Mountain trail formation and the active walker model

We extend the active walker model to address the formation of paths on gradients, which have been observed to have a zigzag form. Our extension includes a new rule which prohibits direct descent or ascent on steep inclines, simulating aversion to falling. Further augmentation of the model stops walkers from changing direction very rapidly as that would likely lead to a fall. The extended model predicts paths with qualitatively similar forms to the observed trails, but only if the terms suppressing sudden direction changes are included. The need to include terms into the model that stop rapid direction change when simulating mountain trails indicates that a similar rule should also be included in the standard active walker model.Comment: Introduction improved. Analysis of discretization errors added. Calculations from alternative scheme include

Renormalization : A number theoretical model

We analyse the Dirichlet convolution ring of arithmetic number theoretic functions. It turns out to fail to be a Hopf algebra on the diagonal, due to the lack of complete multiplicativity of the product and coproduct. A related Hopf algebra can be established, which however overcounts the diagonal. We argue that the mechanism of renormalization in quantum field theory is modelled after the same principle. Singularities hence arise as a (now continuously indexed) overcounting on the diagonals. Renormalization is given by the map from the auxiliary Hopf algebra to the weaker multiplicative structure, called Hopf gebra, rescaling the diagonals.Comment: 15 pages, extended version of talks delivered at SLC55 Bertinoro,Sep 2005, and the Bob Delbourgo QFT Fest in Hobart, Dec 200

Enumeration and Decidable Properties of Automatic Sequences

We show that various aspects of k-automatic sequences -- such as having an unbordered factor of length n -- are both decidable and effectively enumerable. As a consequence it follows that many related sequences are either k-automatic or k-regular. These include many sequences previously studied in the literature, such as the recurrence function, the appearance function, and the repetitivity index. We also give some new characterizations of the class of k-regular sequences. Many results extend to other sequences defined in terms of Pisot numeration systems

Strong light-matter coupling in bulk GaN-microcavities with double dielectric mirrors fabricated by two different methods

Two routes for the fabrication of bulk GaN microcavities embedded between two dielectric mirrors are described, and the optical properties of the microcavities thus obtained are compared. In both cases, the GaN active layer is grown by molecular beam epitaxy on (111) Si, allowing use of selective etching to remove the substrate. In the first case, a three period Al0.2Ga0.8N / AlN Bragg mirror followed by a lambda/2 GaN cavity are grown directly on the Si. In the second case, a crack-free 2,mu m thick GaN layer is grown, and progressively thinned to a final thickness of lambda. Both devices work in the strong coupling regime at low temperature, as evidenced by angle-dependent reflectivity or transmission experiments. However, strong light-matter coupling in emission at room temperature is observed only for the second one. This is related to the poor optoelectronic quality of the active layer of the first device, due to its growth only 250 nm above the Si substrate and its related high defect density. The reflectivity spectra of the microcavities are well accounted for by using transfer matrix calculations. (C) 2010 American Institute of Physics. [doi:10.1063/1.3477450

SEM-EDS analyses of small craters in stardust aluminium foils: implications for the Wild-2 dust distribution

Implications for the Wild-2 dust distribution of the statistical results obtained by SEM-EDS from nearly 300 impact craters on aluminium foils of the Stardust sample tray assembly

On Multiphase-Linear Ranking Functions

Multiphase ranking functions ($\mathit{M{\Phi}RFs}$) were proposed as a means to prove the termination of a loop in which the computation progresses through a number of "phases", and the progress of each phase is described by a different linear ranking function. Our work provides new insights regarding such functions for loops described by a conjunction of linear constraints (single-path loops). We provide a complete polynomial-time solution to the problem of existence and of synthesis of $\mathit{M{\Phi}RF}$ of bounded depth (number of phases), when variables range over rational or real numbers; a complete solution for the (harder) case that variables are integer, with a matching lower-bound proof, showing that the problem is coNP-complete; and a new theorem which bounds the number of iterations for loops with $\mathit{M{\Phi}RFs}$. Surprisingly, the bound is linear, even when the variables involved change in non-linear way. We also consider a type of lexicographic ranking functions, $\mathit{LLRFs}$, more expressive than types of lexicographic functions for which complete solutions have been given so far. We prove that for the above type of loops, lexicographic functions can be reduced to $\mathit{M{\Phi}RFs}$, and thus the questions of complexity of detection and synthesis, and of resulting iteration bounds, are also answered for this class.Comment: typos correcte

Fabrication and Optical Properties of a Fully Hybrid Epitaxial ZnO-Based Microcavity in the Strong Coupling Regime

In order to achieve polariton lasing at room temperature, a new fabrication methodology for planar microcavities is proposed: a ZnO-based microcavity in which the active region is epitaxially grown on an AlGaN/AlN/Si substrate and in which two dielectric mirrors are used. This approach allows as to simultaneously obtain a high-quality active layer together with a high photonic confinement as demonstrated through macro-, and micro-photoluminescence ({\mu}-PL) and reflectivity experiments. A quality factor of 675 and a maximum PL emission at k=0 are evidenced thanks to {\mu}-PL, revealing an efficient polaritonic relaxation even at low excitation power.Comment: 12 pages, 3 figure

Transcutaneous tibial nerve stimulation: 2 years follow-up outcomes in the management of anticholinergic refractory overactive bladder

PURPOSE: To evaluate long-term use, efficacy and tolerability of transcutaneous tibial nerve stimulation (TTNS) in the treatment of refractory overactive bladder (OAB). METHODS: We performed a prospective observational study and included all patients treated in a single center for OAB persisting after first-line anticholinergic treatment, with ≥ 24 months follow-up. The protocol consisted of daily stimulation at home. The primary outcome was treatment persistence. Amelioration was defined as an improvement in urinary symptom profile (USP) score. RESULTS: We assessed 84 consecutive patients. After a mean follow-up of 39.3 months and a mean treatment use of 8.3 months, almost two-thirds of patients (71.8%) had discontinued TTNS. Treatment continuation was > 12 months for 28 patients (33.3%) and > 18 months for 16 patients (19%). TTNS was successful following 3 months of treatment in 60 (71%) patients. Mean USP score stayed significantly lower than baseline until 12 months of treatment, but was not significant anymore after 18 months. Discontinuation therapy reasons were a lack of sufficient symptom relief for 59 (70%) patients, compliance difficulty for 5 (6%) patients and becoming asymptomatic for 6 (8%) patients. No serious adverse events occurred. CONCLUSIONS: The present study confirms the utility of TTNS as a treatment option for patients with resistant OAB. In the long-term use, few patients continued with therapy, mostly because of a decreased effectiveness with time

Generalized shuffles related to Nijenhuis and TD-algebras

Shuffle and quasi-shuffle products are well-known in the mathematics literature. They are intimately related to Loday's dendriform algebras, and were extensively used to give explicit constructions of free commutative Rota-Baxter algebras. In the literature there exist at least two other Rota-Baxter type algebras, namely, the Nijenhuis algebra and the so-called TD-algebra. The explicit construction of the free unital commutative Nijenhuis algebra uses a modified quasi-shuffle product, called the right-shift shuffle. We show that another modification of the quasi-shuffle product, the so-called left-shift shuffle, can be used to give an explicit construction of the free unital commutative TD-algebra. We explore some basic properties of TD-operators and show that the free unital commutative Nijenhuis algebra is a TD-algebra. We relate our construction to Loday's unital commutative dendriform trialgebras, including the involutive case. The concept of Rota-Baxter, Nijenhuis and TD-bialgebras is introduced at the end and we show that any commutative bialgebra provides such objects.Comment: 20 pages, typos corrected, accepted for publication in Communications in Algebr

Patterned silicon substrates: a common platform for room temperature GaN and ZnO polariton lasers

A new platform for fabricating polariton lasers operating at room temperature is introduced: nitride-based distributed Bragg reflectors epitaxially grown on patterned silicon substrates. The patterning allows for an enhanced strain relaxation thereby enabling to stack a large number of crack-free AlN/AlGaN pairs and achieve cavity quality factors of several thousands with a large spatial homogeneity. GaN and ZnO active regions are epitaxially grown thereon and the cavities are completed with top dielectric Bragg reflectors. The two structures display strong-coupling and polariton lasing at room temperature and constitute an intermediate step in the way towards integrated polariton devices