64,184 research outputs found
Brussels-Austin Nonequilibrium Statistical Mechanics in the Early Years: Similarity Transformations between Deterministic and Probabilistic Descriptions
The fundamental problem on which Ilya Prigogine and the Brussels-Austin Group
have focused can be stated briefly as follows. Our observations indicate that
there is an arrow of time in our experience of the world (e.g., decay of
unstable radioactive atoms like Uranium, or the mixing of cream in coffee).
Most of the fundamental equations of physics are time reversible, however,
presenting an apparent conflict between our theoretical descriptions and
experimental observations. Many have thought that the observed arrow of time
was either an artifact of our observations or due to very special initial
conditions. An alternative approach, followed by the Brussels-Austin Group, is
to consider the observed direction of time to be a basics physical phenomenon
and to develop a mathematical formalism that can describe this direction as
being due to the dynamics of physical systems. In part I of this essay, I
review and assess an attempt to carry out an approach that received much of
their attention from the early 1970s to the mid 1980s. In part II, I will
discuss their more recent approach using rigged Hilbert spaces.Comment: 22 pages, Part I of two parts; updated institutional affiliatio
DROP: Dimensionality Reduction Optimization for Time Series
Dimensionality reduction is a critical step in scaling machine learning
pipelines. Principal component analysis (PCA) is a standard tool for
dimensionality reduction, but performing PCA over a full dataset can be
prohibitively expensive. As a result, theoretical work has studied the
effectiveness of iterative, stochastic PCA methods that operate over data
samples. However, termination conditions for stochastic PCA either execute for
a predetermined number of iterations, or until convergence of the solution,
frequently sampling too many or too few datapoints for end-to-end runtime
improvements. We show how accounting for downstream analytics operations during
DR via PCA allows stochastic methods to efficiently terminate after operating
over small (e.g., 1%) subsamples of input data, reducing whole workload
runtime. Leveraging this, we propose DROP, a DR optimizer that enables speedups
of up to 5x over Singular-Value-Decomposition-based PCA techniques, and exceeds
conventional approaches like FFT and PAA by up to 16x in end-to-end workloads
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