Homology cylinders and the acyclic closure of a free group

We give a Dehn-Nielsen type theorem for the homology cobordism group of homology cylinders by considering its action on the acyclic closure, which was defined by Levine, of a free group. Then we construct an additive invariant of those homology cylinders which act on the acyclic closure trivially. We also describe some tools to study the automorphism group of the acyclic closure of a free group generalizing those for the automorphism group of a free group or the homology cobordism group of homology cylinders.Comment: This is the version published by Algebraic & Geometric Topology on 7 April 200

The Magnus representation and higher-order Alexander invariants for homology cobordisms of surfaces

The set of homology cobordisms from a surface to itself with markings of their boundaries has a natural monoid structure. To investigate the structure of this monoid, we define and study its Magnus representation and Reidemeister torsion invariants by generalizing Kirk-Livingston-Wang's argument over the Gassner representation of string links. Moreover, by applying Cochran and Harvey's framework of higher-order (non-commutative) Alexander invariants to them, we extract several pieces of information about the monoid and related objects.Comment: 28 pages. The whole paper has been rewritten, and the title has been change

Adult-onset bulbar ptosis in Joubert syndrome

In this case report, we describe a case of adult-onset bulbar ptosis in a patient with Joubert syndrome. Joubert syndrome is a rare neurodevelopmental disorder with malformations in cerebellum and brainstem. Many ocular abnormalities have been noted in Joubert syndrome, but the association of this syndrome with adult-onset ptosis has not been described to date. This 24-year-old Joubert patient developed a cerebrospinal fluid cyst in her midbrain. She had signs of bilateral third nerve palsy and abducens palsy in the left eye. The bilateral central third nerve palsy causing functional blindness secondary to severe bilateral levator palsy was treated successfully with silicone sling frontalis suspension, as the seventh nerve nucleus was not involved

Process Design for the Production of Ethylene from Ethanol

This project considers using ethanol dehydration as a means to mass-produce ethylene. 2.3MM tonnes of a 95% ethanol / 5% water feed will be converted into 1MM tonnes of 99.96% pure ethylene per year using a series of adiabatic, fixed-bed catalytic reactors operating at 750°F and 600psi. The catalyst is gamma-alumina in the form of 1cm diameter spherical pellets. After the dehydration process, the product will be purified using two flash separation units, an adsorption unit with zeolite 13X sorbent, and finally a cryogenic distillation unit. The plant will be located in São Paulo, Brazil. Because ethanol production in Brazil is seasonal, the plant will operate only 280 days per year at a very high capacity. This includes 30 days worth of on-site feed storage. After conducting an analysis of the sensitivity of the plant’s Net Present Value and Internal Rate of Return to ethylene and ethanol prices, it was determined that while profitability is not attainable in the current market (which prices ethanol at $0.34/lb and ethylene at$0.60/lb), profitability is attainable should ethylene prices rise to $0.64/lb and ethanol prices fall to$0.305/lb

Strong Spherical Asymptotics for Rotor-Router Aggregation and the Divisible Sandpile

The rotor-router model is a deterministic analogue of random walk. It can be used to define a deterministic growth model analogous to internal DLA. We prove that the asymptotic shape of this model is a Euclidean ball, in a sense which is stronger than our earlier work. For the shape consisting of $n=\omega_d r^d$ sites, where $\omega_d$ is the volume of the unit ball in $\R^d$, we show that the inradius of the set of occupied sites is at least $r-O(\log r)$, while the outradius is at most $r+O(r^\alpha)$ for any $\alpha > 1-1/d$. For a related model, the divisible sandpile, we show that the domain of occupied sites is a Euclidean ball with error in the radius a constant independent of the total mass. For the classical abelian sandpile model in two dimensions, with $n=\pi r^2$ particles, we show that the inradius is at least $r/\sqrt{3}$, and the outradius is at most $(r+o(r))/\sqrt{2}$. This improves on bounds of Le Borgne and Rossin. Similar bounds apply in higher dimensions.Comment: [v3] Added Theorem 4.1, which generalizes Theorem 1.4 for the abelian sandpile. [v4] Added references and improved exposition in sections 2 and 4. [v5] Final version, to appear in Potential Analysi

The Effect of Industrialization on Children�s Education. The Experience of Mexico

We use census data to examine the impact of industrialization on children’s education in Mexico. We find no evidence of reverse causality in this case.  We find small positive effects of industrialization on primary education, effects which are larger for domestic manufacturing than for export-intensive assembly (maquiladoras). In contrast, teen-aged girls in Mexican counties (municipios) with more growth in maquiladora employment 1990-2000 have significantly less educational attainment than do girls in low-growth counties. These results shed light on literatures analyzing the impacts of industrialization, foreign investment, and intra-household bargaining powe

Instability and stability properties of traveling waves for the double dispersion equation

In this article we are concerned with the instability and stability properties of traveling wave solutions of the double dispersion equation $~u_{tt} -u_{xx}+a u_{xxxx}-bu_{xxtt} = - (|u|^{p-1}u)_{xx}~$ for $~p>1$, $~a\geq b>0$. The main characteristic of this equation is the existence of two sources of dispersion, characterized by the terms $u_{xxxx}$ and $u_{xxtt}$. We obtain an explicit condition in terms of $a$, $b$ and $p$ on wave velocities ensuring that traveling wave solutions of the double dispersion equation are strongly unstable by blow up. In the special case of the Boussinesq equation ($b=0$), our condition reduces to the one given in the literature. For the double dispersion equation, we also investigate orbital stability of traveling waves by considering the convexity of a scalar function. We provide both analytical and numerical results on the variation of the stability region of wave velocities with $a$, $b$ and $p$ and then state explicitly the conditions under which the traveling waves are orbitally stable.Comment: 16 pages, 4 figure

Manners and method in classical criticism of the early eighteenth century

This article explores a neglected period in the history of classical scholarship: the first decades of the eighteenth century. It focuses on the tension between an evolving idea of method, and the tradition of personal polemic which had been an important part of the culture of scholarship since the Renaissance. There are two case studies: the conflict between Jean Le Clerc and Pieter Burman, and the controversy that followed Richard Bentley's edition of Horace's Odes. Both demonstrate the need to revise current paradigms for writing the history of scholarship, and invite us to reconsider the role of methodology in producing of scholarly authority

On the Sandpile group of the cone of a graph

In this article, we give a partial description of the sandpile group of the cone of the cartesian product of graphs in function of the sandpile group of the cone of their factors. Also, we introduce the concept of uniform homomorphism of graphs and prove that every surjective uniform homomorphism of graphs induces an injective homomorphism between their sandpile groups. As an application of these result we obtain an explicit description of a set of generators of the sandpile group of the cone of the hypercube of dimension d.Comment: 20 pages, 11 figures. The title was changed, other impruvements were made throughout the article. To appear in Linear Algebra and Its Application

Anemia and brain oxygen after severe traumatic brain injury

Purpose: To investigate the relationship between hemoglobin (Hgb) and brain tissue oxygen tension (PbtO2) after severe traumatic brain injury (TBI) and to examine its impact on outcome. Methods: This was a retrospective analysis of a prospective cohort of severe TBI patients whose PbtO2 was monitored. The relationship between Hgb—categorized into four quartiles (≤9; 9-10; 10.1-11; >11g/dl)—and PbtO2 was analyzed using mixed-effects models. Anemia with compromised PbtO2 was defined as episodes of Hgb≤9g/dl with simultaneous PbtO211g/dl as the reference level, and controlling for important physiologic covariates (CPP, PaO2, PaCO2), Hgb≤9g/dl was the only Hgb level that was associated with lower PbtO2 (coefficient −6.53 (95% CI −9.13; −3.94), p<0.001). Anemia with simultaneous PbtO2<20mmHg, but not anemia alone, increased the risk of unfavorable outcome (odds ratio 6.24 (95% CI 1.61; 24.22), p=0.008), controlling for age, GCS, Marshall CT grade, and APACHE II score. Conclusions: In this cohort of severe TBI patients whose PbtO2 was monitored, a Hgb level no greater than 9g/dl was associated with compromised PbtO2. Anemia with simultaneous compromised PbtO2, but not anemia alone, was a risk factor for unfavorable outcome, irrespective of injury severit