Symmetry, Entropy, Diversity and (why not?) Quantum Statistics in Society

We describe society as a nonequilibrium probabilistic system: N individuals occupy W resource states in it and produce entropy S over definite time periods. Resulting thermodynamics is however unusual because a second entropy, H, measures a typically social feature, inequality or diversity in the distribution of available resources. A symmetry phase transition takes place at Gini values 1/3, where realistic distributions become asymmetric. Four constraints act on S: expectedly, N and W, and new ones, diversity and interactions between individuals; the latter result from the two coordinates of a single point in the data, the peak. The occupation number of a job is either zero or one, suggesting Fermi-Dirac statistics for employment. Contrariwise, an indefinite nujmber of individuals can occupy a state defined as a quantile of income or of age, so Bose-Einstein statistics may be required. Indistinguishability rather than anonymity of individuals and resources is thus needed. Interactions between individuals define define classes of equivalence that happen to coincide with acceptable definitions of social classes or periods in human life. The entropy S is non-extensive and obtainable from data. Theoretical laws are compared to data in four different cases of economical or physiological diversity. Acceptable fits are found for all of them.Comment: 13 pages, 2 figure

Electrical Nanoprobing of Semiconducting Carbon Nanotubes using an Atomic Force Microscope

We use an Atomic Force Microscope (AFM) tip to locally probe the electronic properties of semiconducting carbon nanotube transistors. A gold-coated AFM tip serves as a voltage or current probe in three-probe measurement setup. Using the tip as a movable current probe, we investigate the scaling of the device properties with channel length. Using the tip as a voltage probe, we study the properties of the contacts. We find that Au makes an excellent contact in the p-region, with no Schottky barrier. In the n-region large contact resistances were found which dominate the transport properties.Comment: 4 pages, 5 figure

Isotropic, Nematic and Smectic A Phase Behaviour in a Fictitious Field

Phase behaviours of liquid crystals under external fields, conjugate to the nematic order and smectic order, are studied within the framework of mean field approximation developed by McMillan. It is found that phase diagrams, of temperature vs interaction parameter of smectic A order, show several topologically different types caused by the external fields. The influences of the field conjugate to the smectic A phase, which is fictitious field, are precisely discussed.Comment: To be published in J. Phys. Soc. Jpn. vol.73 No.

Projections onto translation—Invariant subspaces of L1(G)

AbstractLet G be a locally compact abelian group. A translation-invariant subspace in L1(G) may or may not be complemented depending on the structure of its hull in Ĝ. Techniques for deciding this complementation problem in a variety of situations are developed and illustrated with examples. A complete characterization is obtained for those ideals with a discrete hull

Computer modeling of large asteroid impacts into continental and oceanic sites: Atmospheric, cratering, and ejecta dynamics

Numerous impact cratering events have occurred on the Earth during the last several billion years that have seriously affected our planet and its atmosphere. The largest cratering events, which were caused by asteroids and comets with kinetic energies equivalent to tens of millions of megatons of TNT, have distributed substantial quantities of terrestrial and extraterrestrial material over much or all of the Earth. In order to study a large-scale impact event in detail, computer simulations were completed that model the passage of a 10 km-diameter asteroid through the Earth's atmosphere and the subsequent cratering and ejecta dynamics associated with impact of the asteroid into two different targets, i.e., an oceanic site and a continental site. The calcuations were designed to broadly represent giant impact events that have occurred on the Earth since its formation and specifically represent an impact cratering event proposed to have occurred at the end of Cretaceous time. Calculation of the passage of the asteroid through a U.S. Standard Atmosphere showed development of a strong bow shock that expanded radially outward. Behind the shock front was a region of highly shock compressed and intensely heated air. Behind the asteroid, rapid expansion of this shocked air created a large region of very low density that also expanded away from the impact area. Calculations of the cratering events in both the continental and oceanic targets were carried to 120 s. Despite geologic differences, impacts in both targets developed comparable dynamic flow fields, and by approx. 29 s similar-sized transient craters approx. 39 km deep and approx. 62 km across had formed. For all practical purposes, the atmosphere was nearly completely removed from the impact area for tens of seconds, i.e., air pressures were less than fractions of a bar out to ranges of over 50 km. Consequently, much of the asteroid and target materials were ejected upward into a near vacuum. Effects of secondary volcanism and return of the ocean over hot oceanic crater floor could also be expected to add substantial solid and vaporized material to the atmosphere, but these conditions were not studied

A reactive system for open terrain navigation: Performance and limitations

We describe a core system for autonomous navigation in outdoor natural terrain. The system consists of three parts: a perception module which processes range images to identify untraversable regions of the terrain, a local map management module which maintains a representation of the environment in the vicinity of the vehicle, and a planning module which issues commands to the vehicle controller. Our approach is to use the concept of 'early traversability evaluation', and on the use of reactive planning for generating commands to drive the vehicle. We argue that our approach leads to a robust and efficient navigation system. We illustrate our approach by an experiment in which a vehicle travelled autonomously for one kilometer through unmapped cross-country terrain

Generation of measures on the torus with good sequences of integers

Let $S= (s_1<s_2<\dots)$ be a strictly increasing sequence of positive integers and denote $\mathbf{e}(\beta)=\mathrm{e}^{2\pi i \beta}$. We say $S$ is good if for every real $\alpha$ the limit $\lim_N \frac1N\sum_{n\le N} \mathbf{e}(s_n\alpha)$ exists. By the Riesz representation theorem, a sequence $S$ is good iff for every real $\alpha$ the sequence $(s_n\alpha)$ possesses an asymptotic distribution modulo 1. Another characterization of a good sequence follows from the spectral theorem: the sequence $S$ is good iff in any probability measure preserving system $(X,\mathbf{m},T)$ the limit $\lim_N \frac1N\sum_{n\le N}f\left(T^{s_n}x\right)$ exists in $L^2$-norm for $f\in L^2(X)$. Of these three characterization of a good set, the one about limit measures is the most suitable for us, and we are interested in finding out what the limit measure $\mu_{S,\alpha}= \lim_N\frac1N\sum_{n\le N} \delta_{s_n\alpha}$ on the torus can be. In this first paper on the subject, we investigate the case of a single irrational $\alpha$. We show that if $S$ is a good set then for every irrational $\alpha$ the limit measure $\mu_{S,\alpha}$ must be a continuous Borel probability measure. Using random methods, we show that the limit measure $\mu_{S,\alpha}$ can be any measure which is absolutely continuous with respect to the Haar-Lebesgue probability measure on the torus. On the other hand, if $\nu$ is the uniform probability measure supported on the Cantor set, there are some irrational $\alpha$ so that for no good sequence $S$ can we have the limit measure $\mu_{S,\alpha}$ equal $\nu$. We leave open the question whether for any continuous Borel probability measure $\nu$ on the torus there is an irrational $\alpha$ and a good sequence $S$ so that $\mu_{S,\alpha}=\nu$.Comment: 44 page

State Differentiation by Transient Truncation in Coupled Threshold Dynamics

Dynamics with a threshold input--output relation commonly exist in gene, signal-transduction, and neural networks. Coupled dynamical systems of such threshold elements are investigated, in an effort to find differentiation of elements induced by the interaction. Through global diffusive coupling, novel states are found to be generated that are not the original attractor of single-element threshold dynamics, but are sustained through the interaction with the elements located at the original attractor. This stabilization of the novel state(s) is not related to symmetry breaking, but is explained as the truncation of transient trajectories to the original attractor due to the coupling. Single-element dynamics with winding transient trajectories located at a low-dimensional manifold and having turning points are shown to be essential to the generation of such novel state(s) in a coupled system. Universality of this mechanism for the novel state generation and its relevance to biological cell differentiation are briefly discussed.Comment: 8 pages. Phys. Rev. E. in pres

Gene identification for the cblD defect of vitamin B12 metabolism

Background Vitamin B12 (cobalamin) is an essential cofactor in several metabolic pathways. Intracellular conversion of cobalamin to its two coenzymes, adenosylcobalamin in mitochondria and methylcobalamin in the cytoplasm, is necessary for the homeostasis of methylmalonic acid and homocysteine. Nine defects of intracellular cobalamin metabolism have been defined by means of somatic complementation analysis. One of these defects, the cblD defect, can cause isolated methylmalonic aciduria, isolated homocystinuria, or both. Affected persons present with multisystem clinical abnormalities, including developmental, hematologic, neurologic, and metabolic findings. The gene responsible for the cblD defect has not been identified. Methods We studied seven patients with the cblD defect, and skin fibroblasts from each were investigated in cell culture. Microcell-mediated chromosome transfer and refined genetic mapping were used to localize the responsible gene. This gene was transfected into cblD fibroblasts to test for the rescue of adenosylcobalamin and methylcobalamin synthesis. Results The cblD gene was localized to human chromosome 2q23.2, and a candidate gene, designated MMADHC (methylmalonic aciduria, cblD type, and homocystinuria), was identified in this region. Transfection of wild-type MMADHC rescued the cellular phenotype, and the functional importance of mutant alleles was shown by means of transfection with mutant constructs. The predicted MMADHC protein has sequence homology with a bacterial ATP-binding cassette transporter and contains a putative cobalamin binding motif and a putative mitochondrial targeting sequence. Conclusions Mutations in a gene we designated MMADHC are responsible for the cblD defect in vitamin B12 metabolism. Various mutations are associated with each of the three biochemical phenotypes of the disorder