LpL^p-improving bounds of maximal functions along planar curves

In this paper, we study the $L^p(\mathbb{R}^2)$-improving bounds, i.e., $L^p(\mathbb{R}^2)\rightarrow L^q(\mathbb{R}^2)$ estimates, of the maximal function $M_{\gamma}$ along a plane curve $(t,\gamma(t))$, where $$M_{\gamma}f(x_1,x_2):=\sup_{u\in [1,2]}\left|\int_{0}^{1}f(x_1-ut,x_2-u \gamma(t))\,\textrm{d}t\right|,$$ and $\gamma$ is a general plane curve satisfying some suitable smoothness and curvature conditions. We obtain $M_{\gamma} : L^p(\mathbb{R}^2)\rightarrow L^q(\mathbb{R}^2)$ if $(\frac{1}{p},\frac{1}{q})\in \Delta\cup \{(0,0)\}$ and $(\frac{1}{p},\frac{1}{q})$ satisfying $1+(1 +\omega)(\frac{1}{q}-\frac{1}{p})>0$, where $\Delta:=\{(\frac{1}{p},\frac{1}{q}):\ \frac{1}{2p}<\frac{1}{q}\leq \frac{1}{p}, \frac{1}{q}>\frac{3}{p}-1 \}$ and $\omega:=\limsup_{t\rightarrow 0^{+}}\frac{\ln|\gamma(t)|}{\ln t}$. This result is sharp except for some borderline cases. As Hickman stated in [J. Funct. Anal. 270 (2016), pp. 560--608], this is a very different situation

Self-Powered Wearable Biosensors

Wearable biosensors hold the potential of revolutionizing personalized healthcare and telemedicine. Advances in chemical sensing, flexible materials, and scalable manufacturing techniques now allow wearables to detect key physiological indicators such as temperature, vital signs, body motion, and molecular biomarkers. With these systems operating on the skin, they enable continuous and noninvasive disease diagnosis and health monitoring. Such complex devices, however, require suitable power sources in order to realize their full capacity. Emerging wearable energy harvesters are attractive for addressing the challenges of a wearable power supply. These harvesters convert various types of ambient energy sources (e.g., biomechanical energy, biochemical energy, and solar energy) into electricity. In some circumstances, the harvested electrical signals can directly be used for active sensing of physiological parameters. On the other hand, single or hybrid wearable energy harvesters, when integrated with power management circuits and energy storage devices, could power additional biosensors as well as signal processing and data transmission electronics. Self-powered sensor systems operate continuously and sustainably without an external power supply are promising candidates in the next generation of wearable electronics and the Internet of Things. This Account highlights recent progress in self-powered wearable sensors toward personalized healthcare, covering biosensors, energy harvesters, energy storage, and power supply strategies. The Account begins with an introduction of our wearable biosensors toward an epidermal detection of physiological information. Advances in structural and material innovations enable wearable systems to measure both biophysical and biochemical indicators conformably, accurately, and continuously. We then discuss emerging technologies in wearable energy harvesting, classified according to their capability to scavenge energy from various sources. These include examples of using energy harvesters themselves as active biosensors. Through seamless integration and efficient power management, self-powered wireless wearable sensor systems allow real-time data acquisition, processing, and transmission for health monitoring. The final section of the Account covers the existing challenges and new opportunities for self-powered wearable sensors in health monitoring and human–machine interfaces toward personalized and precision medicine

Dosage effects of BDNF Val66Met polymorphism on cortical surface area and functional connectivity

The single nucleotide polymorphism (SNP) that leads to a valine-to-methionine substitution at codon 66 (Val66Met) in BDNF is correlated with differences in cognitive and memory functions, as well as with several neurological and psychiatric disorders.MRIstudies have already shown that this genetic variant contributes to changes in cortical thickness and volume, but whether the Val66Met polymorphism affects the cortical surface area of healthy subjects remains unclear. Here, we used multimodal MRI to study whether this polymorphism would affect the cortical morphology and resting-state functional connectivity of a large sample of healthy Han Chinese human subjects. An SNP-wise general linear model analysis revealed a "dosage effect" of the Met allele, specifically a stepwise increase in cortical surface area of the right anterior insular cortex with increasing numbers of the Met allele. Moreover, we found enhanced functional connectivity between the anterior insular and the dorsolateral prefrontal cortices that was linked with the dosage of the Met allele. In conclusion, these data demonstrated a "dosage effect" ofBDNFVal66Met on normal cortical structure and function, suggesting anewpath for exploring the mechanisms underlying the effects of genotype on cognition