18,732 research outputs found
Exact solutions for the two- and all-terminal reliabilities of the Brecht-Colbourn ladder and the generalized fan
The two- and all-terminal reliabilities of the Brecht-Colbourn ladder and the
generalized fan have been calculated exactly for arbitrary size as well as
arbitrary individual edge and node reliabilities, using transfer matrices of
dimension four at most. While the all-terminal reliabilities of these graphs
are identical, the special case of identical edge () and node ()
reliabilities shows that their two-terminal reliabilities are quite distinct,
as demonstrated by their generating functions and the locations of the zeros of
the reliability polynomials, which undergo structural transitions at
Bond-Propagation Algorithm for Thermodynamic Functions in General 2D Ising Models
Recently, we developed and implemented the bond propagation algorithm for
calculating the partition function and correlation functions of random bond
Ising models in two dimensions. The algorithm is the fastest available for
calculating these quantities near the percolation threshold. In this paper, we
show how to extend the bond propagation algorithm to directly calculate
thermodynamic functions by applying the algorithm to derivatives of the
partition function, and we derive explicit expressions for this transformation.
We also discuss variations of the original bond propagation procedure within
the larger context of Y-Delta-Y-reducibility and discuss the relation of this
class of algorithm to other algorithms developed for Ising systems. We conclude
with a discussion on the outlook for applying similar algorithms to other
models.Comment: 12 pages, 10 figures; submitte
Exact Failure Frequency Calculations for Extended Systems
This paper shows how the steady-state availability and failure frequency can
be calculated in a single pass for very large systems, when the availability is
expressed as a product of matrices. We apply the general procedure to
-out-of-:G and linear consecutive -out-of-:F systems, and to a
simple ladder network in which each edge and node may fail. We also give the
associated generating functions when the components have identical
availabilities and failure rates. For large systems, the failure rate of the
whole system is asymptotically proportional to its size. This paves the way to
ready-to-use formulae for various architectures, as well as proof that the
differential operator approach to failure frequency calculations is very useful
and straightforward
Robust, automated sleep scoring by a compact neural network with distributional shift correction.
Studying the biology of sleep requires the accurate assessment of the state of experimental subjects, and manual analysis of relevant data is a major bottleneck. Recently, deep learning applied to electroencephalogram and electromyogram data has shown great promise as a sleep scoring method, approaching the limits of inter-rater reliability. As with any machine learning algorithm, the inputs to a sleep scoring classifier are typically standardized in order to remove distributional shift caused by variability in the signal collection process. However, in scientific data, experimental manipulations introduce variability that should not be removed. For example, in sleep scoring, the fraction of time spent in each arousal state can vary between control and experimental subjects. We introduce a standardization method, mixture z-scoring, that preserves this crucial form of distributional shift. Using both a simulated experiment and mouse in vivo data, we demonstrate that a common standardization method used by state-of-the-art sleep scoring algorithms introduces systematic bias, but that mixture z-scoring does not. We present a free, open-source user interface that uses a compact neural network and mixture z-scoring to allow for rapid sleep scoring with accuracy that compares well to contemporary methods. This work provides a set of computational tools for the robust automation of sleep scoring
Reliability evaluation of scalable complex networks through delta-star conversion
Exact reliability evaluation of large size complex networks becomes intractable with conventional techniques due to the exponential scaling of the computation complexity as the size of network scales up. In this paper we develop a scalable model for the exact evaluation of system reliability of scalable complex networks of the n-tuple bridge type based on scaled delta-star conversion. The number of steps as well as the computation overhead is kept within practical limits as they scale up linearly with the size of the network. The proposed model enables simple numerical evaluation either manually or through spread-sheets
Prototype Backscatter Moessbauer Spectrometer for Measurement of Martian Surface Mineralogy
We have designed and successfully tested a prototype of a backscatter Moessbauer spectrometer (BaMS) targeted for use on the Martian surface to (1) determine oxidation states of iron, and (2) identify and determine relative abundances of iron-bearing mineralogies. No sample preparation is required to perform measurements; it is only necessary to bring sample and instrument into physical contact. The prototype meets our projected specification for a flight instrument in terms of mass, power, and volume. A Moessbauer spectrometer on the Martian surface would provide wide variety of information about the current state of the Martian surface, and this information is described
- โฆ