Lagrange Multiplier Procedure Research Articles

Optimized power control strategy in Massive MIMO for distributed IoT networks

We study a power control strategy for a Massive MIMO enabled IoT system to increase total throughput and to provide better differentiated levels of service to different classes of IoT devices. We use a closed-form signal-to-interference plus noise ratio (SINR) of Massive MIMO and apply the Lagrange multiplier procedure to find the optimum power control coefficients. We investigate several scenarios which include various cell radii and radiation power levels, and verify that the proposed scheme is effective in increasing total throughput and in providing different levels of throughput to different classes of IoT devices. We also apply the power control scheme when each device’s throughput is aggregated from multiple single-antenna access terminals based on the grouping of devices, and compare the cases when the grouping is conducted before and after power control. We show that grouping before power control can provide better differentiated levels of services by allocating different power to each group, while grouping after power control always provides higher total throughput by jointly considering all IoT devices.

Epq Incentive Model for Manufacture - Buyer with Floor Space and Inventory Level Constraints

This paper researches maker and purchaser creation model for deteriorating items with floor space and stock level imperative. Lagrange's multiplier procedure is utilized to take care of this sort of issue. Coordinated framework cost is created for equivalent advantages of both purchaser and producer. So as to decrease the complete stock cost, ideal request amount is resolved and furthermore floor space and stock level requirement ought to be fulfilled. Numerical model is likewise giving to revels the model.

Surface Irradiances Consistent with CERES-Derived Top-of-Atmosphere Shortwave and Longwave Irradiances

Abstract The estimate of surface irradiance on a global scale is possible through radiative transfer calculations using satellite-retrieved surface, cloud, and aerosol properties as input. Computed top-of-atmosphere (TOA) irradiances, however, do not necessarily agree with observation-based values, for example, from the Clouds and the Earth’s Radiant Energy System (CERES). This paper presents a method to determine surface irradiances using observational constraints of TOA irradiance from CERES. A Lagrange multiplier procedure is used to objectively adjust inputs based on their uncertainties such that the computed TOA irradiance is consistent with CERES-derived irradiance to within the uncertainty. These input adjustments are then used to determine surface irradiance adjustments. Observations by the Atmospheric Infrared Sounder (AIRS), Cloud–Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO), CloudSat, and Moderate Resolution Imaging Spectroradiometer (MODIS) that are a part of the NASA A-Train constellation provide the uncertainty estimates. A comparison with surface observations from a number of sites shows that the bias [root-mean-square (RMS) difference] between computed and observed monthly mean irradiances calculated with 10 years of data is 4.7 (13.3) W m−2 for downward shortwave and −2.5 (7.1) W m−2 for downward longwave irradiances over ocean and −1.7 (7.8) W m−2 for downward shortwave and −1.0 (7.6) W m−2 for downward longwave irradiances over land. The bias and RMS error for the downward longwave and shortwave irradiances over ocean are decreased from those without constraint. Similarly, the bias and RMS error for downward longwave over land improves, although the constraint does not improve downward shortwave over land. This study demonstrates how synergetic use of multiple instruments (CERES, MODIS, CALIPSO, CloudSat, AIRS, and geostationary satellites) improves the accuracy of surface irradiance computations.

A Novel Sparse Method for Despeckling SAR Images

This paper presents an algorithm for speckle reduction of synthetic aperture radar (SAR) images within a framework of multiscale curvelet analysis. First, we introduce a novel method to investigate the presence of 2-D heteroscedasticity based on Lagrange multiplier procedure. Employing this test confirms the heteroscedasticity of SAR image curvelet coefficients. Therefore, we employ a generalization of 2-D generalized autoregressive conditional heteroscedastic (2-D GARCH) model, called 2-D GARCH generalized Gaussian (2-D GARCH-GG), to these coefficients. This model preserves the appropriate properties of 2-D GARCH for modeling the curvelet coefficients while extending the dynamic formulation of 2-D GARCH model. Then, we design a novel Bayesian processor based on employing 2-D GARCH-GG model to estimate the noise-free curvelet coefficients. Experiments carried out on synthetic SAR images, as well as on true SAR images, verify the performance improvement in utilizing the new strategy compared with other established despeckle algorithms.

CENTROID NEURAL NETWORK WITH WEIGHTED FEATURES

A Centroid Neural Network with Weighted Features (CNN-WF) is proposed and presented in this paper. The proposed CNN-WF is based on a Centroid Neural Network (CNN), an effective clustering tool that has been successfully applied to various problems. In order to evaluate the importance of each feature in a set of data, a feature weighting concept is introduced to the Centroid Neural Network in the proposed algorithm. The weight update equations for CNN-WF are derived by applying the Lagrange multiplier procedure to the objective function constructed for CNN-WF in this paper. The use of weighted features makes it possible to assess the importance of each feature and to reject features that can be considered as noise in data. Experiments on a synthetic data set and a typical image compression problem show that the proposed CNN-WF can assess the importance of each feature and the proposed CNN-WF outperforms conventional algorithms including the Self-Organizing Map (SOM) and CNN in terms of clustering accuracy.

Energy Efficient Intra-Task Dynamic Voltage Scaling for Realistic CPUs of Mobile Devices *

It is not energy efficient to run a CPU at full speed all the time for all kinds of tasks in mobile devices. This paper proposes two energy efficient intra-task dynamic voltage scaling (DVS) algorithms for CPUs. There are three main contributions in this paper. Firstly, unlike the tedious derivation in PACE [2], we have derived the same optimal speed schedule with minimal energy consumption in a discrete and elegant way by using the Lagrange multiplier procedure. Secondly, the CPU model assumed in PACE is ideal, meaning that such a CPU supports all possible frequencies/voltage levels. We call such CPUs as ideal CPUs. In reality, CPUs only support a limited set of frequency/voltage levels, and we call this kind of CPUs as realistic CPUs. Thirdly, since energy consumption is not a simple function of frequency, it is more reasonable to transform the original nonlinear programming problem to the Multiple-Choice Knapsack Problem (MCKP). Since the problem can be described by a multistage graph, we used dynamic programming to derive an Optimal Schedule for Realistic CPUs (OSRC) with minimal energy consumption for realistic CPUs by using actual power consumption specifications of realistic CPUs. Considering potential computation and transition overheads, we have also proposed a low overhead OSRC (LO-OSRC), which restricts the change of CPU frequency/voltage to only once in the speed schedule. By using actual data from the power consumption specifications of two classical CPUs for evaluation, experimental results have shown that the energy saving of the proposed OSRC (LO-OSRC) is up to 10.3% (9.4%) better than that of PACE for realistic CPUs.

A continuum model of microheterogeneous media

A correct model of media with a microstructure (according to Mindlin's definition), which is defined by the presence of free strains and generalizes the well-known Mindlin, Cosserat and Aero–Kuvshinskii models, is proposed. The correctness of the formulation of the model is determined by using a “kinematic” variational principle, based on a systematic formal description of the kinematics of media, formulation of the kinematic constraints for media of various complexity and the construction of the corresponding strain potential energy using a Lagrange multiplier procedure. A system of constitutive relations is established, and a consistent statement of the boundary-value problem is formulated. It is shown that the model of a medium investigated not only reflects scale effects that are similar to cohesive interactions, but also provides a basis for describing a broad spectrum of adhesive interactions. An interpretation of the physical characteristics responsible for non-classical effects is proposed in the context of an analysis of the physical aspects of the model, and a description of the spectrum of adhesion mechanical parameters is given. ©2009.

Nonlinearities and Fractional Integration in the US Unemployment Rate*

AbstractThis paper proposes a model of the US unemployment rate which accounts for both its asymmetry and its long memory. Our approach introduces fractional integration and nonlinearities simultaneously into the same framework, using a Lagrange multiplier procedure with a standard null‐limit distribution. The empirical results suggest that the US unemployment rate can be specified in terms of a fractionally integrated process, which interacts with some nonlinear functions of labour‐demand variables such as real oil prices and real interest rates. We also find evidence of a long‐memory component. Our results are consistent with a hysteresis model with path dependency rather than a non‐accelerating inflation rate of unemployment (NAIRU) model with an underlying unemployment equilibrium rate, thereby giving support to more activist stabilization policies. However, any suitable model should also include business cycle asymmetries, with implications for both forecasting and policy‐making.

Non-Linearities and Fractional Integration in the US Unemployment Rate

This paper proposes a model of the US unemployment rate which accounts for both its asymmetry and its long memory. Our approach, based on the tests of Robinson (1994), introduces fractional integration and nonlinearities simultaneously into the same framework (unlike earlier studies employing a sequential procedure), using a Lagrange Multiplier procedure with a standard limit distribution. The empirical results suggest that the US unemployment rate can be specified in terms of a fractionally integrated process, which interacts with some non-linear functions of the labour demand variables (real oil prices and real interest rates). We also find evidence of a long-memory component. Our results are consistent with a hysteresis model with path dependency rather than a NAIRU model with an underlying unemployment equilibrium rate, hence giving support to more activist stabilisation policies. However, any suitable model should also include business cycle asymmetries, with implications for both forecasting and policymaking.

Finite Element Method in Dynamics of Flexible Multibody Systems: Modeling of Holonomic Constraints and Energy Conserving Integration Schemes

In this work we discuss an application of the finite elementmethod to modeling of flexible multibody systems employing geometricallyexact structural elements. Two different approaches to handleconstraints, one based on the Lagrange multiplier procedure and anotherbased on the use of release degrees of freedom, are examined in detail.The energy conserving time stepping scheme, which is proved to be wellsuited for integrating stiff differential equations, gouverning themotion of a single flexible link is appropriately modified and extendedto nonlinear dynamics of multibody systems.

Rank-based tests for autoregressive against bilinear serial dependence

Opumal (signed and unsigned) rank-based procedures are derived for the problem of testing autoregiessive AR(l) dependence, with unspecified autoregressive parameter and innovation density, against firstorder diagonal bilinear dependence, The proposed test statistics rely on rank-based versions of the residual spectrum and bispectrum. The resulting tests are asymptotically invariant, hence asymptotically distribution-free, and locally asymptotically most powerful. Their local asymptotic powers and asymptotic relative efficiencies with respect to the Gaussian Lagrange multiplier procedure of Saikkonen and Luukkonen (1988) are provided explicitly.

A Test for Normality of Observations and Regression Residuals

Summary Using the Lagrange multiplier procedure or score test on the Pearson family of distributions we obtain tests for normality of observations and regression disturbances. The tests suggested have optimum asymptotic power properties and good finite sample performance. Due to their simplicity they should prove to be useful tools in statistical analysis.

Implementation and Computational Issues for Combined Models of Location, Destination, Mode, and Route Choice

A unified approach to deriving models of urban location, destination, mode, and route choice is illustrated, and an algorithm based on Evans's approach and the Lagrange multiplier procedure is proposed. By examining derivatives of the Lagrangian function, we show that the Newton—Raphson technique can be implemented for finding the optimal Lagrange multipliers for these models. Procedures for identifying values of generalized cost-function coefficients are studied.

Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation

Traditional econometric models assume a constant one-period forecast variance. To generalize this implausible assumption, a new class of stochastic processes called autoregressive conditional heteroscedastic (ARCH) processes are introduced in this paper. These are mean zero, serially uncorrelated processes with nonconstant variances conditional on the past, but constant unconditional variances. For such processes, the recent past gives information about the one-period forecast variance. A regression model is then introduced with disturbances following an ARCH process. Maximum likelihood estimators are described and a simple scoring iteration formulated. Ordinary least squares maintains its optimality properties in this set-up, but maximum likelihood is more efficient. The relative efficiency is calculated and can be infinite. To test whether the disturbances follow an ARCH process, the Lagrange multiplier procedure is employed. The test is based simply on the autocorrelation of the squared OLS residuals. This model is used to estimate the means and variances of inflation in the U.K. The ARCH effect is found to be significant and the estimated variances increase substantially during the chaotic seventies.

A Test For Heteroscedasticity in a Limited Dependent Variable Model

SummaryLimited Dependent Variable models arise, for example, when the dependent variable is necessarily non‐negative. When these models are estimated under the incorrect assumption of homoscedasticity, serious consequences have been found. It is therefore important to test for its existence. In this paper, we make use of the Lagrange multiplier procedure to derive a test for heteroscedasticity in the Tobit model.

Efficient tests for normality, homoscedasticity and serial independence of regression residuals

We use the Lagrange multiplier procedure to derive efficient joint tests for residual normality, homoscedasticity and serial independence. The tests are simple to compute and asymptotically distributed as χ 2.