87,172 research outputs found
A Survey on Continuous Time Computations
We provide an overview of theories of continuous time computation. These
theories allow us to understand both the hardness of questions related to
continuous time dynamical systems and the computational power of continuous
time analog models. We survey the existing models, summarizing results, and
point to relevant references in the literature
Comparison of POD reduced order strategies for the nonlinear 2D Shallow Water Equations
This paper introduces tensorial calculus techniques in the framework of
Proper Orthogonal Decomposition (POD) to reduce the computational complexity of
the reduced nonlinear terms. The resulting method, named tensorial POD, can be
applied to polynomial nonlinearities of any degree . Such nonlinear terms
have an on-line complexity of , where is the
dimension of POD basis, and therefore is independent of full space dimension.
However it is efficient only for quadratic nonlinear terms since for higher
nonlinearities standard POD proves to be less time consuming once the POD basis
dimension is increased. Numerical experiments are carried out with a two
dimensional shallow water equation (SWE) test problem to compare the
performance of tensorial POD, standard POD, and POD/Discrete Empirical
Interpolation Method (DEIM). Numerical results show that tensorial POD
decreases by times the computational cost of the on-line stage of
standard POD for configurations using more than model variables. The
tensorial POD SWE model was only slower than the POD/DEIM SWE model
but the implementation effort is considerably increased. Tensorial calculus was
again employed to construct a new algorithm allowing POD/DEIM shallow water
equation model to compute its off-line stage faster than the standard and
tensorial POD approaches.Comment: 23 pages, 8 figures, 5 table
Numerical algebraic geometry for model selection and its application to the life sciences
Researchers working with mathematical models are often confronted by the
related problems of parameter estimation, model validation, and model
selection. These are all optimization problems, well-known to be challenging
due to non-linearity, non-convexity and multiple local optima. Furthermore, the
challenges are compounded when only partial data is available. Here, we
consider polynomial models (e.g., mass-action chemical reaction networks at
steady state) and describe a framework for their analysis based on optimization
using numerical algebraic geometry. Specifically, we use probability-one
polynomial homotopy continuation methods to compute all critical points of the
objective function, then filter to recover the global optima. Our approach
exploits the geometric structures relating models and data, and we demonstrate
its utility on examples from cell signaling, synthetic biology, and
epidemiology.Comment: References added, additional clarification
Supporting Regularized Logistic Regression Privately and Efficiently
As one of the most popular statistical and machine learning models, logistic
regression with regularization has found wide adoption in biomedicine, social
sciences, information technology, and so on. These domains often involve data
of human subjects that are contingent upon strict privacy regulations.
Increasing concerns over data privacy make it more and more difficult to
coordinate and conduct large-scale collaborative studies, which typically rely
on cross-institution data sharing and joint analysis. Our work here focuses on
safeguarding regularized logistic regression, a widely-used machine learning
model in various disciplines while at the same time has not been investigated
from a data security and privacy perspective. We consider a common use scenario
of multi-institution collaborative studies, such as in the form of research
consortia or networks as widely seen in genetics, epidemiology, social
sciences, etc. To make our privacy-enhancing solution practical, we demonstrate
a non-conventional and computationally efficient method leveraging distributing
computing and strong cryptography to provide comprehensive protection over
individual-level and summary data. Extensive empirical evaluation on several
studies validated the privacy guarantees, efficiency and scalability of our
proposal. We also discuss the practical implications of our solution for
large-scale studies and applications from various disciplines, including
genetic and biomedical studies, smart grid, network analysis, etc
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