Photon Statistics for Single Molecule Non-Linear Spectroscopy

We consider the theory of the non-linear spectroscopy for a single molecule undergoing stochastic dynamics and interacting with a sequence of two laser pulses. General expressions for photon counting statistics are obtained, and an exact solution to the problem of the Kubo-Anderson process is found. In the limit of impulsive pulses the information on the photon statistics is contained in the molecule's dipole correlation function. The selective limit where temporal resolution is maintained, the semi-classical approximation and the fast modulation limit exhibit general behaviors of this new type of spectroscopy. We show how the design of the external field leads to rich insights on dynamics of individual molecules which are different than those found for an ensemble

Non-normalizable densities in strong anomalous diffusion: beyond the central limit theorem

Strong anomalous diffusion, where $\langle |x(t)|^q \rangle \sim t^{q \nu(q)}$ with a nonlinear spectrum \nu(q) \neq \mbox{const}, is wide spread and has been found in various nonlinear dynamical systems and experiments on active transport in living cells. Using a stochastic approach we show how this phenomena is related to infinite covariant densities, i.e., the asymptotic states of these systems are described by non-normalizable distribution functions. Our work shows that the concept of infinite covariant densities plays an important role in the statistical description of open systems exhibiting multi-fractal anomalous diffusion, as it is complementary to the central limit theorem.Comment: PRL, in pres

Fat residue and use-wear found on Acheulian biface and scraper associated with butchered elephant remains at the site of Revadim, Israel

The archaeological record indicates that elephants must have played a significant role in early human diet and culture during Palaeolithic times in the Old World. However, the nature of interactions between early humans and elephants is still under discussion. Elephant remains are found in Palaeolithic sites, both open-air and cave sites, in Europe, Asia, the Levant, and Africa. In some cases elephant and mammoth remains indicate evidence for butchering and marrow extraction performed by humans. Revadim Quarry (Israel) is a Late Acheulian site where elephant remains were found in association with characteristic Lower Palaeolithic flint tools. In this paper we present results regarding the use of Palaeolithic tools in processing animal carcasses and rare identification of fat residue preserved on Lower Palaeolithic tools. Our results shed new light on the use of Palaeolithic stone tools and provide, for the first time, direct evidence (residue) of animal exploitation through the use of an Acheulian biface and a scraper. The association of an elephant rib bearing cut marks with these tools may reinforce the view suggesting the use of Palaeolithic stone tools in the consumption of large game

From non-Brownian Functionals to a Fractional Schr\"odinger Equation

We derive backward and forward fractional Schr\"odinger type of equations for the distribution of functionals of the path of a particle undergoing anomalous diffusion. Fractional substantial derivatives introduced by Friedrich and co-workers [PRL {\bf 96}, 230601 (2006)] provide the correct fractional framework for the problem at hand. In the limit of normal diffusion we recover the Feynman-Kac treatment of Brownian functionals. For applications, we calculate the distribution of occupation times in half space and show how statistics of anomalous functionals is related to weak ergodicity breaking.Comment: 5 page

Declining Labor and Capital Shares

This paper shows that the decline in the labor share over the past 30 years was not offset by an increase in the capital share. Capital costs are the product of the required rate of return on capital and the value of the capital stock, and the capital share is the ratio of capital costs to gross value added. The capital share is declining, driven by a large decline in the cost of capital. Measured in percentage terms, the decline in the capital share (30%) is much more dramatic than the decline in the labor share (10%). The profit share has increased by more than 12 percentage points. The value of this increase in profits amounts to over $1.1 trillion in 2014, or$14 thousand per employee. The decline in the capital share is unlikely to be driven by unobserved capital. In a standard model, a decline in competition is necessary to generate simultaneous declines in the labor and capital shares. A calibrated model shows that a decline in competition quantitatively matches the data. This paper provides reduced form empirical evidence that a decline in competition plays a significant role in the decline in the labor share. Increases in industry concentration are associated with declines in the labor share. These results suggest that the decline in the shares of labor and capital are due to a decline in competition and call into question the conclusion that the decline in the labor share is an efficient outcome

Comparative gene expression analysis by differential clustering approach: application to the Candida albicans transcription program.

Differences in gene expression underlie many of the phenotypic variations between related organisms, yet approaches to characterize such differences on a genome-wide scale are not well developed. Here, we introduce the "differential clustering algorithm" for revealing conserved and diverged co-expression patterns. Our approach is applied at different levels of organization, ranging from pair-wise correlations within specific groups of functionally linked genes, to higher-order correlations between such groups. Using the differential clustering algorithm, we systematically compared the transcription program of the fungal pathogen Candida albicans with that of the model organism Saccharomyces cerevisiae. Many of the identified differences are related to the differential requirement for mitochondrial function in the two yeasts. Distinct regulation patterns of cell cycle genes and of amino acid metabolic genes were also revealed and, in some cases, could be linked to the differential appearance of cis-regulatory elements in the gene promoter regions. Our study provides a comprehensive framework for comparative gene expression analysis and a rich source of hypotheses for uncharacterized open reading frames and putative cis-regulatory elements in C. albicans

Comment on "Mean First Passage Time for Anomalous Diffusion"

We correct a previously erroneous calculation [Phys. Rev. E 62, 6065 (2000)] of the mean first passage time of a subdiffusive process to reach either end of a finite interval in one dimension. The mean first passage time is in fact infinite.Comment: To appear in Phys. Rev.