13,842 research outputs found
A Minimal Periods Algorithm with Applications
Kosaraju in ``Computation of squares in a string'' briefly described a
linear-time algorithm for computing the minimal squares starting at each
position in a word. Using the same construction of suffix trees, we generalize
his result and describe in detail how to compute in O(k|w|)-time the minimal
k-th power, with period of length larger than s, starting at each position in a
word w for arbitrary exponent and integer . We provide the
complete proof of correctness of the algorithm, which is somehow not completely
clear in Kosaraju's original paper. The algorithm can be used as a sub-routine
to detect certain types of pseudo-patterns in words, which is our original
intention to study the generalization.Comment: 14 page
Structural Equation Modeling and simultaneous clustering through the Partial Least Squares algorithm
The identification of different homogeneous groups of observations and their
appropriate analysis in PLS-SEM has become a critical issue in many appli-
cation fields. Usually, both SEM and PLS-SEM assume the homogeneity of all
units on which the model is estimated, and approaches of segmentation present
in literature, consist in estimating separate models for each segments of
statistical units, which have been obtained either by assigning the units to
segments a priori defined. However, these approaches are not fully accept- able
because no causal structure among the variables is postulated. In other words,
a modeling approach should be used, where the obtained clusters are homogeneous
with respect to the structural causal relationships. In this paper, a new
methodology for simultaneous non-hierarchical clus- tering and PLS-SEM is
proposed. This methodology is motivated by the fact that the sequential
approach of applying first SEM or PLS-SEM and second the clustering algorithm
such as K-means on the latent scores of the SEM/PLS-SEM may fail to find the
correct clustering structure existing in the data. A simulation study and an
application on real data are included to evaluate the performance of the
proposed methodology
Community Detection in Hypergraphs, Spiked Tensor Models, and Sum-of-Squares
We study the problem of community detection in hypergraphs under a stochastic
block model. Similarly to how the stochastic block model in graphs suggests
studying spiked random matrices, our model motivates investigating statistical
and computational limits of exact recovery in a certain spiked tensor model. In
contrast with the matrix case, the spiked model naturally arising from
community detection in hypergraphs is different from the one arising in the
so-called tensor Principal Component Analysis model. We investigate the
effectiveness of algorithms in the Sum-of-Squares hierarchy on these models.
Interestingly, our results suggest that these two apparently similar models
exhibit significantly different computational to statistical gaps.Comment: In proceedings of 2017 International Conference on Sampling Theory
and Applications (SampTA
Choice of State Estimation Solution Process for Medium Voltage Distribution Systems
As distribution networks are turning into active systems, enhanced observability and continuous monitoring becomes essential for effective management and control. The state estimation (SE) tool is therefore now considered as the core component in future distribution management systems. The development of a novel distribution system SE tool is required to accommodate small to very large networks, operable with limited real time measurements and able to execute the computation of large volumes of data in a limited time frame. In this context, the paper investigates the computation time and voltage estimation qualities of three different SE optimization solution methods in order to evaluate their effectiveness as potential distribution SE candidate solutions
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