Exact solution of the Boltzmann equation in the homogeneous color conductivity problem

An exact solution of the Boltzmann equation for a binary mixture of colored Maxwell molecules is found. The solution corresponds to a nonequilibrium homogeneous steady state created by a nonconservative external force. Explicit expressions for the moments of the distribution function are obtained. By using information theory, an approximate velocity distribution function is constructed, which is exact in the limits of small and large field strengths. Comparison is made between the exact energy flux and the one obtained from the information theory distribution.     

An open optimization problem in statistical quality control

We ask the experts in global optimization if there is an efficient solution to an optimization problem in acceptance sampling: Here, one often has incomplete prior information about the quality of incoming lots. Given a cost model, a decision rule for the inspection of a lot may then be designed that minimizes the maximum loss compatible with the available information. The resulting minimax problem is sometimes hard to solve, as the loss functions may have several local maxima which vary in an unpredictable way with the parameters of the decision rule.     

Kinetic energy decomposition scheme based on information theory

We proposed a novel kinetic energy decomposition analysis based on information theory. Since the Hirshfeld partitioning for electron densities can be formulated in terms of Kullback–Leibler information deficiency in information theory, a similar partitioning for kinetic energy densities was newly proposed. The numerical assessments confirm that the current kinetic energy decomposition scheme provides reasonable chemical pictures for ionic and covalent molecules, and can also estimate atomic energies using a correction with viral ratios.     

A central limit theorem in nonlinear filtering

It is shown that the probability law of a diffusion process conditioned on weakly corrupted observations is asymptotically Gaussian when properly scaled. The method of proof involves Fisher information matrices and a Cramér-Rao inequality.     

‘New mathematics’ and teaching

Inside the scientific world it is not always understood that the mood of mathematics, which is a product and a part of culture, can change with time. This is partly why many have been surprised by the coming of the so‐called new mathematics.

In the truly creative mathematical mind two opposite tendencies coexist: the logical and the imaginative. Apparently it seems that new mathematics can be reduced to a purely logical machinery. In fact it contains as much imaginative contributions as classical mathematics. But it is difficult to show simultaneously the logical sequence of propositions and the clumsy progression of research itself. Mathematical exposition does not always follow the ‘ most natural slopes’ of the mind. Unfamiliar presentations often give an impression of ‘ abstraction ‘, more familiar ones an impression of concreteness ‘.

So it appears that difficulties with new mathematics are mostly of psychological origin. Misuses of it can easily raise up intolerance reactions and emotional blocks. Perhaps insisting upon the fact that, here as elsewhere, it is important to be able to guess, to realize that intuition and imagination are essential, could help to make new mathematics better understood, more useful and more able to be considered as a unifing element among sciences.     

Fisher Information of Free-Electron Landau States

An electron in a constant magnetic field has energy levels, known as the Landau levels. One can obtain the corresponding radial wavefunction of free-electron Landau states in cylindrical polar coordinates. However, this system has not been explored so far in terms of an information-theoretical viewpoint. Here, we focus on Fisher information associated with these Landau states specified by the two quantum numbers. Fisher information provides a useful measure of the electronic structure in quantum systems, such as hydrogen-like atoms and under some potentials. By numerically evaluating the generalized Laguerre polynomials in the radial densities, we report that Fisher information increases linearly with the principal quantum number that specifies energy levels, but decreases monotonically with the azimuthal quantum number m. We also present relative Fisher information of the Landau states against the reference density with m=0, which is proportional to the principal quantum number. We compare it with the case when the lowest Landau level state is set as the reference.     

Building and analyzing the US airport network based on en-route location information

From a complex network perspective, this study sets out two aims around the US airport network (USAN) which is built from en-route location information of domestic flights in the US. First, we analyze the structural properties of the USAN with respect to its binary and weighted graphs, and second we explore the airport patterns, which have wide-ranging implications. Results from the two graphs indicate the following. (1) The USAN exhibits scale-free, small-world and disassortative mixing properties, which are consistent with the mainstream perspectives. Besides, we find (2) a remarkable power relationship between the structural measurements in the binary graph and the traffic measurements in the weighted counterpart, namely degree versus capacity and attraction versus volume. On the other hand, investigation of the airport patterns suggests (3) that all the airports can be classified into four categories based on multiple network metrics, which shows a complete typology of the airports. And it further indicates (4) that there is a subtle relationship between the airport traffic and the geographical constraints as well as the regional socioeconomic indicators.     

Rejoinder on “Statistical reasoning with set-valued information: Ontic vs. epistemic views”

This note replies to comments made on our contribution to the Low Quality Data debate.     

Comment on: “Topology identification and adaptive synchronization of uncertain complex networks with adaptive double scaling functions” [Commun Nonlinear Sci Numer Simul 2011;16:3337-43]

In this comment letter we point out that the main result of the recent paper [Xu Y, Zhou W, Fang J, Sun W. Topology identification and adaptive synchronization of uncertain complex networks with adaptive double scaling functions. Commun Nonlinear Sci Numer Simul 2011;16(18):3337-43] has certain errors. The mistakes are corrected and a correct version is presented in this letter. We further indicate that a sufficient condition has been neglected in a series of articles discussing the same topic of network topology identification; hence we hope this letter can help clarify some unclear concepts about this topic.