify study areas [2]. While these macro scale attributes are important for walkability, alone they were considered insufficient for site selection by the CGL team as street characteristics were not considered and the attributes had a bias towards transportation walking. Also, indications from the focus group participants were that walkability is perceptual and therefore some resulting criteria were subjective, for example ‘a pleasant atmosphere contextual to area characteristics’ and therefore difficult to measure objectively. The CGL site selection process presented a number of challenges including limitations with available GIS information, unrepresentative neighbourhood boundaries on GIS datasets, and only one deprived neighbourhood identified as high walkable by the focus group participants. An investigation of the role of high and low walkable environments on resident’s behaviours and health can be used to inform future planning, transport, public health and neighbourhood design policies

An amphipathic helix enables septins to sense micrometer-scale membrane curvature

© The Authors, 2019. This article is distributed under the terms of the Creative Commons Attribution-Noncommercial-Share Alike 4.0 International License. The definitive version was published in Journal of Cell Biology (2019), doi:10.1083/jcb.201807211.Cell shape is well described by membrane curvature. Septins are filament-forming, GTP-binding proteins that assemble on positive, micrometer-scale curvatures. Here, we examine the molecular basis of curvature sensing by septins. We show that differences in affinity and the number of binding sites drive curvature-specific adsorption of septins. Moreover, we find septin assembly onto curved membranes is cooperative and show that geometry influences higher-order arrangement of septin filaments. Although septins must form polymers to stay associated with membranes, septin filaments do not have to span micrometers in length to sense curvature, as we find that single-septin complexes have curvature-dependent association rates. We trace this ability to an amphipathic helix (AH) located on the C-terminus of Cdc12. The AH domain is necessary and sufficient for curvature sensing both in vitro and in vivo. These data show that curvature sensing by septins operates at much smaller length scales than the micrometer curvatures being detected.We thank the Gladfelter laboratory and Danny Lew for useful discussions, Matthias Garten for ideas in setting up the rod assay, and the University of North Carolina EM facility (Victoria Madden and Kristen White) for support with scanning electron microscope. This work was supported by a Howard Hughes Medical Institute Faculty Scholars award to A.S. Gladfelter, and K.S. Cannon was supported in part by a grant from the National Institute of General Medical Sciences under award T32 GM119999.2019-07-0

Variable Spin-down in the Soft Gamma Repeater SGR 1900+14 and Correlations with Burst Activity

We have analyzed Rossi X-ray Timing Explorer Proportional Counter Array observations of the pulsed emission from SGR 1900+14 during September 1996, June - October 1998, and early 1999. Using these measurements and results reported elsewhere, we construct a period history of this source for 2.5 years. We find significant deviations from a steady spin-down trend during quiescence and the burst active interval. Burst and Transient Source Experiment observations of the burst emission are presented and correlations between the burst activity and spin-down rate of SGR 1900+14 are discussed. We find an 80 day interval during the summer of 1998 when the average spin-down rate is larger than the rate elsewhere by a factor ~ 2.3. This enhanced spin-down may be the result of a discontinuous spin-down event or ``braking glitch'' at the time of the giant flare on 27 August 1998. Furthermore, we find a large discrepancy between the pulsar period and average spin-down rate in X-rays as compared to radio observations for December 1998 and January 1999.Comment: 6 pages, 2 figures, submitted to ApJ Letter