Orthogonal Blocks Research Articles

Graph-Based Joint User-Centric Overlapped Clustering and Resource Allocation in Ultradense Networks

With the increase of access point (AP) density and the exponential growth of mobile devices supported by ultradense networks (UDNs), user-centric overlapped clustering relying on AP cooperation is becoming a promising design principle for guaranteeing the quality of service (QoS) required by each user equipment. This ambitious goal can be achieved by the joint design of user-centric overlapped clustering and resource allocation. In this context, both the traffic-load balancing and the limited availability of orthogonal resource blocks (RBs) have to be carefully considered in UDNs. To tackle these challenges, we formulate a joint user-centric overlapped clustering and resource allocation problem with the goal of maximizing the system's spectral efficiency. To efficiently solve this problem, it is decoupled into two subproblems, which can be solved independently with the aid of our graph–theoretical framework. We first develop a novel distributed three-stage user-centric clustering solution, which is aware of the APs’ traffic-loads. Then, based on the overlapped clusters constructed, we propose a novel two-stage graph-based user-centric resource allocation scheme for mitigating the resultant inter-cluster interference, despite the limited availability of orthogonal RBs. Our numerical results confirm the benefits of the proposed framework and show that it outperforms the benchmark solutions in terms of both its per area aggregated user rate and user rate.

Symmetry breaking in mixed integer linear programming formulations for blocking two-level orthogonal experimental designs

Two-level orthogonal designs play an important role in industrial screening experiments, in which the primary goal is to identify the treatment factors with the largest main effects on the output of a process or the performance of a product. Often, the experimental tests suggested by the orthogonal designs cannot be performed on a single day or using a single batch of raw material. This causes day-to-day or batch-to-batch variation in the experimental results, and necessitates the use of orthogonal blocking patterns. These blocking patterns ensure that the factors’ main effects can be estimated independently from the day-to-day or batch-to-batch variation. Finding an optimal orthogonal blocking pattern for an orthogonal design is a major challenge. Recently, mixed integer linear programming has been used for that purpose. While this approach is promising, computational experiments have indicated it is quite slow. We show how to speed up the mixed integer linear programming approach by adding symmetry breaking constraints to the formulation, and study the usefulness of an asymmetric representatives formulation. In other words, we introduce state-of-the-art symmetry breaking approaches in optimal experimental design. We perform extensive computational experiments to test which combinations of symmetry breaking constraints work best. Throughout, we consider two kinds of symmetry: symmetry due to the fact that the blocks can be relabeled without affecting the quality of the blocking pattern, and symmetry due to replicated test combinations.

Cluster‐based resource allocation scheme with QoS guarantee in ultra‐dense networks

Ultra-dense networks (UDN) can provide extremely high throughput and data rate. However, there are severe interference due to dense and random deployment of femto base stations (FBSs). To mitigate interference and allocate network resource efficiently while ensuring quality of service (QoS) of user equipments (UEs), a cluster-based resource allocation scheme for UDN is proposed in this paper. Two stages, clustering and resource allocation, are involved in the scheme. In clustering stage, a modified K-means clustering algorithm is advanced to divide FBSs into different disjoint clusters dynamically according to the density of FBSs. Thus the number of clusters can be adjusted flexibly to fit for the dynamic network topology. In resource allocation stage, a greedy-based compensatory resource allocation algorithm (GCRAA) is further proposed to maximize the throughput of UDN. Herein the orthogonal resource blocks (RBs) are initially assigned among the UEs with a greedy algorithm. In order to ensure the fairness and QoS of UEs, a compensatory resource allocation algorithm is further proposed to allocate the remaining RBs. The simulated results show that the proposed resource allocation scheme can mitigate the interference in UDN effectively, and improve the system throughput while ensuring the QoS for UEs.

Arylboronate Ester Protected Amino Acids as Orthogonal Building Blocks for Fmoc Solid‐Phase Peptide Synthesis

Three new arylboronate ester protected amino acids and their on‐resin deprotection methods have been developed. These useful building blocks were found to exhibit favorable chemical properties that are fully compatible with Fmoc strategy solid‐phase peptide synthesis. Furthermore, the formation of over‐oxidation side‐product methionine was minimized by using N‐methyl‐N‐phenylaniline N‐oxide as the oxidizing reagent. Effective application of the three new amino acids for the synthesis of different types of peptidomimetics has been demonstrated by high‐quality preparation of lipidated peptide MP‐196 C‐C8, on‐resin head‐to‐tail cyclization of desotamide B, and lactam bridging of hPTHrP‐(11–19) through a facile and metal‐free procedure by standard Fmoc solid‐phase peptide synthesis.

Performance evaluation of an adaptive self-organizing frequency reuse approach for OFDMA downlink

Orthogonal frequency division multiple access (OFDMA) is extensively utilized for the downlink of cellular systems such as long term evolution (LTE) and LTE advanced. In OFDMA cellular networks, orthogonal resource blocks can be used within each cell. However, the available resources are rare and so those resources have to be reused by adjacent cells in order to achieve high spectral efficiency. This leads to inter-cell interference (ICI). Thus, ICI coordination among neighboring cells is very important for the performance improvement of cellular systems. Fractional frequency reuse (FFR) has been widely adopted as an effective solution that improves the throughput performance of cell edge users. However, FFR does not account for the varying nature of the channel. Moreover, it exaggerates in caring about the cell edge users at the price of cell inner users. Therefore, effective frequency reuse approaches that consider the weak points of FFR should be considered. In this paper, we present an adaptive self-organizing frequency reuse approach that is based on dividing every cell into two regions, namely, cell-inner and cell-outer regions; and minimizing the total interference encountered by all users in every region. Unlike the traditional FFR schemes, the proposed approach adjusts itself to the varying nature of the wireless channel. Furthermore, we derive the optimal value of the inner radius at which the total throughput of the inner users of the home cell is as close as possible to the total throughput of its outer users. Simulation results show that the proposed adaptive approach has better total throughput of both home cell and all 19 cells than the counterparts of strict FFR, even when all cells are fully loaded, where other algorithms in the literature failed to outperform strict FFR. The improved throughput means that higher spectral efficiency can be achieved; i.e., the spectrum, which is the most precious resource in wireless communication, can be utilized efficiently. In addition, the proposed algorithm can provide significant power saving, that can reach 50% compared to strict FFR, while not penalizing the throughput performance.

Projected mixture designs based on weighing matrices

Prescott (2000) has used augmented pair designs for the projection of response surface designs onto the mixture space and obtained orthogonally blocked designs. Singh (2003) used the Darroch and Waller quadratic model to construct orthogonal designs in two blocks for three and four components. In this paper, we have used quantitative screening designs based on weighing matrices to obtain mixture designs by the method of projection. These mixture designs have been further compared on the basis of uniformity and optimality criteria. Orthogonal blocking of the projected mixture designs has also been presented.

Projected mixture designs based on weighing matrices

Prescott (2000) has used augmented pair designs for the projection of response surface designs onto the mixture space and obtained orthogonally blocked designs. Singh (2003) used the Darroch and Waller quadratic model to construct orthogonal designs in two blocks for three and four components. In this paper, we have used quantitative screening designs based on weighing matrices to obtain mixture designs by the method of projection. These mixture designs have been further compared on the basis of uniformity and optimality criteria. Orthogonal blocking of the projected mixture designs has also been presented.

Mixture designs with orthogonal blocks

ABSTRACTConstructions of blocked mixture designs are considered in situations where BLUEs of the block effect contrasts are orthogonal to the BLUEs of the regression coefficients. Orthogonal arrays (OA), Balanced Arrays (BAs), incidence matrices of balanced incomplete block designs (BIBDs), and partially balanced incomplete block designs (PBIBDs) are used. Designs with equal and unequal block sizes are considered. Also both cases where the constants involved in the orthogonality conditions depend and do not depend on the factors have been taken into account. Some standard (already available) designs can be obtained as particular cases of the designs proposed here.

Evaluation of Orthogonally Blocked Central Composite Designs with Partial Replications

In this work, the orthogonal blocking of the central composite designs is evaluated by considering various equal and unequal replications of the centre point in the factorial (cube) and axial (star) blocks. The A-, D- and G-efficiencies as well as the V-criterion are the single-value design criteria used to examine the prediction performances of the designs. The fraction of design space plot is the graphical method used to display the prediction variance characteristics of these designs throughout the entire design space. The cube and star portions are also replicated to enhance the performance of the designs. The results show that higher and equal replication of the centre points in the blocks as well as more centre points in the star blocks than the cube blocks improve the prediction capabilities of the orthogonally blocked CCD in spherical region.

F-Square Based Four Component D-, A- and E-Optimal Orthogonal Designs for an Additive Quadratic Mixture Model

Orthogonal block designs for Scheffe’s quadratic model have been considered previously by John (Experiments with mixture involving process variables, Technical Report 8, Centre for Statistical Sciences, University of Texas, Austin, TX, 1–17, 1984), Czitrom (Commun Stat Theory Methods 17:105–121, 1988, 18:4561–4581, 1989), Draper et al. (Technometrics 35:268–276, 1993) and Prescott et al. (J Appl Stat 20(1):268–276, 1993). In this paper, we have considered the case of equal volume fractions and have constructed optimal orthogonal designs in two blocks based on F-squares for an additive quadratic mixture model in four components. We have obtained D-, A- and E-optimal orthogonally blocked designs in two blocks for four components when two of the four components are at the same level of mixture composition.

Tethering of Epidermal Growth Factor (EGF) to Beta Tricalcium Phosphate (βTCP) via Fusion to a High Affinity, Multimeric βTCP-Binding Peptide: Effects on Human Multipotent Stromal Cells/Connective Tissue Progenitors.

Transplantation of freshly-aspirated autologous bone marrow, together with a scaffold, is a promising clinical alternative to harvest and transplantation of autologous bone for treatment of large defects. However, survival proliferation, and osteogenic differentiation of the marrow-resident stem and progenitor cells with osteogenic potential can be limited in large defects by the inflammatory microenvironment. Previous studies using EGF tethered to synthetic polymer substrates have demonstrated that surface-tethered EGF can protect human bone marrow-derived osteogenic stem and progenitor cells from pro-death inflammatory cues and enhance their proliferation without detriment to subsequent osteogenic differentiation. The objective of this study was to identify a facile means of tethering EGF to clinically-relevant βTCP scaffolds and to demonstrate the bioactivity of EGF tethered to βTCP using stimulation of the proliferative response of human bone-marrow derived mesenchymal stem cells (hBMSC) as a phenotypic metric. We used a phage display library and panned against βTCP and composites of βTCP with a degradable polyester biomaterial, together with orthogonal blocking schemes, to identify a 12-amino acid consensus binding peptide sequence, LLADTTHHRPWT, with high affinity for βTCP. When a single copy of this βTCP-binding peptide sequence was fused to EGF via a flexible peptide tether domain and expressed recombinantly in E. coli together with a maltose-binding domain to aid purification, the resulting fusion protein exhibited modest affinity for βTCP. However, a fusion protein containing a linear concatamer containing 10 repeats of the binding motif the resulting fusion protein showed high affinity stable binding to βTCP, with only 25% of the protein released after 7 days at 37oC. The fusion protein was bioactive, as assessed by its abilities to activate kinase signaling pathways downstream of the EGF receptor when presented in soluble form, and to enhance the proliferation of hBMSC when presented in tethered form on commercial βTCP bone regeneration scaffolds.

Optimal orthogonal designs in two blocks based on F-squares for mixture inverse model in four components

Orthogonal block designs for Scheffes quadratic model in three and four components have been considered by John (1984), Czitrom (1988, 1989), Draper et al. (1993), Chan and Sandhu (1999), and Ghosh and Liu (1999). Singh (2003) considered optimal orthogonal designs in two blocks for Darroch and Waller's quadratic mixture model in three and four components. Aggarwal et al. (2009) have studied mixture designs in orthogonal blocks using F-squares. A mixtures model with inverse terms was presented by Draper and St. John (1977). In this paper, we have constructed optimal orthogonal designs in two blocks based on F-squares for a mixture inverse model in four components with two component proportions at the same level. Conditions required for orthogonality are also given.

A new method of multi-scale geologic modeling and display

A new method of multi-scale modeling and display of geologic data is introduced to pro- vide information with appropriate detail levels for different types of research. The multi-scale display mode employs a model extending existing 2D methods into 3D space. Geologic models with different scales are organized by segmenting data into orthogonal blocks. A flow diagram illustrates an octree method for upscaling between blocks with different scales. Upscaling data from the smallest unit cells takes into account their average size and the Burgers vector when there are mismatches. A geocellular model of the Chengdao Reservoir of the Shengli Oilfield, China is taken as an illustrative case, showing that the methods proposed can construct a multi-scale geologic model correctly and display data from the multi-scale model effectively in 3D.

Selection of nearly orthogonal blocks in ‘ad-hoc’ experimental designs

The problem of blocking experimental designs is addressed, for both factorial type designs and response surface designs (i.e. for discrete and continuous experimental domains).The focus is to arrange block as orthogonally as possible. To measure the uncorrelatedness between the block and the coefficient estimates, we use directly the corresponding covariance factors.Nevertheless, the blocking of the design may change the variance and covariance of estimates of the remaining coefficients. To take into account this effect, we add the D-criterion to the covariance factors when looking for a design.This defines a multicriteria problem that should be tackled as such because some of the case-studies show that a sequential approach (first to look for a D-optimal design and then block it) leads to designs which are not even D-optimal.With a genetic algorithm, the Pareto-optimal front of the competing criteria is estimated, with the aim of helping in the decision about the design to choose.

Small Box–Behnken designs with orthogonal blocks

Abstract A new method of constructing 3-level second-order designs using incomplete block designs with unequal block sizes is suggested to any number of factors. The method gives orthogonally blocked designs with small run sizes, high D -efficiencies and rotatability measures.

Small Three-Level Second-Order Designs With Orthogonal Blocks

Using suitable incomplete block designs with block size three, orthogonally blocked three-level second-order designs are proposed. These designs have reasonably high D-efficiencies and are often much smaller than the existing designs, in terms of block size and/or the total number of points.

Optimal orthogonal block designs for four-mixture components in two blocks based on F-squares for Becker's models and K-model

Orthogonal block designs in mixture experiments have been extensively studied by various authors. Aggarwal et al. [M.L. Aggarwal, P. Singh, V. Sarin, and B. Husain, Mixture designs in orthogonal blocks using F-squares, METRON – Int. J. Statist. LXVII(2) (2009), pp. 105–128] considered the case of components assuming the same volume fractions and obtained mixture designs in orthogonal blocks using F-squares. In this paper, we have used the class of designs presented by Aggarwal et al. and have obtained D-, A- and E-optimal orthogonal block designs for four components in two blocks for Becker's mixture models and K-model, respectively. Orthogonality conditions for the considered models are also given.

Multilevel dimensionality-reduction methods

When data sets are multilevel (group nesting or repeated measures), different sources of variations must be identified. In the framework of unsupervised analyses, multilevel simultaneous component analysis (MSCA) has recently been proposed as the most satisfactory option for analyzing multilevel data. MSCA estimates submodels for the different levels in data and thereby separates the “within”-subject and “between”-subject variations in the variables. Following the principles of MSCA and the strategy of decomposing the available data matrix into orthogonal blocks, and taking into account the between- and the within data structures, we generalize, in a multilevel perspective, multivariate models in which a matrix of response variables can be used to guide the projections (formed by responses predicted by explanatory variables or by a limited number of their combinations/composites) into choices of meaningful directions. To this end, the current paper proposes the multilevel version of the multivariate regression model and dimensionality-reduction methods (used to predict responses with fewer linear composites of explanatory variables). The principle findings of the study are that the minimization of the loss functions related to multivariate regression, principal-component regression, reduced-rank regression, and canonical-correlation regression are equivalent to the separate minimization of the sum of two separate loss functions corresponding to the between and within structures, under some constraints. The paper closes with a case study of an application focusing on the relationships between mental health severity and the intensity of care in the Lombardy region mental health system.

Innovative green supercritical fluid chromatography development for the determination of polar compounds

In the context of green analytical chemistry, a supercritical fluid chromatography method was developed. In order to prove the potential of this technology, a worst case was selected, i.e. the separation of very polar compounds. For that purpose, an innovative methodology based on design of experiments (DoE) and design space (DS) was previously developed and successfully tested on liquid chromatography. For the first time, this methodology was applied to a supercritical fluid chromatography (SFC) separation. First, a screening design was used to select the stationary phase and the nature of the mobile phase based on a maximization of the number of peaks eluted and a minimization of the number of co-eluted peaks. Then, a central composite design with orthogonal blocks defined a set of experiments used to model the retention times of each peak at the beginning, the apex, and the end. The gradient slope, the isocratic plateau before the gradient, the temperature, and the concentration of trifluoroacetic acid (TFA) in the mobile phase were the potentially influential factors. The critical quality attributes (CQAs), i.e. the separation (S) between peaks of the most critical pair, and the analysis time were the criteria considered to assess the quality of the separation. The DS was computed as the multidimensional subspace where the probability for the separation and analysis time criteria to be within acceptance limits was higher than a defined quality level. The DS was computed propagating the prediction error from the modeled responses to the quality criterion using Monte Carlo simulations. The optimal condition was predicted at a gradient slope of 3.8% min−1 to linearly modify the modifier proportion between 5 and 40%, an isocratic time of 3min, a concentration of TFA of 25mM, and a temperature of 60.5°C. This optimal condition was experimentally tested to confirm the prediction. Furthermore, chromatographic conditions included in the DS and on the limits of the DS were experimentally tested to assess the robustness of the developed SFC method.

Orthogonally blocked mixture component–amount designs via projections of F-squares

Orthogonal block designs for Scheffé’s quadratic model have been considered previously by Draper et al. (1993), John (1984), Lewis et al. (1994) and Prescott, Draper, Dean, and Lewis (1993). Prescott and Draper (2004) obtained mixture component–amount designs via projections of standard mixture designs, viz., the simplex-lattice, the simplex-centroid and the orthogonally blocked mixture designs based on latin squares. Aggarwal, Singh, Sarin, and Husain (2009) considered the case of components assuming equal volume fractions and obtained mixture designs in orthogonal blocks using F-squares. In this paper, we construct orthogonal blocks of two and three mixture component–amount blends by projecting the class of four component mixture designs presented by Aggarwal et al. (2009).