3,663 research outputs found
Prediction, Retrodiction, and The Amount of Information Stored in the Present
We introduce an ambidextrous view of stochastic dynamical systems, comparing
their forward-time and reverse-time representations and then integrating them
into a single time-symmetric representation. The perspective is useful
theoretically, computationally, and conceptually. Mathematically, we prove that
the excess entropy--a familiar measure of organization in complex systems--is
the mutual information not only between the past and future, but also between
the predictive and retrodictive causal states. Practically, we exploit the
connection between prediction and retrodiction to directly calculate the excess
entropy. Conceptually, these lead one to discover new system invariants for
stochastic dynamical systems: crypticity (information accessibility) and causal
irreversibility. Ultimately, we introduce a time-symmetric representation that
unifies all these quantities, compressing the two directional representations
into one. The resulting compression offers a new conception of the amount of
information stored in the present.Comment: 17 pages, 7 figures, 1 table;
http://users.cse.ucdavis.edu/~cmg/compmech/pubs/pratisp.ht
Cosmological Solutions of Low-Energy Heterotic M-Theory
We derive a set of exact cosmological solutions to the D=4, N=1 supergravity
description of heterotic M-theory. Having identified a new and exact SU(3) Toda
model solution, we then apply symmetry transformations to both this solution
and to a previously known SU(2) Toda model, in order to derive two further sets
of new cosmological solutions. In the symmetry-transformed SU(3) Toda case we
find an unusual "bouncing" motion for the M5 brane, such that this brane can be
made to reverse direction part way through its evolution. This bounce occurs
purely through the interaction of non-standard kinetic terms, as there are no
explicit potentials in the action. We also present a perturbation calculation
which demonstrates that, in a simple static limit, heterotic M-theory possesses
a scale-invariant isocurvature mode. This mode persists in certain asymptotic
limits of all the solutions we have derived, including the bouncing solution.Comment: 24 pages, 2 tables, 9 eps figures; minor corrections to conten
Information Accessibility and Cryptic Processes: Linear Combinations of Causal States
We show in detail how to determine the time-reversed representation of a
stationary hidden stochastic process from linear combinations of its
forward-time -machine causal states. This also gives a check for the
-cryptic expansion recently introduced to explore the temporal range over
which internal state information is spread.Comment: 6 pages, 9 figures, 2 tables;
http://users.cse.ucdavis.edu/~cmg/compmech/pubs/iacplcocs.ht
An Informal Summary of a New Formalism for Classifying Spin-Orbit Systems Using Tools Distilled from the Theory of Bundles
We give an informal summary of ongoing work which uses tools distilled from
the theory of fibre bundles to classify and connect invariant fields associated
with spin motion in storage rings. We mention four major theorems. One ties
invariant fields with the notion of normal form, the second allows comparison
of different invariant fields and the two others tie the existence of invariant
fields to the existence of certain invariant sets. We explain how the theorems
apply to the spin dynamics of spin- and spin- particles. Our approach
elegantly unifies the spin-vector dynamics from the T-BMT equation with the
spin-tensor dynamics and other dynamics and suggests an avenue for addressing
the question of the existence of the invariant spin field.Comment: Based on a presentation at Spin2014, The 21st International Symposium
on Spin Physics, Beijing, China, October 2014. To be published in the
International Journal of Modern Physics, Conference Serie
The political economy of opencast mining in Scotland and the north east of England
This is an interdisciplinary, descriptive, empirical study and analysis of the use of opencast mining in a complex process of commercialisation of the coal industry, its impact upon the environment and communities. Much of the initial research was undertaken during a series of public inquiries into opencast mining which provided the wealth of material contained in the thesis. The thesis advanced here is that the State has regulated the supply of coal through positive discrimination for opencast coal in the operation of the planning system and by arbitrary financial regulation of British Coal operations. The argument presented is that despite contrasting approaches and political processes in Scotland and North East England, opencast coal production has been used as a common facilitator towards the commercialisation of the coal industry. Descriptive analysis is given of the changing strategic use of opencast mining across the decades, from its early commercial development and the policy of dual control to its intensive application to assist the coal industry meet government financial and operational directives. The expansion of opencast mining can be attributed to changes in the political economy of the 1970's, the application of the private sector ethos of input-output ratios and management control, the unprecedented (mis)use of secondary planning legislation and the continued use of narrow accountancy procedures. Despite the denials of British Coal, in the North East of England opencast coal output has supplanted deep mined capacity and has been maximised to the limits of the Power Generators* specifications for burning coal to maximise profit and provide a "bank' of assets to attract private investment. The strategy in Scotland shows opencast mining holding the markets during radical reconstruction of the industry, hibernating' investment to make the industry attractive for the private sector. Both strategies have been set within a general "sweetening' operation of the coal industry. The work assesses the changing policy process of environmental planning, planning law and the public inquiry process in relation to opencast coalmining. Two major attitude surveys in Scotland and North East England cover the social context of environmental planning policy, each confirm the marginalisation of the public to decisions made in opencast development. Certain themes define the scope of the thesis: The State’s approach to energy policy and planning policy. British Coal's economic "management' of coal production, as well as the attitudes of the public, public planning officials, British Coal and the National Union of Mineworkers in Scotland and North East England. Scrutiny of the market for coal and British Coal's claims for the need for opencast coal are given full coverage in light of the effects from the expansion of opencast mining on employment, the environment and people. Overall the thesis challenges accepted thinking on economic and planning policy aspects and technical requirements of opencast coal production in relation to deep mined coal
A New and Unifying Approach to Spin Dynamics and Beam Polarization in Storage Rings
With this paper we extend our studies [1] on polarized beams by distilling
tools from the theory of principal bundles. Four major theorems are presented,
one which ties invariant fields with the notion of normal form, one which
allows one to compare different invariant fields, and two that relate the
existence of invariant fields to the existence of certain invariant sets and
relations between them. We then apply the theory to the dynamics of spin-1/2
and spin-1 particles and their density matrices describing statistically the
particle-spin content of bunches. Our approach thus unifies the spin-vector
dynamics from the T-BMT equation with the spin-tensor dynamics and other
dynamics. This unifying aspect of our approach relates the examples elegantly
and uncovers relations between the various underlying dynamical systems in a
transparent way
A detailed and unified treatment of spin-orbit systems using tools distilled from the theory of bundles
We return to our study \cite{BEH} of invariant spin fields and spin tunes for
polarized beams in storage rings but in contrast to the continuous-time
treatment in \cite{BEH}, we now employ a discrete-time formalism, beginning
with the maps of the continuous time formalism. We then
substantially extend our toolset and generalize the notions of invariant spin
field and invariant frame field. We revisit some old theorems and prove several
theorems believed to be new. In particular we study two transformation rules,
one of them known and the other new, where the former turns out to be an
-gauge transformation rule. We then apply the theory to the dynamics of
spin- and spin- particle bunches and their density matrix functions,
describing semiclassically the particle-spin content of bunches. Our approach
thus unifies the spin-vector dynamics from the T-BMT equation with the
spin-tensor dynamics and other dynamics. This unifying aspect of our approach
relates the examples elegantly and uncovers relations between the various
underlying dynamical systems in a transparent way. As in \cite{BEH}, the
particle motion is integrable but we now allow for nonlinear particle motion on
each torus. Since this work is inspired by notions from the theory of bundles,
we also provide insight into the underlying bundle-theoretic aspects of the
well-established concepts of invariant spin field, spin tune and invariant
frame field. Since we neglect, as is usual, the Stern-Gerlach force, the
underlying principal bundle is of product formso that we can present the theory
in a fashion which does not use bundle theory. Nevertheless we occasionally
mention the bundle-theoretic meaningof our concepts and we also mention the
similarities with the geometrical approach to Yang-Mills Theory
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