A Reduced-Order Modeling of Multi-Port RC Networks by Means of Graph Partitioning

A modified reduced-order method for RC networks which takes a division-and-conquest strategy is presented.The whole network is partitioned into a set of sub-networks at first,then each of them is reduced by Krylov subspace techniques,and finally all the reduced sub-networks are incorporated together.With some accuracy,this method can reduce the number of both nodes and components of the circuit comparing to the traditional methods which usually only offer a reduced net with less nodes.This can markedly accelerate the sparse-matrix-based simulators whose performance is dominated by the entity of the matrix or the number of components of the circuits.

THE SUPERIORITY OF EMPIRICAL BAYES ESTIMATION OF PARAMETERS IN PARTITIONED NORMAL LINEAR MODEL

In this article,the empirical Bayes（EB）estimators are constructed for the estimable functions of the parameters in partitioned normal linear model.The superiorities of the EB estimators over ordinary least-squares（LS）estimator are investigated under mean square error matrix（MSEM）criterion.

Understanding and simulating of three-dimensional subsurface hydrological partitioning in an alpine mountainous area, China

Critical zone(CZ)plays a vital role in sustaining biodiversity and humanity.However,flux quantification within CZ,particularly in terms of subsurface hydrological partitioning,remains a significant challenge.This study focused on quantifying subsurface hydrological partitioning,specifically in an alpine mountainous area,and highlighted the important role of lateral flow during this process.Precipitation was usually classified as two parts into the soil:increased soil water content(SWC)and lateral flow out of the soil pit.It was found that 65%–88%precipitation contributed to lateral flow.The second common partitioning class showed an increase in SWC caused by both precipitation and lateral flow into the soil pit.In this case,lateral flow contributed to the SWC increase ranging from 43%to 74%,which was notably larger than the SWC increase caused by precipitation.On alpine meadows,lateral flow from the soil pit occurred when the shallow soil was wetter than the field capacity.This result highlighted the need for three-dimensional simulation between soil layers in Earth system models(ESMs).During evapotranspiration process,significant differences were observed in the classification of subsurface hydrological partitioning among different vegetation types.Due to tangled and aggregated fine roots in the surface soil on alpine meadows,the majority of subsurface responses involved lateral flow,which provided 98%–100%of evapotranspiration(ET).On grassland,there was a high probability(0.87),which ET was entirely provided by lateral flow.The main reason for underestimating transpiration through soil water dynamics in previous research was the neglect of lateral root water uptake.Furthermore,there was a probability of 0.12,which ET was entirely provided by SWC decrease on grassland.In this case,there was a high probability(0.98)that soil water responses only occurred at layer 2(10–20 cm),because grass roots mainly distributed in this soil layer,and grasses often used their deep roots for water uptake during ET.To improve the estimation of soil water dynamics and ET,we established a random forest(RF)model to simulate lateral flow and then corrected the community land model(CLM).RF model demonstrated good performance and led to significant improvements in CLM simulation.These findings enhance our understanding of subsurface hydrological partitioning and emphasize the importance of considering lateral flow in ESMs and hydrological research.

An improved model of partition curve based on accumulation normal distribution function

Extensive studies based on partition curve of gravity separation have been investigated. All created models are merely used to simulate density distribution at the same size fraction. However, they cannot be used to predictive distribution of materials depending on compound feature of density and size. According to this situation, an improved model of partition curve based on accumulation normal distribution, which was distinguished from conventional model of accumulation normal distribution for partition curve, was proposed in this paper. It could simulate density distribution at different size fractions by using the density-size compound index and conflating the partition curves at different size fractions as one partition curve. The feasibility of three compound indexes, including mass index, settlement index and transformation index, were investigated. Specific forms of the improved model were also proposed. It is found that transformation index leads to the best fitting results, while the fitting error is only 1.75 according to the fitting partition curve.

Mathematical Models for a Social Partitioning Problem

In this paper we develop modeling techniques for a social partitioning problem. Different social interaction regulations are imposed during pandemics to prevent the spread of diseases. We suggest partitioning a set of company employees as an effective way to curb the spread, and use integer programming techniques to model it. The goal of the model is to maximize the number of direct interactions between employees who are essential for company’s work subject to the constraint that all employees should be partitioned into components of no more than a certain size implied by the regulations. Then we further develop the basic model to take into account different restrictions and provisions. We also give heuristics for solving the problem. Our computational results include sensitivity analysis on some of the models and analysis of the heuristic performance.

Task Partition Technology of pXCube Cloud Model

Query efficiency is bottleneck of XML data cube aggregate query. pXCube is a kind of XML data cube model based on path calculation. Join operations are avoided in this model, but the query efficiency of fact cell is become a new bottleneck. This paper focuses on parallel technology of cloud computing to improve query efficiency of pXCube. Mixed partitioning strategy for fact and dimensions is applied in pXCube cloud model, and the same partitioned vector is adopted. Query parallel algorithm of pXCube cloud model is presented as well. Experiments show that the query cost of pXCube cloud model decreases with the increasing number of parallel nodes gradually. The query cost of fact fragments of each node are close to or even lower than join operations of dimensions, and the Speedup is with better linear. So the model is well suited for decision supported query.

CONVECTIVE-STRATIFORM RAINFALL PARTITION BY RADIANCE-DERIVED CLOUD CONTENT:A MODELING STUDY

A new scheme that separates convective-stratiform rainfall is developed using threshold values of liquid water path(LWP) and ice water path(IWP).These cloud contents can be predicted with radiances at the Advanced Microwave Sounding Unit(AMSU) channels(23.8,31.4,89,and 150 GHz) through linear regression models.The scheme is demonstrated by an analysis of a two-dimensional cloud resolving model simulation that is imposed by a forcing derived from the Tropical Ocean Global Atmosphere Coupled Ocean-Atmosphere Response Experiment(TOGA COARE).The rainfall is considered convective if associated LWP is larger than 1.91 mm or IWP is larger than1.70 mm.Otherwise,the rainfall is stratiform.The analysis of surface rainfall budget demonstrates that this new scheme is physically meaningful.

A New Formula for Partitions in a Set of Entities into Empty and Nonempty Subsets, and Its Application to Stochastic and Agent-Based Computational Models

In combinatorics, a Stirling number of the second kind S (n,k)? is the number of ways to partition a set of n objects into k nonempty subsets. The empty subsets are also added in the models presented in the article in order to describe properly the absence of the corresponding type i of state in the system, i.e. when its “share” Pi =0?. Accordingly, a new equation for partitions P (N, m)? in a set of entities into both empty and nonempty subsets was derived. The indistinguishableness of particles (N identical atoms or molecules) makes only sense within a cluster (subset) with the size?0≤ni ≥N. The first-order phase transition is indeed the case of transitions, for example in the simplest interpretation, from completely liquid state?typeL = {n1 =N, n2 = 0} to the completely crystalline state??typeC= {n1 =0, n2 = N }. These partitions are well distinguished from the physical point of view, so they are ‘typed’ differently in the model. Finally, the present developments in the physics of complex systems, in particular the structural relaxation of super-cooled liquids and glasses, are discussed by using such stochastic cluster-based models.

Estimation of Partition Coefficients of Fe-S Protein Models： Se Substitutions in Fe4S4Cysn

The SCAP method allows a semiquantitative estimation of the partitioning of many solutes between numerous pairs of solvents. The organic solvent-water partition coefficients P are calculated. For FeaS4Cysn, the organic solvent-water partition coefficients for l-octanol Po, cyclohexane Pch and chloroform Pcf decay 4.46, 6.25 and 4.60 log units per Cys, respectively. The Po is of the same order of magnitude as CDHI （conformationally dependent hydrophobic index） calculations and Pch-cf as computations performed with a method by Leo and Hansch. The logPo-ch-cf mean relative errors are 17%, 25% and-17%, which represent mean and unsigned relative errors of -3% and 20%. On varying the number of Cys, the structures show hydrophobic moments indicative of amphipathic compounds. For Se substitutions in Fe4SeaCys,, Po-ch-cf drop 4.52, 6.30 and 4.66 exponents per Cys. With the reference calculations, Po-ch-cf decay 4.03, 4.80 and 5.76 exponents per Cys. For FeaS4 mSemCys4, the calculated similar partition coefficients and hydrophobic moments, and lower distance in dendrogram suggest a role of Fe-Se clusters in physiological processes. The analysis is extended to lysozyme and its secondary structures.

MEASUREMENT AND CORRELATION OF PARTITION COEFFICIENTS OF UROKINASE IN AQUEOUS TWO-PHASE PEG-POTASSIUM PHOSPHATE SYSTEM

Partition coefficients of Urokinase(UK)were measured in aqueous two-phase systems con-taining polyethylene glycol and potassium phosphate at 273.2K.Based on the Diamond-Hsu model,a modified expression was obtained for the correlation of enzyme partitioning in theabove-mentioned systems.Utilizing a modified form,the partitioning data of UK and heteroproteinwere correlated.The results show that the modified model is simple gives good precision.and will fa-cilitate engineering scale-up of aqueous two-phase systems for certain proteins purification.

Effect of partition coefficient on microsegregation during solidification of aluminium alloys

In the modeling of microsegregation, the partition coefficient is usually calculated using data from the equilibrium phase diagrams. The aim of this study was to experimentally and theoretically analyze the partition coefficient in binary aluminum--copper alloys. The sam- ples were analyzed by differential thermal analysis （DTA）, which were melted and quenched from different temperatures during solidifica- tion. The mass fraction and composition of phases were measured by image processing and scanning electron microscopy （SEM） equipped with an energy-dispersive X-ray spectroscopy （EDS） unit. These data were used to calculate as the experimental partition coefficients with four different methods. The experimental and equilibrium partition coefficients were used to model the concentration profile in the primary phase. The modeling results show that the profiles calculated by the experimental partition coefficients are more consistent with the experi- mental profiles, compared to those calculated using the equilibrium partition coefficients.

Atmospheric concentration characteristics and gas/particle partitioning of PCBs from the North Pacific to the Arctic Ocean

Polychlorinated biphenyls （PCBs） were measured in atmospheric samples collected from the North Pacific to the Arctic Ocean between July and September 2012 to study the atmospheric concentration characteris-tics of PCBs and their gas/particle partitioning. The mean concentration of 26 PCBs （vapor plus particulate phase） （∑PCBs） was 19.116 pg/m^3with a standard deviation of 13.833 pg/m^3. Three most abundant conge-ners were CB-28, -52 and -77, accounting for 43.0% to∑PCBs. The predominance of vapor PCBs （79.0% to∑PCBs） in the atmosphere was observed.∑PCBs were negative correlated with the latitudes and inverse of the absolute temperature （1/T）. The significant correlation for most congeners was also observed between the logarithm of gas/particle partition coefficient （logKp） and 1/T. Shallower slopes （from ∑0.15 to ∑0.46, average ∑0.27） were measured from the regression of the logarithm of sub-cooled liquid vapor pressures （logpoL） and logKP for all samples. The difference of the slopes and intercepts among samples was insignifi-cant （p〉0.1）, implying adsorption and/or absorption processes and the aerosol composition did not differ significantly among different samples. By comparing three models, the J-P adsorption model, the octanol/air partition coefficient （KOA） based model and the soot-air model, the gas/particle partitioning of PCBs in the Arctic atmosphere was simulated more precisely by the soot-air model, and the adsorption onto el-emental carbon is more sensitive than the absorption into organic matters of aerosols, especially for low-chlorinated PCB congeners.

Control synthesis for a class of nonlinear systems based on partition of unity

A partition-of-unity-based approach is proposed to derive an approximate model for a class of nonlinear systems. The precision of the approximate model is analyzed by using the modulus of continuity of continuous functions. The system stability of the approximate model is analyzed by using Lyapunov stability theory. A design algorithm for constructing tracking controllers with tracking performance related to tracking error is given based on the approximate model and the partition of unity method.

A Parameterization of Cooling Rate Calculation under the Non-LTE Condition: Multi-Level Model

Calculations of cooling rate by CO2 15 μm band in the earth's upper mesosphere and lower thermosphere be-come very difficult because of the non-LTE. This is primarily due to the nonlinear vibration-vibrational (VV) transition processes between CO, molecules in different states. This paper suggests that the non-LTE source function be parameterized as a linear combination of two limiting source functions. One limiting source function neglects the VV transitions while the other limiting source function assumes VV transitions being dominant. These two limiting source functions can be derived by linear models. The parameterization schemes proposed here can be applied to the general circulation models including those non-LTE regions.

Trace element partitioning between amphibole and hydrous silicate glasses at 0.6–2.6 GPa

Partitioning behavior between amphibole and silicate glass of thirty-three minor and trace elements(Sc,Ti, V, Cr, Co, Rb, Sr, P, Y, Zr, Nb, Cs, Ba, K, La, Ce, Pr,Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu, Hf, Ta, Pb,Th, and U) have been determined experimentally. Products of crystallization of hydrous basalt melts from 0.6 GPa/860 °C up to 2.6 GPa/970 °C were obtained in a multianvil apparatus. Major and trace element compositions of amphibole and glass were determined with a combination of electron microprobe and laser ablation inductively coupled plasma mass spectrometry. The main mineral phase is calcic amphibole, and the coexisting glass compositions are tonalite, granodiorite, and granite. The compatibility of rare earth elements increase at 915 °C and then decrease at 970 °C, but the compatibility of most of these elements shows a continued, significant increase with increasing pressure. For high-field strength elements, large ion lithophile elements, actinide compatibility decrease with increasing temperature or pressure, but transition metals show a continued increase in compatibility within the temperature–pressure conditions. From mathematical and graphical fitting, we determined best-fit values for the ideal ionic radius(r_0, 1.01–1.04 ?), the strain-free partitioncoefficient(D_0, 1.18–1.58), and apparent Young's modulus(E, 142–370 GPa) for the M4 site in amphibole according to the lattice strain model. The D_0^(M4) for rare earth elements rises at 915 °C and then drops at 970 °C at 0.6 GPa.However, the D_0^(M4) values are positively proportional to the pressure for rare earth elements in the amphibole-glass pairs at 0.6–2.6 GPa and 970 °C. Furthermore, the derived best-fit values for r_0^(M4) and E^(M4) are almost constant and trend to increase with rising temperature and pressure,respectively. The partition coefficient is distinctly different for different melt compositions. The rare earth elements become more enriched in amphibole if the quenched glass is granodiorite or granite compared to the tonalitic glasses.

Neural Network Based Multi-level Fuzzy Evaluation Model for Mechanical Kinematic Scheme

To implement a quantificational evaluation for mechanical kinematic scheme more effectively,a multi-level and multi-objective evaluation model is presented using neural network and fuzzy theory. Firstly,the structure of evaluation model is constructed according to evaluation indicator system. Then evaluation samples are generated and provided to train this model. Thus it can reflect the relation between attributive value and evaluation result,as well as the weight of evaluation indicator. Once evaluation indicators of each candidate are fuzzily quantified and fed into the trained network model,the corresponding evaluation result is outputted and the best alternative can be selected. Under this model,expert knowledge can be effectively acquired and expressed,and the quantificational evaluation can be implemented for kinematic scheme with multi-level evaluation indicator system. Several key problems on this model are discussed and an illustration has demonstrated that this model is feasible and can be regarded as a new idea for solving kinematic scheme evaluation.

Multi-Level Feature-Based Ensemble Model for Target-Related Stance Detection

Stance detection is the task of attitude identification toward a standpoint.Previous work of stance detection has focused on feature extraction but ignored the fact that irrelevant features exist as noise during higher-level abstracting.Moreover,because the target is not always mentioned in the text,most methods have ignored target information.In order to solve these problems,we propose a neural network ensemble method that combines the timing dependence bases on long short-term memory(LSTM)and the excellent extracting performance of convolutional neural networks(CNNs).The method can obtain multi-level features that consider both local and global features.We also introduce attention mechanisms to magnify target information-related features.Furthermore,we employ sparse coding to remove noise to obtain characteristic features.Performance was improved by using sparse coding on the basis of attention employment and feature extraction.We evaluate our approach on the SemEval-2016Task 6-A public dataset,achieving a performance that exceeds the benchmark and those of participating teams.

Multi-level biomechanical models for rehabilitation engineering

Rehabilitation engineering aims in the upmost degree to restore the lost functions for those persons with physical disability. Biomechanical modeling has been widely used for different purposes in rehabilitation engineering to understand the bio-

Effect of Aluminum Hydroxide Adjuvant on the Immunogenicity of the 2009 Pandemic Influenza A/H1N1 Vaccine:Multi-level Modeling of Data with Repeated Measures

Objective To evaluate the effect of the aluminum hydroxide （Al-OH） adjuvant on the 2009 pandemic influenza A/H1N1 （pH1N1） vaccine. Methods In a multicenter, double-blind, randomized, placebo-controlled trial, participants received two doses of split-virion formulation containing 15 ug hemagglutinin antigen, with or without aluminum hydroxide （N-OH）. We classified the participants into six age categories （〉61 years, 41-60 years, 19-40 years, 13-18 years, 8-12 years, and 3-7 years） and obtained four blood samples from each participant on days 0, 21, 35, and 42 following the first dose of immunization. We assessed vaccine immunogenicity by measuring the geometric mean titer （GMT） of hemagglutination inhibiting antibody. We used a two-level model to evaluate the fixed effect of aluminum Al-OH and other factors, accounting for repeated measures. Results The predictions of repeated measurement on GMTs of formulations with or without Al-OH, were 80.35 and 112.72, respectively. Al-OH significantly reduced immunogenicity after controlling for time post immunization, age-group and gender. Conclusion The Al-OH adjuvant does not increase but actually reduces the immunogenicity of the split-virion pH1N1 vaccine.

Parameter-driven Level of Detail Derivation Method for Semantic Building Facade Model

The relentless progress in the research of geographic spatial data models and their application scenarios is propelling an unprecedented rich Level of Detail(LoD)in realistic 3D representation and smart cities.This pursuit of rich details not only adds complexity to entity models but also poses significant computational challenges for model visualization and 3D GIS.This paper introduces a novel method for deriving multi-LOD models,which can enhance the efficiency of spatial computing in complex 3D building models.Firstly,we extract multiple facades from a 3D building model(LoD3)and convert them into individual semantic facade models.Through the utilization of the developed facade layout graph,each semantic facade model is then transformed into a parametric model.Furthermore,we explore the specification of geometric and semantic details in building facades and define three different LODs for facades,offering a unique expression.Finally,an innovative heuristic method is introduced to simplify the parameterized facade.Through rigorous experimentation and evaluation,the effectiveness of the proposed parameterization methodology in capturing complex geometric details,semantic richness,and topological relationships of 3D building models is demonstrated.