Partition Size Research Articles

Statistically significant tests of multiparticle quantum correlations based on randomized measurements

We consider statistical methods based on finite samples of locally randomized measurements in order to certify different degrees of multiparticle entanglement in intermediate-scale quantum systems. We first introduce hierarchies of multi-qubit criteria, satisfied by states which are separable with respect to partitions of different size, involving only second moments of the underlying probability distribution. Then, we analyze in detail the statistical error of the estimation in experiments and present several approaches for estimating the statistical significance based on large deviation bounds. The latter allows us to characterize the measurement resources required for the certification of multiparticle correlations, as well as to analyze given experimental data in detail.

Chain Decompositions of q, t-Catalan Numbers: Tail Extensions and Flagpole Partitions

This article is part of an ongoing investigation of the combinatorics of $q,t$-Catalan numbers $\textrm{Cat}_n(q,t)$. We develop a structure theory for integer partitions based on the partition statistics dinv, deficit, and minimum triangle height. Our goal is to decompose the infinite set of partitions of deficit $k$ into a disjoint union of chains $\mathcal{C}_{\mu}$ indexed by partitions of size $k$. Among other structural properties, these chains can be paired to give refinements of the famous symmetry property $\textrm{Cat}_n(q,t)=\textrm{Cat}_n(t,q)$. Previously, we introduced a map that builds the tail part of each chain $\mathcal{C}_{\mu}$. Our first main contribution here is to extend this map to construct larger second-order tails for each chain. Second, we introduce new classes of partitions called flagpole partitions and generalized flagpole partitions. Third, we describe a recursive construction for building the chain $\mathcal{C}_{\mu}$ for a (generalized) flagpole partition $\mu$, assuming that the chains indexed by certain specific smaller partitions (depending on $\mu$) are already known. We also give some enumerative and asymptotic results for flagpole partitions and their generalized versions.

Trace Metal Partitioning in the Salinity Gradient of the Highly Stratified Estuary: A Case Study in the Krka River Estuary (Croatia)

A size partitioning of several trace metals (Zn, Cd, Pb, Cu, Ni, Co, Mn, Fe and Al) between five size fractions (<3 kDa, 3 kDa–0.1 µm, 0.1 µm–1.2 µm, 1.2 µm–5 µm and >5 µm) was studied in the vertical salinity gradient of the highly stratified Krka River estuary. The results indicated a dominant river source for Zn, Co, Mn, Fe and Al and a diluting effect on Cd, Pb and Ni. The truly dissolved fraction (<3 kDa) dominated the Zn, Cd, Cu, Ni and Co pool, and a large part of Pb, Mn, Fe and Al was present in >5 µm particles. Pb, Mn, Fe and Al were closely related, showing a precipitation and colloidal aggregation in the surface layers and dissolution in the seawater layer. The highest percentage (30–37%) of colloids (3 kDa–0.1 µm) in the dissolved pool was found for Pb, Cu, Fe and Al. Differences in size distribution between low and high river flow periods revealed that Zn, Pb, Co, Mn, Fe and Al are introduced by the river mostly in the 3 kDa–5 µm size range. Therefore, a low percentage of colloidally bound metals compared to other coastal areas can be explained by a limited riverine input of terrigenous material, characteristic for this estuary. Correlation with PARAFAC components revealed associations of Cu with protein-like substances and Co with humic-like substances. The accumulation of Cu at the freshwater-seawater interface coupled with an increase of its colloidal fraction was observed, apparently governed by biologically produced organic ligands.

Detection of Embryonic Trisomy 21 in the First Trimester Using Maternal Plasma Cell-Free RNA.

Prenatal trisomy 21 (T21) screening commonly involves testing a maternal blood sample for fetal DNA aneuploidy. It is reliable but poses a cost barrier to universal screening. We hypothesized maternal plasma RNA screening might provide similar reliability but at a lower cost. Discovery experiments used plasma cell-free RNA from 20 women 11–13 weeks tested by RNA and miRNA microarrays followed by qRT-PCR. Thirty-six mRNAs and 18 small RNAs of the discovery cDNA were identified by qPCR as potential markers of embryonic T21. The second objective was validation of the RNA predictors in 998 independent pregnancies at 11–13 weeks including 50 T21. Initial analyses identified 9–15 differentially expressed RNA with modest predictive power (AUC < 0.70). The 54 RNAs were then subjected to machine learning. Eleven algorithms were trained on one partition and tested on an independent partition. The three best algorithms were identified by Kappa score and the effects of training/testing partition size and dataset class imbalance on prediction were evaluated. Six to ten RNAs predicted T21 with AUCs up to 1.00. The findings suggest that maternal plasma collected at 11–13 weeks, tested by qRT-PCR, and classified by machine learning, may accurately predict T21 for a lower cost than plasma DNA, thus opening the door to universal screening.

On the strange kinetic aesthetic of rectangular shape partitions

Abstract In this paper, we focus on shape partitions. We show that for any fixed k, one can symbolically characterize the shape partition on a k × n rectangular grid by a context-free grammar. We explicitly give this grammar for k = 2 and k = 3 (for k = 1, this corresponds to compositions of integers). From these grammars, we deduce the number of shape partitions for the k × n rectangular grids for k ∈ {1, 2, 3} and every n, as well as the limiting Gaussian distribution of the number of connected components. This also enables us to randomly and uniformly generate shape partitions of large size.

Multikernel Capsule Network for Schizophrenia Identification.

Schizophrenia seriously affects the quality of life. To date, both simple (e.g., linear discriminant analysis) and complex (e.g., deep neural network) machine-learning methods have been utilized to identify schizophrenia based on functional connectivity features. The existing simple methods need two separate steps (i.e., feature extraction and classification) to achieve the identification, which disables simultaneous tuning for the best feature extraction and classifier training. The complex methods integrate two steps and can be simultaneously tuned to achieve optimal performance, but these methods require a much larger amount of data for model training. To overcome the aforementioned drawbacks, we proposed a multikernel capsule network (MKCapsnet), which was developed by considering the brain anatomical structure. Kernels were set to match partition sizes of the brain anatomical structure in order to capture interregional connectivities at the varying scales. With the inspiration of the widely used dropout strategy in deep learning, we developed capsule dropout in the capsule layer to prevent overfitting of the model. The comparison results showed that the proposed method outperformed the state-of-the-art methods. Besides, we compared performances using different parameters and illustrated the routing process to reveal characteristics of the proposed method. MKCapsnet is promising for schizophrenia identification. Our study first utilized the capsule neural network for analyzing functional connectivity of magnetic resonance imaging (MRI) and proposed a novel multikernel capsule structure with the consideration of brain anatomical parcellation, which could be a new way to reveal brain mechanisms. In addition, we provided useful information in the parameter setting, which is informative for further studies using a capsule network for other neurophysiological signal classification.

Impact of data partitioning in groundwater level prediction using artificial neural network for multiple wells

Information on groundwater level (GWL) fluctuation is very important for general planning and water resources management. In recent times, Artificial Neural Network (ANN) has gained popularity as alternative modelling tool to the existing physical based models in groundwater level forecasting. In ANN modelling, the most widely and successfully used data partitioning approach of the hold-out cross validation has been a critical factor that affects the performance of the model. This study is focused on evaluating and comparing the impact of different data size partitioning in groundwater level prediction using ANN methods. The study considered all the possible partitioning percentages for the train-test sets which are (90-10), (80-20), (70-30), (60-40) and (50-50). These five different partitions have been analysed and tested on 13 different boreholes (BH) using Backpropagation Neural Network (BPNN), Radial Basis Function Neural Network (RBFNN), Generalised Regression Neural Network (GRNN) and Group Method of Data Handling (GMDH). The results indicated that (70-30) and (80-20) were the most dominant partitions to produce optimum GWL prediction models for the BHs. Overall, it was noticed that RBFNN was superior when (70-30) and (80-20) partitions were employed, whereas BPNN was the best for the (60-40) and (50-50) partitions. This study demonstrates that the performance of ANN method is heavily dependent on the partition percentage used in the model formulation. Therefore, the main contribution of this study was to bring to light how different data partitioning size impacts on the effectiveness of the ANN in GWL prediction.

Context-Aware Phylogenetic Trees for Phylogeny-Based Taxonomy Visualization.

Sustained efforts in next-generation sequencing technologies are changing the field of taxonomy. The increase in the number of resolved genomes has made the traditional taxonomy of species antiquated. With phylogeny-based methods, taxonomies are being updated and refined. Although such methods bridge the gap between phylogeny and taxonomy, phylogeny-based taxonomy currently lacks interactive visualization approaches. Motivated by enriching and increasing the consistency of evolutionary and taxonomic studies alike, we propose Context-Aware Phylogenetic Trees (CAPT) as an interactive web tool to support users in exploration- and validation-based tasks. To complement phylogenetic information with phylogeny-based taxonomy, we offer linking two interactive visualizations which compose two simultaneous views: the phylogenetic tree view and the taxonomic icicle view. Thanks to its space-filling properties, the icicle visualization follows the intuition behind taxonomies where different hierarchical rankings with equal number of child elements can be represented with same-sized rectangular areas. In other words, it provides partitions of different sizes depending on the number of elements they contain. The icicle view integrates seven taxonomic rankings: domain, phylum, class, order, family, genus, and species. CAPT enriches the clades in the phylogenetic tree view with context from the genomic data and supports interactive techniques such as linking and brushing to highlight correspondence between the two views. Four different use cases, extracted from the Genome Taxonomy DataBase, were employed to create four scenarios using our approach. CAPT was successfully used to explore the phylogenetic trees as well as the taxonomic data by providing context and using the interaction techniques. This tool is essential to increase the accuracy of categorization of newly identified species and validate updated taxonomies. The source code and data are freely available at https://github.com/ghattab/CAPT.

Assessment of the flat-top stable GFEM for free vibration analysis

The stable Generalized Finite Element Method, SGFEM, has been used for numerical stabilization of the generalized finite element method during enrichment process of shape functions. However, some troubles persist in dynamic analysis. The flat-top strategy is an alternative to hold up the SGFEM but, despite its good performance in quasi-static problems, for dynamic problems some points remain opened, such as the accuracy of natural frequencies, the computational effort to reach a desired degree of precision (for each natural frequency), and the conditioning of mass and stiffness matrices. The main objective of this work is to assess the performance of the flat-top SGFEM in the context of free vibration analysis Based in many numerical simulations, the sensitivity of the method is verified for different parameters, such as, the size of the flat-top partition of unity (PU) intervals, the smoothness of enriched functions, and the stabilization parameter. Despite the flat-top SGFEM improves the numerical stability for modal analysis, it is shown that the convergence rates can be degraded.

The waiting-time distribution for network partitions in cascading failures in power networks

Network redundancy is one of the spatial properties critical to robustness against cascading failures in power networks. Waiting-time distributions for network partitions in cascading failures explain how spatial network structures affect the cascading behaviors temporally. Two waiting time events associated with the first and largest network partitions in cascading failures are studied. With synthetic power networks, waiting-time distributions of network partitions can be systematically analyzed for various network redundancies. Waiting-time distributions take longer from the local redundancy to the global redundancy. Meanwhile, the largest network partition during a cascading failure may not be unique. In power networks with larger global redundancies, the multiple largest network partitions happen more likely, and the sizes of the largest partitions decrease while their number increases statistically. Simulations in realistic power networks demonstrate the same spatio-temporal behaviors as revealed in synthetic power networks.

Resource partitioning may limit interspecific competition among Arctic fish species during early life

Arctic cod (Boreogadus saida) strongly dominates the ichthyoplankton assemblages of High Arctic seas, hence competition with other native species seldom has been studied. Yet, interspecific competition could negatively impact the survival of early life stages of fishes in Arctic areas where higher diversity prevails. We surveyed the ichthyoplankton community of the Greenland Sea, in August–September 2017. Gadids (mostly Arctic cod, with a low number of ice cod Arctogadus glacialis) and non-gadids (bigeye sculpin Triglops nybelini and gelatinous snailfish Liparis fabricii) co-dominated age-0 fish assemblages. Here, we document their diet, prey selectivity, horizontal and vertical distributions as well as that of their prey to assess resource partitioning and the potential for interspecific competition. All fish species occupied the top 30 m of the water column, but Arctic cod occurred in highest abundances over the continental slope, whereas other species distributed almost exclusively over the continental shelf. A particle track analysis suggests that Arctic cod larvae could have hatched in the open waters of the Northeast Water Polynya, drifted with the East Greenland Current, and benefited from the high secondary production associated with these oceanographic features. The diet of gadids did not overlap significantly with the diet of non-gadids, but strong selectivity for Pseudocalanus spp. and Calanus spp. copepodites among the larvae suggests potential competition for these key prey items, although limited by size partitioning of the prey. We thus conclude that interspecific competition among early life stages of Arctic fishes is limited for now. However, changing conditions and the northward range expansion of boreal species following climate change could increase competition and, in turn, negatively affect the recruitment of Arctic ichthyoplankton.

Quantum state transfer on the complete bipartite graph

Previously it was shown that (almost) perfect state transfer can be achieved on the complete bipartite graph by a discrete-time coined quantum walk based algorithm when both the sender and receiver vertices are in the same partition of the graph and when the sender and receiver are in opposite partitions of the same size. By changing the coin operator, we analyze the state transfer problem and we show that it is still possible to achieve state transfer with high fidelity even when the sender and receiver are in different partitions with different sizes. Moreover, it is also possible to use an active switch approach using lackadaisical quantum walks where the marked vertex is switched between the sender and receiver during the algorithm.

Pathwise Convergent Approximation for the Fractional SDEs

Fractional stochastic differential equation (FSDE)-based random processes are used in a wide spectrum of scientific disciplines. However, in the majority of cases, explicit solutions for these FSDEs do not exist and approximation schemes have to be applied. In this paper, we study one-dimensional stochastic differential equations (SDEs) driven by stochastic process with Hölder continuous paths of order 1/2&lt;γ&lt;1. Using the Lamperti transformation, we construct a backward approximation scheme for the transformed SDE. The inverse transformation provides an approximation scheme for the original SDE which converges at the rate h2γ, where h is a time step size of a uniform partition of the time interval under consideration. This approximation scheme covers wider class of FSDEs and demonstrates higher convergence rate than previous schemes by other authors in the field.

Pivotal discrepancy measures for Bayesian modelling of spatio-temporal data

Within the field of geostatistics, Gaussian processes are a staple for modelling spatial and spatio-temporal data. Statistical literature is rich with estimation methods for the mean and covariance of such processes (in both frequentist and Bayesian contexts). Considerably less attention has been paid to developing goodness-of-fit tests for assessment of model adequacy. Jun et al. (Environmetrics 25(8):584–595, 2014) introduced a statistical test that uses pivotal discrepancy measures to assess goodness-of-fit in the Bayesian context. We present a modification and generalization of their statistical test. The initial method involves spatial partitioning of the data, followed by evaluation of a pivotal discrepancy measure at each posterior draw to obtain a posterior distribution of pivotal statistics. Order statistics from this distribution are used to obtain approximate p-values. Jun et al. (Environmetrics 25(8):584–595, 2014) use arbitrary partitions based on pre-existing spatial boundaries. The partitions are made to be of equal size. Our contribution is two-fold. We use K-means clustering to create the spatial partitions and we generalise Jun et al.’s approach to incorporate unequal partition sizes. Observations from a spatial or spatio-temporal process are partitioned using an appropriate feature vector that incorporates the geographic location of the observations into subsets (not necessarily of the same size). The method’s viability is illustrated in a simulation study, and in an application to hoki (Macruronus novaezelandiae) catch data from a survey of the sub-Antarctic region.

Optimal Network Partition and Edge Server Placement for Distributed State Estimation

This paper investigates network partition and edge server placement problem to exploit the benefit of edge computing for distributed state estimation. A constrained many-objective optimization problem is formulated to minimize the cost of edge server deployment, operation, and maintenance, avoid the difference in the partition sizes, reduce the level of coupling between connected partitions, and maximize the inner cohesion of each partition. Capacities of edge server are constrained against underload and overload. To efficiently solve the problem, an improved non-dominated sorting genetic algorithm III (NSGA-III) is developed, with a specifically designed directed mutation operator based on topological characteristics of the partitions to accelerate convergence. Case study validates that the proposed formulations effectively characterize the practical concerns and reveal their trade-offs, and the improved algorithm outperforms existing representative ones for large-scale networks in converging to a near-optimal solution. The optimized result contributes significantly to real-time distributed state estimation.

A Practical Energy/Power Reduction Approach for Parallel Decimal Multiplier

Decimal computation is highly demanded in many human-centric applications such as banking, accounting, tax calculation, and currency conversion. Hence the design and implementation of radix-10 arithmetic units attract the attention of many researchers. Among the basic decimal arithmetic operations, multiplication is not only a frequent operation but also has high complexity and considerable power consumption. Therefore, this paper concentrates on this issue and studies a general design methodology that reduces power/energy consumption via localizing switching activity without compromising target performance. This method decomposes a digit multiplier into smaller ones, like Karatsuba’s algorithm, while the multiplicand and the multiplier can be partitioned into different sizes. We take advantage of various size partitions in two types of symmetric and asymmetric, which final designs provide specific characteristics. All designs were implemented using VHDL and synthesized in the Design-Compiler toolbox with TSMC 130 nm Technology file. The results are significant; in respect to the original design, by a random test vector, 25% power reduction is achieved with no effect on latency and a negligible area penalty. Moreover, the experimental results indicate a potential for considerable reduction of power dissipation based on statistical properties of possible input data.

Cloud-Based Framework for Spatio-Temporal Trajectory Data Segmentation and Query

Trajectory segmentation is a technique of dividing sequential trajectory into segments. These segments are building blocks to various applications. Hence a system framework is essential to support trajectory segment indexing, storage, and query. When the size of segments is beyond the computing capacity of a single processing node, a distributed solution is proposed. In this article, we develop a distributed trajectory segmentation framework that includes a greedy-split segmentation method. This framework consists of distributed in-memory processing and a cluster of graph storage respectively. For fast trajectory queries, we design a distributed spatial R-tree index of trajectory segments. Using the indexes, we build scalable query operations from both in-memory processing and access to graph storage. Based on this framework, we define two metrics to measure trajectory similarity and chance of collision. These two metrics are further applied to identify moving groups of trajectories. We quantitatively evaluate the effects of data partition, parallelism, and data size on the system. We identify the bottleneck factors at the data partition stage and validate two mitigation techniques to data skew. The evaluation demonstrates our distributed segmentation method and the system framework scale as the growth of the workload and the size of the parallel cluster.

A Compressed Data Partition and Loop Scheduling Scheme for Neural Networks

Neural networks (NNs) have been widely adopted in various application domains, ranging from image and video recognition to natural language processing. Recent studies reveal that deeper NNs with more parameters greatly enhance the output accuracy. However, complex NNs incur intensive memory accesses. Since the weights of even a single layer can exceed the on-chip storage capacity, the data usually need to be partitioned. Compression can effectively reduce the storage space requirements. However, there is no research considering the partition of the spare matrix. In this paper, we propose a sparse NN data partition and loop scheduling scheme. We establish the compression efficiency model of the matrix sparse algorithm and design a partition selection method based on sparsity characteristics analyzed by the compression efficiency model. Finally, we design a loop scheduling scheme based on the proper partition size. The experiment results show that the average memory access of each layer can be compressed to 68% of the original; additionally, the throughput of the three networks is increased to an average of 1.66 times.

A Complexity Aware Scheduler With Dynamic Slot Allocation for Cloud Video Transcoding

For a multimedia cloud computing platform, it needs to perform video transcoding to provide bandwidth-compatible bit-streams for users. In configuring a MapReduce system, it allocates slots to workers with the assumption of homogeneous worker power and performs task scheduling by assuming equal task time complexity. However, the computing power of a practical cluster of workers and the time complexity of tasks is time-varying in any case. The task-scheduling algorithm has to well manipulate these heterogeneous cloud resources and task complexity. We first find a good partition size for a video transcoding job for efficient processing. We proposed a Complexity-Aware Scheduling (CAS) algorithm that reorders task assignment priorities according to task complexity to maintain load-balancing operations. By utilizing a Neural Network model to refine the task complexity estimation for the CAS(CASNN), the scheduling and transcoding speedup performances can further be improved. Based on the CASNN, we proposed a Dynamically Adjusting Slot number allocation (DAS) method, DASCASNN, to adjust the slots according to resource utilization status to improve the processing performance. Experimental results show the proposed DASCASNN can help reduce 30% of the transcoding time on average as compared to available schedulers and increase the resource utilization rates from 82.7% to 98%.

Index Dependent Nested Loops Parallelization with an Even Distributed Number of Steps

Parallel processing of algorithms is an effective way to achieve higher performance on multiprocessor systems rather. During parallelization, it is critical to minimize the difference between the processing time for threads. It is necessary to choose a method that can efficiently distribute the workload evenly across the threads. This paper deals with a special kind of nested loops where the internal loop iterator depends on the outer loop iterator. In such cases, the process can be represented as an upper (or lower) triangular matrix. This paper introduces a method for partitioning the outer loop according to the indices in an almost optimal manner, so that the partial loops in each thread will take nearly the same number of steps. In addition, we examine the potential of a perfect partition and try to determine the maximum (but still meaningful) partition size.