•Theoretical investigations on correlation dimension (CD) and approximate entropy (AE) are conducted.•CD and AE have a “bilateral reduction” effect.•Kurtosis and negative entropy have a “unilateral ...reduction” effect.•CD with any dimension and AE with smaller dimension become smaller when a signal is getting sparser or more deterministic.
The sparsity of signals is of great concern in various research domains. In mechanical systems and signal processing, repetitive transients are the symptoms of localized gear and bearing faults and they are sparse signals. During the recent years, sparsity measures, such as kurtosis and Shannon entropy, have been thoroughly studied to quantify repetitive transients for machine condition monitoring. Spectral kurtosis and spectral negative Shannon entropy are two typical examples of sparsity measures for machine condition monitoring. Besides sparsity measures, complexity measures including correlation dimension (CD) and approximate entropy (AE) have been experimentally studied during the recent years. However, theoretical investigations on these two complexity measures for machine condition monitoring are seldom reported. This paper aims to fill this research gap and propose some new theorems and proofs to show that CD and AE have a “bilateral reduction” effect, which is a proper measure of entropy. Specifically, CD with any dimension and AE with smaller dimension become smaller when a signal is getting sparser or more deterministic, which is significantly different from sparsity measures that are monotonically increasing when a signal is getting from more deterministic to sparser. This new discovery is able to help readers fully understand the main difference between sparsity measures and complexity measures. In view of this discovery, it is suggested that the concept of blind fault component separation should be used to separate low-frequency periodic components (a deterministic signal) from high-frequency repetitive transients (a sparse signal) before complexity measures are used for machine condition monitoring. This suggestion aims to avoid the uncertainty of machine condition monitoring caused by low-frequency periodic components and high-frequency repetitive transients.
Flexible optimization on video coding computational complexity is imperative to adapt to diverse terminals in video streaming, especially with high definition videos and increasingly comprehensive ...encoders. Until now, few efforts have been contributed to the encoder of multiview videos, which complicates its encoding structure with duplex frame display. To address this issue, we propose a flexible complexity optimization framework in this paper. In the first place, the proposed algorithm flexibly reduces the encoder complexity at different external-defined complexity constraints; furthermore, it is also committed to compression efficiency optimization at different complexity levels. The framework is achieved by a hybrid approach: complexity allocation , which allocates the external-defined complexity constraint to all views, hierarchical layers and frames based on linear programming; and complexity regulation , which dynamically adjusts local candidate partitions to fulfil the targeted local complexity constraint, with a probability-driven Alternate Partition Cost (APC) minimization. The overall algorithm is implemented on the popular multiview encoder, Multiview High Efficiency Video Coding (MV-HEVC), with promising Rate-Distortion (RD) performances at different complexity constraints, which are also superior to two recent complexity optimization algorithms.
As products and their manufacturing systems have become more sophisticated and complex, both industry and academia have widely discussed complexity in product design and manufacturing to understand ...its impact. However, the impact of complexity on manufacturing performance has not been clearly articulated in the previous empirical studies despite the widely expected negative relationship between them. As a response, this paper considers static complexity, which is due to inherent structural characteristics in product design and manufacturing, to elucidate the impact of design and manufacturing complexity on manufacturing performance. Metrics to properly capture design and manufacturing complexity in a product family are proposed and applied to a screwdriver product family case. Then, regression analysis is performed to identify the impact of complexity on manufacturing performance under different demand levels and manufacturing strategies. As a result, the negative impacts of design and manufacturing complexity on lead time and total production cost and their changes commensurate to the increase in demand are observed under the make-to-order policy. On the other hand, similar negative impacts are not statistically significant under the make-to-stock policy. These results indicate that static complexity negatively affects manufacturing performance only in the make-to-order system; and the inventory held of common parts in the make-to-stock system decreases the influence of static complexity on manufacturing performance.
Molecular machine learning has been maturing rapidly over the last few years. Improved methods and the presence of larger datasets have enabled machine learning algorithms to make increasingly ...accurate predictions about molecular properties. However, algorithmic progress has been limited due to the lack of a standard benchmark to compare the efficacy of proposed methods; most new algorithms are benchmarked on different datasets making it challenging to gauge the quality of proposed methods. This work introduces MoleculeNet, a large scale benchmark for molecular machine learning. MoleculeNet curates multiple public datasets, establishes metrics for evaluation, and offers high quality open-source implementations of multiple previously proposed molecular featurization and learning algorithms (released as part of the DeepChem open source library). MoleculeNet benchmarks demonstrate that learnable representations are powerful tools for molecular machine learning and broadly offer the best performance. However, this result comes with caveats. Learnable representations still struggle to deal with complex tasks under data scarcity and highly imbalanced classification. For quantum mechanical and biophysical datasets, the use of physics-aware featurizations can be more important than choice of particular learning algorithm.
Droplet organelles? Courchaine, Edward M; Lu, Alice; Neugebauer, Karla M
The EMBO journal,
01 August 2016, Volume:
35, Issue:
15
Journal Article
Peer reviewed
Open access
Cells contain numerous, molecularly distinct cellular compartments that are not enclosed by lipid bilayers. These compartments are implicated in a wide range of cellular activities, and they have ...been variously described as bodies, granules, or organelles. Recent evidence suggests that a liquid–liquid phase separation (LLPS) process may drive their formation, possibly justifying the unifying term “droplet organelle”. A veritable deluge of recent publications points to the importance of low‐complexity proteins and RNA in determining the physical properties of phase‐separated structures. Many of the proteins linked to such structures are implicated in human diseases, such as amyotrophic lateral sclerosis (ALS). We provide an overview of the organizational principles that characterize putative “droplet organelles” in healthy and diseased cells, connecting protein biochemistry with cell physiology.
Non‐membrane‐bound cellular structures such as nucleoli, stress granules, Cajal and P bodies have been long established. Recent data reviewed by Neugebauer and colleagues delineate liquid–liquid phase separation processes that underlie the dynamic nature of these organelles composed of low‐complexity proteins and RNA.
Dislocations are commonly present and important in metals but their effects have not been fully recognized in oxide ceramics. The large strain energy raised by the rigid ionic/covalent bonding in ...oxide ceramics leads to dislocations with low density (∼10
mm
), thermodynamic instability and spatial inhomogeneity. In this paper, we report ultrahigh density (∼10
mm
) of edge dislocations that are uniformly distributed in oxide ceramics with large compositional complexity. We demonstrate the dislocations are progressively and thermodynamically stabilized with increasing complexity of the composition, in which the entropy gain can compensate the strain energy of dislocations. We also find cracks are deflected and bridged with ∼70% enhancement of fracture toughness in the pyrochlore ceramics with multiple valence cations, due to the interaction with enlarged strain field around the immobile dislocations. This research provides a controllable approach to establish ultra-dense dislocations in oxide ceramics, which may open up another dimension to tune their properties.
In this Letter, the authors propose a low-complexity search method for carrier frequency offset (CFO) estimation in generalised frequency division multiplexing (GFDM). The proposed technique does not ...have any limitations on CFO acquisition range while providing an accurate estimate. Compared with the existing solutions in the literature with the lowest complexity, the proposed technique brings at least an order of magnitude complexity reduction without any performance penalty. Finally, the numerical results and comparisons with the existing literature in terms of performance and complexity attest the efficacy of the proposed method.
A strategy is proposed for characterizing the worst-case performance of algorithms for solving nonconvex smooth optimization problems. Contemporary analyses characterize worst-case performance by ...providing, under certain assumptions on an objective function, an upper bound on the number of iterations (or function or derivative evaluations) required until a
p
th-order stationarity condition is approximately satisfied. This arguably leads to conservative characterizations based on certain objectives rather than on ones that are typically encountered in practice. By contrast, the strategy proposed in this paper characterizes worst-case performance separately over regions comprising a search space. These regions are defined generically based on properties of derivative values. In this manner, one can analyze the worst-case performance of an algorithm independently from any particular class of objectives. Then, once given a class of objectives, one can obtain a tailored complexity analysis merely by delineating the types of regions that comprise the search spaces for functions in the class. Regions defined by first- and second-order derivatives are discussed in detail and example complexity analyses are provided for a few standard first- and second-order algorithms when employed to minimize convex and nonconvex objectives of interest. It is also explained how the strategy can be generalized to regions defined by higher-order derivatives and for analyzing the behavior of higher-order algorithms.
In simulation-based realization of complex systems, we are forced to address the issue of computational complexity. One critical issue that must be addressed is the approximation of reality using ...surrogate models to replace expensive simulation models of engineering problems. In this paper, we critically review over 200 papers. We find that a framework for selecting appropriate surrogate modeling methods for a given function with specific requirements has been lacking. Having such a framework for surrogate model users, specifically practitioners in industry, is very important because there is very limited information about the performance of different models before applying them on the problem. Our contribution in this paper is to address this gap by creating practical guidance based on a trade-off among three main drivers, namely, size (how much information is necessary to compute the surrogate model), accuracy (how accurate the surrogate model must be) and computational time (how much time is required for the surrogate modeling process). Using the proposed guidance a huge amount of time is saved by avoiding time-consuming comparisons before selecting the appropriate surrogate model. To make this contribution, we review the state-of-the-art surrogate modeling literature to answer the following three questions: (1) What are the main classes of the design of experiment (DOE) methods, surrogate modeling methods and model-fitting methods based on the requirements of size, computational time, and accuracy? (2) Which surrogate modeling method is suitable based on the critical characteristics of the requirements of size, computational time and accuracy? (3) Which DOE is suitable based on the critical characteristics of the requirements of size, computational time and accuracy? Based on these three characteristics, we find six different qualitative categories for the surrogate models through a critical evaluation of the literature. These categories provide a framework for selecting an efficient surrogate modeling process to assist those who wish to select more appropriate surrogate modeling techniques for a given function. It is also summarized in Table
4
and Figs.
2
,
3
. MARS, response surface models, and kriging are more appropriate for large problems, acquiring less computation time and high accuracy, respectively. Also, Latin Hypercube
,
fractional factorial designs and D-Optimal designs are appropriate experimental designs. Our contribution is to propose a qualitative evaluation and a mental model which is based on quantitative results and findings of authors in the published literature. The value of such a framework is in providing practical guide for researchers and practitioners in industry to choose the most appropriate surrogate model based on incomplete information about an engineering design problem. Another contribution is to use three drivers, namely, computational time, accuracy, and problem size instead of using a single measure that authors generally use in the published literature.
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