Trajectories of frailty with aging: Coordinated analysis of five longitudinal studies

Background and Objectives There is an urgent need to better understand frailty and it’s predisposing factors. Although numerous cross-sectional studies have identified various risk and protective factors of frailty, there is a limited understanding of longitudinal frailty progression. Furthermore, discrepancies in the methodologies of these studies hamper comparability of results. Here, we use a coordinated analytical approach in five independent cohorts to evaluate longitudinal trajectories of frailty and the effect of three previously identified critical risk factors: sex, age, and education. Research Design and Methods We derived a frailty index (FI) for five cohorts based on the accumulation of deficits approach. Four linear and quadratic growth curve models were fit in each cohort independently. Models were adjusted for sex/gender, age, years of education, and a sex/gender-by-age interaction term. Results Models describing linear progression of frailty best fit the data. Annual increases in FI ranged from 0.002 in the InCHIANTI cohort to 0.009 in the LASA. Women had consistently higher levels of frailty than men in all cohorts, ranging from an increase in the mean FI in women from 0.014 in the HRS cohort to 0.046 in the LASA cohort. However, the associations between sex/gender and rate of frailty progression were mixed. There was significant heterogeneity in within-person trajectories of frailty about the mean curves. Discussion and Implications Our findings of linear longitudinal increases in frailty highlight important avenues for future research. Specifically, we encourage further research to identify potential effect modifiers or groups that would benefit from targeted or personalized interventions.

Weak Multiplex Percolation

In many systems consisting of interacting subsystems, the complex interactions between elements can be represented using multilayer networks. However percolation, key to understanding connectivity and robustness, is not trivially generalised to multiple layers. This Element describes a generalisation of percolation to multilayer networks: weak multiplex percolation. A node belongs to a connected component if at least one of its neighbours in each layer is in this component. The authors fully describe the critical phenomena of this process. In two layers with finite second moments of the degree distributions the authors observe an unusual continuous transition with quadratic growth above the threshold. When the second moments diverge, the singularity is determined by the asymptotics of the degree distributions, creating a rich set of critical behaviours. In three or more layers the authors find a discontinuous hybrid transition which persists even in highly heterogeneous degree distributions, becoming continuous only when the powerlaw exponent reaches $1+1/(M-1)$ for $M$ layers.

On Degenerate Doubly Nonnegative Projection Problems

The doubly nonnegative (DNN) cone, being the set of all positive semidefinite matrices whose elements are nonnegative, is a popular approximation of the computationally intractable completely positive cone. The major difficulty for implementing a Newton-type method to compute the projection of a given large-scale matrix onto the DNN cone lies in the possible failure of the constraint nondegeneracy, a generalization of the linear independence constraint qualification for nonlinear programming. Such a failure results in the singularity of the Jacobian of the nonsmooth equation representing the Karush–Kuhn–Tucker optimality condition that prevents the semismooth Newton–conjugate gradient method from solving it with a desirable convergence rate. In this paper, we overcome the aforementioned difficulty by solving a sequence of better conditioned nonsmooth equations generated by the augmented Lagrangian method (ALM) instead of solving one aforementioned singular equation. By leveraging the metric subregularity of the normal cone associated with the positive semidefinite cone, we derive sufficient conditions to ensure the dual quadratic growth condition of the underlying problem, which further leads to the asymptotically superlinear convergence of the proposed ALM. Numerical results on difficult randomly generated instances and from the semidefinite programming library are presented to demonstrate the efficiency of the algorithm for computing the DNN projection to a very high accuracy.

Relaxation of the Boussinesq system and applications to the Rayleigh–Taylor instability

We consider the evolution of two incompressible fluids with homogeneous densities $$\rho _{-}<\rho _+$$ ρ - < ρ + subject to gravity described by the inviscid Boussinesq equations and provide the explicit relaxation of the associated differential inclusion. The existence of a subsolution to the relaxation allows one to conclude the existence of turbulently mixing solutions to the original Boussinesq system. As a specific application we investigate subsolutions emanating from the classical Rayleigh-Taylor initial configuration where the two fluids are separated by a horizontal interface with the heavier fluid being on top of the lighter. It turns out that among all self-similar subsolutions the criterion of maximal initial energy dissipation selects a linear density profile and a quadratic growth of the mixing zone. The subsolution selected this way can be extended in an admissible way to exist for all times. We provide two possible extensions with different long-time limits. The first one corresponds to a total mixture of the two fluids, the second corresponds to a full separation with the lighter fluid on top of the heavier. There is no motion in either of the limit states.

Equilibrium of Surfaces in a Vertical Force Field

In this paper, we study $$\varphi $$ φ -minimal surfaces in $$\mathbb {R}^3$$ R 3 when the function $$\varphi $$ φ is invariant under a two-parametric group of translations. Particularly those which are complete graphs over domains in $$\mathbb {R}^2$$ R 2 . We describe a full classification of complete flat-embedded $$\varphi $$ φ -minimal surfaces if $$\varphi $$ φ is strictly monotone and characterize rotational $$\varphi $$ φ -minimal surfaces by its behavior at infinity when $$\varphi $$ φ has a quadratic growth.

Inspection—Corruption Game of Illegal Logging and Other Violations: Generalized Evolutionary Approach

Games of inspection and corruption are well developed in the game-theoretic literature. However, there are only a few publications that approach these problems from the evolutionary point of view. In previous papers of this author, a generalization of the replicator dynamics of the evolutionary game theory was suggested for inspection modeling, namely the pressure and resistance framework, where a large pool of small players plays against a distinguished major player and evolves according to certain myopic rules. In this paper, we develop this approach further in a setting of the two-level hierarchy, where a local inspector can be corrupted and is further controlled by the higher authority (thus combining the modeling of inspection and corruption in a unifying setting). Mathematical novelty arising in this investigation involves the analysis of the generalized replicator dynamics (or kinetic equation) with switching, which occurs on the “efficient frontier of corruption”. We try to avoid parameters that are difficult to observe or measure, leading to some clear practical consequences. We prove a result that can be called the “principle of quadratic fines”: We show that if the fine for violations (both for criminal businesses and corrupted inspectors) is proportional to the level of violations, the stable rest points of the dynamics support the maximal possible level of both corruption and violation. The situation changes if a convex fine is introduced. In particular, starting from the quadratic growth of the fine function, one can effectively control the level of violations. Concrete settings that we have in mind are illegal logging, the sales of products with substandard quality, and tax evasion.

Eluciadation of the Plant Morphological and Biochemical Characterization of Bhela (Semecarpus Anacardium L.): An Underutilized Plant of Tropics

Semecarpus anacardium L. is a potential underutilized edible, highly nutritious fruit crop with ample medicinal properties grown in some localized pockets of India. Being a hardy crop, it can be easily used for climate resilient horticulture adaptation. But due to inadequate knowledge it is remains in underused position. Therefore the investigation was carried out to study the morphological and biochemical characteristics of the plant which will help in further improvement of the crop. The plant followed quadratic growth curve in different vegetative characters and leaf chlorophyll in both the years. Positive correlation was observed in different vegetative characters with different weather parameters during first year whereas in second year negatively correlation was recorded with sunshine hours only. The vegetative growth almost ceased during winter season, slow to moderate growth during summer and rapid growth was noticed from rainy to autumn season during experimentation. Leaf chlorophyll content followed an increasing trend during April to November and whereas a decreasing trend from December-March. It bears only terminally in older shoot from May to June with very lower fruit set and retention yield. The ripened fruits of Bhela showed high (23.94 ºbrix) TSS, total sugar, protein (21.08%), total carbohydrate, crude fat (34.91%) and food energy value (445.43 kcal/g). The observed performance of the crop with regards to plant morphology, growth rate and fruit quality was indicative for commercial exploitation in future.

Precision SMEFT bounds from the VBF Higgs at high transverse momentum

We study the production of Higgs bosons at high transverse momenta via vector-boson fusion (VBF) in the Standard Model Effective Field Theory (SMEFT). We find that contributions from four independent operator combinations dominate in this limit. These are the same ‘high energy primaries’ that control high energy diboson processes, including Higgs-strahlung. We perform detailed collider simulations for the diphoton decay mode of the Higgs boson as well as the three final states arising from the ditau channel. Using the quadratic growth of the SMEFT contributions relative to the Standard Model (SM) contribution, we project very stringent bounds on these operators that far surpass the corresponding bounds from the LEP experiment.

Mathematical Modelling, Analysis of Novel Corona Disease, and Its Effect on the Human Being

The present study is about the outbreak of novel Corona disease (COVID-19). The study proposes the mathematical modelling of COVID-19 disease as quadratic growth. Correlation coefficient associated with the characteristic of the modelling trend has been obtained by least square method using matlab function. Analysis of variance show the model proposed is significant. The study gave the information about the transmission of the disease and the prevention observed by the medical practitioner. The graphical representation has shown the outcome of the spread of the disease in India. This disease can be of respiratory type, pneumonia type, or asymptotic carrier type. The simulation result obtained is in accordance to the quadratic model fitted and can be used for the prediction of the growth. Results obtained on the basis of R2 were of approximately 97% in agreement. The only possibilities to avoid the spread of the disease is to monitor self-isolation, maintain cleanliness, improve immunity, and be protected.

Higher differentiability results for solutions to a class of non-autonomous obstacle problems with sub-quadratic growth conditions

We establish some higher differentiability results of integer and fractional order for solutions to non-autonomous obstacle problems of the form min ⁡ { ∫ Ω f ⁢ ( x , D ⁢ v ⁢ ( x ) ) : v ∈ K ψ ⁢ ( Ω ) } , \min\biggl{\{}\int_{\Omega}f(x,Dv(x)):v\in\mathcal{K}_{\psi}(\Omega)\biggr{\}}, where the function 𝑓 satisfies 𝑝-growth conditions with respect to the gradient variable, for 1 < p < 2 1<p<2 , and K ψ ⁢ ( Ω ) \mathcal{K}_{\psi}(\Omega) is the class of admissible functions v ∈ u 0 + W 0 1 , p ⁢ ( Ω ) v\in u_{0}+W^{1,p}_{0}(\Omega) such that v ≥ ψ v\geq\psi a.e. in Ω, where u 0 ∈ W 1 , p ⁢ ( Ω ) u_{0}\in W^{1,p}(\Omega) is a fixed boundary datum. Here we show that a Sobolev or Besov–Lipschitz regularity assumption on the gradient of the obstacle 𝜓 transfers to the gradient of the solution, provided the partial map x ↦ D ξ ⁢ f ⁢ ( x , ξ ) x\mapsto D_{\xi}f(x,\xi) belongs to a suitable Sobolev or Besov space. The novelty here is that we deal with sub-quadratic growth conditions with respect to the gradient variable, i.e. f ⁢ ( x , ξ ) ≈ a ⁢ ( x ) ⁢ | ξ | p f(x,\xi)\approx a(x)\lvert\xi\rvert^{p} with 1 < p < 2 1<p<2 , and where the map 𝑎 belongs to a Sobolev or Besov–Lipschitz space.