Non-uniform Partitioning Research Articles

On bounded solutions of linear systems of differential equations with unbounded coefficients

This paper deals with a problem of finding a bounded solution of a system of nonhomogeneous linear differential equations with an unbounded matrix of coefficients on a finite interval. The right-hand side of the equation belongs to a space of continuous functions bounded with some weight; the weight function is chosen taking into account the behavior of the coefficient matrix. The problem is studied using a modified version of the parameterization method with non-uniform partitioning. Necessary and sufficient conditions of well-posedness of the problem are obtained in terms of a bilaterally infinite matrix of special structure.

Relationship between Concrete Hole Shape and Meso-Crack Evolution Based on Stereology Theory and CT Scan under Compression.

To achieve more accurate prediction of the potential failure location and to conduct a deeper analysis of the failure mechanism of concrete constructions, it is critical to probe the evolution process of internal meso-cracks that bear various intensities of load. While a computer Tomography (CT) test provides a non-destructive detection technique for obtaining the internal meso-damage state of concrete, traditional image processing and Digital Image Correlation (DIC) are ineffective in extracting meso-damage information from concrete CT images. On the other hand, by observing the shape change law of concrete’s internal holes under load, it is proposed to use the hole roundness and area fraction formula, developed based on the stereology principle and morphology, to characterize and predict the potential failure location. Four features particularly addressed include the CT image as a whole, image equal partitioning, crack and non-crack areas, and representative holes. The approach is to explore the variation law of critical hole shape parameters, especially the hole roundness under different loading stages, and analyze the relationship between the change in hole shapes and the final macro-crack positions. It is found that compared with the average area fraction, the average hole roundness value of cross section images is more sensitive to the change in stress. In both uniform partitioning and non-uniform partitioning, the average hole roundness value near the final macro-crack location exhibits an increase trend with the stress, while the smoothing effect caused by the hole roundness averaging always exists. Near the final macro-crack location, the roundness of each individual hole is positively associated with the stress, while away from the final macro-crack location such a relation may not be observed. This trend expounds the evolution process of meso-damage in concrete, and the finding can be used to predict the accurate locations of macro-cracks.

In vitro study on the partitioning of red blood cells using a microchannel network.

To investigate the partitioning properties of red blood cells (RBCs) in the bifurcating capillary vessels, an in vitro experiment was performed to perfuse human RBC suspensions into the microfluidic channels with a width of <10μm. Two types of microchannel geometries were established. One is a single model comprising one parent and two daughter channels with different widths, and the other is a network model that had a symmetric geometry with four consecutive divergences and convergences. In addition to the fractional RBC flux at each bifurcation, changes in hematocrit levels and flow velocity before and after the bifurcation were investigated. In the single model, non-uniform partitioning of RBCs was observed, and this result was in good agreement with that of the empirical model. Furthermore, in the network model, the RBC distribution in the cross-section before the bifurcation significantly affected RBC partitioning in the two channels after the bifurcation. Hence, there was a large RBC heterogeneity in the capillary network. The hematocrit levels between the channels differed for more than one order of magnitude. Therefore, the findings of the current research could facilitate a better understanding of RBC partitioning properties in the microcirculatory system.

New Algorithm to Solve Mixed Integer Quadratically Constrained Quadratic Programming Problems Using Piecewise Linear Approximation

Techniques and methods of linear optimization underwent a significant improvement in the 20th century which led to the development of reliable mixed integer linear programming (MILP) solvers. It would be useful if these solvers could handle mixed integer nonlinear programming (MINLP) problems. Piecewise linear approximation (PLA) is one of most popular methods used to transform nonlinear problems into linear ones. This paper will introduce PLA with brief a background and literature review, followed by describing our contribution before presenting the results of computational experiments and our findings. The goals of this paper are (a) improving PLA models by using nonuniform domain partitioning, and (b) proposing an idea of applying PLA partially on MINLP problems, making them easier to handle. The computational experiments were done using quadratically constrained quadratic programming (QCQP) and MIQCQP and they showed that problems under PLA with nonuniform partition resulted in more accurate solutions and required less time compared to PLA with uniform partition.

Collaborative execution of fluid flow simulation using non-uniform decomposition on heterogeneous architectures

The demand for computing power, along with the diversity of computational problems, culminated in a variety of heterogeneous architectures. Among them, hybrid architectures combine different specialized hardware into a single chip, comprising a System-on-Chip (SoC). Since these architectures usually have limited resources, efficiently splitting data and tasks between the different hardware is primal to improve performance. In this context, we explore the non-uniform decomposition of the data domain to improve fluid flow simulation performance on heterogeneous architectures. We evaluate two hybrid architectures: one comprised of a general-purpose x86 CPU and a graphics processing unit (GPU) integrated into a single chip (AMD Kaveri SoC), and another comprised by a general-purpose ARM CPU and a Field Programmable Gate Array (FPGA) integrated into the same chip (Intel Arria 10 SoC). We investigate the effects on performance and energy efficiency of data decomposition on each platform’s devices on a collaborative execution. Our case study is the well-known Lattice Boltzmann Method (LBM), where we apply the technique and analyze the performance and energy efficiency of five kernels on both devices on each platform. Our experimental results show that non-uniform partitioning improves the performance of LBM kernels by up to 11.40% and 15.15% on AMD Kaveri and Intel Arria 10, respectively. While AMD’s Kaveri platform’s performance efficiency is of up to 10.809 MLUPS with an energy efficiency of 142.881 MLUPKJ, Intel’s Arria 10 platform’s is of up to 1.12 MLUPS and 82.272 MLUPKJ.

Minimization of WCRT with Recovery Assurance from Hardware Trojans for Tasks on FPGA-based Cloud

Dynamic partial reconfiguration (DPR) enabled FPGA-based Cloud architecture acts as a flexible and efficient shared environment to facilitates application support to users’ request at low cost. While on one hand we need to handle a variety of tasks, such as periodic or sporadic, deadline or non-deadline, high or low critical tasks from the point of producing correct results, on the other hand we are constrained to use untrusted FPGA-based application IP blocks procured from various third-party vendors, which may contain hardware Trojan horse (HTH) affecting throughput and reliability of the Cloud. We propose Trojan-aware processing of tasks by monitored execution of a task on different untrusted cores, and then one more execution is done upon detection of hardware Trojan effects. For this stringent scheduling environment, the proposed dynamic scheduling algorithm is also properly extended to guarantee successful recovery from Trojan effects for all accepted tasks. Experimental results show that our algorithm improves worst-case-response-time for all tasks including non-deadline tasks and achieves lower task rejection rate for the deadline tasks, through judicious non-uniform partitioning of FPGAs based on supported jobs and subsequent better resource utilization, compared to that for existing Trojan-aware scheduling techniques.

In vitro investigations of red blood cell phase separation in a complex microchannel network

Microvascular networks feature a complex topology with multiple bifurcating vessels. Nonuniform partitioning (phase separation) of red blood cells (RBCs) occurs at diverging bifurcations, leading to a heterogeneous RBC distribution that ultimately affects the oxygen delivery to living tissues. Our understanding of the mechanisms governing RBC heterogeneity is still limited, especially in large networks where the RBC dynamics can be nonintuitive. In this study, our quantitative data for phase separation were obtained in a complex in vitro network with symmetric bifurcations and 176 microchannels. Our experiments showed that the hematocrit is heterogeneously distributed and confirmed the classical result that the branch with a higher blood fraction received an even higher RBC fraction (classical partitioning). An inversion of this classical phase separation (reverse partitioning) was observed in the case of a skewed hematocrit profile in the parent vessels of bifurcations. In agreement with a recent computational study [P. Balogh and P. Bagchi, Phys. Fluids 30,051902 (2018)], a correlation between the RBC reverse partitioning and the skewness of the hematocrit profile due to sequential converging and diverging bifurcations was reported. A flow threshold below which no RBCs enter a branch was identified. These results highlight the importance of considering the RBC flow history and the local RBC distribution to correctly describe the RBC phase separation in complex networks.

Securing RSA against power analysis attacks through non‐uniform exponent partitioning with randomisation

This study presents an approach to compute randomised modular exponentiation through non-uniform exponent partitioning. The exponent has been first partitioned into multiple parts and then shuffled by Fisher Yates method. Thereafter, every partition randomly computes modular exponentiation followed by a final modulo operation to generate the desired result. The shuffling has been introduced to randomise the execution order of individual modular exponentiation. This work is implemented in Rivest-Shamir-Adleman (RSA) and Chinese remainder theorem RSA as they are modular exponentiation based public key cryptosystems. The results have been analysed during decryption with different key sizes. The results indicate that the proposed work can generate non-uniform partitions of the exponent which could not be easily anticipated even in multiple iterations. Also, the shuffling method could completely randomise the execution order of modular exponentiation operations. With non-uniform exponent partitions and randomised modular exponentiation, the proposed work could challenge all the variances of power analysis attacks.

Self-adaptive type-1/type-2 hybrid fuzzy reasoning techniques for two-factored stock index time-series prediction

Considerable research outcomes on stock index time-series prediction using classical (type-1) fuzzy sets are available in the literature. However, type-1 fuzzy sets cannot fully capture the uncertainty involved in prediction because of its limited representation capability. This paper fills the void. Here, we propose four chronologically improved methods of time-series prediction using interval type-2 fuzzy sets. The first method is concerned with prediction of the (main factor) variation time-series using interval type-2 fuzzy reasoning. The second method considers secondary factor variation as an additional condition in the antecedent of the rules used for prediction. Another important aspect of the first and the second methods is non-uniform partitioning of the dynamic range of the time-series using evolutionary algorithm, so as to ensure that each partition includes at least one data point. The third method considers uniform partitioning without imposing any restriction on the number of data points in a partition. The partitions are here modeled by type-1 fuzzy sets, if there exists a single block of contiguous data, and by interval type-2 fuzzy sets, if there exists two or more blocks of contiguous data in a partition. The fourth method keeps provision for tuning of membership functions using recent data from the given time-series to influence the prediction results with the current trends. Experiments undertaken confirm that the fourth technique outperforms the first three techniques and also the existing techniques with respect to root-mean-square error metric.

Connectivity Restoration in Wireless Sensor Networks via Space Network Coding

The problem of finding the number and optimal positions of relay nodes for restoring the network connectivity in partitioned Wireless Sensor Networks (WSNs) is Non-deterministic Polynomial-time hard (NP-hard) and thus heuristic methods are preferred to solve it. This paper proposes a novel polynomial time heuristic algorithm, namely, Relay Placement using Space Network Coding (RPSNC), to solve this problem, where Space Network Coding, also called Space Information Flow (SIF), is a new research paradigm that studies network coding in Euclidean space, in which extra relay nodes can be introduced to reduce the cost of communication. Unlike contemporary schemes that are often based on Minimum Spanning Tree (MST), Euclidean Steiner Minimal Tree (ESMT) or a combination of MST with ESMT, RPSNC is a new min-cost multicast space network coding approach that combines Delaunay triangulation and non-uniform partitioning techniques for generating a number of candidate relay nodes, and then linear programming is applied for choosing the optimal relay nodes and computing their connection links with terminals. Subsequently, an equilibrium method is used to refine the locations of the optimal relay nodes, by moving them to balanced positions. RPSNC can adapt to any density distribution of relay nodes and terminals, as well as any density distribution of terminals. The performance and complexity of RPSNC are analyzed and its performance is validated through simulation experiments.

A novel stock trading prediction and recommendation system

The prices of the stock are influence by many factors and emerge extremely nonlinear structure. Therefore, the stock trading prediction and recommendation is an extremely challenging task. In this paper, a novel stock trading prediction and recommendation system is proposed in user-friendly form. The recommendation system can inform the user whether is to buy or sell the stocks in the next step. Information granulation is applied to transform raw time series into meaningful and interpretable granules, and the more effective non-uniform partitioning method for prediction is presented. The system first determines the intervals based on information granules, and then define the fuzzy sets and fuzzify the historical data. Third, construct fuzzy relationships and assign weights to each period. Finally, the prediction and recommendation is implemented. The experimental results show the proposed system yields better prediction performance, and increases profit-making opportunities.

Observer-Based Stabilization Control of Time-Delay T-S Fuzzy Systems via the Non-Uniform Delay Partitioning Approach

It is well known that intelligent control technology plays an important role in the design of many control systems, and intelligent control has aroused wide attention from scholars. Fuzzy control is also the case because fuzzy control is one branch of intelligent control. The Takagi-Sugeno (T-S) fuzzy model is an effective approach when dealing with complex nonlinear systems, and the advantages of fuzzy controller design is that the linear control methods can be used. In addition, nonlinearity and time delay are inherent and not all states are available in many practical system. Therefore, the observer-based stabilization control for time-delay T-S fuzzy systems is of great significance. With the help of the non-uniform delay partitioning approach, a novel method is put forward to analyze the stability of the time-delay T-S fuzzy system and design the observer-based feedback controller via the parallel distributed compensation (PDC) scheme. The sufficient conditions of asymptotic stability for both nominal and uncertain time-delay T-S fuzzy system are derived based on the Lyapunov stability theory and linear matrix inequality (LMI) techniques. What is more, the solving methods to obtain the controller gain matrices, observer gain matrices, and upper bound of time delay are presented. Two illustrative examples are given to demonstrate the effectiveness and verify the superiority of our developed methods. From the simulation results, it can be found that the most prominent advantages of our proposed methods lie on larger delay bound and less decision variables compared with other related methods. The problem of observer-based stabilization control for continuous nonlinear time-delay systems is investigated in this paper, and the delay-dependent stability criteria are derived to achieve greater delay bound by virtual of the non-uniform delay partitioning approach. Numerical examples further confirmed the effectiveness and advantages of our developed methods.

Lateral heterogeneity of the proton potential along the thylakoid membranes of chloroplasts

This work is devoted to critical analysis and reexamination of the problem of lateral heterogeneity of the trans-thylakoid pH difference (ΔpH=pHout−pHin) in thylakoid membranes of chloroplasts. Correct measurements of ΔpH may be complicated by nonuniform partitioning of the protons pumped into the lumen of granal (stacked) and stroma-exposed thylakoids. We have compared results of ΔpH estimations in isolated bean chloroplasts by two different methods. One of the methods is based on the use of pH-sensitive spin-probes. Another approach relies on the analysis of pH-dependent post-illumination reduction of P700+ - oxidized reaction center of photosystem I (PSI). Both methods lead to virtually the same values of ΔpH, as measured in the state of photosynthetic control when the ATP synthase complexes are inactive (ΔpH~2.3–2.5 at pHout~8). Under the photophosphorylation conditions (metabolic state 3), ΔpH decreases due to the proton drain from the lumen to stroma via active ATP synthases (ΔpH~1–2 at pHout~8). In this state, ΔpH values derived from kinetic data are smaller than ΔpH measured with the pH-probing amines. Such a discrepancy can be explained by the coexistence of thylakoids with different pHin established in granal and stromal thylakoids. The kinetic method is equivalent to the use of a “local pH-meter”, which is sensitive to less significant decrease in pHin inside the stroma-exposed thylakoids. Otherwise, pH-indicating probes give information on pHin values averaged out at both granal and stromal thylakoids. Experimental results have been analyzed within the framework of our mathematical model developed for simulation of electron and proton transport processes in laterally heterogeneous thylakoids. The model provides a reasonable description of experimental data, supporting the notion that the long-range diffusion of protons within the lumen and obstructed diffusion of mobile electron carriers (PQH2 and Pc) influence the lateral profiles of pH along the thylakoid membranes. The model predicts significant alkalization of the inter-thylakoid gap and the establishment of nonuniform lateral profiles of ΔpH under the photophosphorylation conditions. These results are discussed in the context of the problem of energy coupling in laterally heterogeneous lamellar system of chloroplasts.

Red blood cell phase separation in symmetric and asymmetric microchannel networks: effect of capillary dilation and inflow velocity.

The non-uniform partitioning or phase separation of red blood cells (RBCs) at a diverging bifurcation of a microvascular network is responsible for RBC heterogeneity within the network. The mechanisms controlling RBC heterogeneity are not yet fully understood and there is a need to improve the basic understanding of the phase separation phenomenon. In this context, in vitro experiments can fill the gap between existing in vivo and in silico models as they provide better controllability than in vivo experiments without mathematical idealizations or simplifications inherent to in silico models. In this study, we fabricated simple models of symmetric/asymmetric microvascular networks; we provided quantitative data on the RBC velocity, line density and flux in the daughter branches. In general our results confirmed the tendency of RBCs to enter the daughter branch with higher flow rate (Zweifach-Fung effect); in some cases even inversion of the Zweifach-Fung effect was observed. We showed for the first time a reduction of the Zweifach-Fung effect with increasing flow rate. Moreover capillary dilation was shown to cause an increase of RBC line density and RBC residence time within the dilated capillary underlining the possible role of pericytes in regulating the oxygen supply.

An Optimal Microarchitecture for Stencil Computation Acceleration Based on Nonuniform Partitioning of Data Reuse Buffers

High-level synthesis (HLS) tools have made significant progress in compiling high-level descriptions of computation into highly pipelined register-transfer level specifications. The high-throughput computation raises a high data demand. To prevent data accesses from being the bottleneck, on-chip memories are used as data reuse buffers to reduce off-chip accesses. Also memory partitioning is explored to increase the memory bandwidth by scheduling multiple simultaneous memory accesses to different memory banks. Prior work on memory partitioning of data reuse buffers is limited to uniform partitioning. In this paper, we perform an early-stage exploration of nonuniform memory partitioning. We use the stencil computation, a popular communication-intensive application domain, as a case study to show the potential benefits of nonuniform memory partitioning. Our novel method can always achieve the minimum memory size and the minimum number of memory banks, which cannot be guaranteed in any prior work. We develop a generalized microarchitecture to decouple stencil accesses from computation, and an automated design flow to integrate our microarchitecture with the HLS-generated computation kernel for a complete accelerator.

Effect of phase interactions on crystal stress evolution over crystal orientation space under elastoplastic deformation of two-phase polycrystalline solids

It has been known for decades that crystal stress directions move toward the vertices of the single crystal yield surface (SCYS) during plastic flow of polycrystalline solids to satisfy the deformation compatibility among crystals. The alignment of crystal stress with a SCYS vertex is affected not only by plastic anisotropy, but also by other factors such as elastic anisotropy, loading direction, and grain interactions. Among the factors contributing to the degree of alignment, the effect of phase interactions on the crystal stress evolution during plastic flow has not been extensively investigated. In this research, the effect of phase interactions on the crystal stress direction evolution is investigated using simulations of an elastoplastically deforming two-phase (Cu/Fe) polycrystalline solid calibrated to a neutron diffraction experiment. By mapping the simulated crystal stresses over the crystal orientation space, crystal-orientation-dependent nonuniform partitioning of the crystal stress between phases can be observed. An analysis of the distribution of angles between the SCYS vertex and the crystal stress based on the simulation of the two-phase material shows that the crystal stress evolution pattern during plastic flow is strongly affected by phase interactions. These interactions result in low alignment and greater dispersion angles between the crystal stresses and SCYS vertices, particularly in the strong phase.

An improved multiple-attractor cellular automata classifier with a tree frame based on CART

From the view of a cell, the partition of a pattern space is a uniform partition. It is difficult to meet the needs of spatial non-uniform partitioning. In this paper, a cellular automaton classifier with a tree structure is proposed, by combining multiple-attractor cellular automata with the algorithm CART. The method of construction of the characteristic matrix of the multiple-attractor cellular automata is studied on the basis of particle swarm optimization. This method builds multiple-attractor cellular automata as tree nodes. This kind of classifier can be used to solve the non-uniform partition problem and obtain a good classification performance by using a pseudo-exhaustive field with a few bits, and so can restrain the over-fitting. The feasibility and the effectiveness of this method have been verified by experiments.

Data size reduction with symbolic aggregate approximation for electrical load pattern grouping

Data size reduction techniques may be helpful in the process of categorising the electrical load consumption patterns on the basis of their shape. Starting from a macro-class of consumers defined according to certain general criteria on the type of consumers and the period of the year or week, the representative load pattern (RLP) of each consumer can be built by considering the data points in the time domain or a reduced number of features. This study exploits the effects of using the symbolic aggregate approximation (SAX) method to form the reduced set of features. The portion of the time–amplitude plane defining the RLP is partitioned into sub-portions on the basis of the characteristics of the whole data set. A specific partitioning of the time axis is proposed on the basis of the cumulative distribution function of the RLP variations in time. Each RLP is then coded according to the SAX principles. The resulting codes are then used into a hierarchical clustering procedure. The validity of the clustering results obtained by using the SAX data representation with the proposed non-uniform partitioning of the time axis is presented and discussed, including comparisons with the results obtained from other data size reduction techniques.

An Improved Keyframe Extraction Method Based on HSV Colour Space

Video segmentation and keyframe extraction are the basis of Content-based Video Retrieval (CBVR), in which keyframe selection is at the very core of CBVR. At shot level, key-frame extraction provides sufficient indexing and browsing of large video databases. In this paper, we proposed two improved approaches of key-frame extraction for video summarization. In our first synthesis method based on histogram-based method and pixel-based method, videos were firstly segmented into shots according to video content, by our improved histogram-based method, with the use of histogram intersection and nonuniform partitioning and weighting. Then, the obtained results are secondly detected to optimize the results. On the other hand, we realized an improved clustering algorithm for video shot segmentation, in consideration of video characteristics. Within each shot, key-frames were determined with the calculation of image entropy of every frame in HSV colour space. Our simulation results in section 4 prove that extracted key frames with our method are compact and faithful to the original video. Moreover, according to the types of test videos, different methods for shot segmentation are highly recommended.

New Delay-Interval-Dependent Exponential Stability for Stochastic Neural Networks with Interval Time-Varying Delay and Distributed Delay

This paper deals with the problem of exponential stability for a class of stochastic neural networks with interval time-varying delay and distributed delay. Based on the idea of nonuniform partitioning for the delay interval, new delay-interval-dependent stability conditions are proposed in terms of linear matrix inequalities (LMIs) by constructing novel Augmented Lyapunov–Krasovskii functionals. Some numerical examples are presented to show the effectiveness and improvement of the proposed method.