15,738 research outputs found
Active matter beyond mean-field: Ring-kinetic theory for self-propelled particles
A ring-kinetic theory for Vicsek-style models of self-propelled agents is
derived from the exact N-particle evolution equation in phase space. The theory
goes beyond mean-field and does not rely on Boltzmann's approximation of
molecular chaos. It can handle pre-collisional correlations and cluster
formation which both seem important to understand the phase transition to
collective motion. We propose a diagrammatic technique to perform a small
density expansion of the collision operator and derive the first two equations
of the BBGKY-hierarchy. An algorithm is presented that numerically solves the
evolution equation for the two-particle correlations on a lattice. Agent-based
simulations are performed and informative quantities such as orientational and
density correlation functions are compared with those obtained by ring-kinetic
theory. Excellent quantitative agreement between simulations and theory is
found at not too small noises and mean free paths. This shows that there is
parameter ranges in Vicsek-like models where the correlated closure of the
BBGKY-hierarchy gives correct and nontrivial results. We calculate the
dependence of the orientational correlations on distance in the disordered
phase and find that it seems to be consistent with a power law with exponent
around -1.8, followed by an exponential decay. General limitations of the
kinetic theory and its numerical solution are discussed
Doctor of Philosophy
dissertationX-ray computed tomography (CT) is a widely popular medical imaging technique that allows for viewing of in vivo anatomy and physiology. In order to produce high-quality images and provide reliable treatment, CT imaging requires the precise knowledge of t
Cell shape analysis of random tessellations based on Minkowski tensors
To which degree are shape indices of individual cells of a tessellation
characteristic for the stochastic process that generates them? Within the
context of stochastic geometry and the physics of disordered materials, this
corresponds to the question of relationships between different stochastic
models. In the context of image analysis of synthetic and biological materials,
this question is central to the problem of inferring information about
formation processes from spatial measurements of resulting random structures.
We address this question by a theory-based simulation study of shape indices
derived from Minkowski tensors for a variety of tessellation models. We focus
on the relationship between two indices: an isoperimetric ratio of the
empirical averages of cell volume and area and the cell elongation quantified
by eigenvalue ratios of interfacial Minkowski tensors. Simulation data for
these quantities, as well as for distributions thereof and for correlations of
cell shape and volume, are presented for Voronoi mosaics of the Poisson point
process, determinantal and permanental point processes, and Gibbs hard-core and
random sequential absorption processes as well as for Laguerre tessellations of
polydisperse spheres and STIT- and Poisson hyperplane tessellations. These data
are complemented by mechanically stable crystalline sphere and disordered
ellipsoid packings and area-minimising foam models. We find that shape indices
of individual cells are not sufficient to unambiguously identify the generating
process even amongst this limited set of processes. However, we identify
significant differences of the shape indices between many of these tessellation
models. Given a realization of a tessellation, these shape indices can narrow
the choice of possible generating processes, providing a powerful tool which
can be further strengthened by density-resolved volume-shape correlations.Comment: Chapter of the forthcoming book "Tensor Valuations and their
Applications in Stochastic Geometry and Imaging" in Lecture Notes in
Mathematics edited by Markus Kiderlen and Eva B. Vedel Jense
Fuzzy Techniques for Decision Making 2018
Zadeh's fuzzy set theory incorporates the impreciseness of data and evaluations, by imputting the degrees by which each object belongs to a set. Its success fostered theories that codify the subjectivity, uncertainty, imprecision, or roughness of the evaluations. Their rationale is to produce new flexible methodologies in order to model a variety of concrete decision problems more realistically. This Special Issue garners contributions addressing novel tools, techniques and methodologies for decision making (inclusive of both individual and group, single- or multi-criteria decision making) in the context of these theories. It contains 38 research articles that contribute to a variety of setups that combine fuzziness, hesitancy, roughness, covering sets, and linguistic approaches. Their ranges vary from fundamental or technical to applied approaches
Learning Task Specifications from Demonstrations
Real world applications often naturally decompose into several sub-tasks. In
many settings (e.g., robotics) demonstrations provide a natural way to specify
the sub-tasks. However, most methods for learning from demonstrations either do
not provide guarantees that the artifacts learned for the sub-tasks can be
safely recombined or limit the types of composition available. Motivated by
this deficit, we consider the problem of inferring Boolean non-Markovian
rewards (also known as logical trace properties or specifications) from
demonstrations provided by an agent operating in an uncertain, stochastic
environment. Crucially, specifications admit well-defined composition rules
that are typically easy to interpret. In this paper, we formulate the
specification inference task as a maximum a posteriori (MAP) probability
inference problem, apply the principle of maximum entropy to derive an analytic
demonstration likelihood model and give an efficient approach to search for the
most likely specification in a large candidate pool of specifications. In our
experiments, we demonstrate how learning specifications can help avoid common
problems that often arise due to ad-hoc reward composition.Comment: NIPS 201
A Robust Distance Measurement and Dark Energy Constraints from the Spherically-Averaged Correlation Function of Sloan Digital Sky Survey Luminous Red Galaxies
We measure the effective distance to z=0.35, D_V(0.35), from the overall
shape of the spherically-averaged two-point correlation function of the Sloan
Digital Sky Survey (SDSS) Data Release 7 (DR7) luminous red galaxy (LRG)
sample. We find D_V(0.35)=1428_{-73}^{+74} without assuming a dark energy model
or a flat Universe. We find that the derived measurement of
r_s(z_d)/D_V(0.35)=0.1143 \pm 0.0030 (the ratio of the sound horizon at the
drag epoch to the effective distance to z=0.35) is more tightly constrained and
more robust with respect to possible systematic effects. It is also nearly
uncorrelated with \Omega_m h^2.
Combining our results with the cosmic microwave background and supernova
data, we obtain \Omega_k=-0.0032^{+0.0074}_{-0.0072} and
w=-1.010^{+0.046}_{-0.045} (assuming a constant dark energy equation of state).
By scaling the spherically-averaged correlation function, we find the Hubble
parameter H(0.35)=83^{+13}_{-15} km s^{-1}Mpc^{-1} and the angular diameter
distance D_A(0.35)=1089^{+93}_{-87} Mpc.
We use LasDamas SDSS mock catalogs to compute the covariance matrix of the
correlation function, and investigate the use of lognormal catalogs as an
alternative. We find that the input correlation function can be accurately
recovered from lognormal catalogs, although they give larger errors on all
scales (especially on small scales) compared to the mock catalogs derived from
cosmological N-body simulations.Comment: revised, 12 pages, 12 figure
Sparse neural networks with large learning diversity
Coded recurrent neural networks with three levels of sparsity are introduced.
The first level is related to the size of messages, much smaller than the
number of available neurons. The second one is provided by a particular coding
rule, acting as a local constraint in the neural activity. The third one is a
characteristic of the low final connection density of the network after the
learning phase. Though the proposed network is very simple since it is based on
binary neurons and binary connections, it is able to learn a large number of
messages and recall them, even in presence of strong erasures. The performance
of the network is assessed as a classifier and as an associative memory
Modelling fraud detection by attack trees and Choquet integral
Modelling an attack tree is basically a matter of associating a logical ÒndÓand a logical ÒrÓ but in most of real world applications related to fraud management the Ònd/orÓlogic is not adequate to effectively represent the relationship between a parent node and its children, most of all when information about attributes is associated to the nodes and the main problem to solve is how to promulgate attribute values up the tree through recursive aggregation operations occurring at the Ònd/orÓnodes. OWA-based aggregations have been introduced to generalize ÒndÓand ÒrÓoperators starting from the observation that in between the extremes Òor allÓ(and) and Òor anyÓ(or), terms (quantifiers) like ÒeveralÓ ÒostÓ ÒewÓ ÒomeÓ etc. can be introduced to represent the different weights associated to the nodes in the aggregation. The aggregation process taking place at an OWA node depends on the ordered position of the child nodes but it doesnÕ take care of the possible interactions between the nodes. In this paper, we propose to overcome this drawback introducing the Choquet integral whose distinguished feature is to be able to take into account the interaction between nodes. At first, the attack tree is valuated recursively through a bottom-up algorithm whose complexity is linear versus the number of nodes and exponential for every node. Then, the algorithm is extended assuming that the attribute values in the leaves are unimodal LR fuzzy numbers and the calculation of Choquet integral is carried out using the alpha-cuts.Fraud detection; attack tree; ordered weighted averaging (OWA) operator; Choquet integral; fuzzy numbers.
Probability Transform Based on the Ordered Weighted Averaging and Entropy Difference
Dempster-Shafer evidence theory can handle imprecise and unknown information, which has attracted many people. In most cases, the mass function can be translated into the probability, which is useful to expand the applications of the D-S evidence theory. However, how to reasonably transfer the mass function to the probability distribution is still an open issue. Hence, the paper proposed a new probability transform method based on the ordered weighted averaging and entropy difference. The new method calculates weights by ordered weighted averaging, and adds entropy difference as one of the measurement indicators. Then achieved the transformation of the minimum entropy difference by adjusting the parameter r of the weight function. Finally, some numerical examples are given to prove that new method is more reasonable and effective
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Gaussian process regression for virtual metrology of microchip quality and the resulting strategic sampling scheme
Manufacturing of integrated circuits involves many sequential processes, often ex- ecuted to nanoscale tolerances, and the yield depends on the often unmeasured quality of intermediate steps. In the high-throughput industry of fabricating microelectronics on semi-conducting wafers, scheduling measurements of product quality before the electrical test of the complete IC can be expensive. We therefore seek to predict metrics of product quality based on sensor readings describing the environment within the relevant tool during the processing of each wafer, or to apply the concept of virtual metrology (VM) to monitor these intermediate steps. We model the data using Gaussian process regression (GPR), adapted to simultaneously learn the nonlinear dynamics that govern the quality characteristic, as well as their operating space, expressed by a linear embedding of the sensor traces’ features. Such Bayesian models predict a distribution for the target metric, such as a critical dimension, so one may assess the model’s credibility through its predictive uncertainty. Assuming measurements of the quality characteristic of interest are budgeted, we seek to hasten convergence of the GPR model to a credible form through an active sampling scheme, whereby the predictive uncertainty informs which wafer’s quality to measure next. We evaluate this convergence when predicting and updating online, as if in a factory, using a large dataset for plasma-enhanced chemical vapor deposition (PECVD), with measured thicknesses for ~32,000 wafers. By approximately optimizing the information extracted from this seemingly repetitive data describing a tightly controlled process, GPR achieves ~10% greater accuracy on average than a baseline linear model based on partial least squares (PLS). In a derivative study, we seek to discern the degree of drift in the process over the several months the data spans. We express this drift by how unusual the relevant features, as embedded by the GPR model, appear as the in- puts compensate for degrading conditions. This method detects the onset of consistently unusual behavior that extends to a bimodal thickness fault, anticipating its flagging by as much as two days.Mechanical Engineerin
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