1,095 research outputs found
Addressing the Bard: Learning Ideas
The Scottish Poetry Library has published a new, provocative and
exciting anthology of Burns poems, launched in the Year of
Homecoming and of Burns’s 250th anniversary.
What makes this anthology different is that twelve contemporary
poets have been asked to select one of Burns’s poems and to
respond to it.
The result is an eclectic collection with some unexpected choices
and responses that enlighten, challenge and amuse us. All of the
response poems provide insight into Burns’s original work and
some may have a more direct resonance with modern readers.
In addition to the book itself, these supporting resources are
being provided on the Learning and Teaching Scotland website.
The material has been developed by Liz Niven, poet, writer, and
Scots-language educator, and Maureen Farrell, an English
teacher and now teacher educator from the University of Glasgow
Fluctuations and Transients in Quantum-Resonant Evolution
The quantum-resonant evolution of the mean kinetic energy (MKE) of the kicked
particle is studied in detail on different time scales for {\em general}
kicking potentials. It is shown that the asymptotic time behavior of a
wave-packet MKE is typically a linear growth with bounded fluctuations having a
simple number-theoretical origin. For a large class of wave packets, the MKE is
shown to be exactly the superposition of its asymptotic behavior and transient
logarithmic corrections. Both fluctuations and transients can be significant
for not too large times but they may vanish identically under some conditions.
In the case of incoherent mixtures of plane waves, it is shown that the MKE
never exhibits asymptotic fluctuations but transients usually occur.Comment: REVTEX, 12 page
Recurrent proofs of the irrationality of certain trigonometric values
We use recurrences of integrals to give new and elementary proofs of the
irrationality of pi, tan(r) for all nonzero rational r, and cos(r) for all
nonzero rational r^2. Immediate consequences to other values of the elementary
transcendental functions are also discussed
Origins of the Combinatorial Basis of Entropy
The combinatorial basis of entropy, given by Boltzmann, can be written , where is the dimensionless entropy, is the
number of entities and is number of ways in which a given
realization of a system can occur (its statistical weight). This can be
broadened to give generalized combinatorial (or probabilistic) definitions of
entropy and cross-entropy: and , where is the probability of a given
realization, is a convenient transformation function, is a
scaling parameter and an arbitrary constant. If or
satisfy the multinomial weight or distribution, then using
and , and asymptotically
converge to the Shannon and Kullback-Leibler functions. In general, however,
or need not be multinomial, nor may they approach an
asymptotic limit. In such cases, the entropy or cross-entropy function can be
{\it defined} so that its extremization ("MaxEnt'' or "MinXEnt"), subject to
the constraints, gives the ``most probable'' (``MaxProb'') realization of the
system. This gives a probabilistic basis for MaxEnt and MinXEnt, independent of
any information-theoretic justification.
This work examines the origins of the governing distribution ....
(truncated)Comment: MaxEnt07 manuscript, version 4 revise
On Maltsev digraphs
The original publication is available at www.springerlink.com Copyright SpringerWe study digraphs preserved by a Maltsev operation, Maltsev digraphs. We show that these digraphs retract either onto a directed path or to the disjoint union of directed cycles, showing that the constraint satisfaction problem for Maltsev digraphs is in logspace, L. (This was observed in [19] using an indirect argument.) We then generalize results in [19] to show that a Maltsev digraph is preserved not only by a majority operation, but by a class of other operations (e.g., minority, Pixley) and obtain a O(V G4)-time algorithm to recognize Maltsev digraphs. We also prove analogous results for digraphs preserved by conservative Maltsev operations which we use to establish that the list homomorphism problem for Maltsev digraphs is in L. We then give a polynomial time characterisation of Maltsev digraphs admitting a conservative 2-semilattice operation. Finally, we give a simple inductive construction of directed acyclic digraphs preserved by a Maltsev operation.Peer reviewe
Grover's Quantum Search Algorithm and Diophantine Approximation
In a fundamental paper [Phys. Rev. Lett. 78, 325 (1997)] Grover showed how a
quantum computer can find a single marked object in a database of size N by
using only O(N^{1/2}) queries of the oracle that identifies the object. His
result was generalized to the case of finding one object in a subset of marked
elements. We consider the following computational problem: A subset of marked
elements is given whose number of elements is either M or K, M<K, our task is
to determine which is the case. We show how to solve this problem with a high
probability of success using only iterations of Grover's basic step (and no
other algorithm). Let m be the required number of iterations; we prove that
under certain restrictions on the sizes of M and K the estimation m <
(2N^{1/2})/(K^{1/2}-M^{1/2}) obtains. This bound sharpens previous results and
is known to be optimal up to a constant factor. Our method involves
simultaneous Diophantine approximations, so that Grover's algorithm is
conceptualized as an orbit of an ergodic automorphism of the torus. We comment
on situations where the algorithm may be slow, and note the similarity between
these cases and the problem of small divisors in classical mechanics.Comment: 8 pages, revtex, Title change
Electron-electron interaction corrections to the thermal conductivity in disordered conductors
We evaluate the electron-electron interaction corrections to the electronic
thermal conductivity in a disordered conductor in the diffusive regime. We use
a diagrammatic many-body method analogous to that of Altshuler and Aronov for
the electrical conductivity. We derive results in one, two and three dimensions
for both the singlet and triplet channels, and in all cases find that the
Wiedemann-Franz law is violated.Comment: 8 pages, 2 figures Typos corrected in formulas (15) and (A.4) and
Table 1; discussion of previous work in introduction extended; reference
clarifying different definitions of parameter F adde
Sums of products of Ramanujan sums
The Ramanujan sum is defined as the sum of -th powers of the
primitive -th roots of unity. We investigate arithmetic functions of
variables defined as certain sums of the products
, where are polynomials with
integer coefficients. A modified orthogonality relation of the Ramanujan sums
is also derived.Comment: 13 pages, revise
Maximum-Entropy Weighting of Multi-Component Earth Climate Models
A maximum entropy-based framework is presented for the synthesis of
projections from multiple Earth climate models. This identifies the most
representative (most probable) model from a set of climate models -- as defined
by specified constraints -- eliminating the need to calculate the entire set.
Two approaches are developed, based on individual climate models or ensembles
of models, subject to a single cost (energy) constraint or competing
cost-benefit constraints. A finite-time limit on the minimum cost of modifying
a model synthesis framework, at finite rates of change, is also reported.Comment: Inspired by discussions at the Mathematical and Statistical
Approaches to Climate Modelling and Prediction workshop, Isaac Newton
Institute for Mathematical Sciences, Cambridge, UK, 11 Aug. to 22 Dec. 2010.
Accepted for publication in Climate Dynamics, 8 August 201
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