923 research outputs found
Reconstructing Extended Perfect Binary One-Error-Correcting Codes from Their Minimum Distance Graphs
The minimum distance graph of a code has the codewords as vertices and edges
exactly when the Hamming distance between two codewords equals the minimum
distance of the code. A constructive proof for reconstructibility of an
extended perfect binary one-error-correcting code from its minimum distance
graph is presented. Consequently, inequivalent such codes have nonisomorphic
minimum distance graphs. Moreover, it is shown that the automorphism group of a
minimum distance graph is isomorphic to that of the corresponding code.Comment: 4 pages. Accepted for publication in IEEE Transactions on Information
Theor
SiSeRHMap v1.0: A simulator for mapped seismic response using a hybrid model
SiSeRHMap is a computerized methodology capable of drawing up prediction maps of
seismic response. It was realized on the basis of a hybrid model which combines different
approaches and models in a new and non-conventional way. These approaches
5 and models are organized in a code-architecture composed of five interdependent
modules. A GIS (Geographic Information System) Cubic Model (GCM), which is a layered
computational structure based on the concept of lithodynamic units and zones,
aims at reproducing a parameterized layered subsoil model. A metamodeling process
confers a hybrid nature to the methodology. In this process, the one-dimensional linear
10 equivalent analysis produces acceleration response spectra of shear wave velocitythickness
profiles, defined as trainers, which are randomly selected in each zone. Subsequently,
a numerical adaptive simulation model (Spectra) is optimized on the above
trainer acceleration response spectra by means of a dedicated Evolutionary Algorithm
(EA) and the Levenberg–Marquardt Algorithm (LMA) as the final optimizer. In the fi15
nal step, the GCM Maps Executor module produces a serial map-set of a stratigraphic
seismic response at different periods, grid-solving the calibrated Spectra model. In addition,
the spectra topographic amplification is also computed by means of a numerical
prediction model. This latter is built to match the results of the numerical simulations
related to isolate reliefs using GIS topographic attributes. In this way, different sets
20 of seismic response maps are developed, on which, also maps of seismic design response
spectra are defined by means of an enveloping technique
The Statistical Physics of Athermal Materials
At the core of equilibrium statistical mechanics lies the notion of
statistical ensembles: a collection of microstates, each occurring with a given
a priori probability that depends only on a few macroscopic parameters such as
temperature, pressure, volume, and energy. In this review article, we discuss
recent advances in establishing statistical ensembles for athermal materials.
The broad class of granular and particulate materials is immune from the
effects of thermal fluctuations because the constituents are macroscopic. In
addition, interactions between grains are frictional and dissipative, which
invalidates the fundamental postulates of equilibrium statistical mechanics.
However, granular materials exhibit distributions of microscopic quantities
that are reproducible and often depend on only a few macroscopic parameters. We
explore the history of statistical ensemble ideas in the context of granular
materials, clarify the nature of such ensembles and their foundational
principles, highlight advances in testing key ideas, and discuss applications
of ensembles to analyze the collective behavior of granular materials
Against Pointillisme about Mechanics
This paper forms part of a wider campaign: to deny pointillisme. That is the
doctrine that a physical theory's fundamental quantities are defined at points
of space or of spacetime, and represent intrinsic properties of such points or
point-sized objects located there; so that properties of spatial or
spatiotemporal regions and their material contents are determined by the
point-by-point facts.
More specifically, this paper argues against pointillisme about the concept
of velocity in classical mechanics; especially against proposals by Tooley,
Robinson and Lewis. A companion paper argues against pointillisme about
(chrono)-geometry, as proposed by Bricker.
To avoid technicalities, I conduct the argument almost entirely in the
context of ``Newtonian'' ideas about space and time, and the classical
mechanics of point-particles, i.e. extensionless particles moving in a void.
But both the debate and my arguments carry over to relativistic physics.Comment: 41 pages Late
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