Admissible Set Research Articles

Optimization of the integro-differential hyperbolic model

We consider a model of processes in viscoelastic media. The force arising inside the body may depend not only on the current values but also on the entire time history of the motion (for example, polymers, emulsions, and suspensions exhibit memory properties). Such processes often lead to the necessity of studying hyperbolic integro-differential equations with Volterra integral term. The main goal is to prove the existence and uniqueness of generalized solutions to the corresponding initial-boundary value problem, as well as to investigate the existence of optimal control for systems described by these models. The main results are obtained using the method of a priori inequalities in negative norms. In particular, we justify inequalities in negative norms for the integro-differential operator in certain functional spaces. The work begins with a short description of relevant results with similar formulations and referencing works with physical justification of the model. Afterwards, we describe the problem statement, constraints on equation parameters, and functional spaces used for the investigation. Below are the main results, in particular definitions of generalized solutions and properties on the well-posed of the initial-boundary value problem as well as the existence of optimal control. Control is carried out through the right-hand side of the equation using a certain special operator. It is possible to examine specific examples of such control operators (illustrating various control mechanisms) and the corresponding control spaces. By utilizing proven inequalities and relying on general results of S.I. Lyashko from the theory of a priori inequalities in negative norms, we establish sufficient conditions for the existence of optimal control. In particular, we impose the restrictions on the admissible set of controls and the quality criterion.

Finite-time synchronization of complex dynamic networks with impulsive control and actuator saturation: An LMI approach

This paper investigates the finite-time synchronization (FTS) of complex dynamic networks (CDNs) with impulsive control subject to actuator saturation. We develop a novel method that integrates the impulsive comparison principle and improved convex hull representation lemma of saturated function to derive LMI-based sufficient conditions for FTS, which are easy to verify. We also estimate the admissible set of initial values to ensure the validity of the lemma. Unlike previous work, we relax the monotonicity assumption on the Lyapunov function, which broadens our results’ applicability. Moreover, we formulate and solve an optimization problem to enlarge the admissible set under the LMI constraints, using YALMIP toolbox in MATLAB software. Finally, several numerical examples are proposed to demonstrate our results’ effectiveness and superiority.

On the Maximal Output Admissible Set for Linear Distributed Systems

On the Maximal Output Admissible Set for Linear Distributed Systems

Weakly coupled systems of semilinear σ$$ \sigma $$‐evolution equations with friction and visco‐elastic type damping

In the present paper, we are interested to study global (in time) existence of small data Sobolev solutions to the Cauchy problem for a weakly coupled system of two semilinear ‐evolution equations with friction and visco‐elastic type damping, where for . We study model (1.1) (see below) in several cases with respect to the regularity for the data: First, we assume data . By using estimates of Sobolev solutions to related linear models with vanishing right‐hand side, we explain the admissible range of exponents in (1.1) which allow to prove the global (in time) existence of small data Sobolev solutions. Then we suppose that the data belong to , where now , . So the data have additional regularity to the first assumed integrability. We restrict ourselves to data from energy space (on the basis of ) and from energy space with additional suitable higher regularity. We compare in our statements the admissible set of exponents and in the power nonlinearities with the so‐called modified Fujita exponent. Finally, some blow‐up results complete the paper.

Monitor-based synthesis in enforcing disjunctive generalised mutual exclusion constraints

This paper focuses on enforcing disjunctive generalised mutual exclusion constraints, referred to as OR-GMEC, on Petri net models. In this case, the legal marking set is non-convex, while the admissible marking set can either be convex or non-convex. The study presents a necessary condition for the existence of a monitor-based solution for a non-convex admissible marking set. Subsequently, the disjunctive constraints are developed to derive an optimal supervisory controller, and an algorithm is proposed for solution computation. The design procedure includes off-line computation mechanisms, yielding an optimal (maximally permissive) supervisor with only a few monitors. The key advantage of the suggested approach is that, unlike the current techniques, the number of monitors in the supervisor’s structure does not rise as the number of constraints increases.

High-order accurate positivity-preserving and well-balanced discontinuous Galerkin schemes for ten-moment Gaussian closure equations with source terms

This paper proposes novel high-order accurate discontinuous Galerkin (DG) schemes for the one- and two-dimensional ten-moment Gaussian closure equations with source terms defined by a known potential function. Our DG schemes exhibit the desirable capability of being well-balanced (WB) for a known hydrostatic equilibrium state while simultaneously preserving positive density and positive-definite anisotropic pressure tensor. The well-balancedness is built on carefully modifying the solution states in the Harten–Lax–van Leer–contact (HLLC) flux, and appropriate reformulation and discretization of the source terms. Our novel modification technique overcomes the difficulties posed by the anisotropic effects, maintains the high-order accuracy, and ensures that the modified solution state remains within the physically admissible state set. We provide the rigorous positivity-preserving analyses of our WB DG schemes, based on several key properties of the admissible state set, the HLLC flux and the HLLC solver, as well as the geometric quasilinearization (GQL) approach in Wu and Shu (2023) [52], which was originally applied to analyze the admissible state set and the physical-constraints-preserving schemes for the relativistic magnetohydrodynamic equations in Wu and Tang (2017) [54], to address the difficulties arising from the nonlinear constraints on the pressure tensor. Moreover, the proposed WB DG schemes satisfy the weak positivity for the cell averages, implying the use of a simple scaling limiter to enforce the physical admissibility of the DG solution polynomials at certain points of interest. Extensive numerical experiments are conducted to validate the preservation of equilibrium states, accuracy in capturing small perturbations to such states, robustness in solving problems involving low density or low pressure, and high resolution for both smooth and discontinuous solutions.

On Complexity Bounds for the Maximal Admissible Set of Linear Time-Invariant Systems

On Complexity Bounds for the Maximal Admissible Set of Linear Time-Invariant Systems

A thermodynamically consistent machine learning-based finite element solver for phase-field approach

In this article, a thermodynamics-based data-driven approach utilizing machine learning is proposed to accelerate multiscale phase-field simulations. To obtain training data, the interface propagation kinetics, integrated into a physics-based phase-field model, are monolithically solved using a finite element method-based code developed within the Python-based open-source platform FEniCS. The admissible sets of internal state variables (e.g., stress, strain, order parameter, and its gradient) are extracted from the simulations and then utilized to identify the deformation fields of the microstructure at a given state in a thermodynamics-based artificial neural network. Finally, the high performance of the proposed machine learning-enhanced solver is illustrated through detailed comparisons with nanostructural calculations at the nanoscale. Unlike previous methods, the current analysis is not restricted by specific morphologies and boundary conditions, given the length and time scales required to reproduce these results.

Less conservative robust reference governors and their applications

The applications of reference governors to systems with unmeasured set-bounded disturbances can lead to conservative solutions. This conservatism can be reduced by estimating the disturbance from output measurements and canceling it in the nominal control law. In this paper, a reference governor based on such an approach is considered and time-varying, disturbance and state estimation errors bounding sets are derived. Consequently, the traditional implementation of a reference governor, which exploits a constraint admissible positively-invariant set of constant commands and initial states, is replaced by one which utilizes a time-dependent sequence of similar sets (which are not necessary nested). Examples are reported which include two applications to longitudinal control of aircraft that illustrate handling of elevator uncertainty and wing icing.

Balloon aortic valvuloplasty bridge to transcatheter aortic valve replacement is associated with worse in-hospital mortality

BackgroundBalloon aortic valvuloplasty (BAV) has gained renewed interest as a bridge to transcatheter aortic valve replacement (TAVR) for patients with aortic stenosis (AS). However, it is unclear whether they patients should undergo TAVR directly or receive a staged bridge to BAV before TAVR is unclear. We used a national database to examine the association between BAV and TAVR in patients with TAVR and its effect on in-hospital mortality. MethodsUsing the nationwide inpatient database of the Japanese registry of all cardiac and vascular diseases and the combination of the diagnosis procedure combination, we retrospectively analyzed 27,600 patients with AS who underwent TAVR between October 2013 and March 2021. Outcomes of the direct TAVR group (n = 27,387) were compared with those of the BAV bridge to TAVR group (n = 213), which received BAV at least 1 day before TAVR. ResultsThe median age was 85 (interquartile range: 82–88) years, with 33.3% (n = 9188) being male. Unplanned/emergent admissions increased with TAVR, whereas the use of BAV bridge to TAVR decreased. The in-hospital mortality rate was 1.3% and decreased over time. However, the BAV bridge to TAVR had a significantly higher in-hospital mortality than direct TAVR (5.6% vs. 1.3%; p < .0001). Factors associated with in-hospital mortality included age, body mass index, chronic renal disease, percutaneous coronary intervention, and BAV bridge to TAVR. ConclusionsIn unplanned/emergent and planned admission settings, the in-hospital mortality rate for BAV bridge to TAVR is worse than that for direct TAVR. Practical criteria for BAV bridge to TAVR should be proposed to improve outcomes.

Design Principles for Perfect Adaptation in Biological Networks with Nonlinear Dynamics.

Establishing a mapping between the emergent biological properties and the repository of network structures has been of great relevance in systems and synthetic biology. Adaptation is one such biological property of paramount importance that promotes regulation in the presence of environmental disturbances. This paper presents a nonlinear systems theory-driven framework to identify the design principles for perfect adaptation with respect to external disturbances of arbitrary magnitude. Based on the prior information about the network, we frame precise mathematical conditions for adaptation using nonlinear systems theory. We first deduce the mathematical conditions for perfect adaptation for constant input disturbances. Subsequently, we translate these conditions to specific necessary structural requirements for adaptation in networks of small size and then extend to argue that there exist only two classes of architectures for a network of any size that can provide local adaptation in the entire state space, namely, incoherent feed-forward (IFF) structure and negative feedback loop with buffer node (NFB). The additional positiveness constraints further narrow the admissible set of network structures. This also aids in establishing the global asymptotic stability for the steady state given a constant input disturbance. The proposed method does not assume any explicit knowledge of the underlying rate kinetics, barring some minimal assumptions. Finally, we also discuss the infeasibility of certain IFF networks in providing adaptation in the presence of downstream connections. Moreover, we propose a generic and novel algorithm based on non-linear systems theory to unravel the design principles for global adaptation. Detailed and extensive simulation studies corroborate the theoretical findings.

Multi-criteria optimization calculations to improve the efficiency of an agricultural moving power units in fleet

BACKGROUND: Due to the fact that the development of one target function for separately assessing each agricultural machine used in the fleet seems insufficient to fully assess the efficiency of agricultural moving power units in fleet, a multi-criteria formulation of the problem was applied using the previously developed hardware and software complex MOVI 1.4 and the development of computer programs to carry out their optimization calculations of the efficiency of the agricultural moving power units in fleet the example of a specific farm. AIMS: The goal of the work is to develop software tools for carrying out multi-criteria optimization calculations in order to increase the efficiency of agricultural moving power units in fleet in the context of digitalization of agriculture. METHODS: The analysis is based on the collection of scientific publications, scientific articles and other sources of information on the development of research and experimental design work on the creation of intelligent transport and technical means and the improvement of methodological and software for multi-criteria optimization calculations of the efficiency of the agricultural moving power units in fleet. Methods of scientific generalization and statistical processing of available information and analytical materials from domestic and foreign sources were also used. RESULTS: To calculate the values of quality criteria for the MES fleet, an interface subprogram for MOVI 1.4 was developed in the Pascal programming language, adequate for implementing calculations based on mathematical models of criteria at trial points. After introducing functional and criterion restrictions, an admissible set and a set of Pareto-optimal solutions were constructed, and correlation graphs between quality criteria were constructed. The scientific novelty lies in the development of computer programs for multi-criteria justification of the efficiency of the agricultural moving power units in fleet. CONCLUSION: The practical value lies in the fact that the developed mathematical and software tools can be successfully used for multi-criteria optimization of the efficiency of an agricultural moving power units in fleet using the example of specific agricultural organizations, regions or the country as a whole.

A solution for abstract decision problems based on maximum flow value

An abstract decision problem is an ordered pair where the first component is a nonempty and finite set of alternatives from which a society has to make a choice and the second component is an irreflexive relation on that set representing a dominance relation. A crucial problem is to find a reasonable solution that allows to select, for any given abstract decision problem, some of the alternatives. A variety of solutions have been proposed over the years. In this paper we propose a new solution, called maximum flow value set, that naturally stems from the work by Bubboloni and Gori (The flow network method, Social Choice and Welfare 51, pp. 621–656, 2018) and that is based on the concept of maximum flow value in a digraph. We analyze its properties and its relation with other solutions such as the core, the admissible set, the uncovered set, the Copeland set and the generalized stable set. We also show that the maximum flow value set allows to define a new Condorcet social choice correspondence strictly related to the Copeland social choice correspondence and fulfilling lots of desirable properties.

A Case of Rapidly Progressive Proliferative Diabetic Retinopathy in the Setting of Severe Anorexia Nervosa

Purpose: To report a case of rapidly progressive diabetic retinopathy in the setting of admission for severe anorexia nervosa. Methods: Case report Results: A 21-year-old female with type 1 diabetes mellitus and mild nonproliferative diabetic retinopathy of both eyes was admitted for severe anorexia nervosa with a BMI of 12.5 and hemoglobin A1c of 10.6. Three months after admission, the patient reported visual complaints and was found to have severe nonproliferative diabetic retinopathy in the right eye and proliferative diabetic retinopathy with vitreous hemorrhage in the left eye. She was lost to follow-up for 4 months, then presented to clinic with bilateral proliferative diabetic retinopathy and a tractional retinal detachment of the right eye. Conclusion: There is a potential relationship between severe eating disorders and rapid worsening of diabetic retinopathy. Patients with type 1 diabetes who have acute complications due to eating disorders should be evaluated by an ophthalmologist to monitor for rapid progression of retinopathy.

A retrospective audit of adult and paediatric anaphylaxis management from two Australian metropolitan mixed emergency departments

BackgroundAnaphylaxis is a potentially life-threatening allergic reaction, with presentations to emergency departments (EDs) increasing across Australia. Understanding the features of those presenting with anaphylaxis and aspects related to its optimal clinical management across the admission, treatment and discharge settings is needed to minimise its impact. We aimed to evaluate the nature and management of presentations related to anaphylaxis across two Australian EDs.MethodsRetrospective audit of paediatric and adult patients presenting to a community or tertiary level ED with anaphylaxis from 1 May 2018 to 30 April 2019. Data extracted from medical records included demographic characteristics, causative agents, clinical features, treatments administered across community, ambulance or ED settings, as well as post-discharge care arrangements including provision of Adrenaline Auto-Injector (AAI) and Allergy/Anaphylaxis Action Plan (AAP).ResultsA total of 369 (107 paediatric and 262 adult) ED presentations were identified. A total of 94 (36%) adult and 46 (43%) paediatric patients received pre-hospital adrenaline, with a further 91 (35%) adult and 29 (27%) paediatric patients receiving a dose of adrenaline in the ED. The most commonly administered treatment in ED were corticosteroids, given to 157 (60%) adult and 55 (51%) paediatric patients. Among those requiring an AAI for discharge, 123/210 (59%) adult and 57/91 (63%) of paediatric patients left hospital with an AAI. In contrast, among those requiring an allergy/anaphylaxis action plan (AAP) on discharge, 61/206 (30%) adult and 30/90 (33%) of paediatric patients left hospital with one. Factors associated with an increased likelihood of receiving AAI on discharge in paediatric and adult patients included receipt of any adrenaline, receipt of two or more doses of adrenaline, and longer duration of hospital stay. Adults presenting within business hours were more likely to be discharged with AAI, but no such difference was observed for paediatric patients. Similar findings were evident for provision of AAP on discharge.ConclusionThese findings demonstrate the need to improve assessment and treatment in the ED. In particular, the observed large variability in provision of AAI and AAP on discharge presents opportunities to explore strategies to improve awareness and provision of these critical components of post-discharge care.

Implementation of asynchronous mode in a linear periodic system with the nontrivial lower left block of averaging of the coefficient matrix

A linear control system with a periodic matrix of coefficients and program control is considered. The matrix under control is constant, rectangular (the number of columns does not exceed the number of rows) and its rank is not maximum, i. e. less than the number of columns. It is assumed that the control is periodic, and the module of its frequencies, i. e. the smallest additive group of real numbers, including all Fourier exponents of this control, is contained in the frequency module of the coefficient matrix. The following task is posed: to construct such a control from an admissible set that switches the system to asynchronous mode, i. e. the system must have periodic solutions such that the intersection of the frequency moduli of the solution and the coefficient matrix is trivial. The problem posed is called the problem of synthesis of asynchronous mode. The solution to the formulated problem significantly depends on the structure of the average value of the coefficient matrix. In particular, its solution is known for systems with zero average. In addition, solvability conditions were obtained in the case when the matrix under control has zero rows, the averaging of the coefficient matrix is reduced to the form with upper left diagonal block and with zero remaining blocks. In this paper we consider a more general case with a nontrivial left lower block. Assuming an incomplete column rank of the matrix function composed from the rows of oscillation path of the coefficient matrix, we construct the control explicitly. This control switches the system to asynchronous mode.

On almost-prime k-tuples

Let [Formula: see text] denote the divisor function and [Formula: see text] be an admissible set. We prove that there are infinitely many [Formula: see text] for which the product [Formula: see text] is square-free and [Formula: see text], where [Formula: see text] is asymptotic to [Formula: see text]. It improves a previous result of Ram Murty and Vatwani, replacing [Formula: see text] by [Formula: see text]. The main ingredients in our proof are the higher rank Selberg sieve and Irving–Wu–Xi estimate for the divisor function in arithmetic progressions to smooth moduli.

Tractable algorithms for strong admissibility

Much like admissibility is the key concept underlying preferred semantics, strong admissibility is the key concept underlying grounded semantics, as membership of a strongly admissible set is sufficient to show membership of the grounded extension. As such, strongly admissible sets and labellings can be used as an explanation of membership of the grounded extension, as is for instance done in some of the proof procedures for grounded semantics. In the current paper, we present two polynomial algorithms for constructing relatively small strongly admissible labellings, with associated min–max numberings, for a particular argument. These labellings can be used as relatively small explanations for the argument’s membership of the grounded extension. Although our algorithms are not guaranteed to yield an absolute minimal strongly admissible labelling for the argument (as doing so would have implied an exponential complexity), our best performing algorithm yields results that are only marginally larger. Moreover, the runtime of this algorithm is an order of magnitude smaller than that of the existing approach for computing an absolute minimal strongly admissible labelling for a particular argument. As such, we believe that our algorithms can be of practical value in situations where the aim is to construct a minimal or near-minimal strongly admissible labelling in a time-efficient way.

On Two Simple, Three-Parameter, Three-Dimensional, Non-Exchangeable Copulas

In this paper, we use the notion of a copula to provide theoretical contributions to the development of three-dimensional dependence models. In particular, we suggest two new three-dimensional copulas whose forms are simple and adaptable; they are based on polynomials, power functions, and three tuning parameters. In order to rely on the existing literature, we mention that the second copula can be viewed as a generalization of the three-dimensional Farlie- Gumbel-Morgenstern copula. Both copulas have the feature of being non-exchangeable (for most of the parameter values). Theoretical results are demonstrated, including wide admissible sets of values for the parameters and closed-form expressions for the medial correlation and Spearman’s rho. By using our methodology, the limitations imposed by the exchangeable property, which are typical of traditional three-dimensional copulas in the literature, are thus overcome, and new approaches to dependence modeling are opened up.

A Relaxed Version of the Cutting Method with Approximation of the Constraint Region

A cutting method was proposed for solving the convex programming problem. The method assumes that the constraint region of the problem is embedded into some polyhedral sets for constructing iteration points. It involves the construction of a sequence of approximations that belongs to the admissible set and is relaxed, as well as implies that the ε-solution of the initial problem is fixed after a finite number of steps. The method also allows to obtain mixed convergent algorithms by using, if desired, any known or new relaxation algorithms for constructing the main iteration points.