Partitioning Principle Research Articles

1.06 Tbit/s space division multiplexing self-homodyne coherent transmission with high spectral efficiency probabilistic shaping multidimensional modulation

We propose a probabilistic shaping multidimensional (MD) modulation format for self-homodyne coherent transmission systems. The redundancy of the MD signal is separated and transmitted together with the optical pilot tone (PT). The 4D/8D/12D modulation is constructed at the transmitter based on the amplitude translation (AT)-set partitioning (SP) principle and the probabilistic amplitude shaping (PAS) structure. Moreover, the hard-decision (HD) and soft-decision (SD) decoders for MD signals are introduced. We implement 20 GBaud 4D/8D/12D probabilistic shaping (PS) 16384-level quadrature amplitude modulation (QAM) transmission over 22.5 km uncoupled multicore fiber to analyze the performance. The experimental results show that it is possible for the MD signal to provide spectral efficiency (SE) gain up to 3.31 bit/s/Hz/4D-sym. The maximum SE transmitted is up to 57.29 bit/s/Hz, i.e., 17.5 bit/s/Hz/4D-sym, with a bit rate of 1.06 Tbit/s.

Determination and comparison of freely dissolved PAHs using different types of passive samplers in freshwater

Polycyclic aromatic hydrocarbons (PAHs) are well-known for their recalcitrant properties and biotoxicity in organisms, leading to serious environmental and health problems. Despite various analytical methods available, accurate determination of the bioavailable fraction is warranted in order to evaluate the precise toxic potentials of these compounds. Currently, the passive sampler is used worldwide to measure the bioavailable PAHs in the environment using the equilibrium partitioning principle. In this study, we co-deployed different types of passive samplers, which are linear low-density polyethylene (LLDPE) and low-density polyethylene (LDPE), to determine freely dissolved concentrations (Cfree) of PAHs using the performance reference compounds (PRCs) in Kentucky Lake (KL), Ohio River (OH), and Mississippi River (MS). The fractional equilibrium (feq) of BeP-d12 was observed to be high in LLDPE compared with LDPE in OH and MS. In contrast, the feq of all PRCs was similar in both passive samplers in KL due to slow flow velocity. The sum of average freely dissolved PAH concentrations in LLDPE and LDPE during the exposure period were 2.89 and 1.27 ng/L in KL, 8.13 and 3.31 ng/L in OH, and 5.19 and 3.82 ng/L in MS, respectively. The results revealed that LLDPE is a suitable alternative tool to LDPE for both short-term and long-term monitoring of PAHs.

Distributed Collaborative Optimization of a Multi-Region Integrated Energy System Based on Edge Computing Unit

The coordinated optimization scheduling of the integrated energy systems is vital in multi-energy complementarity and hierarchical utilization. However, the centralized optimization is inferior to the distributed optimization of the large-scale multiregion integrated energy system (MRIES) in data processing capacity and information security. This study proposes a distributed computing architecture based on the edge computing unit (ECU), which takes the energy hub as the main body and sets the partitioning principle and method of MRIES. The ECU can finally realize the whole-system collaborative optimization of MRIES, which contains electrical, natural gas, and district heating networks through internal autonomous optimization and boundary information interaction with the cloud computing center. At the same time, an improved nested algorithm based on the consensus-alternating direction method of multipliers is proposed, which ensures the convergence of the mixed-integer linear program and effectively improves the convergence speed. Combining the advantages of the model and algorithm provides a theoretical and algorithmic support for the optimization research of the MRIES.

A Stepwise Procedure for Toxicity Studies Based on Ratio of two means

This paper proposes a stepwise confidence set procedure for identifying equivalence or safety of compounds in a toxicity study under heteroscedasticity of variances for a normally distributed data. The problem of statistical methodology for drug safety is the control of the familywise error rate (FWER). Hence, we construct a confidence set procedure for toxicological evaluation and incorporating the partitioning principle with a case of heteroscedascity of variances under normal assumption. Our simulation studies demonstrated that the power of the procedures for heterogeneity of variances increases with increasing in ratio of means.

Identifying Minimum Effective Dose Under Heteroscedasticity

We propose a stepwise confidence procedure for identifying minimum effective dose (MED) without multiplicity adjustment.Stepwise procedures strongly control the familywise error rate (FWER) which is a critical requirement for statistical methodologies in identification of MED. The partitioning principle is invoked to validate the control of the FWER. Our simulation study indicates that the FWER was properly controlled in the case with balanced design but failed in some cases of sample sizes for situations of unbalanced design. In addition, the power of the procedure increases with increasing mean of ratio differences and the sample sizes.

Simultaneous confidence intervals for ranks using the partitioning principle

We consider the problem of constructing simultaneous confidence intervals (CIs) for the ranks of n means based on their estimates together with the (known) standard errors of those estimates. We present a generic method based on the partitioning principle in which the parameter space is partitioned into disjoint subsets and then each one of them is tested at level α. The resulting CIs have then a simultaneous coverage of 1−α. We show that any procedure which produces simultaneous CIs for ranks can be written as a partitioning procedure. We present a first example where we test the partitions using the likelihood ratio (LR) test. Then, in a second example we show that a recently proposed method for simultaneous CIs for ranks using Tukey’s honest significant difference test has an equivalent procedure based on the partitioning principle. By embedding these two methods inside our generic partitioning procedure, we obtain improved variants. We illustrate the performance of these methods through simulations and real data analysis on hotel ratings. While the novel method that uses the LR test and its variant produce shorter CIs when the number of means is small, the Tukey-based method and its variant produce shorter CIs when the number of means is high.

Biostatistical Assessment of Mutagenicity Studies: A Stepwise Confidence Procedure

The paper addresses the issue of identifying the maximum safe dose in the context of noninferiority trials where several doses of toxicological compounds exist. Statistical methodology for identifying the maximum safe dose is available for three-arm noninferiority designs with only one experimental drug treatment. Extension of this methodology for several experimental groups exists but with multiplicity adjustment. However, if the experimental or the treatment groups can be ordered a priori according to their treatment effect, then multiplicity adjustment is unneeded. Assuming homogeneity of variances across dose group in normality settings, we employed the generalized Fieller’s confidence interval method in a multiple comparison stepwise procedure by incorporating the partitioning principle in order to control the familywise error rate (FWER). Simulation results revealed that the procedure properly controlled the FWER in strong sense. Also, the power of our procedure increases with increasing sample size and the ratio of mean differences. We illustrate our procedure with mutagenicity dataset from a clinical study.

Partitioning Apomixis Components to Understand and Utilize Gametophytic Apomixis.

Apomixis is a method of reproduction to generate clonal seeds and offers tremendous potential to fix heterozygosity and hybrid vigor. The process of apomictic seed development is complex and comprises three distinct components, viz., apomeiosis (leading to formation of unreduced egg cell), parthenogenesis (development of embryo without fertilization) and functional endosperm development. Recently, in many crops, these three components are reported to be uncoupled leading to their partitioning. This review provides insight into the recent status of our understanding surrounding partitioning apomixis components in gametophytic apomictic plants and research avenues that it offers to help understand the biology of apomixis. Possible consequences leading to diversity in seed developmental pathways, resources to understand apomixis, inheritance and identification of candidate gene(s) for partitioned components, as well as contribution towards creation of variability are all discussed. The potential of Panicum maximum, an aposporous crop, is also discussed as a model crop to study partitioning principle and effects. Modifications in cytogenetic status, as well as endosperm imprinting effects arising due to partitioning effects, opens up new opportunities to understand and utilize apomixis components, especially towards synthesizing apomixis in crops.

ПРОЕКТИРОВАНИЕ МУЛЬТИМОДАЛЬНОЙ ТРАНСПОРТНОЙ СЕТИ

Objective: To create a methodology for designing a multimodal transport network under various scenarios of socioeconomic development of the Russian Federation and its regions which take into account the influence of factors that create initial-information indeterminacy in decisionmaking. Methods: System theory, partitioning principle, theory of sets, theory of probability and mathematical statistics, basics of information theory, graph theory and reliability theory; as well as methods of system analysis, mathematic simulation of processes and systems, mathematical logic, decision-making, dynamical programming, multi-objective optimization, economic evaluation of efficiency of design solutions were applied. Results: The authors developed and proposed a concept for designing methodology of multimodal transport networks, systemic presentation of multimodal transport networks, four-level partitioning and set-theoretical presentation of multimodal transport networks layout, mathematical simulation of multimodal transport network development strategy which takes into account the scenario of socioeconomic development of a region under study, balanced system of indices for evaluation of multimodal transport network development strategy and managing the trajectory of change of its layout and capacity in accordance with set strategic objectives, method for forming layout of multimodal transport network, method for forming a variety of possible strategies of gradual changing of layout and capacity of multimodal transport network objects, method for forming an area of efficient multimodal transport network development strategies, technology for decision-makers’ work with efficient strategy area for decision-making. Practical relevance: This methodology can be used in investment evaluation and technical and economic feasibility study of strategies of multimodal transport networks’ layout and capacity change strategies as an aggregate of multimodal transport corridors designed with the purpose of implementation of strategic tasks of development of a country’s single transport network.

Further investigation into lithium recovery from salt lake brines with different feed characteristics by electrodialysis

Although lithium resources are abundant in the salt lakes located in West China, the majority of these resources have a high Mg/Li ratio, which is problematic because traditional precipitation methods are unsuitable for lithium recovery from this type of brine. In our previous work, constant-current electrodialysis (ED) was applied to comprehensively investigate the effects of operating conditions on the Li+/Mg2+ separation, however, the experimental study considering the feed characteristic diversity and the theoretical analysis of the ionic transfer process considering the feed composition complexity were remained to be perfected. This work focused on resolving the remained questions therein. Initially, we determined the ion-exchange isotherm of the CSO membrane. The selective affinity towards divalent cation was validated, which laid the foundation for the development of the electric double layer (EDL). Then, we investigated the effects of applied voltage on the separation performance and optimized the power mode. The constant-voltage was verified to be a superior power mode compared to the constant-current applied in our previous work. Thereafter, the feed solutions characterized by different Mg/Li ratios, Na/Li ratios, and sulfate concentrations were treated by constant-voltage ED, wherein the partitioning principle was further explained via a thermodynamic analysis of the aqueous species distribution of ions. The results showed that in a high-salinity aqueous system, mass transfer was significantly affected by the complexity of the ions’ existing forms, which notably determined the steric hindrance and charge effect. As a specific transfer phenomenon, we found that sulfate ions provided large benefit to lithium recovery in the salt lake brine system. A natural brine experiment also showed that lithium recovery can be effectively achieved by ED. These observations indicated that ED has a wide adaptability for lithium recovery from brines with different feed characteristics.

A Comparative Study of Synchronous Current Control Schemes Based on FCS-MPC and PI-PWM for a Two-Motor Three-Phase Drive

A two-motor drive, supplied by a five-leg inverter, is considered in this paper. The independent control of machines with full dc-bus voltage utilization is typically achieved using an existing pulsewidth modulation (PWM) technique in conjunction with field-oriented control, based on PI current control. However, model predictive control (MPC), based on a finite number of control inputs [finite-control-set MPC (FCS-MPC)], does not utilize a pulsewidth modulator. This paper introduces three FCS-MPC schemes for synchronous current control in this drive system. The first scheme uses all of the available switching states. The second and third schemes are aimed at reducing the computational burden and utilize a reduced set of voltage vectors and a duty ratio partitioning principle, respectively. Steady-state and transient performances are analyzed and compared both against each other and with respect to the field-oriented control based on PI controllers and PWM. All analyses are experimental and use the same experimental rig and test conditions. Comparison of the predictive schemes leads to the conclusion that the first two schemes have the fastest transient response. The third scheme has a much smaller current ripple while achieving perfect control decoupling between the machines and is of low computational complexity. Nevertheless, at approximately the same switching loss, the PI-PWM control yields the lowest current ripple but with slower electrical transient response.

Partitioning of trait variation among communities: measures of apportionment and differentiation based on binary sampling

The notion that trait variation is partitioned among communities essentially rests on the supposition that the total variation in the metacommunity exceeds the variation within the communities due to differences between their trait distributions (the partitioning principle). Two elementary perspectives of partitioning can be distinguished: apportionment (members of the same community tend to hold the same trait state) and differentiation (members of different communities tend to hold different trait states). While the apportionment perspective reaches its extreme when each community is monomorphic (fixation), the differentiation perspective does so if communities share no trait states. Even though both perspectives can be shown to be involved in the analysis of community dynamics, their assessment is still almost completely limited to the apportionment perspective (chiefly G ST and its relatives). To overcome this limitation, methods of quantifying both partitioning perspectives are developed for qualitatively and quantitatively varying traits, where variation is represented by the differences in type resulting from sampling two individuals. It is shown that the validity of the partitioning principle and the design of corresponding measures crucially depend on proper specification of the modes of sampling and specification of differences between types that follow a concavity principle. This approach allows comparison between measures of apportionment and measures of differentiation. Such comparisons enable conclusions about the share that random (drift) and directional (selection, migration) processes have in the partitioning of variation among communities. One of the more far-reaching conclusions is that effects of forces apportioning variation outperform the effects of forces of differentiation, if the average similarity within communities exceeds the average difference between them.

An Extension of the Holm Procedure Based on Partitioning Principle for Adaptive Treatment Selection Designs with Structured Hypotheses

Multiple comparisons are attracting increasing attention in the evaluation of statistical evidence in clinical trials including at least one or any combination of (i) multiple hypotheses, (ii) repeated hypotheses testing at interim analyses, and (iii) mid-course design adaptations. In this paper, we discuss an efficient and sensible multiple testing procedure for two-stage adaptive treatment selection designs including structured hypotheses. Specifically, we extend the Holm procedure for serial gatekeeping structured hypotheses in adaptive clinical trials. The proposed approach is based on the idea of combining partition testing with the inverse normal combination test. A clinical trial example is used to illustrate the implementation of the proposed procedure.

Bregman Hyperplane Trees for Fast Approximate Nearest Neighbor Search

This article presents a new approximate index structure, the Bregman hyperplane tree, for indexing the Bregman divergence, aiming to decrease the number of distance computations required at query processing time, by sacrificing some accuracy in the result. The experimental results on various high-dimensional data sets demonstrate that the proposed index structure performs comparably to the state-of-the-art Bregman ball tree in terms of search performance and result quality. Moreover, this method results in a speedup of well over an order of magnitude for index construction. The authors also apply their space partitioning principle to the Bregman ball tree and obtain a new index structure for exact nearest neighbor search that is faster to build and a slightly slower at query processing than the original.

A Modeling Method of Wideband Devices Based on Modified Nodal Analysis

According to the simplified circuit partitioning principle, this paper improves the Modified Nodal Analysis(MNA) of wideband Equivalent Circuit Model(ECM). The form of upconversion impedance is transformed from series into parallel. The results show that in the parallel form, the verification process of impedance type has been eliminated and it will not introduce new nodes. At the same time, the amount of computation has been reduced. The maximum relative error of measured data with this model fit is less than 0.693%. The simulation results and ECM test data are consistent with better at 0 to 8GHz frequency range.

General solutions to consistency problems in multiple hypothesis testing

Coherence and consonance are the two important concepts to ensure consistent conclusions drawn from multiple tests. Unlike coherence, consonance of a multiple testing procedure (MTP) has not yet received much attention. Although most of the MTPs used in practice are consonant, cases still exist that dissonant tests have to be used due to their unique advantages, for example, the likelihood ratio tests and sum tests. Consonance adjustments are necessary for such tests to avoid difficulty in interpretation. Moreover, in terms of detecting elementary hypotheses, a consonant test procedure is uniformly more powerful than the corresponding dissonant one. In this paper, several general methods using the partitioning principle to construct (strongly) consonant and strongly coherent MTPs are proposed. As a result, any dissonant (but coherent) multiple level α test can be improved by a consonant one without any cost in terms of inferences on elementary hypotheses.

Three-sided hypothesis testing: Simultaneous testing of superiority, equivalence and inferiority

We propose three-sided testing, a testing framework for simultaneous testing of inferiority, equivalence and superiority in clinical trials, controlling for multiple testing using the partitioning principle. Like the usual two-sided testing approach, this approach is completely symmetric in the two treatments compared. Still, because the hypotheses of inferiority and superiority are tested with one-sided tests, the proposed approach has more power than the two-sided approach to infer non-inferiority or non-superiority. Applied to the classical point null hypothesis of equivalence, the three-sided testing approach shows that it is sometimes possible to make an inference on the sign of the parameter of interest, even when the null hypothesis itself could not be rejected. Relationships with confidence intervals are explored, and the effectiveness of the three-sided testing approach is demonstrated in a number of recent clinical trials.

Alternative Confidence Regions for Bonferroni‐Based Closed‐Testing Procedures that are not Alpha‐Exhaustive

This article complements the results in Guilbaud (Biometrical Journal 2008; 50:678-692). Simultaneous confidence regions were derived in that article that correspond to any given multiple testing procedure (MTP) in a fairly large class of consonant closed-testing procedures based on marginal p-values and weighted Bonferroni tests for intersection hypotheses. This class includes Holm's MTP, the fixed-sequence MTP, gatekeeping MTPs, fallback MTPs, multi-stage fallback MTPs, and recently proposed MTPs specified through a graphical representation and associated rejection algorithm. More general confidence regions are proposed in this article. These regions are such that for certain underlying MTPs which are not alpha-exhaustive, they lead to confidence assertions that may be sharper than rejection assertions for some rejected null hypotheses H when not all Hs are rejected, which is not the case with the previously proposed regions. In fact, various alternative confidence regions may be available for such an underlying MTP. These results are shown through an extension of the previous direct arguments (without invoking the partitioning principle), and under the same general setup; so for instance, estimated quantities and marginal confidence regions are not restricted to be of any particular kinds/dimensions. The relation with corresponding confidence regions of Strassburger and Bretz (Statistics in Medicine 2008; 27:4914-4927) is described. The results are illustrated with fallback and parallel-gatekeeping MTPs.

Partition testing in dose–response studies with multiple endpoints

Dose-response studies with multiple endpoints can be formulated as closed testing or partition testing problems. When the endpoints are primary and secondary, whether the order in which the doses are to be tested is pre-determined or sample determined lead to different partitioning of the parameter space corresponding to the null hypotheses to be tested. We use the case of two doses and two endpoints to illustrate how to apply the partitioning principle to construct multiple tests that control the appropriate error rate. Graphical representation can be useful in visualizing the decision process.

A unifying approach to non‐inferiority, equivalence and superiority tests via multiple decision processes

Two approaches of multiple decision processes are proposed for unifying the non-inferiority, equivalence and superiority tests in a comparative clinical trial for a new drug against an active control. One is a method of confidence set with confidence coefficient 0.95 improving the conventional 0.95 confidence interval in the producer's risk and also the consumer's risk in some cases. It requires to include 0 within the region as well as to clear the non-inferiority margin so that a trial with somewhat large number of subjects and inappropriately large non-inferiority margin for proving non-inferiority of a drug that is actually inferior should be unsuccessful. The other is the closed testing procedure which combines the one- and two-sided tests by applying the partitioning principle and justifies the switching procedure by unifying the non-inferiority, equivalence and superiority tests. In particular regarding the non-inferiority, the proposed method justifies simultaneously the old Japanese Statistical Guideline (one-sided 0.05 test) and the International Guideline ICH E9 (one-sided 0.025 test). The method is particularly attractive, changing the strength of the evidence of relative efficacy of the test drug against a control at five levels according to the achievement of the clinical trial. The meaning of the non-inferiority test and also the rationale of switching from it to superiority test will be discussed.