On blowup for Yang-Mills fields

We study development of singularities for the spherically symmetric Yang-Mills equations in $d+1$ dimensional Minkowski spacetime for $d=4$ (the critical dimension) and $d=5$ (the lowest supercritical dimension). Using combined numerical and analytical methods we show in both cases that generic solutions starting with sufficiently large initial data blow up in finite time. The mechanism of singularity formation depends on the dimension: in $d=5$ the blowup is exactly self-similar while in $d=4$ the blowup is only approximately self-similar and can be viewed as the adiabatic shrinking of the marginally stable static solution. The threshold for blowup and the connection with critical phenomena in the gravitational collapse (which motivated this research) are also briefly discussed.Comment: 4 pages, 3 figures, submitted to Physical Review Letter

Cross-Entropy Clustering

We construct a cross-entropy clustering (CEC) theory which finds the optimal number of clusters by automatically removing groups which carry no information. Moreover, our theory gives simple and efficient criterion to verify cluster validity. Although CEC can be build on an arbitrary family of densities, in the most important case of Gaussian CEC: {\em -- the division into clusters is affine invariant; -- the clustering will have the tendency to divide the data into ellipsoid-type shapes; -- the approach is computationally efficient as we can apply Hartigan approach.} We study also with particular attention clustering based on the Spherical Gaussian densities and that of Gaussian densities with covariance s \I. In the letter case we show that with $s$ converging to zero we obtain the classical k-means clustering

Integrals of motion and the shape of the attractor for the Lorenz model

In this paper, we consider three-dimensional dynamical systems, as for example the Lorenz model. For these systems, we introduce a method for obtaining families of two-dimensional surfaces such that trajectories cross each surface of the family in the same direction. For obtaining these surfaces, we are guided by the integrals of motion that exist for particular values of the parameters of the system. Nonetheless families of surfaces are obtained for arbitrary values of these parameters. Only a bounded region of the phase space is not filled by these surfaces. The global attractor of the system must be contained in this region. In this way, we obtain information on the shape and location of the global attractor. These results are more restrictive than similar bounds that have been recently found by the method of Lyapunov functions.Comment: 17 pages,12 figures. PACS numbers : 05.45.+b / 02.30.Hq Accepted for publication in Physics Letters A. e-mails : [email protected] & [email protected]

Community-based health insurance and social protection policy

Of all the risks facing poor households, health risks pose the greatest threat to their lives and livelihoods. A health shock adds health expenditures to the burden of the poor precisely at the time when they can afford it the least.One of the ways that poor communities manage health risks, in combination with publicly financed health care services, are community-based health insurance schemes (CBHIs). These are small scale, voluntary health insurance programs, organized and managed in a participatory manner. They are designed to be simple and affordable, and to draw on resources of social solidarity and cohesion to overcome problems of small risk pools, moral hazard, fraud, exclusion and cost-escalation. Less than 10 percent of the informal sector population in the developing nations has health coverage from a CBHI, but the number of such schemes is growing rapidly. On average, CBHIs recover between a quarter to a half of health service costs. As a social protection device, they have been shown to be effective in reducing out-of-pocket payments of their members, and in improving access to health services. Many schemes do fail. Problems, such as weak management, poor quality government health services, and the limited resources that local population can mobilize to finance health care, can impede success.Health Economics&Finance,Health Monitoring&Evaluation,Poverty Assessment,Safety Nets and Transfers,Insurance&Risk Mitigation

Extreme Entropy Machines: Robust information theoretic classification

Most of the existing classification methods are aimed at minimization of empirical risk (through some simple point-based error measured with loss function) with added regularization. We propose to approach this problem in a more information theoretic way by investigating applicability of entropy measures as a classification model objective function. We focus on quadratic Renyi's entropy and connected Cauchy-Schwarz Divergence which leads to the construction of Extreme Entropy Machines (EEM). The main contribution of this paper is proposing a model based on the information theoretic concepts which on the one hand shows new, entropic perspective on known linear classifiers and on the other leads to a construction of very robust method competetitive with the state of the art non-information theoretic ones (including Support Vector Machines and Extreme Learning Machines). Evaluation on numerous problems spanning from small, simple ones from UCI repository to the large (hundreads of thousands of samples) extremely unbalanced (up to 100:1 classes' ratios) datasets shows wide applicability of the EEM in real life problems and that it scales well