Unequal Sizes Research Articles

Capacity-Achieving Private Information Retrieval Schemes From Uncoded Storage Constrained Servers With Low Sub-Packetization

This paper investigates reducing sub-packetization of capacity-achieving schemes for uncoded Storage Constrained Private Information Retrieval (SC-PIR) systems. In the SC-PIR system, a user aims to download one out of K files from N servers while revealing nothing about the identity of the requested file to any individual server, in which the K files are stored at the N servers in an uncoded form and each server can store up to μK equivalent files, where μ is the normalized storage capacity of each server. We first prove that there exists a capacity-achieving SC-PIR scheme for a given storage design if and only if all the packets are stored exactly at M\triangleq μN servers for μ such that M=μN ∈ {2,3,...,N}. Then, the optimal sub-packetization for capacity-achieving linear SC-PIR schemes is characterized as the solution to an optimization problem, which is typically hard to solve since it involves non-continuous indicator functions. Moreover, a new notion of array called Storage Design Array (SDA) is introduced for the SC-PIR system. With any given SDA, an associated capacity-achieving SC-PIR scheme is constructed. Next, the SC-PIR schemes that have equal-size packets are investigated. Furthermore, the optimal equal-size sub-packetization among all capacity-achieving linear SC-PIR schemes characterized by Woolsey et al. is proved to be \frac N(M-1)gcd(N,M), which is achieved by a construction of SDA. Finally, by allowing unequal size of packets, a greedy SDA construction is proposed, where the sub-packetization of the associated SC-PIR scheme is upper bounded by \frac N(M-1)gcd(N,M). Among all capacity-achieving linear SC-PIR schemes, the sub-packetization is optimal when min{M,N-M}|N or M=N, and within a multiplicative gap \frac min{M,N-M}gcd(N,M) of the optimal one in general. In particular, for the special case N=d·M±1 where the positive integer d ≥ 2, we propose another SDA construction to obtain lower sub-packetization.

Methods for dealing with unequal cluster sizes in cluster randomized trials: A scoping review.

In a cluster-randomized trial (CRT), the number of participants enrolled often varies across clusters. This variation should be considered during both trial design and data analysis to ensure statistical performance goals are achieved. Most methodological literature on the CRT design has assumed equal cluster sizes. This scoping review focuses on methodology for unequal cluster size CRTs. EMBASE, Medline, Google Scholar, MathSciNet and Web of Science databases were searched to identify English-language articles reporting on methodology for unequal cluster size CRTs published until March 2021. We extracted data on the focus of the paper (power calculation, Type I error etc.), the type of CRT, the type and the range of parameter values investigated (number of clusters, mean cluster size, cluster size coefficient of variation, intra-cluster correlation coefficient, etc.), and the main conclusions. Seventy-nine of 5032 identified papers met the inclusion criteria. Papers primarily focused on the parallel-arm CRT (p-CRT, n = 60, 76%) and the stepped-wedge CRT (n = 14, 18%). Roughly 75% of the papers addressed trial design issues (sample size/power calculation) while 25% focused on analysis considerations (Type I error, bias, etc.). The ranges of parameter values explored varied substantially across different studies. Methods for accounting for unequal cluster sizes in the p-CRT have been investigated extensively for Gaussian and binary outcomes. Synthesizing the findings of these works is difficult as the magnitude of impact of the unequal cluster sizes varies substantially across the combinations and ranges of input parameters. Limited investigations have been done for other combinations of a CRT design by outcome type, particularly methodology involving binary outcomes-the most commonly used type of primary outcome in trials. The paucity of methodological papers outside of the p-CRT with Gaussian or binary outcomes highlights the need for further methodological development to fill the gaps.

Optimal design of cluster randomized trials allowing unequal allocation of clusters and unequal cluster size between arms.

There are sometimes cost, scientific, or logistical reasons to allocate individuals unequally in an individually randomized trial. In cluster randomized trials we can allocate clusters unequally and/or allow different cluster size between trial arms. We consider parallel group designs with a continuous outcome, and optimal designs that require the smallest number of individuals to be measured given the number of clusters. Previous authors have derived the optimal allocation ratio for clusters under different variance and/or intracluster correlations (ICCs) between arms, allowing different but prespecified cluster sizes by arm. We derive closed-form expressions to identify the optimal proportions of clusters and of individuals measured for each arm, thereby defining optimal cluster sizes, when cluster size can be chosen freely. When ICCs differ between arms but the variance is equal, the optimal design allocates more than half the clusters to the arm with the higher ICC, but (typically only slightly) less than half the individuals and hence a smaller cluster size. We also describe optimal design under constraints on the number of clusters or cluster size in one or both arms. This methodology allows trialists to consider a range for the number of clusters in the trial and for each to identify the optimal design. Except if there is clear prior evidence for the ICC and variance by arm, a range of values will need to be considered. Researchers should choose a design with adequate power across the range, while also keeping enough clusters in each arm to permit the intended analysis method.

Measure of Slope Rotatability for Second Order Response Surface Designs Under Tri-Diagonal Correlation Error Structure Using Symmetrical Unequal Block Arrangements with Two Unequal Block Sizes

In this paper, measure of slope rotatability for second order response surface designs using symmetrical unequal block arrangements with two unequal block sizes under tri-diagonal correlation error structure is suggested and illustrated with examples.

Design a Hybrid FPGA Architecture for Visible Digital Image Watermarking in Spatial and Frequency Domain

Hybrid field programmable gate array (FPGA) implementation is proposed to improve the performance of visible image watermarking systems. The visible watermarking process is implemented as pixel by pixel operation under a spatial domain or vector operation in the frequency domain. The proposed approach is mainly designed for watermarking the images taken from digital cameras of various sizes. The padding technique is used for unequal sizes of the watermark image and original host image. The architecture data path consists of eight and six stages of pipeline capable of watermarking on the pixel-based operation and vector-based operation, respectively. The dual image watermarking architecture data path consists of a 13-stage pipeline. Pipeline and parallelism mechanisms are used to improve throughput. To improve the performance in discrete cosine transform operations at the frequency domain, the shift-add technique replaces the conventional multipliers. The clock gating technique is employed to reduce the power by preventing unnecessary switching in a path. Hardware implementation of the algorithm is tested in Intel Cyclone FPGA with the device of EP4CGX22CF19C6, with which the throughput achieved is 1.27[Formula: see text]Gbits/s with a total area utilization of 35[Formula: see text]digital signal processing (DSP) blocks, 378 look-up tables (LUTs) and 486 registers.

Kant’s Mereological Account of Greater and Lesser Actual Infinities

Abstract Recent work on Kant’s conception of space has largely put to rest the view that Kant is hostile to actual infinity. Far from limiting our cognition to quantities that are finite or merely potentially infinite, Kant characterizes the ground of all spatial representation as an actually infinite magnitude. I advance this reevaluation a step further by arguing that Kant judges some actual infinities to be greater than others: he claims, for instance, that an infinity of miles is strictly smaller than an infinity of earth-diameters. This inequality follows from Kant’s mereological conception of magnitudes (quanta): the part is (analytically) less than the whole, and an infinity of miles is equal to only a part of an infinity of earth-diameters. This inequality does not, however, imply that Kant’s infinities have transfinite and unequal sizes (quantitates). Because Kant’s conception of size (quantitas) is based on the Eudoxian theory of proportions, infinite magnitudes (quanta) cannot be assigned exact sizes. Infinite magnitudes are immeasurable, but some are greater than others.

CRTpowerdist: An R package to calculate attained power and construct the power distribution for cross-sectional stepped-wedge and parallel cluster randomized trials

BackgroundThe attained power, calculated conditional on the realized allocation, of a clinical trial may differ from the expected power, obtained pre-randomization through averaging over all potential allocations that could be generated by the randomization algorithm (RA). For example, a two-arm trial using a RA that is expected to allocate 20 participants to each arm will attain less than the expected power if by chance it allocates 25 and 15 participants to the arms. Cluster randomized trials with unequal cluster sizes have elevated risk of realizing an allocation that yields an attained power much lower than the expected power when modest numbers of clusters are randomized. MethodWe developed the R package CRTpowerdist, which implements both simulations and approximate analytic formulae to calculate the attained powers associated with different realized allocations and constructs the pre-randomization power distribution associated with the RA to facilitate assessing the risk of obtaining inadequate power. The package covers unequal cluster-size, cross-sectional stepped-wedge and parallel cluster randomized trials, with or without stratification. Allowed outcome types are: continuous (Gaussian), binary (Binomial) and count (Poisson). The analytic formulae-based calculations are also implemented in a Shiny app. ResultsThe functionality of the CRTpowerdist is illustrated for each type of trial design. The examples show how to obtain the attained power, the power distribution, and the risk of low attained power, using both simulation and analytic formulae. ConclusionFor cluster randomized trials with unequal cluster sizes, the CRTpowerdist package can assist users in identifying an appropriate randomization algorithm by enabling the user to assess the risk that a randomization algorithm will lead to an allocation with inadequate attained power. The Shiny app makes these assessments accessible to researchers who are unable or do not wish to use the CRTpowerdist package.

Constraining PERMANOVA and LDM to within-set comparisons by projection improves the efficiency of analyses of matched sets of microbiome data

BackgroundMatched-set data arise frequently in microbiome studies. For example, we may collect pre- and post-treatment samples from a set of individuals, or use important confounding variables to match data from case participants to one or more control participants. Thus, there is a need for statistical methods for data comprised of matched sets, to test hypotheses against traits of interest (e.g., clinical outcomes or environmental factors) at the community level and/or the operational taxonomic unit (OTU) level. Optimally, these methods should accommodate complex data such as those with unequal sample sizes across sets, confounders varying within sets, and continuous traits of interest.MethodsPERMANOVA is a commonly used distance-based method for testing hypotheses at the community level. We have also developed the linear decomposition model (LDM) that unifies the community-level and OTU-level tests into one framework. Here we present a new strategy that can be used with both PERMANOVA and the LDM for analyzing matched-set data. We propose to include an indicator variable for each set as covariates, so as to constrain comparisons between samples within a set, and also permute traits within each set, which can account for exchangeable sample correlations. The flexible nature of PERMANOVA and the LDM allows discrete or continuous traits or interactions to be tested, within-set confounders to be adjusted, and unbalanced data to be fully exploited.ResultsOur simulations indicate that our proposed strategy outperformed alternative strategies, including the commonly used one that utilizes restricted permutation only, in a wide range of scenarios. Using simulation, we also explored optimal designs for matched-set studies. The flexibility of PERMANOVA and the LDM for a variety of matched-set microbiome data is illustrated by the analysis of data from two real studies.ConclusionsIncluding set indicator variables and permuting within sets when analyzing matched-set data with PERMANOVA or the LDM is a strategy that performs well and is capable of handling the complex data structures that frequently occur in microbiome studies.3i1UxvTTxBo8cNUR6xzMG1Video

Reevaluating the SIBTEST Classification Heuristics for Dichotomous Differential Item Functioning.

A simulation study was conducted to investigate the heuristics of the SIBTEST procedure and how it compares with ETS classification guidelines used with the Mantel-Haenszel procedure. Prior heuristics have been used for nearly 25 years, but they are based on a simulation study that was restricted due to computer limitations and that modeled item parameters from estimates of ACT and ASVAB tests from 1987 and 1984, respectively. Further, suggested heuristics for data fitting a two-parameter logistic model (2PL) have essentially went unused since their original presentation. This simulation study incorporates a wide range of data conditions to recommend heuristics for both 2PL and three-parameter logistic (3PL) data that correspond with ETS's Mantel-Haenszel heuristics. Levels of agreement between the new SIBTEST heuristics and Mantel-Haenszel heuristics were similar for 2PL data and higher than prior SIBTEST heuristics for 3PL data. The new recommendations provide higher true-positive rates for 2PL data. Conversely, they displayed decreased true-positive rates for 3PL data. False-positive rates, overall, remained below the level of significance for the new heuristics. Unequal group sizes resulted in slightly larger false-positive rates than balanced designs for both prior and new SIBTEST heuristics, with rates less than alpha levels for equal ability distributions and unbalanced designs versus false-positive rates slightly higher than alpha with unequal ability distributions and unbalanced designs.

A Monte Carlo Simulation Study on the Influence of Unequal Group Sizes on Parameter Estimation in Multilevel Confirmatory Factor Analysis

ABSTRACT Unequal group sizes (imbalance) and small sample sizes are common in multilevel confirmatory factor analyses (ML-CFA). This simulation study examined the influence of imbalance combined with small sample sizes on both levels on estimation performance in ML-CFA. Imbalance did not influence estimation performance given the minimum sample size requirements. Greater sample sizes on one level compensated for smaller sample sizes on the respective other level. Additionally, the degree of intraclass correlation () interacted with sample sizes. Based on the results of the simulation study, recommendations for practical applications are delineated. For instance, at least 100 Level-2 units with an average cluster size of four or 150 Level-2 units with an average cluster size of two are recommended given an of .30 or above.

Rodent Species Diversity and Occurrence of Leishmania in Northeastern Iran

The aim of the current study was to survey the species diversity and Leishmania infection of rodents in the Gonbad -e- Kavoos City and County, northeastern Iran, during 2018–2019. Totally, 20 rural and four urban areas endemic for leishmaniasis were selected and visited monthly. Rodent species diversity indices were calculated in different spatial and temporal scales. Species richness was also calculated using rarefaction curves to estimate the number of species in unequal sample sizes. A total of 167 rodents belonging to 7 species, 6 genera, and 2 families were collected. Rattus rattus (34.7%) and Rattus norvegicus (18.6%) were identified as dominant species. The largest Margalef and Menhinick species richness (DMg = 1.55; DMn = 1.01) and the highest value of the Shannon index (H′ = 1.71) were observed in rural areas. Seasonal abundance of the rodents varied among species and showed that the highest richness (DMg = 1.27; DMn = 0.65) occurred in spring and the highest value of Shannon index (H′ = 1.72) was noted in summer. Rarefaction curves confirmed that the highest species richness occurred in summer and spring in the rural area. Seasonal fluctuations of R. rattus and R. norvegicus have a significant impact on the changes in rodent species diversity. Investigations of Leishmania infection showed that amastigote forms of Leishmania were observed in 15.4% of smears taken from Rhombomys opimus and Meriones libycus and examined under the light microscope. The highest rate of Leishmania infection was observed during the summer.

Brand familiarity vs profit-sharing rate: which has a stronger impact on Muslim customers’ intention to invest in an Islamic bank?

PurposeThe purpose of this study is to examine the impact of brand familiarity and profit-sharing rate on Muslim customers’ brand trust, perceived financial risk, perceived value and intention to invest in an Islamic bank.Design/methodology/approachA between-subjects experimental design was applied in the study. Six experiments involving two brand familiarity levels and three profit-sharing rates were conducted using a total of 217 samples. Randomization was applied in the study, which generated unequal sample sizes for each group of experiments.FindingsThe findings of this experimental study demonstrated that Muslim customers’ familiarity with the bank’s brand has a significant impact on their brand trust and intention to invest in an Islamic bank. The study also found that the profit-sharing rate has a significant impact on the perceived value both with and without interaction with brand familiarity.Research limitations/implicationsThe current study applies an independent measured design or a between-subjects experimental design, that resulted in unequal sample sizes. In addition, the study also does not control for the types of bank accounts owned by respondents. The design may invite the presence of confounding variables that exist due to individual differences and environmental variables.Practical implicationsThe results show that Islamic bank managers should care about the brand familiarity issue, which strongly influences customers’ brand trust and customer intention to invest in an Islamic bank. In addition, Islamic bank managers should pay attention to the profit-sharing rate given to customers, as it interacts with brand familiarity in influencing customers’ perceived value.Originality/valueThis study examined the impact of brand familiarity and profit-sharing rate on Muslim consumers’ brand trust, perceived risk, perceived value and intention to save in an Islamic bank. The paper provides a shred of empirical evidence to the theoretical relationship between the subjective and objective cues that influence the formation of customers’ trust, perceived financial risk, perceived value and intention in the Islamic bank context.

A Dual stopband two-sided frequency selective surface for mobile shielding applications

A two-sided frequency selective surface (FSS) is proposed to shield two bands of the mobile frequencies (EGSM-900 and DCS-1800). The FSS consists of an array of square concentric-rings cells printed on both sides of the substrate to offer better shielding of the two mobile frequencies. The CST Microwave suit is used for the simulations. The equivalent circuit model for the two-sided FSS is analysed and the transmission frequency in terms of the two stop frequencies is estimated. The obtained shielding is better than 40 dB across the two bands. The proposed FSS can be used to reduce mobile radiation or to isolate halls from nearby mobile base stations. The bandwidth of the FSS cell can be increased by using ring pairs of unequal sizes on the two sides of the substrate.

Introduction to Bayesian methods

The concepts of Bayesian analysis are introduced by discussing a 2 × 2 confusion matrix with unequal sample sizes for each class.

A hybridization strategy using equal and unequal clustering schemes to mitigate idle listening for lifetime maximization of wireless sensor network

The main focus in the designing of wireless sensor networks (WSNs) applications and protocols is minimizing energy dissipation while at the same time maximizing the network lifetime. In this paper, we investigate the idle listening and hotspot problems with respect to the clustering routing technique in WSNs. Some of the studies in clustering centered around equal clustering scheme while others were based on unequal clustering scheme. Equal clustering scheme avoids inter-cluster idle listening as the intra-cluster data collection can be completed at the same time across all clusters in the network but lead to hotspot problem due to additional traffic relay experienced by cluster heads near the base station. Similarly, unequal clustering addresses hotspot problem but lead to inter-cluster idle listening due to the use of global network-wide intra-cluster collection among clusters of unequal sizes and densities. In this paper we proposed a zone-based clustering scheme referred to as hybrid equal and unequal clustering (HEUC) that jointly address inter-cluster idle listening and hotspot problems to maximize the lifetime of WSNs. To achieve this, the network area is firstly partitioned into zones. The size of clusters in the same zone is designed to be equal and cluster size increases across zones as the distance from the BS increases. Secondly, the density of nodes deployed in each cluster per zone is obtained in such a way that the distribution of nodes in zones away from BS increases according to the radius increase in clusters across the zones. Thirdly, a deterministic deployment strategy is used to deploy nodes into various clusters. Fourthly, we implement a zone-wise intra-cluster data collection strategy that allows intra-cluster data collection to be completed at once to address inter-cluster idle listening. Lastly, a multihop routing is used for data forwarding to BS. The result shows that our proposed HEUC has 38% and 51% lifetime improvement against EBULRP and AECR respectively.

Common and distinct neural connectivity in attention-deficit/hyperactivity disorder and alcohol use disorder studied using resting-state functional magnetic resonance imaging.

A link between attention-deficit/hyperactivity disorder (ADHD) and alcohol use disorder (AUD) has been widely demonstrated. In this study, we used neuroimaging to investigate the connectivity traits that may contribute to the comorbidity of these disorders. The study included an AUD group (N=18), an ADHD group (N=17), a group with AUD+ADHD comorbidity (N=12) and a control group (N=18). We used resting-state functional connectivity in a seed-based approach in the default mode networks, the dorsal attention network, and the salience network. Within the default mode networks, all affected groups shared greater connectivity toward the temporal gyrus when compared to the control group. Regarding the dorsal attention network, the Brodmann area 6 presented greater connectivity for each affected group in comparison with the control group, displaying the strongest aberrations in the AUD+ADHD group. In the salience network, the prefrontal cortex showed decreased connectivity in each affected group compared to the control group. Despite the small and unequal sample sizes, our findings show evidence of common neurobiological alterations in AUD and ADHD, supporting the hypothesis that ADHD could be a risk factor for the development of AUD. The results highlight the importance of an early ADHD diagnosis and treatment to reduce the risk of a subsequent AUD.

High-Low Level Support Vector Regression Prediction Approach (HL-SVR) for Data Modeling with Input Parameters of Unequal Sample Sizes

Support vector regression (SVR) has been widely used to reduce the high computational cost of computer simulation. SVR assumes the input parameters have equal sample sizes, but unequal sample sizes are often encountered in engineering practices. To solve this issue, a new prediction approach based on SVR, namely as high-low level SVR approach (HL-SVR) is proposed for data modeling of input parameters of unequal sample sizes in this paper. The proposed approach consists of low-level SVR models for the input parameters of larger sample sizes and high-level SVR model for the input parameters of smaller sample sizes. For each training point of the input parameters of smaller sample sizes, one low-level SVR model is built based on its corresponding input parameters of larger sample sizes and their responses of interest. The high-level SVR model is built based on the obtained responses from the low-level SVR models and the input parameters of smaller sample sizes. A number of numerical examples are used to validate the performance of HL-SVR. The experimental results indicate that HL-SVR can produce more accurate prediction results than SVR. The proposed approach is applied to the stress analysis of dental implant, in which the structural parameters have massive samples but the material of implant can only be selected from Ti and its alloys. The obtained prediction results of the HL-SVR approach are much better than SVR. The proposed approach can be used for the design, optimization, and analysis of engineering systems with input parameters of unequal sample sizes.

Extraction and characterization of pectin from fruit peels of Irvingia gabonensis and pulp of Cola milleni and Theobroma cacao as precursor for industrial applications

Pectin is a complex polysaccharide that makes up about one third of the cell wall of higher plants. It was extracted from fruit peels of Irvingia gabonensis and pulp of Cola milleni and Theobroma cacao using acid extraction and alcohol precipitation methods. The effects of temperature and time on the yield and physicochemical properties of the extracted pectin were evaluated. Optimum yields of pectin from C. milleni, I. gabonensis, and T. Cacao were 10.73%, 19.83%, and 11.73% respectively at extracting period of 150 min and temperature of 100 °C. Although there was significant difference in moisture content, degree of esterification, equivalent weight, and methoxyl content of the extracted pectins, there was no significant difference in yield, protein, and ash content at 95% confidence interval. The monosaccharide composition of the three pectins shows that the extracted pectin composed of galacturonic acid and minor neutral sugars. Major functional groups in the extracted pectin show peaks in the region between 1000 and 2000 cm−1. The bands observed between 1627–1651 cm−1 and 1739–1793 cm−1 indicated the presence of the carbonyl group stretching. The surface morphologies of the extracted pectins show irregular shapes, non-smooth surfaces, and unequal sizes which also reveals more silica nodes in cocoa pulp pectin than in other pectins. Thermogravimetric analysis of the pectin samples shows multi-step stages of thermal decomposition, indicating wide range of thermal stability. The overall results specified that the pectins extracted from these plants are suitable for industrial applications.

Shorting And Drying Technology Unit For Improving The Effectiveness Of Black Onion Process

In 2016, the development of Gempar Tunggal Micro Small and Medium Enterprises (MSMEs) that involved in the processing of black onions began. The raw materials are obtained from the Medan City market center, but sometimes it also come from Brebes and Semarang. The goods manufacture that resulted are sold to Aceh, Kalimantan and Sulawesi. However, because it was a home industry, the manufacturing system that was developed still very simple. Therefore, some weakness were identified, in particular the percentage of damaged or defective finished goods reaching 25 percent before its sold, various levels of maturity and work processes and supervision that drained attention and energy. In addition, the cost of using electricity is also high. It was found from the literature study by the Abdimas team of USU that there are 3 parameters that affect the processing of onions, namely garlic which is sensitive to temperature, humidity and exposure period of temperature and humidity. Often, due to the unequal size of the raw onion amount, the maturity of the onions is not homogenous distributed made the bigger the raw material of the onion impacted the faster it will ripen. Another problem that found during manufacturing process is the water vapor was not completely evaporated from the furnace. Basic technology that was developed by Abdimas USU team, namely the manual gravity onion sorting and drying unit was already used by Partners in the production process. As the result, it was successfully reducing broken onions. Lastly, homogenous maturity due to dividing process the onions by scale obtained.

Evaluating Measure of Reformed Rotatability for Second Degree Polynomial Using a Pair of Incomplete Block Designs with Two Unequal Block Sizes

In this paper, a study on evaluating measure of reformed rotatability for second degree polynomial using a pair of incomplete block designs with two unequal block sizes (like symmetrical unequal block arrangements with two unequal block sizes) is suggested which enables us to assess the degree of reformed (modified) rotatability for a given response surface design.