13,717 research outputs found

### Scaling behavior in economics: I. Empirical results for company growth

We address the question of the growth of firm size. To this end, we analyze
the Compustat data base comprising all publicly-traded United States
manufacturing firms within the years 1974-1993. We find that the distribution
of firm sizes remains stable for the 20 years we study, i.e., the mean value
and standard deviation remain approximately constant. We study the distribution
of sizes of the ``new'' companies in each year and find it to be well
approximated by a log-normal. We find (i) the distribution of the logarithm of
the growth rates, for a fixed growth period of one year, and for companies with
approximately the same size $S$ displays an exponential form, and (ii) the
fluctuations in the growth rates -- measured by the width of this distribution
$\sigma_1$ -- scale as a power law with $S$, $\sigma_1\sim S^{-\beta}$. We find
that the exponent $\beta$ takes the same value, within the error bars, for
several measures of the size of a company. In particular, we obtain:
$\beta=0.20\pm0.03$ for sales, $\beta=0.18\pm0.03$ for number of employees,
$\beta=0.18\pm0.03$ for assets, $\beta=0.18\pm0.03$ for cost of goods sold, and
$\beta=0.20\pm0.03$ for property, plant, & equipment.Comment: 16 pages LateX, RevTeX 3, 10 figures, to appear J. Phys. I France
(April 1997

### Scaling behavior in economics: II. Modeling of company growth

In the preceding paper we presented empirical results describing the growth
of publicly-traded United States manufacturing firms within the years
1974--1993. Our results suggest that the data can be described by a scaling
approach. Here, we propose models that may lead to some insight into these
phenomena. First, we study a model in which the growth rate of a company is
affected by a tendency to retain an ``optimal'' size. That model leads to an
exponential distribution of the logarithm of the growth rate in agreement with
the empirical results. Then, we study a hierarchical tree-like model of a
company that enables us to relate the two parameters of the model to the
exponent $\beta$, which describes the dependence of the standard deviation of
the distribution of growth rates on size. We find that $\beta = -\ln \Pi / \ln
z$, where $z$ defines the mean branching ratio of the hierarchical tree and
$\Pi$ is the probability that the lower levels follow the policy of higher
levels in the hierarchy. We also study the distribution of growth rates of this
hierarchical model. We find that the distribution is consistent with the
exponential form found empirically.Comment: 19 pages LateX, RevTeX 3, 6 figures, to appear J. Phys. I France
(April 1997

### Resilience of Complex Networks to Random Breakdown

Using Monte Carlo simulations we calculate $f_c$, the fraction of nodes which
are randomly removed before global connectivity is lost, for networks with
scale-free and bimodal degree distributions. Our results differ with the
results predicted by an equation for $f_c$ proposed by Cohen, et al. We discuss
the reasons for this disagreement and clarify the domain for which the proposed
equation is valid

### Vulnerability and Protection of Critical Infrastructures

Critical infrastructure networks are a key ingredient of modern society. We
discuss a general method to spot the critical components of a critical
infrastructure network, i.e. the nodes and the links fundamental to the perfect
functioning of the network. Such nodes, and not the most connected ones, are
the targets to protect from terrorist attacks. The method, used as an
improvement analysis, can also help to better shape a planned expansion of the
network.Comment: 4 pages, 1 figure, 3 table

### Discrimination between pure states and mixed states

In this paper, we discuss the problem of determining whether a quantum system
is in a pure state, or in a mixed state. We apply two strategies to settle this
problem: the unambiguous discrimination and the maximum confidence
discrimination. We also proved that the optimal versions of both strategies are
equivalent. The efficiency of the discrimination is also analyzed. This scheme
also provides a method to estimate purity of quantum states, and Schmidt
numbers of composed systems

### Critical Phenomena and Thermodynamic Geometry of RN-AdS Black Holes

The phase transition of Reissner-Nordstr\"om black holes in
$(n+1)$-dimensional anti-de Sitter spacetime is studied in details using the
thermodynamic analogy between a RN-AdS black hole and a van der Waals liquid
gas system. We first investigate critical phenomena of the RN-AdS black hole.
The critical exponents of relevant thermodynamical quantities are evaluated. We
find identical exponents for a RN-AdS black hole and a Van der Waals liquid gas
system. This suggests a possible universality in the phase transitions of these
systems. We finally study the thermodynamic behavior using the equilibrium
thermodynamic state space geometry and find that the scalar curvature diverges
exactly at the van der Waals-like critical point where the heat capacity at
constant charge of the black hole diverges.Comment: 18 pages, 5 figure

### Quantifying photosynthetic rates of microphytobenthos using the triple isotope composition of dissolved oxygen

Author Posting. © Association for the Sciences of Limnology and Oceanography, 2013. This article is posted here by permission of Association for the Sciences of Limnology and Oceanography for personal use, not for redistribution. The definitive version was published in Limnology and Oceanography: Methods 11 (2013): 360-373, doi:10.4319/lom.2013.11.360.Microphytobenthos are important mediators of nutrient and carbon fluxes in coastal environments. However, quantifying production rates by microphytobenthos is difficult, and existing methods necessitate perhaps erroneous assumptions that dark respiration equals light respiration. Here we present a new method for quantifying photosynthetic rates of microphytobenthos, i.e., gross primary production, by using the triple isotope composition of dissolved oxygen in benthic flux chambers. Because the triple oxygen isotope signature is sensitive to photosynthesis, but not to respiration, this method allows quantification of gross photosynthetic oxygen fluxes by microphytobenthos without assumptions about respiration. We present results from field experiments in Waquoit Bay, Massachusetts, that illustrate the method.We gratefully
acknowledge funding for this work by the Coastal Ocean Institute of
Woods Hole Oceanographic Institution and the National Science
Foundation (OCE-82964400). EH was supported by a National Defense
Science and Engineering Graduate Fellowship award

### Methods for measuring the citations and productivity of scientists across time and discipline

Publication statistics are ubiquitous in the ratings of scientific
achievement, with citation counts and paper tallies factoring into an
individual's consideration for postdoctoral positions, junior faculty, tenure,
and even visa status for international scientists. Citation statistics are
designed to quantify individual career achievement, both at the level of a
single publication, and over an individual's entire career. While some academic
careers are defined by a few significant papers (possibly out of many), other
academic careers are defined by the cumulative contribution made by the
author's publications to the body of science. Several metrics have been
formulated to quantify an individual's publication career, yet none of these
metrics account for the dependence of citation counts and journal size on time.
In this paper, we normalize publication metrics across both time and discipline
in order to achieve a universal framework for analyzing and comparing
scientific achievement. We study the publication careers of individual authors
over the 50-year period 1958-2008 within six high-impact journals: CELL, the
New England Journal of Medicine (NEJM), Nature, the Proceedings of the National
Academy of Science (PNAS), Physical Review Letters (PRL), and Science. In
comparing the achievement of authors within each journal, we uncover
quantifiable statistical regularity in the probability density function (pdf)
of scientific achievement across both time and discipline. The universal
distribution of career success within these arenas for publication raises the
possibility that a fundamental driving force underlying scientific achievement
is the competitive nature of scientific advancement.Comment: 25 pages in 1 Column Preprint format, 7 Figures, 4 Tables. Version
II: changes made in response to referee comments. Note: change in definition
of "Paper shares.

### Scaling for the Percolation Backbone

We study the backbone connecting two given sites of a two-dimensional lattice
separated by an arbitrary distance $r$ in a system of size $L$. We find a
scaling form for the average backbone mass: $\sim L^{d_B}G(r/L)$, where
$G$ can be well approximated by a power law for $0\le x\le 1$: $G(x)\sim
x^{\psi}$ with $\psi=0.37\pm 0.02$. This result implies that $\sim
L^{d_B-\psi}r^{\psi}$ for the entire range $0<r<L$. We also propose a scaling
form for the probability distribution $P(M_B)$ of backbone mass for a given
$r$. For $r\approx L, P(M_B)$ is peaked around $L^{d_B}$, whereas for $r\ll L,
P(M_B)$ decreases as a power law, $M_B^{-\tau_B}$, with $\tau_B\simeq 1.20\pm
0.03$. The exponents $\psi$ and $\tau_B$ satisfy the relation
$\psi=d_B(\tau_B-1)$, and $\psi$ is the codimension of the backbone,
$\psi=d-d_B$.Comment: 3 pages, 5 postscript figures, Latex/Revtex/multicols/eps

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