7,427 research outputs found
Complexity of Two-Dimensional Patterns
In dynamical systems such as cellular automata and iterated maps, it is often
useful to look at a language or set of symbol sequences produced by the system.
There are well-established classification schemes, such as the Chomsky
hierarchy, with which we can measure the complexity of these sets of sequences,
and thus the complexity of the systems which produce them.
In this paper, we look at the first few levels of a hierarchy of complexity
for two-or-more-dimensional patterns. We show that several definitions of
``regular language'' or ``local rule'' that are equivalent in d=1 lead to
distinct classes in d >= 2. We explore the closure properties and computational
complexity of these classes, including undecidability and L-, NL- and
NP-completeness results.
We apply these classes to cellular automata, in particular to their sets of
fixed and periodic points, finite-time images, and limit sets. We show that it
is undecidable whether a CA in d >= 2 has a periodic point of a given period,
and that certain ``local lattice languages'' are not finite-time images or
limit sets of any CA. We also show that the entropy of a d-dimensional CA's
finite-time image cannot decrease faster than t^{-d} unless it maps every
initial condition to a single homogeneous state.Comment: To appear in J. Stat. Phy
Automated Microbial Metabolism Laboratory Final report
Photosynthesis activity during phosphate soil analysi
"Dressing" lines and vertices in calculations of matrix elements with the coupled-cluster method and determination of Cs atomic properties
We consider evaluation of matrix elements with the coupled-cluster method.
Such calculations formally involve infinite number of terms and we devise a
method of partial summation (dressing) of the resulting series. Our formalism
is built upon an expansion of the product of cluster amplitudes
into a sum of -body insertions. We consider two types of insertions:
particle/hole line insertion and two-particle/two-hole
random-phase-approximation-like insertion. We demonstrate how to ``dress''
these insertions and formulate iterative equations. We illustrate the dressing
equations in the case when the cluster operator is truncated at single and
double excitations. Using univalent systems as an example, we upgrade
coupled-cluster diagrams for matrix elements with the dressed insertions and
highlight a relation to pertinent fourth-order diagrams. We illustrate our
formalism with relativistic calculations of hyperfine constant and
electric-dipole transition amplitude for Cs atom. Finally,
we augment the truncated coupled-cluster calculations with otherwise omitted
fourth-order diagrams. The resulting analysis for Cs is complete through the
fourth-order of many-body perturbation theory and reveals an important role of
triple and disconnected quadruple excitations.Comment: 16 pages, 7 figures; submitted to Phys. Rev.
Geometry of effective Hamiltonians
We give a complete geometrical description of the effective Hamiltonians
common in nuclear shell model calculations. By recasting the theory in a
manifestly geometric form, we reinterpret and clarify several points. Some of
these results are hitherto unknown or unpublished. In particular, commuting
observables and symmetries are discussed in detail. Simple and explicit proofs
are given, and numerical algorithms are proposed, that improve and stabilize
common methods used today.Comment: 1 figur
Estimating the Expected Value of Partial Perfect Information in Health Economic Evaluations using Integrated Nested Laplace Approximation
The Expected Value of Perfect Partial Information (EVPPI) is a
decision-theoretic measure of the "cost" of parametric uncertainty in decision
making used principally in health economic decision making. Despite this
decision-theoretic grounding, the uptake of EVPPI calculations in practice has
been slow. This is in part due to the prohibitive computational time required
to estimate the EVPPI via Monte Carlo simulations. However, recent developments
have demonstrated that the EVPPI can be estimated by non-parametric regression
methods, which have significantly decreased the computation time required to
approximate the EVPPI. Under certain circumstances, high-dimensional Gaussian
Process regression is suggested, but this can still be prohibitively expensive.
Applying fast computation methods developed in spatial statistics using
Integrated Nested Laplace Approximations (INLA) and projecting from a
high-dimensional into a low-dimensional input space allows us to decrease the
computation time for fitting these high-dimensional Gaussian Processes, often
substantially. We demonstrate that the EVPPI calculated using our method for
Gaussian Process regression is in line with the standard Gaussian Process
regression method and that despite the apparent methodological complexity of
this new method, R functions are available in the package BCEA to implement it
simply and efficiently
Trans-Rational Cash: Ghost-Money, Hong Kong, and Nonmodern Networks
In this essay, I examine through Bruno Latour's concept of nonmodern networks the intersections of the hyper-modernity of Hong Kong's ‘real’ money economy with that of an economy of ghost-money that, through the act of burning, serves as an offering to the dead and the divine. The essay reconfigures Latour's ‘modern constitution’ as it relates to philosophy, myth and modernity as they are organised around the values of a currency that trespass all boundaries.postprin
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