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

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

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

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

The reaction to nailing or cementing of the femur in rats. A microangiographic and fluorescence study.

Bone reaction to cement and to a cementless stem was studied in the rat femur with histological fluorescence and microangiographic techniques. Periosteal and endosteal apposition, and consequent remodelling, appeared as a reaction to reaming rather than caused by cement or a cementless stem. Every change in bone began with proliferation, progression and orientation of the vessels. Endosteal apposition was absent in cemented femurs because the entire medulla was occupied by the acrylic cement, but remodelling of the subendosteal cortex followed medullary revascularisation which was far advanced after 90 days. In cementless stems, endosteal apposition of primary woven bone and remodelling was the basis for bony ingrowth and anchorage through bony bridges. Our results suggest that the pattern of blood supply is relevant to the structural organisation of mature lamellar bone around the implant. Cemented stems have maximum anchorage and stability as soon as they are inserted, but this decreases with time as revascularisation occurs. Cementless stems can reach maximum integration later after insertion, and revascularisation is less critical because they usually do not fill the canal completely

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

The effects of mechanical forces on bones and joints. Experimental study on the rat tail.

We have used an experimental model employing the bent tail of rats to investigate the effects of mechanical forces on bones and joints. Mechanical strain could be applied to the bones and joints of the tail without direct surgical exposure or the application of pins and wires. The intervertebral disc showed stretched annular lamellae on the convex side, while the annulus fibrosus on the concave side was pinched between the inner corners of the vertebral epiphysis. In young rats with an active growth plate, a transverse fissure appeared at the level of the hypertrophic cell layer or the primary metaphyseal trabecular zone. Metaphyseal and epiphyseal trabeculae on the compressed side were thicker and more dense than those of the distracted part of the vertebra. In growing animals, morphometric analysis of hemiepiphyseal and hemimetaphyseal areas, and the corresponding trabecular bone density, showed significant differences between the compressed and distracted sides. No differences were observed in adult rats. We found no significant differences in osteoclast number between compressed and distracted sides in either age group. Our results provide quantitative evidence of the working of 'Wolff's law'. The differences in trabecular density are examples of remodelling by osteoclasts and osteoblasts; our finding of no significant difference in osteoclast numbers between the hemiepiphyses in the experimental and control groups suggests that the response of living bone to altered strain is mediated by osteoblasts

Inhibitory effect of salmon calcitonin on bone resorption: morphological study of the tibial growth plate in rats.

Salmon calcitonin (sCT) at doses of 100 and 50 UI given subcutaneously to growing rats produced in vivo evidence of osteoclastic activity inhibition. Histological assessment was carried out by measuring the perichondrial ring of Lacroix height, and a dose-correlated effect was found. These aspects were coupled with an increase in the osteoclast number and suggested that in studies with bone resorption inhibitors, morphological evaluation based on osteoclasts count is not reliable. The changes of the metaphysis suggested also that sCT affects the activity of hypertrophic chondrocytes of the growth plate. Plasma calcium levels did not differ significantly between treated rats and controls; an increased phosphatemia was observed in sCT-treated animals