Towards Informative Statistical Flow Inversion

This is the accepted version of 'Towards Informative Statistical Flow Inversion', archived originally at arXiv:0705.1939v1 [cs.NI] 14 May 2007.A problem which has recently attracted research attention is that of estimating the distribution of flow sizes in internet traffic. On high traffic links it is sometimes impossible to record every packet. Researchers have approached the problem of estimating flow lengths from sampled packet data in two separate ways. Firstly, different sampling methodologies can be tried to more accurately measure the desired system parameters. One such method is the sample-and-hold method where, if a packet is sampled, all subsequent packets in that flow are sampled. Secondly, statistical methods can be used to ``invert'' the sampled data and produce an estimate of flow lengths from a sample. In this paper we propose, implement and test two variants on the sample-and-hold method. In addition we show how the sample-and-hold method can be inverted to get an estimation of the genuine distribution of flow sizes. Experiments are carried out on real network traces to compare standard packet sampling with three variants of sample-and-hold. The methods are compared for their ability to reconstruct the genuine distribution of flow sizes in the traffic

Efficient unified Montgomery inversion with multibit shifting

Computation of multiplicative inverses in finite fields GF(p) and GF(2/sup n/) is the most time-consuming operation in elliptic curve cryptography, especially when affine co-ordinates are used. Since the existing algorithms based on the extended Euclidean algorithm do not permit a fast software implementation, projective co-ordinates, which eliminate almost all of the inversion operations from the curve arithmetic, are preferred. In the paper, the authors demonstrate that affine co-ordinate implementation provides a comparable speed to that of projective co-ordinates with careful hardware realisation of existing algorithms for calculating inverses in both fields without utilising special moduli or irreducible polynomials. They present two inversion algorithms for binary extension and prime fields, which are slightly modified versions of the Montgomery inversion algorithm. The similarity of the two algorithms allows the design of a single unified hardware architecture that performs the computation of inversion in both fields. They also propose a hardware structure where the field elements are represented using a multi-word format. This feature allows a scalable architecture able to operate in a broad range of precision, which has certain advantages in cryptographic applications. In addition, they include statistical comparison of four inversion algorithms in order to help choose the best one amongst them for implementation onto hardware

Inference of internal stress in a cell monolayer

We combine traction force data with Bayesian inversion to obtain an absolute estimate of the internal stress field of a cell monolayer. The method, Bayesian inversion stress microscopy (BISM), is validated using numerical simulations performed in a wide range of conditions. It is robust to changes in each ingredient of the underlying statistical model. Importantly, its accuracy does not depend on the rheology of the tissue. We apply BISM to experimental traction force data measured in a narrow ring of cohesive epithelial cells, and check that the inferred stress field coincides with that obtained by direct spatial integration of the traction force data in this quasi-one-dimensional geometry.Comment: 38 pages, 14 figure

Generalized Post-Widder inversion formula with application to statistics

In this work we derive an inversion formula for the Laplace transform of a density observed on a curve in the complex domain, which generalizes the well known Post-Widder formula. We establish convergence of our inversion method and derive the corresponding convergence rates for the case of a Laplace transform of a smooth density. As an application we consider the problem of statistical inference for variance-mean mixture models. We construct a nonparametric estimator for the mixing density based on the generalized Post-Widder formula, derive bounds for its root mean square error and give a brief numerical example

Quantum mutual entropy for Jaynes-Cummings model

The dynamics of an atom on the Jaynes-Cummings model has been studied by an atomic inversion, von Neumann entropy and so on. In this letter, we will treat the Jaynes-Cummings model as a problem in non-equilibrium statistical mechanics and apply quantum mutual entropy to study the irreversible dynamics of a state for the atom on this model.Comment: RevTeX, 4 pages with a figure(eps file), submitted to Physical Review Letter

Interpretation of HINODE SOT/SP asymmetric Stokes profiles observed in quiet Sun network and internetwork

We present the first interpretation of the Stokes profile asymmetries measured in the FeI 630 nm lines by SOT/SP, in both quiet Sun internetwork (IN) and network regions. The inversion is carried out under the hypothesis of MISMA, where the unresolved structure is assumed to be optically thin. We analyze a 29.52"x31.70" subfield carefully selected to be representative of the properties of a 302"x162" quiet Sun field-of-view at disk center. The inversion code is able to reproduce the observed asymmetries in a very satisfactory way. The inversion code interprets 25% of inverted profiles as emerging from pixels in which both positive and negative polarities coexist. kG field strengths are found at the base of the photosphere in both network and IN; in the case of the latter, both kG fields and hG fields are admixed. When considering the magnetic properties at the mid photosphere most kG fields are gone, and the statistics is dominated by hG fields. We constrain the magnetic field of only 4.5% of the analyzed photosphere (and this percentage reduces to 1.3% when referred to all pixels, including those with low polarization not analyzed). The rest of the plasma is consistent with the presence of weak fields not contributing to the detected polarization signals. The average flux densities derived in the full subfield and in IN regions are higher than the ones derived from the same dataset by Milne-Eddington inversion. The existence of large asymmetries in SOT/SP polarization profiles is uncovered. These are not negligible in quiet Sun data. The MISMA inversion code reproduces them in a satisfactory way, and provides a statistical description of the magnetized IN and network which partly differs and complements the results obtained so far. From this it follows the importance of having a complete interpretation of the line profile shapes.Comment: 11 pages, 9 figures, 1 table - Accepted for publication on A&