178,503 research outputs found
Automated Discharging Arguments for Density Problems in Grids
Discharging arguments demonstrate a connection between local structure and
global averages. This makes it an effective tool for proving lower bounds on
the density of special sets in infinite grids. However, the minimum density of
an identifying code in the hexagonal grid remains open, with an upper bound of
and a lower bound of . We present a new, experimental framework for producing discharging
arguments using an algorithm. This algorithm replaces the lengthy case analysis
of human-written discharging arguments with a linear program that produces the
best possible lower bound using the specified set of discharging rules. We use
this framework to present a lower bound of on
the density of an identifying code in the hexagonal grid, and also find several
sharp lower bounds for variations on identifying codes in the hexagonal,
square, and triangular grids.Comment: This is an extended abstract, with 10 pages, 2 appendices, 5 tables,
and 2 figure
Polynomial Response Surface Approximations for the Multidisciplinary Design Optimization of a High Speed Civil Transport
Surrogate functions have become an important tool in multidisciplinary design optimization to deal with noisy functions, high computational cost, and the practical difficulty of integrating legacy disciplinary computer codes. A combination of mathematical, statistical, and engineering techniques, well known in other contexts, have made polynomial surrogate functions viable for MDO. Despite the obvious limitations imposed by sparse high fidelity data in high dimensions and the locality of low order polynomial approximations, the success of the panoply of techniques based on polynomial response surface approximations for MDO shows that the implementation details are more important than the underlying approximation method (polynomial, spline, DACE, kernel regression, etc.). This paper surveys some of the ancillary techniquesâstatistics, global search, parallel computing, variable complexity modelingâthat augment the construction and use of polynomial surrogates
Galaxy Tracers and Velocity Bias
This paper examines several methods of tracing galaxies in N-body simulations
and their effects on the derived galaxy statistics, especially measurements of
velocity bias. Using two simulations with identical initial conditions, one
following dark matter only and the other following dark matter and baryons,
both collisionless and collisional methods of tracing galaxies are compared to
one another and against a set of idealized criteria. None of the collisionless
methods proves satisfactory, including an elaborate scheme developed here to
circumvent previously known problems. The main problem is that galactic
overdensities are both secularly and impulsively disrupted while orbiting in
cluster potentials. With dissipation, the baryonic tracers have much higher
density contrasts and much smaller cross sections, allowing them to remain
distinct within the cluster potential. The question remains whether the
incomplete physical model introduces systematic biases. Statistical measures
determined from simulations can vary significantly based solely on the galaxy
tracing method utilized. The two point correlation function differs most on
sub-cluster scales with generally good agreement on larger scales. Pairwise
velocity dispersions show less uniformity on all scales addressed here. All
tracing methods show a velocity bias to varying degrees, but the predictions
are not firm: either the tracing method is not robust or the statistical
significance has not been demonstrated. Though theoretical arguments suggest
that a mild velocity bias should exist, simulation results are not yet
conclusive.Comment: ApJ, in press, 23 pages, plain TeX, 8 of 13 figures included, all
PostScript figures (4.8 MB) available via anonymous ftp from
ftp://astro.princeton.edu/summers/tracers . Also available as POPe-616 on
http://astro.princeton.edu/~library/prep.htm
Desirable properties for XML update mechanisms
The adoption of XML as the default data interchange format and the standardisation of the XPath and XQuery languages has resulted in significant research in the development and implementation of XML databases capable of processing queries efficiently. The ever-increasing deployment of XML in industry and the real-world requirement to support efficient updates to XML documents has more recently prompted research in dynamic XML labelling schemes. In this paper, we provide an overview of the recent research in dynamic XML labelling schemes. Our motivation is to define a set of properties that represent a more holistic dynamic labelling scheme and present our findings through an evaluation matrix for most of the existing schemes that provide update functionality
Bond graph based sensitivity and uncertainty analysis modelling for micro-scale multiphysics robust engineering design
Components within micro-scale engineering systems are often at the limits of commercial miniaturization and this can cause unexpected behavior and variation in performance. As such, modelling and analysis of system robustness plays an important role in product development. Here schematic bond graphs are used as a front end in a sensitivity analysis based strategy for modelling robustness in multiphysics micro-scale engineering systems. As an example, the analysis is applied to a behind-the-ear (BTE) hearing aid.
By using bond graphs to model power flow through components within different physical domains of the hearing aid, a set of differential equations to describe the system dynamics is collated. Based on these equations, sensitivity analysis calculations are used to approximately model the nature and the sources of output uncertainty during system operation. These calculations represent a robustness evaluation of the current hearing aid design and offer a means of identifying potential for improved designs of multiphysics systems by way of key parameter identification
Data-driven modeling of the olfactory neural codes and their dynamics in the insect antennal lobe
Recordings from neurons in the insects' olfactory primary processing center,
the antennal lobe (AL), reveal that the AL is able to process the input from
chemical receptors into distinct neural activity patterns, called olfactory
neural codes. These exciting results show the importance of neural codes and
their relation to perception. The next challenge is to \emph{model the
dynamics} of neural codes. In our study, we perform multichannel recordings
from the projection neurons in the AL driven by different odorants. We then
derive a neural network from the electrophysiological data. The network
consists of lateral-inhibitory neurons and excitatory neurons, and is capable
of producing unique olfactory neural codes for the tested odorants.
Specifically, we (i) design a projection, an odor space, for the neural
recording from the AL, which discriminates between distinct odorants
trajectories (ii) characterize scent recognition, i.e., decision-making based
on olfactory signals and (iii) infer the wiring of the neural circuit, the
connectome of the AL. We show that the constructed model is consistent with
biological observations, such as contrast enhancement and robustness to noise.
The study answers a key biological question in identifying how lateral
inhibitory neurons can be wired to excitatory neurons to permit robust activity
patterns
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