SMM: Leveraging Metadata for Contextually Salient Multi-Variate Motif Discovery

A common challenge in multimedia data understanding is the unsupervised discovery of recurring patterns, or motifs, in time series data. The discovery of motifs in uni-variate time series is a well studied problem and, while being a relatively new area of research, there are also several proposals for multi-variate motif discovery. Unfortunately, motif search among multiple variates is an expensive process, as the potential number of sub-spaces in which a pattern can occur increases exponentially with the number of variates. Consequently, many multi-variate motif search algorithms make simplifying assumptions, such as searching for motifs across all variates individually, assuming that the motifs are of the same length, or that they occur on a fixed subset of variates. In this paper, we are interested in addressing a relatively broad form of multi-variate motif detection, which seeks frequently occurring patterns (of possibly differing lengths) in sub-spaces of a multi-variate time series. In particular, we aim to leverage contextual information to help select contextually salient patterns and identify the most frequent patterns among all. Based on these goals, we first introduce the contextually salient multi-variate motif (CS-motif) discovery problem and then propose a salient multi-variate motif (SMM) algorithm that, unlike existing methods, is able to seek a broad range of patterns in multi-variate time series.

Attracting sets for one class of asymptotically compact systems with pulsed perturbation

The authors consider the pulsed dynamical systems generated by evolutionary processes. The trajectories of these processes undergo the pulsed perturbation when the energy functional reaches some fixed limit value. The generalization of the classical theory of global attractors of infinite dimensional dynamical systems in case of systems with impulse actions is carried out. It is established that for the dissipative pulsed dynamical system generated by the asymptotically compact semigroup, there exists a uniform attractor, i.e., a compact uniformly attracting set, minimal among all such sets in the phase space of the system. The result is applied to the weakly nonlinear wave equation with dissipation, the trajectories of which are subjected to impulsive perturbations upon attainment of a certain fixed subset in the phase space, so called the impulse set.

Designing optimal route for the distribution chain of a rural LPG delivery system

A practical distribution system that arises in the context of delivering liquefied petroleum gas (LPG) through cylinders is considered in this study. To meet all the challenging constraints, the model is explicitly considered as a simultaneous pickup and delivery single commodity truncated vehicle routing problem with the homogeneous fleet of vehicles. The aim of this problem is to find the optimal routes for the set of vehicles locating at the distributing agency (DA), which offers simultaneous pickup and delivery operations over single commodity (i.e. LPG cylinders) to a fixed subset (need not serve all delivery centers) of delivery centers at rural level. The model is designed using zero-one integer linear programming. For proper treatment of the present model, an exact Lexi-search algorithm (LSA) has been developed. A comparative study is performed between the LSA and existing results for the relaxed version of the present model. Further, the efficiency of the LSA is tested through numerical experiments over small and medium CVRP benchmark test instances. The extensive computational results have shown that the LSA is productive and revealed that the real solutions have more consistent than the integral solutions in the presence of truncation constraint.

Time-Frequency Representation Based on Robust Local Mean Decomposition

Fourier transform based frequency representation makes an underlying assumption of stationarity and linearity for the target signal whose spectrum is to be computed, and thus it is unable to track time varying characteristics of non-stationary signals that also widely exist in the physical world. Time-frequency representation (TFR) is a technique to reveal useful information included in the signals, and thus the TFR methods are very attractive to the scientific and engineering world. Local mean decomposition (LMD) is a TFR technique used in many fields, e.g. machinery fault diagnosis. Similar to Hilbert-Huang transform, it is an alternative approach to demodulate amplitude-modulation (AM) and frequency-modulation (FM) signals into a set of components, each of which is the product of an instantaneous envelope signal and a pure FM signal. TFR can then be derived by the instantaneous envelope signal and the pure FM signal. However, LMD based TFR technique still has two limitations, i.e. the end effect and the mode mixing problems. Solutions for the two limitations greatly depend on three critical parameters of LMD that are boundary condition, envelope estimation, and sifting stopping criterion. Most reported studies aiming to improve performance of LMD have focused on only one parameter a time, and thus they ignore the fact that the three parameters are not independent to each other, and all of them are needed to address the end effect and the mode mixing problems in LMD. In this paper, a robust optimization approach is proposed to improve performance of LMD through an integrated framework of parameter selection in terms of boundary condition, envelope estimation, and sifting stopping criterion. The proposed optimization approach includes three components. First, the mirror extending method is employed to deal with the boundary condition problem. Second, moving average is used as the smooth algorithm for envelope estimation of local mean and local magnitude in LMD. The fixed subset size is the only parameter that usually needs to be predefined with a prior knowledge. In this step, a self-adaptive method based on the statistics theory is proposed to automatically determine a fixed subset size of moving average for accurate envelope estimation. Third, based on the first and the second steps, a soft sifting stopping criterion is proposed to enable LMD to achieve a self-adaptive stop for each sifting process. In this last step, we define an objective function that considers both global and local characteristics of a target signal. Based on the objective function, a heuristic mechanism is proposed to automatically determine the optimal number of sifting iterations in the sifting process. Finally, numerical simulation results show the effectiveness of the robust LMD in terms of mining time-frequency representation information.

Natural Partial Orders on Transformation Semigroups with Fixed Sets

LetXbe a nonempty set. For a fixed subsetYofX, letFixX,Ybe the set of all self-maps onXwhich fix all elements inY. ThenFixX,Yis a regular monoid under the composition of maps. In this paper, we characterize the natural partial order onFix(X,Y)and this result extends the result due to Kowol and Mitsch. Further, we find elements which are compatible and describe minimal and maximal elements.

LED Chip Deformation Measurement During the Operation Using the X-Ray CT Digital Volume Correlation

A high-power LED can generate tremendous heat under the operation, which causes the LED chip undergo large deformation. LED Wire Bonds may undergo deformation because of the mismatch between the LED chip and substrate. Presently, measurements of deformation and strain in operational electronics are limited to measurement on a cut-plane using techniques including digital image correlation and moiré interferometry based techniques. There is need for tools and techniques that can help quantify the in-situ chip deformation and interconnects inside the LED. Digital Volume Correlation (DVC) has been used in conjunction with X-ray Micro-CT for three-dimensional measurement of deformation and strain in LEDs under operational stresses. The Digital Volume Correlation has been used to correlate the undeformed image with deformed images by computing correlation functions throughout each voxel. The deformed images have been generated by CT scanning over the object while the LED is operational. The correlation function computation starts at specific fixed subset window in the reference image, and searches every possible subset window in the deformed image to identify the deformation in the electronic structure. Once the displacement components have been derived, the strain components have been computed by calculating the gradients of the displacement field. In this paper, the full strain field, both in-plane and out-plane strain, will be presented, and the LED chip deformation shape will be analyzed.

New Results on a Generalized Coupon Collector Problem Using Markov Chains

In this paper we study a generalized coupon collector problem, which consists of determining the distribution and the moments of the time needed to collect a given number of distinct coupons that are drawn from a set of coupons with an arbitrary probability distribution. We suppose that a special coupon called the null coupon can be drawn but never belongs to any collection. In this context, we obtain expressions for the distribution and the moments of this time. We also prove that the almost-uniform distribution, for which all the nonnull coupons have the same drawing probability, is the distribution which minimizes the expected time to obtain a fixed subset of distinct coupons. This optimization result is extended to the complementary distribution of the time needed to obtain the full collection, proving by the way this well-known conjecture. Finally, we propose a new conjecture which expresses the fact that the almost-uniform distribution should minimize the complementary distribution of the time needed to obtain any fixed number of distinct coupons.

New Results on a Generalized Coupon Collector Problem Using Markov Chains

In this paper we study a generalized coupon collector problem, which consists of determining the distribution and the moments of the time needed to collect a given number of distinct coupons that are drawn from a set of coupons with an arbitrary probability distribution. We suppose that a special coupon called the null coupon can be drawn but never belongs to any collection. In this context, we obtain expressions for the distribution and the moments of this time. We also prove that the almost-uniform distribution, for which all the nonnull coupons have the same drawing probability, is the distribution which minimizes the expected time to obtain a fixed subset of distinct coupons. This optimization result is extended to the complementary distribution of the time needed to obtain the full collection, proving by the way this well-known conjecture. Finally, we propose a new conjecture which expresses the fact that the almost-uniform distribution should minimize the complementary distribution of the time needed to obtain any fixed number of distinct coupons.

Asymptotic Behavior for a Class of Nonclassical Parabolic Equations

This paper is devoted to the qualitative analysis of a class of nonclassical parabolic equations ut-εΔut-ωΔu+f(u)=g(x) with critical nonlinearity, where ε∈[0,1] and ω>0 are two parameters. Firstly, we establish some uniform decay estimates for the solutions of the problem for g(x)∈H-1(Ω), which are independent of the parameter ε. Secondly, some uniformly (with respect to ε∈[0,1]) asymptotic regularity about the solutions has been established for g(x)∈L2(Ω), which shows that the solutions are exponentially approaching a more regular, fixed subset uniformly (with respect to ε∈[0,1]). Finally, as an application of this regularity result, a family {ℰε}ε∈[0,1] of finite dimensional exponential attractors has been constructed. Moreover, to characterize the relation with the reaction diffusion equation (ε=0), the upper semicontinuity, at ε=0, of the global attractors has been proved.