Continuous Family Research Articles

Evaluation of a Patient-Centered Fall-Prevention Tool Kit to Reduce Falls and Injuries

Falls represent a leading cause of preventable injury in hospitals and a frequently reported serious adverse event. Hospitalization is associated with an increased risk for falls and serious injuries including hip fractures, subdural hematomas, or even death. Multifactorial strategies have been shown to reduce falls in acute care hospitals, but evidence for fall-related injury prevention in hospitals is lacking. To assess whether a fall-prevention tool kit that engages patients and families in the fall-prevention process throughout hospitalization is associated with reduced falls and injurious falls. This nonrandomized controlled trial using stepped wedge design was conducted between November 1, 2015, and October 31, 2018, in 14 medical units within 3 academic medical centers in Boston and New York City. All adult inpatients hospitalized in participating units were included in the analysis. A nurse-led fall-prevention tool kit linking evidence-based preventive interventions to patient-specific fall risk factors and designed to integrate continuous patient and family engagement in the fall-prevention process. The primary outcome was the rate of patient falls per 1000 patient-days in targeted units during the study period. The secondary outcome was the rate of falls with injury per 1000 patient-days. During the interrupted time series, 37 231 patients were evaluated, including 17 948 before the intervention (mean [SD] age, 60.56 [18.30] years; 9723 [54.17%] women) and 19 283 after the intervention (mean [SD] age, 60.92 [18.10] years; 10 325 [53.54%] women). There was an overall adjusted 15% reduction in falls after implementation of the fall-prevention tool kit compared with before implementation (2.92 vs 2.49 falls per 1000 patient-days [95% CI, 2.06-3.00 falls per 1000 patient-days]; adjusted rate ratio 0.85; 95% CI, 0.75-0.96; P = .01) and an adjusted 34% reduction in injurious falls (0.73 vs 0.48 injurious falls per 1000 patient-days [95% CI, 0.34-0.70 injurious falls per 1000 patient-days]; adjusted rate ratio, 0.66; 95% CI, 0.53-0.88; P = .003). In this nonrandomized controlled trial, implementation of a fall-prevention tool kit was associated with a significant reduction in falls and related injuries. A patient-care team partnership appears to be beneficial for prevention of falls and fall-related injuries. ClinicalTrials.gov Identifier: NCT02969343.

Performance of reconstruction factors for a class of new complex continuous wavelets

In this paper, we determine the factors necessary for the reconstruction of the signal from its continuous wavelet transform performed using the new complex continuous wavelet family by making use of admissible conditions and studied some of its properties. We also make a comparative assessment of its performance with the existing complex continuous wavelets, such as Morlet, Paul and DOG, in terms of reconstruction capability. The reconstruction was performed on three data sets, namely, a signal with a mixture of low and high frequencies, a non-stationary signal (synthetic) and an ECG signal. The results show that the proposed family of wavelets reconstruction capability is comparable with Morlet, Paul and DOG wavelets. Further, we investigate an alternate reconstruction formula without making use of admissibility condition and compare its efficiency of reconstruction with the standard (restricted) Morlet wavelet.

Solvability and Controllability Of Nonlinear Second - Order Control Systems Using Fixed Point Theorem

In this work, the nonlinear 2-order systems in Banach-spaces are introduced. Thence the sufficient conditions for existence and controllability of solutions for these systems are established using a strongly continuous cosine family of bounded linear operations on Banach-space and fixed-point theorem by Schauder. Moreover, examples which illustrate mathematical justification of above results are given.

A new approach in index theory

In this paper, we define an analytical index for a continuous family of Fredholm operators parameterized by a topological space $${\mathbb {X}}$$ into a Hilbert space H, as a sequence of integers, extending naturally the usual definition of the index and we prove the homotopy invariance of the index. We give also an extension of the Weyl theorem for normal continuous families and we prove that if H is separable, then the space of B-Fredholm operators on H is path connected.

Generalized Grad–Shafranov equation for non-axisymmetric MHD equilibria

The structure of static MHD equilibria that admit continuous families of Euclidean symmetries is well understood. Such field configurations are governed by the classical Grad–Shafranov equation, which is a single elliptic partial differential equation in two space dimensions. By revealing a hidden symmetry, we show that in fact all smooth solutions of the equilibrium equations with non-vanishing pressure gradients away from the magnetic axis satisfy a generalization of the Grad–Shafranov equation. In contrast to solutions of the classical Grad–Shafranov equation, solutions of the generalized equation are not automatically equilibria, but instead only satisfy force balance averaged over the one-parameter hidden symmetry. We then explain how the generalized Grad–Shafranov equation can be used to reformulate the problem of finding exact three-dimensional smooth solutions of the equilibrium equations as finding an optimal volume-preserving symmetry.

Renormalization of Galilean electrodynamics

We study the quantum properties of a Galilean-invariant abelian gauge theory coupled to a Schrödinger scalar in 2+1 dimensions. At the classical level, the theory with minimal coupling is obtained from a null-reduction of relativistic Maxwell theory coupled to a complex scalar field in 3+1 dimensions and is closely related to the Galilean electromagnetism of Le-Bellac and Lévy-Leblond. Due to the presence of a dimensionless, gauge-invariant scalar field in the Galilean multiplet of the gauge-field, we find that at the quantum level an infinite number of couplings is generated. We explain how to handle the quantum corrections systematically using the background field method. Due to a non-renormalization theorem, the beta function of the gauge coupling is found to vanish to all orders in perturbation theory, leading to a continuous family of fixed points where the non-relativistic conformal symmetry is preserved.

Loewner evolution of hedgehogs and 2-conformal measures of circle maps

AbstractLet f be a germ of a holomorphic diffeomorphism with an irrationally indifferent fixed point at the origin in ${\mathbb C}$ (i.e. $f(0) = 0, f'(0) = e^{2\pi i \alpha }, \alpha \in {\mathbb R} - {\mathbb Q}$ ). Pérez-Marco [Fixed points and circle maps. Acta Math.179(2) (1997), 243–294] showed the existence of a unique continuous monotone one-parameter family of non-trivial invariant full continua containing the fixed point called Siegel compacta, and gave a correspondence between germs and families $(g_t)$ of circle maps obtained by conformally mapping the complement of these compacts to the complement of the unit disk. The family of circle maps $(g_t)$ is the orbit of a locally defined semigroup $(\Phi _t)$ on the space of analytic circle maps, which we show has a well-defined infinitesimal generator X. The explicit form of X is obtained by using the Loewner equation associated to the family of hulls $(K_t)$ . We show that the Loewner measures $(\mu _t)$ driving the equation are 2-conformal measures on the circle for the circle maps $(g_t)$ .

Continuous family of exact Dispersive Quasi-Normal Modal (DQNM) expansions for dispersive photonic structures.

In photonics, Dispersive Quasi-Normal Modes (DQNMs) refer to optical resonant modes, solutions of spectral problems associated with Maxwell's equations for open photonic structures involving dispersive media. Since these DQNMs are the constituents determining optical responses, studying DQNM expansion formalisms is the key to model the physical properties of a considered system. In this paper, we emphasize the non-uniqueness of the expansions related to the over-completeness of the set of modes and discuss a family of DQNM expansions depending on continuous parameters that can be freely chosen. These expansions can be applied to dispersive, anisotropic, and even non-reciprocal materials. As an example, we particularly demonstrate the modal analysis on a 2-D scattering model where the permittivity of a silicon object is drawn directly from actual measurement data.

Left orderable surgeries of double twist knots II

AbstractA slope r is called a left orderable slope of a knot $K \subset S^3$ if the 3-manifold obtained by r-surgery along K has left orderable fundamental group. Consider double twist knots $C(2m, \pm 2n)$ and $C(2m+1, -2n)$ in the Conway notation, where $m \ge 1$ and $n \ge 2$ are integers. By using continuous families of hyperbolic ${\mathrm {SL}}_2(\mathbb {R})$ -representations of knot groups, it was shown in [8, 16] that any slope in $(-4n, 4m)$ (resp. $ [0, \max \{4m, 4n\})$ ) is a left orderable slope of $C(2m, 2n)$ (resp. $C(2m, - 2n)$ ) and in [6] that any slope in $(-4n,0]$ is a left orderable slope of $C(2m+1,-2n)$ . However, the proofs of these results are incomplete, since the continuity of the families of representations was not proved. In this paper, we complete these proofs, and, moreover, we show that any slope in $(-4n, 4m)$ is a left orderable slope of $C(2m+1,-2n)$ detected by hyperbolic ${\mathrm {SL}}_2(\mathbb {R})$ -representations of the knot group.

Topological transition on the conformal manifold

Despite great successes in the study of gapped phases, a comprehensive understanding of the gapless phases and their transitions is still under developments. In this paper, we study a general phenomenon in the space of (1+1)$d$ critical phases with fermionic degrees of freedom described by a continuous family of conformal field theories (CFT), a.k.a. the conformal manifold. Along a one-dimensional locus on the conformal manifold, there can be a transition point, across which the fermionic CFTs on the two sides differ by stacking an invertible fermionic topological order (IFTO), point-by-point along the locus. At every point on the conformal manifold, the order and disorder operators have power-law two-point functions, but their critical exponents cross over with each other at the transition point, where stacking the IFTO leaves the fermionic CFT unchanged. We call this continuous transition on the fermionic conformal manifold a topological transition. By gauging the fermion parity, the IFTO stacking becomes a Kramers-Wannier duality between the corresponding bosonic CFTs. Both the IFTO stacking and the Kramers-Wannier duality are induced by the electromagnetic duality of the (2+1)$d$ $\mathbb{Z}_2$ topological order. We provide several examples of topological transitions, including the familiar Luttinger model of spinless fermions (i.e. the $c=1$ massless Dirac fermion with the Thirring interaction), and a new class of $c=2$ examples describing $U(1)\times SU(2)$-protected gapless phases.

Reducibility sets for sequences of matrices

Our main aim is to give a complete characterization of the reducibility sets of continuous 1-parameter families of sequences of matrices, which turn out to be the Fσ -sets. We also show that for any Fσ -set containing zero, one can find a family with this reducibility set. In addition, we obtain corresponding results for the reducibility-stability set and we give an optimal condition for the reducibility to a diagonal matrix in terms of the Lyapunov exponents.

Women leadership in Vietnamese higher education institutions: An exploratory study on barriers and enablers for career enhancement

Barriers and enablers that the women leaders experience in the higher education (HE) sector have been a widely researched topic in many developed countries. However, the research on this topic is very limited in developing countries such as Vietnam. Despite the Gender Equality Law introduced in 2006 by the Vietnamese government to promote equal opportunities to women and also reducing the Gender Gap Index score of 70% in Vietnam, there are few women in leadership roles in several sectors including HE. This explanatory study has been conducted in nine universities in Vietnam to understand the barriers that prevent women from taking up leadership roles and the factors that motivate them in their career advancement to become a leader. The qualitative study was conducted with 21 participants (19 women and two men) working as senior leaders, middle managers, and lecturers in these universities. The study found that the main barriers in women’s career enhancement were work-life imbalance, subordinates’ perceptions regarding women leaders, social networking, and personal factors. The factors which motivated women leaders to advance in their career path were continuous family and mentor support, changing mindset of employers, and potential leadership competency of women leaders. The findings of this study would be beneficial for the Vietnamese HE institutions to determine policies and programs, which can support women’s career advancement to leadership roles bringing diversity and inclusion at these institutions. The results might be a steppingstone to achieve the United Nations Sustainable Development Goal 5 on gender equality in Vietnam, which is one of the world’s fastest-growing economies.

Periodic orbits of a Hamiltonian system related with the Friedmann–Robertson–Walker system in rotating coordinates

We provide sufficient conditions on the four parameters of a Hamiltonian system, related with the Friedmann–Robertson–Walker Hamiltonian system in a rotating reference frame, which guarantee the existence of 12 continuous families of periodic orbits, parameterized by the values of the Hamiltonian, which born at the equilibrium point localized at the origin of coordinates. The main tool for finding analytically these families of periodic orbits is the averaging theory for computing periodic orbits adapted to the Hamiltonian systems. The technique here used can be applied to arbitrary Hamiltonian systems.

Beyond Beatty sequences: Complementary lattices

AbstractBy taking square lattices as a two-dimensional analogue to Beatty sequences, we are motivated to define and explore the notion of complementary lattices. In particular, we present a continuous one-parameter family of complementary lattices. This main result then yields several novel examples of complementary sequences, along with a geometric proof of the fundamental property of Beatty sequences.

Central Configurations and Action Minimizing Orbits in Kite Four-Body Problem

In the current article, we study the kite four-body problems with the goal of identifying global regions in the mass parameter space which admits a corresponding central configuration of the four masses. We consider two different types of symmetrical configurations. In each of the two cases, the existence of a continuous family of central configurations for positive masses is shown. We address the dynamical aspect of periodic solutions in the settings considered and show that the minimizers of the classical action functional restricted to the homographic solutions are the Keplerian elliptical solutions. Finally, we provide numerical explorations via Poincaré cross-sections, to show the existence of periodic and quasiperiodic solutions within the broader dynamical context of the four-body problem.

Family support is beneficial to the management and prognosis of patients with obstructive sleep apnoea.

This study aimed to explore the correlations between continuous positive airway pressure (CPAP) treatment-related self-efficacy and family support among patients with obstructive sleep apnoea (OSA) to provide a basis for improving patients' CPAP treatment compliance. From May to Dec 2017, a cross-sectional study was conducted in the emergency wards, otorhinolaryngology wards, respiratory wards, and outpatient clinic of our hospital. A total of 112 patients with OSA treated with home ventilators were administered with the Self-efficacy Measure for Sleep Apnoea (SEMSA) and Perceived Social Support from Family (PSS-Fa) Scale. On the SEMSA, participants had a disease risk perception score of 2.61±0.31, an outcome expectation score of 2.44±0.17, and a self-efficacy score of 2.55±0.13. Mean total score on PSS-Fa was 10.15±2.73, with 10.7%, 45.5% and 43.8% of participants showing a low level, a medium level, and a high level of family support, respectively. Outcome expectation and self-efficacy were positively correlated with family support. The self-efficacy and outcome expectation of patients with OSA are positively correlated with their level of family support.

Scale-dependent Rayleigh–Taylor dynamics with variable acceleration by group theory approach

Rayleigh–Taylor instability (RTI) has critical importance for a broad range of plasma processes, from supernovae to fusion. In most instances, RTI is driven by variable acceleration, whereas the bulk of existing studies have considered only constant and impulsive acceleration. This work focuses on RTI driven by acceleration with a power-law time-dependence. We review the existing theoretical approaches, apply the group theory approach to solve this long-standing problem, and yield the unified framework for the scale-dependent dynamics of Rayleigh–Taylor (RT) bubbles and RT spikes. For the early-time linear dynamics, we provide the dependence of RTI evolution on the acceleration parameters and the initial conditions. For the late-time nonlinear dynamics, we find a continuous family of asymptotic solutions, directly link the interface velocity to the interface morphology and the interfacial shear, derive solutions for the regular bubbles and for the singular spikes, and study the stability of these solutions. The properties of special nonlinear solutions in the RT family are scrupulously described, including the critical, Taylor, Layzer-drag, and Atwood solutions. It is shown that the fastest Atwood bubble is regular and stable, and the fastest Atwood spike is singular and unstable. The essentially multi-scale and interfacial character of RT dynamics is demonstrated. The former can be understood by viewing the RT coherent structure of bubbles and spikes as a standing wave with the growing amplitude. The latter implies that RT flow has effectively no motion of the fluids away from the interface and has intense motion of the fluids near the interface, with shear-driven vortical structures appearing at the interface. Our theory agrees with available observations and elaborates extensive benchmarks for future research and for better understanding of RT driven phenomena in plasmas.

Asymptotic growth of the 4d mathcal{N} = 4 index and partially deconfined phases

We study the Cardy-like asymptotics of the 4d mathcal{N} = 4 index and demonstrate the existence of partially deconfined phases where the asymptotic growth of the index is not as rapid as in the fully deconfined case. We then take the large-N limit after the Cardy-like limit and make a conjecture for the leading asymptotics of the index. While the Cardy-like behavior is derived using the integral representation of the index, we demonstrate how the same results can be obtained using the Bethe ansatz type approach as well. In doing so, we discover new non-standard solutions to the elliptic Bethe ansatz equations including continuous families of solutions for SU(N ) theory with N ≥ 3. We argue that the existence of both standard and continuous non-standard solutions has a natural interpretation in terms of vacua of mathcal{N} = 1∗ theory on ℝ3× S1.

Complete Ricci Solitons via Estimates on the Soliton Potential

Abstract In this paper, a growth estimate on the soliton potential is shown for a large class of cohomogeneity one manifolds. This is used to construct continuous families of complete steady and expanding Ricci solitons in the setups of Lü–Page–Pope [24] and Dancer–Wang [17]. It also provides a different approach to the two summands system [30] that applies to all known geometric examples.

Adaptive Isostable Reduction of Nonlinear PDEs With Time Varying Parameters

Isostable reduction is a powerful technique for characterizing the transient behavior of a weakly forced, nonlinear dynamical systems in relation to a stable attractor. Practically, this reduction strategy requires small magnitude inputs so that the state remains close to the underlying attractor; when inputs become too large the reduction becomes unusable. Here, we develop an adaptive isostable coordinate framework that is valid for a continuous family of system parameters. Relations are derived that capture changes to the isostable coordinates in response to parameter changes. This information is subsequently used to define a reduction strategy valid for large magnitude but slowly varying inputs. The proposed reduction framework is compared to well-established linear and nonlinear proper orthogonal decomposition (POD) reduction techniques for simulations of the 1-dimensional nonlinear Burgers' equation with time-varying Dirichlet boundary conditions. In numerical simulations the proposed reduction strategy only requires a single mode to accurately capture system behavior. By contrast, the linear POD reduction performs poorly while the nonlinear POD strategy requires several modes to achieve comparable performance.