1,660 research outputs found
Limit-(quasi)periodic point sets as quasicrystals with p-adic internal spaces
Model sets (or cut and project sets) provide a familiar and commonly used
method of constructing and studying nonperiodic point sets. Here we extend this
method to situations where the internal spaces are no longer Euclidean, but
instead spaces with p-adic topologies or even with mixed Euclidean/p-adic
topologies.
We show that a number of well known tilings precisely fit this form,
including the chair tiling and the Robinson square tilings. Thus the scope of
the cut and project formalism is considerably larger than is usually supposed.
Applying the powerful consequences of model sets we derive the diffractive
nature of these tilings.Comment: 11 pages, 2 figures; dedicated to Peter Kramer on the occasion of his
65th birthda
Generalized quasiperiodic Rauzy tilings
We present a geometrical description of new canonical -dimensional
codimension one quasiperiodic tilings based on generalized Fibonacci sequences.
These tilings are made up of rhombi in 2d and rhombohedra in 3d as the usual
Penrose and icosahedral tilings. Thanks to a natural indexing of the sites
according to their local environment, we easily write down, for any
approximant, the sites coordinates, the connectivity matrix and we compute the
structure factor.Comment: 11 pages, 3 EPS figures, final version with minor change
Fluctuations in the Site Disordered Traveling Salesman Problem
We extend a previous statistical mechanical treatment of the traveling
salesman problem by defining a discrete "site disordered'' problem in which
fluctuations about saddle points can be computed. The results clarify the basis
of our original treatment, and illuminate but do not resolve the difficulties
of taking the zero temperature limit to obtain minimal path lengths.Comment: 17 pages, 3 eps figures, revte
Critical temperature of a fully anisotropic three-dimensional Ising model
The critical temperature of a three-dimensional Ising model on a simple cubic
lattice with different coupling strengths along all three spatial directions is
calculated via the transfer matrix method and a finite size scaling for L x L
oo clusters (L=2 and 3). The results obtained are compared with available
calculations. An exact analytical solution is found for the 2 x 2 oo Ising
chain with fully anisotropic interactions (arbitrary J_x, J_y and J_z).Comment: 17 pages in tex using preprint.sty for IOP journals, no figure
On FPL configurations with four sets of nested arches
The problem of counting the number of Fully Packed Loop (FPL) configurations
with four sets of a,b,c,d nested arches is addressed. It is shown that it may
be expressed as the problem of enumeration of tilings of a domain of the
triangular lattice with a conic singularity. After reexpression in terms of
non-intersecting lines, the Lindstr\"om-Gessel-Viennot theorem leads to a
formula as a sum of determinants. This is made quite explicit when
min(a,b,c,d)=1 or 2. We also find a compact determinant formula which generates
the numbers of configurations with b=d.Comment: 22 pages, TeX, 16 figures; a new formula for a generating function
adde
How a co-actorâs task affects monitoring of own errors: evidence from a social event-related potential study
Efficient flexible behavior requires continuous monitoring of performance for possible deviations from the intended goal of an action. This also holds for joint action. When jointly performing a task, one needs to not only know the otherâs goals and intentions but also generate behavioral adjustments that are dependent on the other personâs task. Previous studies have shown that in joint action people not only represent their own task but also the task of their co-actor. The current study investigated whether these so-called shared representations affect error monitoring as reflected in the response-locked error-related negativity (Ne/ERN) following own errors. Sixteen pairs of participants performed a social go/no-go task, while EEG and behavioral data were obtained. Responses were compatible or incompatible relative to the go/no-go action of the co-actor. Erroneous responses on no-go stimuli were examined. The results demonstrated increased Ne/ERN amplitudes and longer reaction times following errors on compatible compared to incompatible no-go stimuli. Thus, Ne/ERNs were larger after errors on trials that did not require a response from the co-actor either compared to errors on trials that did require a response from the co-actor. As the task of the other person is the only difference between these two types of errors, these findings show that people also represent their co-actorâs task during error monitoring in joint action. An extension of existing models on performance monitoring in individual action is put forward to explain the current findings in joint action. Importantly, we propose that inclusion of a co-actorâs task in performance monitoring may facilitate adaptive behavior in social interactions enabling fast anticipatory and corrective actions
A theorem on the absence of phase transitions in one-dimensional growth models with onsite periodic potentials
We rigorously prove that a wide class of one-dimensional growth models with
onsite periodic potential, such as the discrete sine-Gordon model, have no
phase transition at any temperature . The proof relies on the spectral
analysis of the transfer operator associated to the models. We show that this
operator is Hilbert-Schmidt and that its maximum eigenvalue is an analytic
function of temperature.Comment: 6 pages, no figures, submitted to J Phys A: Math Ge
Overlapping Unit Cells in 3d Quasicrystal Structure
A 3-dimensional quasiperiodic lattice, with overlapping unit cells and
periodic in one direction, is constructed using grid and projection methods
pioneered by de Bruijn. Each unit cell consists of 26 points, of which 22 are
the vertices of a convex polytope P, and 4 are interior points also shared with
other neighboring unit cells. Using Kronecker's theorem the frequencies of all
possible types of overlapping are found.Comment: LaTeX2e, 11 pages, 5 figures (8 eps files), uses iopart.class. Final
versio
Finite precision measurement nullifies the Kochen-Specker theorem
Only finite precision measurements are experimentally reasonable, and they
cannot distinguish a dense subset from its closure. We show that the rational
vectors, which are dense in S^2, can be colored so that the contradiction with
hidden variable theories provided by Kochen-Specker constructions does not
obtain. Thus, in contrast to violation of the Bell inequalities, no
quantum-over-classical advantage for information processing can be derived from
the Kochen-Specker theorem alone.Comment: 7 pages, plain TeX; minor corrections, interpretation clarified,
references update
Needle & knot : binder boilerplate tied up
To lighten the burden of programming language mechanization, many approaches have been developed that tackle the substantial boilerplate which arises from variable binders. Unfortunately, the existing approaches are limited in scope. They typically do not support complex binding forms (such as multi-binders) that arise in more advanced languages, or they do not tackle the boilerplate due to mentioning variables and binders in relations. As a consequence, the human mechanizer is still unnecessarily burdened with binder boilerplate and discouraged from taking on richer languages.
This paper presents Knot, a new approach that substantially extends the support for binder boilerplate. Knot is a highly expressive language for natural and concise specification of syntax with binders. Its meta-theory constructively guarantees the coverage of a considerable amount of binder boilerplate for well-formed specifications, including that for well-scoping of terms and context lookups. Knot also comes with a code generator, Needle, that specializes the generic boilerplate for convenient embedding in COQ and provides a tactic library for automatically discharging proof obligations that frequently come up in proofs of weakening and substitution lemmas of type-systems.
Our evaluation shows, that Needle & Knot significantly reduce the size of language mechanizations (by 40% in our case study). Moreover, as far as we know, Knot enables the most concise mechanization of the POPLmark Challenge (1a + 2a) and is two-thirds the size of the next smallest. Finally, Knot allows us to mechanize for instance dependentlytyped languages, which is notoriously challenging because of dependent contexts and mutually-recursive sorts with variables
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