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To explore family perspectives on physical restraint practices and their minimization in an adult intensive care unit. A qualitative descriptive study with one-on-one semi-structured interviews. A deductive content analysis approach was undertaken using the Theoretical Domains Framework. A 20-bed medical, surgical, trauma ICU in Toronto, Canada. Fifteen family members were interviewed. Three themes emerged: (i) barriers and facilitators to restraint minimization. Barriers noted by families included patient agitation posing risks of losing endotracheal tubes, nurse reluctance to remove restraints, lack of family involvement, limited knowledge of alternatives, and a noisy environment. Facilitators included family involvement in decision-making, timely extubation, use of less restrictive alternatives such as mittens, mandating shorter periods of restraints application, and environmental modifications; (ii) unilateral decision-making regarding physical restraint use, where clinicians made decisions with inadequate communication with families nor obtaining consent; and (iii) the emotional impact of physical restraint use, with families experiencing sadness and shock and believing the patient would feel similarly. This qualitative study highlights significant issues surrounding the use of physical restraints, particularly the lack of family involvement in decision-making, the emotional toll on families, and various barriers and facilitators to minimizing restraint use. Effective communication and collaboration between clinicians and families are crucial to addressing these issues. Our findings underscore the critical need to enhance communication between clinicians and families, alongside consent processes. Identifying barriers and facilitators at various levels can inform individualized strategies to reduce restraint use, including integrating alternatives like mittens and involving families in care. Timely introduction of alternatives and family involvement are vital to prevent further emotional distress for families. Prioritizing the reduction of restraint duration is crucial, particularly in settings emphasizing harm minimization.

The magnetic susceptibility of tissue can be determined in gradient echo MRI by deconvolving the local magnetic field with the magnetic field generated by a unit dipole. This Quantitative Susceptibility Mapping (QSM) problem is unfortunately ill-posed. By transforming the problem to the Fourier domain, the susceptibility appears to be undersampled only at points where the dipole kernel is zero, suggesting that a modest amount of additional information may be sufficient for uniquely resolving susceptibility. A Morphology Enabled Dipole Inversion (MEDI) approach is developed that exploits the structural consistency between the susceptibility map and the magnitude image reconstructed from the same gradient echo MRI. Specifically, voxels that are part of edges in the susceptibility map but not in the edges of the magnitude image are considered to be sparse. In this approach an L1 norm minimization is used to express this sparsity property. Numerical simulations and phantom experiments are performed to demonstrate the superiority of this L1 minimization approach over the previous L2 minimization method. Preliminary brain imaging results in healthy subjects and in patients with intracerebral hemorrhages illustrate that QSM is feasible in practice. [Display omitted] ► We present a dipole inversion for quantitative susceptibility mapping (QSM). ► The structural consistency between anatomy and susceptibility is used for inversion. ► We implement the structural consistency in the L1- and L2-norm minimization. ► The L1-norm is superior to the L2-norm for QSM accuracy and quality. ► High quality QSM is feasible for imaging brain structures and hemorrhages.

In this paper, the problem of non-rigid structure estimation in trajectory space from monocular vision is investigated. Similar to the Point Trajectory Approach (PTA), based on characteristic points’ trajectories described by a predefined Discrete Cosine Transform (DCT) basis, the structure matrix was also calculated by using a factorization method. To further optimize the non-rigid structure estimation from monocular vision, the rank minimization problem about structure matrix is proposed to implement the non-rigid structure estimation by introducing the basic low-rank condition. Moreover, the Accelerated Proximal Gradient (APG) algorithm is proposed to solve the rank minimization problem, and the initial structure matrix calculated by the PTA method is optimized. The APG algorithm can converge to efficient solutions quickly and lessen the reconstruction error obviously. The reconstruction results of real image sequences indicate that the proposed approach runs reliably, and effectively improves the accuracy of non-rigid structure estimation from monocular vision.

In this paper, we prove the existence of finite-energy electrically and magnetically charged vortex solutions in the full Chern-Simons-Higgs theory, for which both the Maxwell term and the Chern-Simons term are present in the Lagrangian density. We consider both Abelian and non-Abelian cases. The solutions are smooth and satisfy natural boundary conditions. Existence is established via a constrained minimization procedure applied on indefinite action functionals. This work settles a long-standing open problem concerning the existence of dually charged vortices in the classical gauge field Higgs model minimally extended to contain a Chern-Simons term.

This note develops theory and a solution technique for a quadratically constrained eigenvalue minimization problem. This class of problems arises in the numerical solution of fully-nonlinear boundary value problems of Monge–Ampère type. Though it is most important in the three dimensional case, the solution method is directly applicable to systems of arbitrary dimension. The focus here is on solving the minimization subproblem which is part of a method to numerically solve a Monge–Ampère type equation. These subproblems must be evaluated many times in this numerical solution technique and thus efficiency is of utmost importance. A novelty of this minimization algorithm is that it is finite, of complexity , with the exception of solving a very simple rational function of one variable. This function is essentially the same for any dimension. This result is quite surprising given the nature of the constrained minimization problem.

The purposes of this paper are to establish an alternative forward-backward method with penalization terms called new forward-backward penalty method (NFBP) and to investigate the convergence behavior of the new method via numerical experiment. It was proved that the proposed method (NFBP) converges in norm to a zero point of the monotone inclusion problem involving the sum of a maximally monotone operator and the normal cone of the set of zeros of another maximally monotone operator. Under the observation of some appropriate choices for the available properties of the considered functions and scalars, we can generate a suitable method that weakly ergodic converges to a solution of the monotone inclusion problem. Further, we also provide a numerical example to compare the new forward-backward penalty method with the algorithm introduced by Attouch [Attouch, H., Czarnecki, M.-O. and Peypouquet, J., Coupling forward-backward with penalty schemes and parallel splitting for constrained variational inequalities, SIAM J. Optim., 21 (2011), 1251-1274].

In this paper, we introduce two implicit and explicit hybrid viscositylike approximation methods for solving a general monotone variational inequality, which covers their monotone variational inequality withC=Has a special case. We use the contractions to regularize the general monotone variational inequality, where the monotone operators are the generalized complements of nonexpansive mappings and the solutions are sought in the set of fixed points of another nonexpansive mapping. Such general monotone variational inequality includes some monotone inclusions and some convex optimization problems to be solved over the fixed point sets of nonexpansive mappings. Both implicit and explicit hybrid viscosity-like approximation methods are shown to be strongly convergent. In the meantime, these results are applied to deriving the strong convergence theorems for a general monotone variational inequality with minimization constraint. An application in hierarchical minimization is also included. 2010Mathematics Subject Classification:90C25, 47H05, 47H09, 65J15. Key words and phrases: Hybrid viscosity-like approximation method, General monotone variational inequality, Nonexpansive mapping, Projection, Minimization constraint.

There are problems in linear elasticity theory whose corresponding deformations, usually associated with singular stress fields, are open to question because they are not one-to-one and predict self-intersection. Recently, a theory has been advanced to handle such situations, which consists in minimizing the quadratic energy functional of linear elasticity subject to the constraint of local injectivity. In particular, the Jacobian of the deformation gradient is required to be not less than an arbitrarily small positive quantity, and, thus, the local orientation is preserved. Here, this theory is applied to the classical Lekhnitskii problem of an elastic aelotropic circular disk which is loaded on its boundary by a uniform radial pressure. Without the injectivity constraint, this classical linear problem has a unique solution. This example, with the injectivity constraint, already has been considered in previous works, but radial symmetry was assumed in order to reduce the problem from 2D to 1D. Here, making use of an interior penalty formulation, a numerical scheme is implemented that solves a full 2D problem. Remarkably, it is shown that there are values of the material moduli for which the minimal potential energy solution is no longer symmetric, producing a strong azimuthal shear and nominally a 180° rotation of an internal central core of the disk. Although the elastic strain energy is quadratic and convex, the strongly nonlinear character of the constraint allows for bifurcation instabilities.

The unique construction of stress as a constraint reaction in a rigid body loaded on its boundary in a state of equilibrium is described through the use of the elementary variational problem of minimum potential energy. We suppose that the body is naturally constrained to be strain free and this leads to a non-trivial constrained minimization problem. Our construction is based on an application of a Riesz-like representation theorem within the context of the classical Lagrange multiplier theorem of variational calculus.[PUBLICATION ABSTRACT]

In this work we discuss the existence of nonconstant periodic solutions for nonautonomous singular second order differential equations in the presence of impulses. Our approach is variational.