40,854 research outputs found
On random tomography with unobservable projection angles
We formulate and investigate a statistical inverse problem of a random
tomographic nature, where a probability density function on is
to be recovered from observation of finitely many of its two-dimensional
projections in random and unobservable directions. Such a problem is distinct
from the classic problem of tomography where both the projections and the unit
vectors normal to the projection plane are observable. The problem arises in
single particle electron microscopy, a powerful method that biophysicists
employ to learn the structure of biological macromolecules. Strictly speaking,
the problem is unidentifiable and an appropriate reformulation is suggested
hinging on ideas from Kendall's theory of shape. Within this setup, we
demonstrate that a consistent solution to the problem may be derived, without
attempting to estimate the unknown angles, if the density is assumed to admit a
mixture representation.Comment: Published in at http://dx.doi.org/10.1214/08-AOS673 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Monetary economics from econophysics perspective
This is an invited article for the Discussion and Debate special issue of The
European Physical Journal Special Topics on the subject "Can Economics Be a
Physical Science?" The first part of the paper traces the personal path of the
author from theoretical physics to economics. It briefly summarizes
applications of statistical physics to monetary transactions in an ensemble of
economic agents. It shows how a highly unequal probability distribution of
money emerges due to irreversible increase of entropy in the system. The second
part examines deep conceptual and controversial issues and fallacies in
monetary economics from econophysics perspective. These issues include the
nature of money, conservation (or not) of money, distinctions between money vs.
wealth and money vs. debt, creation of money by the state and debt by the
banks, the origins of monetary crises and capitalist profit. Presentation uses
plain language understandable to laypeople and may be of interest to both
specialists and general public.Comment: 23 pages, 1 figur
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