Narrow Results

Consider a nonlinear wave equation for a massless scalar field with self-interaction in the spatially flat Friedmann–Lemaître–Robertson–Walker spacetimes. For the case of accelerated expansion, we show that the blow-up in a finite time occurs for the equation with arbitrary power nonlinearity as well as upper bounds of the lifespan of blow-up solutions. Comparing to the case of the Minkowski spacetime, we discuss how the scale factor affects the lifespan of blow-up solutions of the equation.

In this paper, the lifespan under the generalized uncertainty principle (GUP) of rotating black hole is derived through the corrected radiation energy flux and the first law of the thermodynamics of black hole. The radiation energy flux indicates that there exist the highest temperature and the minimum mass both of which are relevant to the initial mass of the black hole in the final stage of the radiation. The lifespan of rotating black hole includes three terms: the dominant term is just the lifespan in the flat spacetime; the other two terms are individually induced by the rotation and the GUP.

The emergence of cloud computing in big data era has exerted a substantial impact on our daily lives. The conventional reliability-aware workflow scheduling (RWS) is capable of improving or maintaining system reliability by fault tolerance techniques such as replication and checkpointing based recovery. However, the fault tolerant techniques used in RWS would inevitably result in higher system energy consumption, longer execution time, and worse thermal profiles that would in turn lead to a decreased hardware lifespan. To mitigate the lifetime-energy-makespan issues of RWS in cloud computing systems for big data, we propose a novel methodology that decomposes the complicated studied problem. In this methodology, we provide three procedures to solve the energy consumption, execution makespan, and hardware lifespan issues in cloud systems executing real-time workflow applications. We implement numerous simulation experiments to validate the proposed methodology for RWS. Simulation results clearly show that the proposed RWS strategies outperform comparative approaches in reducing energy consumption, shortening execution makespan, and prolonging system lifespan while maintaining high reliability. The improvements on energy saving, reduction on makespan, and increase in lifespan can be up to 23.8%, 18.6%, and 69.2%, respectively. Results also show the potentiality of the proposed method to develop a distributed analysis system for big data that serves satellite signal processing, earthquake early warning, and so on.

Of all cancers, pancreatic cancer has a significantly low rate of survival, mostly due to lack of early screening. Thus, once detected, pancreatic cancer is usually in later stages, reducing the likelihood of full recovery. The most common treatment strategy is chemotherapy, although several immunotherapeutic drugs show promising results in extending the patient’s lifespan. In this paper, we provide a validated mathematical model for the pancreatic cancer after fitting the parameter values, such as tumor growth rate, inverse carrying capacity, activation and decay rate of pancreatic stellate cells, with the use of the experimental data presented by Cioffi et al. cioffi2015inhibition For treatments with the chemotherapeutic drugs, Abraxane and Gemcitabine, and the immunotherapeutic drug, Anti-CD47, we modified the model accurately and compared the simulation results with the experimental data not only to model pancreatic cancer treatment correctly but also to move forward with other drug trials. Then, we include the cancer stem cells, which are known to initiate tumors and cause a relapse post-chemotherapy, per cancer stem cell hypothesis so that cancer progression can be assessed based on this phenomenon. In addition, we investigate optimal drug protocols. We find out that the most effective treatment is dual therapy due to extending survival time when compared to other drugs. Moreover, this study reveals that drug dose is more effectual than frequency of drug injection on account of different treatment scheduling with the same dose over a week. The model could be a starting point to investigate pancreatic cancer progression based on cancer stem cell hypothesis and shed light on novel drug discoveries.

Aims: This study investigated the relationship between electroencephalograph (EEG) power and basal metabolic rate (BMR) over the human lifespan, to better understand the mechanisms involved in the decline of neural activity with age.

Methods: Eyes-open EEG power was calculated in standard frequency bands and averaged across recording sites in 1831 healthy subjects aged 6 to 86 years, from the Brain Resource International Database. In a subset of 175 subjects, structural MRI scans were also undertaken to determine the role of grey matter. Cerebral metabolic rate (CMR) was estimated using two models of EEG power, based on: (1) normalization of BMR by total body mass, and (2) scaling by cortical grey matter.

Results: Regression analysis revealed a linear relationship between the CMR estimates and EEG power under both models. In the full sample, CMR explained 65% of the variance in delta power, and 53% of the variance in theta power over the age span.

Discussion: The results demonstrate that the large EEG signals in early childhood are associated with a higher BMR during that age.

Integrative Significance: The use of cross-modal measurements in this study highlights the utility of capturing data in an integrative framework to reveal fundamental physiological relationships.

We consider smooth solutions of radial exterior Cauchy–Neumann problems with small initial data for radial quasilinear wave equations in three space dimensions, when the size of the initial data tends to 0. We obtain rather precise information on the lifespan, analogous with well known Cauchy problem results of Hörmander and John.

We consider the Cauchy–Dirichlet problem for semilinear wave equations in a three space-dimensional domain exterior to a bounded and non-trapping obstacle. We obtain a detailed estimate for the lower bound of the lifespan of classical solutions when the size of initial data tends to zero, in a similar spirit to that of the works of John and Hörmander where the Cauchy problem was treated. We show that our estimate is sharp at least for radially symmetric case.

We consider a toy model for a damped water waves system in a domain ${\mathrm{\Omega }}_t\subset 𝕋\times ℝ$. The toy model is based on the paradifferential formulation of the water waves system derived in the work of Alazard–Burq–Zuily [On the water-waves equations with surface tension, Duke Math. J.158 (2011) 413–499]. The form of damping we consider is a modified sponge layer proposed for the $3d$ water waves system by Clamond et al. in [An efficient model for three-dimensional surface wave simulations. Part II: Generation and absorption, J. Comput. Phys.205 (2005) 686–705]. We show that, in the case of small Cauchy data, solutions to the toy model exhibit a quadratic lifespan. This is done via proving energy estimates with Klainerman vector fields.

For a special class of quasilinear wave equations with small initial data which satisfy the nondegenerate assumption, the authors prove that the radially symmetric solution develops singularities in the second order derivatives in finite time while the first order derivatives and the solution itself remain continuous and small. More precisely, it turns out that this solution is a "geometric blowup solution of cusp type", according to the terminology posed by S. Alinhac^[2].

Objective: Epimedium flavonoids (EF), the raw extract of medicinal herb Epimedium, have been shown to have broad beneficial effects in the elderly including those with neurodegeneration. The goal of this study is to investigate whether EF is protective against proteotoxicity and whether it extends healthspan in C. elegans.

Methods: Animals were treated with EF supplemented in the growth medium. Two C. elegans models of human proteotoxic disease, CL4176 expressing an aggregated amyloid-$\beta$ (1–42) peptide (A$\beta$1–42) and AM140 expressing a polyglutamine (polyQ) protein, were exploited to test the anti-proteotoxicity of EF. Proteotoxicity-induced paralysis in CL4176 and AM140 was evaluated. Lifespan, stress resistance, and locomotion were tested in wild-type N2 C. elegans. Lifespan assays were also performed in CF1038, a daf-16 null mutant strain. DAF-16 nuclear translocation was analyzed in TJ356, a strain expressing a functional DAF-16::GFP fusion protein. The mRNA levels of downstream targets of DAF-16 were measured by qPCR.

Results: EF significantly reduced A$\beta$1–42- and polyQ-induced paralysis in CL4176 and AM140, indicating the anti-proteotoxic potency of EF. EF significantly extended the lifespan and promoted stress resistance and locomotion in N2, demonstrating a healthspan extension effect of EF. DAF-16 nuclear localization and its downstream targets, sod-3 and hsp-16.2 mRNA levels, were significantly elevated with EF. EF did not increase the lifespan of daf-16 null mutant CF1038, revealing a DAF-16-dependent mechanism of EF effect on lifespan.

Conclusion: We found that EF, a natural extract from a widely used medicinal herb Epimedium, protects against proteotoxicity and extends the healthspan via DAF-16 in C. elegans. Our work may provide molecular insights into the clinical benefits of EF and Epimedium.