Full Constraints Research Articles

Generalized separable parameter space techniques for fitting 1K‐5K serial compartment models

Kinetic modeling is widely used to analyze dynamic imaging data, estimating kinetic parameters that quantify functional or physiologic processes in vivo. Typical kinetic models give rise to nonlinear solution equations in multiple dimensions, presenting a complex fitting environment. This work generalizes previously described separable nonlinear least-squares techniques for fitting serial compartment models with up to three tissue compartments and five rate parameters. The approach maximally separates the linear and nonlinear aspects of the modeling equations, using a formulation modified from previous basis function methods to avoid a potential mathematical degeneracy. A fast and robust algorithm for solving the linear subproblem with full user-defined constraints is also presented. The generalized separable parameter space technique effectively reduces the dimensionality of the nonlinear fitting problem to one dimension for 2K-3K compartment models, and to two dimensions for 4K-5K models. Exhaustive search fits, which guarantee identification of the true global minimum fit, required approximately 10 ms for 2K-3K and 1.1 s for 4K-5K models, respectively. The technique is also amenable to fast gradient-descent iterative fitting algorithms, where the reduced dimensionality offers improved convergence properties. The objective function for the separable parameter space nonlinear subproblem was characterized and found to be generally well-behaved with a well-defined global minimum. Separable parameter space fits with the Levenberg-Marquardt algorithm required fewer iterations than comparable fits for conventional model formulations, averaging 1 and 7 ms for 2K-3K and 4K-5K models, respectively. Sensitivity to initial conditions was likewise reduced. The separable parameter space techniques described herein generalize previously described techniques to encompass 1K-5K compartment models, enable robust solution of the linear subproblem with full user-defined constraints, and are amenable to rapid and robust fitting using iterative gradient-descent type algorithms.

Decentralized control of nonlinear interconnected systems under both amplitude and rate saturations

In this paper, we design a decentralized controller for a class of nonlinear interconnected systems under both amplitude and rate limited actuators. Since the input amplitude can be treated as a state of the actuator dynamics, in the presence of both amplitude and rate constraints, each closed-loop subsystem would be regarded as a partial state and input constrained system. Then, based on the linear differential inclusion method, we propose linear matrix inequality (LMI) conditions to design the decentralized state feedback controller that can handle the partial state and full rate constraints. Furthermore, we estimate the domain of attraction of both subsystems and the overall systems using the Cartesian product of the ellipsoidal sets. A numerical example is presented to demonstrate the validity of the proposed controller.

QCD on an Infinite Lattice

We construct a mathematically well–defined framework for the kinematics of Hamiltonian QCD on an infinite lattice in \({\mathbb{R}^3}\) , and it is done in a C*-algebraic context. This is based on the finite lattice model for Hamiltonian QCD developed by Kijowski, Rudolph e.a.. To extend this model to an infinite lattice, we need to take an infinite tensor product of nonunital C*-algebras, which is a nonstandard situation. We use a recent construction for such situations, developed by Grundling and Neeb. Once the field C*-algebra is constructed for the fermions and gauge bosons, we define local and global gauge transformations, and identify the Gauss law constraint. The full field algebra is the crossed product of the previous one with the local gauge transformations. The rest of the paper is concerned with enforcing the Gauss law constraint to obtain the C*-algebra of quantum observables. For this, we use the method of enforcing quantum constraints developed by Grundling and Hurst. In particular, the natural inductive limit structure of the field algebra is a central component of the analysis, and the constraint system defined by the Gauss law constraint is a system of local constraints in the sense of Grundling and Lledo. Using the techniques developed in that area, we solve the full constraint system by first solving the finite (local) systems and then combining the results appropriately. We do not consider dynamics.

Linear stratified approach using full geometric constraints for 3D scene reconstruction and camera calibration

This paper presents a new linear framework to obtain 3D scene reconstruction and camera calibration simultaneously from uncalibrated images using scene geometry. Our strategy uses the constraints of parallelism, coplanarity, colinearity, and orthogonality. These constraints can be obtained in general man-made scenes frequently. This approach can give more stable results with fewer images and allow us to gain the results with only linear operations. In this paper, it is shown that all the geometric constraints used in the previous works performed independently up to now can be implemented easily in the proposed linear method. The study on the situations that cannot be dealt with by the previous approaches is also presented and it is shown that the proposed method being able to handle the cases is more flexible in use. The proposed method uses a stratified approach, in which affine reconstruction is performed first and then metric reconstruction. In this procedure, the additional constraints newly extracted in this paper have an important role for affine reconstruction in practical situations.

Synthetic Constraint of Soil C Dynamics Using 50 Years of 14C and Net Primary Production (NPP) in a New Zealand Grassland Site

Time-series radiocarbon measurements have substantial ability to constrain the size and residence time of the soil C pools commonly represented in ecosystem models. 14C remains unique in its ability to constrain the size and turnover rate of the large stabilized soil C pool with roughly decadal residence times. The Judgeford soil, near Wellington, New Zealand, provides a detailed 11-point 14C time series enabling observation of the incorporation and loss of bomb 14C in surface soil from 1959–2002. Calculations of the flow of C through the plant-soil system can be improved further by combining the known constraints of net primary productivity (NPP) and 14C-derived C turnover. We show the Biome-BGC model provides good estimates of NPP for the Judgeford site and estimates NPP from 1956–2010. Synthesis of NPP and 14C data allows parameters associated with the rapid turnover “active” soil C pool to be estimated. This step is important because it demonstrates that NPP and 14C can provide full data-based constraint of pool sizes and turnover rates for the 3 pools of soil C used in nearly all ecosystem and global C-cycle models.

A Modal Analysis of Eccentric Shaft of Caster Vibration Device

The model of eccentric shaft of caster vibration device is built by finite element software ANSYS, and bearings are regarded as rigid constraints and elastic constraints.Firstly, regarding the bearings as rigid constraints, the nodes on the parts of eccentric shaft, which match with bearing,are exerted full constraints. Secondly, regarding bearings as elastic constraints, spring, which is built by elastic element combination 14, are used to replace the bearings. In addition, the full constraints are exerted on the one side of spring,and axial constraint are exerted on the other side. Afterwards make the modal analysis of eccentric shaft.Solve and extract the first six natural frequency and modal shape.Watch and analyse the breaking formal of eccentric shaft as it is in different mode. The basis are settled for instantaneous and harmonic analysis.

The Schwinger Dyson equations and the algebra of constraints of random tensor models at all orders

Random tensor models for a generic complex tensor generalize matrix models in arbitrary dimensions and yield a theory of random geometries. They support a 1/N expansion dominated by graphs of spherical topology. Their Schwinger Dyson equations, generalizing the loop equations of matrix models, translate into constraints satisfied by the partition function. The constraints have been shown, in the large N limit, to close a Lie algebra indexed by colored rooted D-ary trees yielding a first generalization of the Virasoro algebra in arbitrary dimensions. In this paper we complete the Schwinger Dyson equations and the associated algebra at all orders in 1/N. The full algebra of constraints is indexed by D-colored graphs, and the leading order D-ary tree algebra is a Lie subalgebra of the full constraints algebra.

A new iterative-doubling Greedy–Lookahead algorithm for the single container loading problem

The aim of the Single Container Loading Problem (SCLP) is to pack three-dimensional boxes into a three-dimensional container so as to maximize the volume utilization of the container. We propose a new block building approach that constructs packings by placing one block (of boxes) at a time until no more boxes can be loaded. The key to obtaining high quality solutions is to select the right block to place into the right free space cuboid (or residual space) in the container. We propose a new heuristic for evaluating the fitness of residual spaces, and use a tree search to decide the best residual space-block pair at each step. The resultant algorithm outperforms the best known algorithms based on the 1600 commonly used benchmark instances even when given fewer computational resources. We also adapted our approach to address the full support constraint. The computational results for the full support support variant on the 1600 instances similarly show a significant improvement over existing techniques even when given substantially fewer computational resources.

Minimizing ISP Network Energy Cost: Formulation and Solutions

According to several studies, the power consumption of the Internet accounts for up to 10% of the worldwide energy consumption and is constantly increasing. The global consciousness on this problem has also grown, and several initiatives are being put into place to reduce the power consumption of the ICT sector in general. In this paper, we face the problem of minimizing power consumption for Internet service provider (ISP) networks. In particular, we propose and assess strategies to concentrate network traffic on a minimal subset of network resources. Given a telecommunication infrastructure, our aim is to turn off network nodes and links while still guaranteeing full connectivity and maximum link utilization constraints. We first derive a simple and complete formulation, which results into an NP-hard problem that can be solved only for trivial cases. We then derive more complex formulations that can scale up to middle-sized networks. Finally, we provide efficient heuristics that can be used for large networks. We test the effectiveness of our algorithms on both real and synthetic topologies, considering the daily fluctuations of Internet traffic and different classes of users. Results show that the power savings can be significant, e.g., larger than 35%.

Validation of the Texture-Based ALAMEL and VPSC Models by Measured Anisotropy of Plastic Yielding

Several multilevel plasticity models that make use of the crystallographic texture have been developed in the past for the prediction of deformation textures. State-of-the-art models that consider grain interaction, such as Alamel and VPSC, are known to give superior deformation texture predictions compared to the well-known (full constraint) Taylor model. In this paper, these models are assessed on a different basis, namely their ability to predict plastic anisotropy in single-phase steel sheet. A wide range of mechanical tests is considered: uniaxial tension, plane strain tension, simple shear and sheet normal compression. Furthermore, the sensitivity of the anisotropy predictions is analyzed, considering the variability in textures measured by routine XRD. The considered grain interaction models clearly produce improved predictions of plastic anisotropy over the Taylor model.

Yield Strength Anisotropy of Steel Sheet Induced by Grain Shape and Crystal Anisotropy

In crystal plasticity models the crystal anisotropy of the yield strength is accounted for by the yield locus. In the present paper the full constraint Taylor model is used to calculate the yield strength anisotropy of a heavily cold rolled and annealed IF steel. In addition to the crystallographically induced anisotropy also the grain shape anisotropy was taken into account. To this purpose a model is presented in which the grain size that appears in the Hall-Petch relation is substituted by an effective grain size that is dependent of the grain-shape morphology and the crystal orientation. The grain shape of a specific crystal orientation is approximated by an ellipsoid volume of which the major axes are obtained from experimental data. The effective grain size of a specific crystal orientation is determined by the intersection of the most active crystal slip plane of this orientation and the ellipsoid volume.

Hyperspectral Unmixing via $L_{1/2}$ Sparsity-Constrained Nonnegative Matrix Factorization

Hyperspectral unmixing is a crucial preprocessing step for material classification and recognition. In the last decade, nonnegative matrix factorization (NMF) and its extensions have been intensively studied to unmix hyperspectral imagery and recover the material end-members. As an important constraint for NMF, sparsity has been modeled making use of the L1 regularizer. Unfortunately, the L1 regularizer cannot enforce further sparsity when the full additivity constraint of material abundances is used, hence limiting the practical efficacy of NMF methods in hyperspectral unmixing. In this paper, we extend the NMF method by incorporating the L1/2 sparsity constraint, which we name L1/2 -NMF. The L1/2 regularizer not only induces sparsity but is also a better choice among Lq(0 <; q <; 1) regularizers. We propose an iterative estimation algorithm for L1/2-NMF, which provides sparser and more accurate results than those delivered using the L1 norm. We illustrate the utility of our method on synthetic and real hyperspectral data and compare our results to those yielded by other state-of-the-art methods.

STATCOM/SVC impact on the performance of transmission line distance protection

AbstractThe impact of 48‐pulse STATCOM/SVC on the apparent impedance seen by the transmission line distance relay is investigated in this paper. Analytical results are presented and verified by detailed simulations. The STATCOM/SVC control systems are modeled in full details and practical constraints are applied. It is shown that the presence of a current limiter in the control system of STATCOM could significantly mitigate the impact of STATCOM on the relay's calculated apparent impedance. Six different phase‐to‐phase and phase‐to‐ground measuring units of the distance relay are simulated to resemble the behavior of the relay. It is shown that the impact of SVC on the apparent impedance seen by the phase‐to‐ground fault measuring units is more pronounced. Different power system operating conditions, STATCOM/SVC control system settings and fault scenarios are considered in the simulations. The STATCOM/SVC effects on the distance relay tripping characteristics are also analyzed. © 2011 Institute of Electrical Engineers of Japan. Published by John Wiley &amp; Sons, Inc.

A novel yield locus description by combining the Taylor and the relaxed Taylor theory for sheet steels

Recently, several flexible constitutive equations have been proposed for sheet forming simulations. However, various mechanical tests are required to determine the material parameters needed for such models. In the present work, effort has been made to investigate the correlation between the polycrystal plasticity based yield loci and those determined from mechanical tests, in order to define yield functions easily and accurately with minimum experimental work. The results for different materials indicate that, in many cases, the Hill’48 quadratic yield function conventionally fitted with the plastic anisotropy R-values deviates significantly from measured yield loci. The Hill’48 yield function fitted with the uniaxial and biaxial yield stresses is quite close to the measured one, but with large deviation in the strain ratios for strong anisotropic materials. A careful comparison of the measured yield loci and those calculated from the Taylor full constraint model and the relaxed model indicates that the yield loci derived from the Taylor full constraint model capture the shape of the measured ones in general, but they are less elongated in the stretching direction, and the stretching factor is usually smaller than that derived from the relaxed Taylor model. The measured biaxial points are between those calculated from the two Taylor models. Based on the two yield loci derived from the Taylor models, a new combined model referred to as CTFP is proposed. The new model retains roughly the shape of the yield loci derived from the Taylor full constraint model, but the size is scaled using the averaged biaxial points of each model in the stretching regime. The proposed new description has been validated using several forming steel grades. This model can be used as virtual experiment for complicated mechanical tests, such as the plane strain tension, balanced biaxial stretching and shear test. The stress and strain data from the virtual experiments, together with the stress and plastic anisotropy measured in the uniaxial tensile test, are easily deployed as input data for other constitutive equations used in sheet metal forming simulations. Forming limit diagrams were predicted using different material constitutive models. The difference between the measured FLD and the calculated ones is remarkable. A profound analysis of the phenomena and a systematic study of intrinsic material parameters on the FLDs is needed.

A Theoretical Study on Forming Limit Diagram Predictions Using Viscoplastic Polycrystalline Plasticity Models

The Forming Limit Diagrams (FLDs) of textured polycrystalline sheet metals were investigated using micro-macro averaging and two types of grain-interaction models: Full-Constraint (FC) and Self-consistent (SC) schemes, in conjunction with the Marciniak–Kuczynski (MK) approach. By referring to previous FLD studies based on the FC-Taylor model ─ Wu and coworkers [Effect of an initial cube texture on sheet metal formability, Materials Science and Engineering A, 364:182–7, 2004] and Inal and coworkers [Forming Limit comparison for FCC and BCC sheets, International Journal of Plasticity, 21:1255-1266, 2005] ─ we found that the MK-FC strategy leads to unrealistic results. In the former case, the researchers found that an increasing spread about the cube texture produces unexpectedly high limit strains. In the latter work, Inal et al. predicted a remarkably low forming-limit curve for a FCC material and an extremely high forming-limit curve for a BCC material, in the biaxial-stretching range. Our investigations show that simulations performed with the MK-VPSC approach successfully predict more reliable results. For the BCC structure, the MK-VPSC predictions do not give the extreme values predicted when calculations are carried out with the MK-FC approach. In the FCC case, with decreasing textural intensity ─ from the ideal cube texture, through dispersions around the cube texture with increasing cut-off angles, to a random texture ─ a smooth transition in increasing limit strains was obtained. Furthermore, these results suggest that the selected constitutive model is critical for predicting the behavior of materials that exhibit a qualitative change in crystallographic texture, and hence, evolve anisotropically during mechanical deformation.

Strain Mode Dependence of Deformation Texture Developments: Microstructural Origin

Fully recrystallized commercial-purity aluminum sheets were deformed by limiting dome height tests, the following strain modes: uniaxial tension (US), near plane strain tension (PS), and equibiaxial tension (BS) were identified using standard procedure. The deformation texture developments differed significantly depending on the strain mode. Although the full constraints Taylor (FCT) model captured the texture developments in US, it failed to reproduce deformation textures in PS and especially in BS. The Advanced LAMEL (ALAMEL) model and the crystal plasticity finite element method (CPFEM) were, however, successful with respect to all three strain modes. Microtexture data brought out interesting observations of orientation gradients. First, the orientation gradients increased from US to PS to BS. Second, such gradients were mostly around initial (or prior deformation) grain boundary regions. A simple algorithm, and an associated computer program, was developed to demarcate such near boundary gradient zones (NBGZs). The area fraction and severity of NBGZ seemed to affect the texture development; FCT was reasonably successful at low NBGZ, whereas high NBGZ required the ALAMEL and the CPFEM models that are capable of addressing strain heterogeneity and grain interactions.

Slip Deformation Analysis Based on Full Constraints Model for &amp;alpha;-Titanium Alloy at Low Temperature

The effects of restricted slip conditions on both the Taylor factor and plastic work rate under the condition of tensile yielding have been analyzed in � -titanium alloys at low temperatures, using the full constraints model. The role of secondary slip systems, i.e., the hai basal slip and hc þ ai pyramidal slip, was clarified, when the hai prismatic slip was dominant. Although no influence of secondary slip conditions on the Taylor factor was detected, the plastic work rate was sensitive to the operating secondary slip systems. When the basal system was chosen as the secondary slip system, the plastic work rate increased in all tensile axes, especially around h0001i. In addition, no basal slip operation decreased the plastic strain energy. The plastic work rate was the highest along the h0001i tensile axis, and the operation of the hc þ ai pyramidal slip was necessary to achieve plastic deformation along c axis. High elastic strain energy, therefore, must accumulate to a high level around h0001i, because the pyramidal slip is hardly active owing to its very high critical resolved shear stress. [doi:10.2320/matertrans.L-M2011815]

The evolution of the Dillamore orientation in 80% rolled copper

The Dillamore orientation, {4 4 11}〈11 11 8〉, which is calculated by the full constraints Taylor model ( d e 11 = - d e 33 , d e 22 = 0 , d e ij = 0 for i ≠ j , with the subscripts 1, 2, and 3 indicating the rolling, transverse, and normal directions, respectively) is stable under plane-strain compression of face-centered cubic (fcc) metals. However, the Dillamore component has been little reported in rolling textures of fcc metals. The component has been observed along with the generally observed Goss {1 1 0}〈0 0 1〉, brass {1 1 0}〈1 1 2〉, copper {1 1 2}〈1 1 1〉, and S {1 2 3}〈6 3 4〉 components in the texture of 80% rolled copper sheet. The texture was measured by electron backscatter diffraction.

21 years of Biologically Effective Dose

In 1989 the British Journal of Radiology published a review proposing the term biologically effective dose (BED), based on linear quadratic cell survival in radiobiology. It aimed to indicate quantitatively the biological effect of any radiotherapy treatment, taking account of changes in dose-per-fraction or dose rate, total dose and (the new factor) overall time. How has it done so far? Acceptable clinical results have been generally reported using BED, and it is in increasing use, although sometimes mistaken for "biologically equivalent dose", from which it differs by large factors, as explained here. The continuously bending nature of the linear quadratic curve has been questioned but BED has worked well for comparing treatments in many modalities, including some with large fractions. Two important improvements occurred in the BED formula. First, in 1999, high linear energy transfer (LET) radiation was included; second, in 2003, when time parameters for acute mucosal tolerance were proposed, optimum overall times could then be "triangulated" to optimise tumour BED and cell kill. This occurs only when both early and late BEDs meet their full constraints simultaneously. New methods of dose delivery (intensity modulated radiation therapy, stereotactic body radiation therapy, protons, tomotherapy, rapid arc and cyberknife) use a few large fractions and obviously oppose well-known fractionation schedules. Careful biological modelling is required to balance the differing trends of fraction size and local dose gradient, as explained in the discussion "How Fractionation Really Works". BED is now used for dose escalation studies, radiochemotherapy, brachytherapy, high-LET particle beams, radionuclide-targeted therapy, and for quantifying any treatments using ionising radiation.

Semi‐global stabilization of discrete‐time systems subject to non‐right invertible constraints

AbstractThis paper investigates time‐invariant linear systems subject to input and state constraints. We study discrete‐time systems with full or partial constraints on both input and state. It has been shown earlier that the solvability conditions of stabilization problems are closely related to important concepts such as the right invertibility or non‐right invertibility of the constraints, the location of constraint invariant zeros, and the order of constraint infinite zeros. In this paper, for general time‐invariant linear systems with non‐right invertible constraints, necessary and sufficient conditions are developed under which semi‐global stabilization in the admissible set can be achieved by state feedback. Sufficient conditions are also developed for such a stabilization in the case where measurement feedback is used. Such sufficient conditions are almost necessary. Controllers for both state feedback and measurement feedback are constructed as well. Copyright © 2009 John Wiley &amp; Sons, Ltd.