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 $\epsilon$-machine causal states. This also gives a check for the $k$-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-$1/2$ and spin-$1$ 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

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

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 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 $\rm{Poincar\acute{e}}$ 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 $SO(3)$-gauge transformation rule. We then apply the theory to the dynamics of spin-$1/2$ and spin-$1$ 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