Applying dissipative dynamical systems to pseudorandom number generation: Equidistribution property and statistical independence of bits at distances up to logarithm of mesh size

The behavior of a family of dissipative dynamical systems representing transformations of two-dimensional torus is studied on a discrete lattice and compared with that of conservative hyperbolic automorphisms of the torus. Applying dissipative dynamical systems to generation of pseudorandom numbers is shown to be advantageous and equidistribution of probabilities for the sequences of bits can be achieved. A new algorithm for generating uniform pseudorandom numbers is proposed. The theory of the generator, which includes proofs of periodic properties and of statistical independence of bits at distances up to logarithm of mesh size, is presented. Extensive statistical testing using available test packages demonstrates excellent results, while the speed of the generator is comparable to other modern generators.Comment: 6 pages, 3 figures, 3 table

Learning Poisson Binomial Distributions

We consider a basic problem in unsupervised learning: learning an unknown \emph{Poisson Binomial Distribution}. A Poisson Binomial Distribution (PBD) over $\{0,1,\dots,n\}$ is the distribution of a sum of $n$ independent Bernoulli random variables which may have arbitrary, potentially non-equal, expectations. These distributions were first studied by S. Poisson in 1837 \cite{Poisson:37} and are a natural $n$-parameter generalization of the familiar Binomial Distribution. Surprisingly, prior to our work this basic learning problem was poorly understood, and known results for it were far from optimal. We essentially settle the complexity of the learning problem for this basic class of distributions. As our first main result we give a highly efficient algorithm which learns to \eps-accuracy (with respect to the total variation distance) using \tilde{O}(1/\eps^3) samples \emph{independent of $n$}. The running time of the algorithm is \emph{quasilinear} in the size of its input data, i.e., \tilde{O}(\log(n)/\eps^3) bit-operations. (Observe that each draw from the distribution is a $\log(n)$-bit string.) Our second main result is a {\em proper} learning algorithm that learns to \eps-accuracy using \tilde{O}(1/\eps^2) samples, and runs in time (1/\eps)^{\poly (\log (1/\eps))} \cdot \log n. This is nearly optimal, since any algorithm {for this problem} must use \Omega(1/\eps^2) samples. We also give positive and negative results for some extensions of this learning problem to weighted sums of independent Bernoulli random variables.Comment: Revised full version. Improved sample complexity bound of O~(1/eps^2

Les premiers cycles dans un graphe en evolution

SIGLECNRS 14802 E / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc

Patupilone (Epothilone B) for recurrent glioblastoma: Clinical outcome and translational analysis of a single-institution phase I/II trial

Background: Patients with glioblastoma (GBM) inevitably develop recurrent or progressive disease after initial multimodal treatment and have a median survival of 6-9 months from time of progression. To date, there is no accepted standard treatment for GBM relapse or progression. Patupilone (EPO906) is a novel natural microtubule-stabilizing cytotoxic agent that crosses the blood-brain barrier and has been found to have preclinical activity in glioma models. Methods: This is a single-institution, early-phase I/II trial of GBM patients with tumor progression who qualified for second surgery with the goal of evaluating efficacy and safety of the single-agent patupilone (10 mg/m(2), every 3 weeks). Patients received patupilone 1 week prior to second surgery and every 3 weeks thereafter until tumor progression or toxicity. Primary end points were progression-free survival (PFS) and overall survival (OS) at 6 months as well as patupilone concentration in tumor tissue. Secondary end points were toxicity, patupilone concentration in plasma and translational analyses for predictive biomarkers. Results: Nine patients with a mean age of 54.6 ± 8.6 years were recruited between June 2008 and April 2010. Median survival and 1-year OS after second surgery were 11 months (95% CI, 5-17 months) and 45% (95% CI, 14-76), respectively. Median PFS was 1.5 months (95% CI, 1.3-1.7 months) and PFS6 was 22% (95% CI, 0-46), with 2 patients remaining recurrence-free at 9.75 and 22 months. At the time of surgery, the concentration of patupilone in tumor tissue was 30 times higher than in the plasma. Tumor response was not predictable by the tested biomarkers. Treatment was generally well tolerated with no hematological, but cumulative, though reversible sensory neuropathy grade ≤3 was seen in 2 patients (22%) at 8 months and grade 4 diarrhea in the 2nd patient (11%). Non-patupilone-related peri-operative complications occurred in 2 patients resulting in discontinuation of patupilone therapy. There were no neurocognitive changes 3 months after surgery compared to baseline. Conclusions: In recurrent GBM, patupilone can be given safely pre- and postoperatively. The drug accumulates in the tumor tissue. The treatment results in long-term PFS in some patients. Patupilone represents a valuable novel compound which deserves further evaluation in combination with radiation therapy in patients with GBM