Lie point symmetries and first integrals: the Kowalevsky top

We show how the Lie group analysis method can be used in order to obtain first integrals of any system of ordinary differential equations. The method of reduction/increase of order developed by Nucci (J. Math. Phys. 37, 1772-1775 (1996)) is essential. Noether's theorem is neither necessary nor considered. The most striking example we present is the relationship between Lie group analysis and the famous first integral of the Kowalevski top.Comment: 23 page

Estimating Dynamic Traffic Matrices by using Viable Routing Changes

Abstract: In this paper we propose a new approach for dealing with the ill-posed nature of traffic matrix estimation. We present three solution enhancers: an algorithm for deliberately changing link weights to obtain additional information that can make the underlying linear system full rank; a cyclo-stationary model to capture both long-term and short-term traffic variability, and a method for estimating the variance of origin-destination (OD) flows. We show how these three elements can be combined into a comprehensive traffic matrix estimation procedure that dramatically reduces the errors compared to existing methods. We demonstrate that our variance estimates can be used to identify the elephant OD flows, and we thus propose a variant of our algorithm that addresses the problem of estimating only the heavy flows in a traffic matrix. One of our key findings is that by focusing only on heavy flows, we can simplify the measurement and estimation procedure so as to render it more practical. Although there is a tradeoff between practicality and accuracy, we find that increasing the rank is so helpful that we can nevertheless keep the average errors consistently below the 10% carrier target error rate. We validate the effectiveness of our methodology and the intuition behind it using commercial traffic matrix data from Sprint's Tier-1 backbon

Síndromes Miastênicas Congênitas E Miastenia Grave São Diagnósticos Desafiadores Na Prática Neurológica

74969569

Ermakov's Superintegrable Toy and Nonlocal Symmetries

We investigate the symmetry properties of a pair of Ermakov equations. The system is superintegrable and yet possesses only three Lie point symmetries with the algebra sl(2,R). The number of point symmetries is insufficient and the algebra unsuitable for the complete specification of the system. We use the method of reduction of order to reduce the nonlinear fourth-order system to a third-order system comprising a linear second-order equation and a conservation law. We obtain the representation of the complete symmetry group from this system. Four of the required symmetries are nonlocal and the algebra is the direct sum of a one-dimensional Abelian algebra with the semidirect sum of a two-dimensional solvable algebra with a two-dimensional Abelian algebra. The problem illustrates the difficulties which can arise in very elementary systems. Our treatment demonstrates the existence of possible routes to overcome these problems in a systematic fashion.Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

DoWitcher: Effective Worm Detection and Containment in the Internet Core

Enterprise networks are increasingly offloading the responsibility for worm detection and containment to the carrier networks. However, current approaches to the zero-day worm detection problem such as those based on content similarity of packet payloads are not scalable to the carrier link speeds (OC-48 and up-wards). In this paper, we introduce a new system, namely DoWitcher, which in contrast to previous approaches is scalable as well as able to detect the stealthiest worms that employ low-propagation rates or polymorphisms to evade detection. DoWitcher uses an incremental approach toward worm detection: First, it examines the layer-4 traffic features to discern the presence of a worm anomaly; Next, it determines a flow-filter mask that can be applied to isolate the suspect worm flows and; Finally, it enables full-packet capture of only those flows that match the mask, which are then processed by a longest common subsequence algorithm to extract the worm content signature. Via a proof-of-concept implementation on a commercially available network analyzer processing raw packets from an OC-48 link, we demonstrate the capability of DoWitcher to detect low-rate worms and extract signatures for even the polymorphic worm

Oculofacial alterations in NBAS-SOPH like mutations: Case report

PURPOSE:: To describe the clinical features of a rare case of NBAS-SOPH-like mutations; to emphasize special aspects of the ocular and oro-facial regions. METHODS:: Case report. CASE DESCRIPTION:: We present a 5-year-old girl initially examined for her dysmorphic features, mental delay, strabismus, and high myopia. During the funduscopic examination, we observed optic atrophy with narrow thinned arterioles with the light brown reflex of the central retina. A genetic assessment revealed NBAS-SOPH like mutation. An assessment by a team of orthodontists defined typical characteristics. CONCLUSIONS:: NBAS mutations can also cause complex disease with a broad clinical spectrum ranging from isolated recurrent acute liver failure (RALF) to a multisystemic phenotype. Due to the heterogeneity of the expressions, a multispeciality approach to this situation is recommended

Analytic Behaviour of Competition among Three Species

We analyse the classical model of competition between three species studied by May and Leonard ({\it SIAM J Appl Math} \textbf{29} (1975) 243-256) with the approaches of singularity analysis and symmetry analysis to identify values of the parameters for which the system is integrable. We observe some striking relations between critical values arising from the approach of dynamical systems and the singularity and symmetry analyses.Comment: 14 pages, to appear in Journal of Nonlinear Mathematical Physic

drag forces in statistically stationary and homogeneous submerged granular flows

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