A variable transformation method for solving linear absolute-value objective-function problems with linear constraints

Consensus for multi-agent systems with inherent nonlinear dynamics under directed topologies

BackgroundRestricted mean survival time (RMST) quantifies survival benefits in single-endpoint analysis, while restricted mean time lost (RMTL) measures event-related time loss in competing risks settings. Both provide clinically intuitive interpretations of treatment effects without relying on proportional hazards assumptions or parametric distributions. While existing RMST/RMTL methods focus primarily on two-group comparisons, multi-arm trials are common in practice. However, asymptotic approaches for these metrics suffer from inflated type I error in small samples, limiting their reliability.MethodsWe propose a global test framework using variable transformation methods (e.g., log, clog-log, arcsine square root, logit), which is applicable to multi-group comparisons of RMST and extends to RMTL in the presence of competing risks. Monte-Carlo simulations were conducted to evaluate type I error and power under various scenarios, and two illustrative examples were provided.ResultsSimulations demonstrated that transformed RMST and RMTL global tests effectively controlled type I error across small samples and high censoring rates, while improving power compared to untransformed methods. For single-endpoint analysis, the RMST arcsine square root transformation is recommended. In competing risks settings, RMTL logit transformation is preferred when the event of interest occurs more frequently than competing events, whereas clog-log transformation performs better when competing events dominate.ConclusionsThe proposed transformation-based global tests offer researchers a flexible, assumption-free tool to compare treatment effects across multiple groups with enhanced reliability and interpretability. Additionally, an R package "compRM" was developed to implement the proposed methods.

This research has first established that it is based on multiple methodologies developed to tackle the areas of engineering cargo handling systems, both at port and on-board vessels, as well as in the area of organisational self-assessment. It continued in reviewing the current status and future aspects of marine safety assessment together with an examination of a few major accidents. The major problems identified in marine safety assessment in this research are associated with inappropriate treatment of uncertainty in data and human error issues during the risk modelling estimation process and the calculation of failure probabilities. Following the identification of the research needs, this thesis has developed several analytical models for the safety assessment of cargo handling systems and organisational assessment structure. Such models can be effectively integrated into a risk-based framework using the marine formal safety assessment, safety case concepts. Bayesian network (BN) and evidential reasoning (ER) approaches applicable to cargo handling engineering systems have been proposed for systematically and effectively addressing uncertainty due to randomness and vagueness in data respectively. ER test cases for both a vessel selection process and a comparison of the safety maturity of different organisations in terms of self-assessment have been produced within a domain in which main and sub criteria have been developed for assessment reasons a long with the combination of the proposed model with existing organisational models. BN test case for a Liquefied Petroleum Gas (LPG) reliquefaction plant has been produced within a cause-effect domain in which Bayes' theorem is the focal mechanism of inference processing. A methodology aiming in finding the probability of failure when having variables ruled by uncertainty is established using certain variable transformation methods through the First and Second order reliability methodologies. Form/Sorm produces a most likely failure point, which is demonstrated through the application at a port cargo handling crane system. The outcomes have the potential to facilitate the decision-making process in a risk-based framework. Finally, the results of the research are summarised and areas where further research is required to improve the developed methodologies are outlined.

A reliability model is proposed to solve the problem of hybrid uncertainty with both random and interval variables in slope engineering. A hybrid uncertainty model based on the dimension reduction method and Taylor expansion is constructed to approximate the limit state function. Using the polynomial theorem and variable transformation method, the origin and center moments’ interval of the limit state function are calculated. Moment information is applied to the expansion of a three-parameter Weibull distribution, and the cumulative distribution function and probability density function of limit state function are determined. As a result, the failure probability interval of the slope is calculated. The interval uncertainty problem is transformed into an interval certainty problem using Taylor expansion without solving for the statistical moment of limit state function using multiple integrals and iteratively searching for the most probable failure points. The numerical results from two slopes show that the proposed method is effective and feasible.

Household consumption or income surveys do not typically cover refugee populations. In the rare cases where refugees are included, inconsistencies between different data sources could interfere with comparable poverty estimates. We test the performance of a recently developed cross-survey imputation method to estimate poverty for a sample of refugees in Colombia, combining household income surveys collected by the Government of Colombia and administrative (ProGres) data collected by the United Nations High Commissioner for Refugees in 2019 and 2022. We find that certain variable transformation methods can help resolve these inconsistencies. Estimation results with our preferred variable standardization method are robust to different imputation methods, including the normal linear regression method, the empirical distribution of the errors method, and the probit and logit methods. Several common machine learning techniques generally perform worse than our proposed imputation methods. We also find that we can reasonably impute poverty rates using an older household income survey and a more recent ProGres dataset for most of the poverty lines. These results provide relevant inputs into designing better surveys and administrative datasets on refugees in various country settings.

Bäcklund transformation (BT) is an intrinsic property of nonlinear integrable system. Generally, it is an interesting and challenging work to investigate BT of a nonlinear system, especially for the non-polynomial form. In this paper, we introduce an analytic method for constructing BTs of the generalized nonlinear wave equations (NLWEs) of the form utt=auxx+h(u). The BTs with arbitrary parameters are provided explicitly, so the integrability of the equation is verified accordingly. Then, the nonlinear superposition formulas (NSFs) of the NLWEs are given in terms of such BTs, and the infinite number of exact explicit solutions to the equations are obtained based on the BTs and the NSFs. Furthermore, the BTs of the other types of NLWEs of the form uxt=h(u) can be provided directly by the variable transformation method.

In this paper, synchronization of an inertial neural network with time-varying delays is investigated. Based on the variable transformation method, we transform the second-order differential equations into the first-order differential equations. Then, using suitable Lyapunov-Krasovskii functionals and Jensen's inequality, the synchronization criteria are established in terms of linear matrix inequalities. Moreover, a feedback controller is designed to attain synchronization between the master and slave models, and to ensure that the error model is globally asymptotically stable. Numerical examples and simulations are presented to indicate the effectiveness of the proposed method. Besides that, an image encryption algorithm is proposed based on the piecewise linear chaotic map and the chaotic inertial neural network. The chaotic signals obtained from the inertial neural network are utilized for the encryption process. Statistical analyses are provided to evaluate the effectiveness of the proposed encryption algorithm. The results ascertain that the proposed encryption algorithm is efficient and reliable for secure communication applications.

In this paper, the problem of robust stability analysis for a type of uncertain stochastic switched inertial neural networks (SSINNs) with time‐varying delay is investigated. First, the original second‐order system is converted into first‐order differential equations using the variable transformation method. Next, some sufficient conditions in terms of linear matrix inequalities (LMIs) are obtained using Lyapunov‐Krasovskii functional (LKF), state‐dependent switching (SDS) method, and Jensen's integral inequality for estimating integral inequalities so that the augmented system is robust, global, and asymptotically stable in the mean square for the uncertain SSINNs with time‐varying delay. It is shown that the stability of the above considered system composed of all unstable subsystems can be achieved by using the SDS law. Finally, two numerical simulations are provided to demonstrate the effectiveness of the proposed SDS law.

Linear reachability problems and minimal solutions to linear Diophantine equation systems

A VARIABLE METRIC METHOD FOR LINEARLY CONSTRAINED MINIMIZATION PROBLEMS

The linear constrained regulation problem for discrete-time systems is studied and a design algorithm for a linear constrained state-feedback controller is developed. The approach presented is based on the properties of positive invariant polyhedral sets of linear systems. The first part of the paper deals with the problem of the existence of linear state-feedback control laws that transfer asymptotically to the origin all initial stales belonging to a polyhedral subset of the state space while linear constraints on the control vector are satisfied. Then, an optimization approach for the derivation of a solution to the linear constrained regulation problem is established.

The linear reachability problem is to decide whether there is an execution path in a given finite state transition system such that the counts of labels on the path satisfy a given linear constraint. Using results on minimal solutions (in nonnegative integers) for linear Diophantine systems, we obtain new complexity results for the problem, as well as for other linear counting problems of finite state transition systems and timed automata. In contrast to previously known results, the complexity bounds obtained in this paper are polynomial in the size of the transition system in consideration, when the linear constraint is fixed.

The impact of power supply integrity on a design has become a critical issue, not only for functional verification, but also for performance verification. Traditional analysis has typically applied a worst case voltage drop at all points along a circuit path which leads to a very conservative analysis. We also show that in certain cases, the traditional analysis can be optimistic, since it ignores the possibility of voltage shifts between driver and receiver gates. In this paper, we propose a new analysis approach for computing the maximum path delay under power supply fluctuations. Our analysis is based on the use of superposition, both spatially across different circuit blocks, and temporally in time. We first present an accurate model of path delay variations under supply drops, considering both the effect of local supply reduction at individual gates and voltage shifts between driver/receiver pairs. We then formulate the path delay maximization problem as a constrained linear optimization problem, considering the effect of both IR drop and LdI/dt drops. We show how correlations between currents of different circuit blocks can be incorporated in this formulation using linear constraints. The proposed methods were implemented and tested on benchmark circuits, including an industrial power supply grid and we demonstrate a significant improvement in the worst-case path delay increase.

Simulating (elastically) deformable models that can collide with each other and with the environment remains a challenging task. The resulting contact problems can be elegantly approached using Lagrange multipliers to represent the unknown magnitude of the response forces. Typical methods construct and solve a Linear Complementarity Problem (LCP) to obtain the response forces. This requires the inverse of the generalized mass matrix, which is generally hard to obtain for deformable-body problems. In this article, we tackle such contact problems by directly solving the Mixed Linear Complementarity Problem (MLCP) and omitting the construction of an LCP matrix. Since a convex quadratic program with linear constraints is equivalent to an MLCP, we propose to use a Conjugate Residual (CR) solver as the backbone of our collision response system. By dynamically updating the set of active constraints, the MLCP with inequality constraints can be solved efficiently. We also propose a simple yet efficient preconditioner that ensures faster convergence. Finally, our approach is faster than existing methods (at the same accuracy), and it allows accurate treatment of friction.

On the dual of linear inverse problems