524,538 research outputs found
Network as a computer: ranking paths to find flows
We explore a simple mathematical model of network computation, based on
Markov chains. Similar models apply to a broad range of computational
phenomena, arising in networks of computers, as well as in genetic, and neural
nets, in social networks, and so on. The main problem of interaction with such
spontaneously evolving computational systems is that the data are not uniformly
structured. An interesting approach is to try to extract the semantical content
of the data from their distribution among the nodes. A concept is then
identified by finding the community of nodes that share it. The task of data
structuring is thus reduced to the task of finding the network communities, as
groups of nodes that together perform some non-local data processing. Towards
this goal, we extend the ranking methods from nodes to paths. This allows us to
extract some information about the likely flow biases from the available static
information about the network.Comment: 12 pages, CSR 200
The NASA/industry Design Analysis Methods for Vibrations (DAMVIBS) program: Boeing Helicopters airframe finite element modeling
Mathematical models based on the finite element method of structural analysis, as embodied in the NASTRAN computer code, are routinely used by the helicopter industry to calculate airframe static internal loads used for sizing structural members. Historically, less reliance has been placed on the vibration predictions based on these models. Beginning in the early 1980's NASA's Langley Research Center initiated an industry wide program with the objective of engendering the needed trust in vibration predictions using these models and establishing a body of modeling guides which would enable confident future prediction of airframe vibration as part of the regular design process. Emphasis in this paper is placed on the successful modeling of the Army/Boeing CH-47D which showed reasonable correlation with test data. A principal finding indicates that improved dynamic analysis requires greater attention to detail and perhaps a finer mesh, especially the mass distribution, than the usual stress model. Post program modeling efforts show improved correlation placing key modal frequencies in the b/rev range with 4 percent of the test frequencies
Generating Mathematical Derivations with Large Language Models
The derivation of mathematical results in specialised fields using Large
Language Models (LLMs) is an emerging research direction that can help identify
models' limitations, and potentially support mathematical discovery. In this
paper, we leverage a symbolic engine to generate derivations of equations at
scale, and investigate the capabilities of LLMs when deriving goal equations
from premises. Specifically, we employ in-context learning for GPT and
fine-tune a range of T5 models to compare the robustness and generalisation of
pre-training strategies to specialised models. Empirical results show that
fine-tuned FLAN-T5-large (MathT5) outperforms GPT models on all static and
out-of-distribution test sets in terms of absolute performance. However, an
in-depth analysis reveals that the fine-tuned models are more sensitive to
perturbations involving unseen symbols and (to a lesser extent) changes to
equation structure. In addition, we analyse 1.7K equations and over 200
derivations to highlight common reasoning errors such as the inclusion of
incorrect, irrelevant, and redundant equations, along with the tendency to skip
derivation steps. Finally, we explore the suitability of existing metrics for
evaluating mathematical derivations finding evidence that, while they capture
general properties such as sensitivity to perturbations, they fail to highlight
fine-grained reasoning errors and essential differences between models.
Overall, this work demonstrates that training models on synthetic data can
improve their mathematical capabilities beyond larger architectures.Comment: 13 page
Harder, better, faster, stronger: understanding and improving the tractability of large energy system models
Energy system models based on linear programming have been growing in size
with the increasing need to model renewables with high spatial and temporal
detail. Larger models lead to high computational requirements. Furthermore,
seemingly small changes in a model can lead to drastic differences in runtime.
Here, we investigate measures to address this issue. We review the mathematical
structure of a typical energy system model, and discuss issues of sparsity,
degeneracy and large numerical range. We introduce and test a method to
automatically scale models to improve numerical range. We test this method as
well as tweaks to model formulation and solver preferences, finding that
adjustments can have a substantial impact on runtime. In particular, the
barrier method without crossover can be very fast, but affects the structure of
the resulting optimal solution. We conclude with a range of recommendations for
energy system modellers
Marginal empirical likelihood and sure independence feature screening
We study a marginal empirical likelihood approach in scenarios when the
number of variables grows exponentially with the sample size. The marginal
empirical likelihood ratios as functions of the parameters of interest are
systematically examined, and we find that the marginal empirical likelihood
ratio evaluated at zero can be used to differentiate whether an explanatory
variable is contributing to a response variable or not. Based on this finding,
we propose a unified feature screening procedure for linear models and the
generalized linear models. Different from most existing feature screening
approaches that rely on the magnitudes of some marginal estimators to identify
true signals, the proposed screening approach is capable of further
incorporating the level of uncertainties of such estimators. Such a merit
inherits the self-studentization property of the empirical likelihood approach,
and extends the insights of existing feature screening methods. Moreover, we
show that our screening approach is less restrictive to distributional
assumptions, and can be conveniently adapted to be applied in a broad range of
scenarios such as models specified using general moment conditions. Our
theoretical results and extensive numerical examples by simulations and data
analysis demonstrate the merits of the marginal empirical likelihood approach.Comment: Published in at http://dx.doi.org/10.1214/13-AOS1139 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Evaluation of methods to account for release from nanofiber scaffolds
Electrospinning is a common technique utilized to form fibers from the micro- to nanometer range. Nanofibers form through electrospinning can be utilized as scaffolds since the fiber structures are similar to the structures within the extracellular matrix. Researchers use additives, such as growth factors, to help facilitate cell proliferation and function. Also, researchers are attempting to use electrospun fibers for drug delivery and as wound dressings since the electrospun fibers have high surface area to volume ratio. In both situations, the release of either the additive or the drug needs to be controlled so that the fibers would release the additive or drug in a desired manner. To understand the release from the electrospun fibers, researchers develop mathematical models that rely on the release data. Additionally, researchers utilize models based on Fick\u27s second law of diffusion to predict release in cylindrical coordinates. This work aims to understand the release from electrospun fibers by finding the relationship between Fick\u27s second law of diffusion and the mathematical models from experimental data. Three different release studies for electrospun fibers are investigated. Predicted mutual diffusion coefficients are developed so that the coefficients could be used for future predictive releases
Stochastic processes for modelling bridge deterioration
Traditionally, bridge management systems were designed using Markov chain models. Recently, researchers applied the gamma process successfully to structural deterioration problems. The stochastic process captures the temporal variability of degradation, and has been applied to a range of problems in structures. We report on a study for the modelling of the condition of bridges in the state of NSW. The study encompasses large amounts of data spanning more than 15 years. We argue for the applicability of the gamma process and other stochastic processes. While the gamma process has been adopted in the past decade on grounds of mathematical tractability and physical motivation, we also observe another distribution for the deterioration at different times. The finding promotes the stochastic process modelling direction taken in the past decade and brings forth new models for the time-dependent reliability analysis of bridges. © 2009 Taylor & Francis Group, London
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