Portable electronic devices (PEDs) are promising information‐exchange platforms for real‐time responses. Their performance is becoming more and more sensitive to energy consumption. Rechargeable batteries are the primary energy source of PEDs and hold the key to guarantee their desired performance stability. With the remarkable progress in battery technologies, multifunctional PEDs have constantly been emerging to meet the requests of our daily life conveniently. The ongoing surge in demand for high‐performance PEDs inspires the relentless pursuit of even more powerful rechargeable battery systems in turn. In this review, we present how battery technologies contribute to the fast rise of PEDs in the last decades. First, a comprehensive overview of historical advances in PEDs is outlined. Next, four types of representative rechargeable batteries and their impacts on the practical development of PEDs are described comprehensively. The development trends toward a new generation of batteries and the future research focuses are also presented.

Various studies have assessed the clinicopathological and prognostic value of Notch1 and Notch3 expression in Non-small cell lung cancer (NSCLC), but their results remain controversial. This meta-analysis was conducted to address the above issues by using a total of 19 studies involving 3663 patients. The correlations between Notch1 and Notch3 expression and clinicopathological features and NSCLC prognosis were analyzed. The meta-analysis indicated that higher expression of Notch1 was associated with greater possibility of lymph node metastasis and higher TNM stages. Moreover, patients with Notch1 overexpression and Notch3 overexpression showed significantly poor overall survival (Notch1: HR, 1.29; 95% CI, 1.06–1.57, p = 0.468 and I2 = 0.0%; Notch3: HR, 1.57; 95%CI, 1.04-2.36, p = 0.445 and I2 = 0.0%). Furthermore, there are statistically significant association between overall survival of NSCLC patients and the expression of Notch signaling ligand DLL3 and target gene HES1. Our meta-analysis supports that Notch signaling is a valuable bio-marker to predict progression and targeting Notch signaling could benefit subpopulation of NSCLC patients.

Like classical block codes, a locally repairable code also obeys the Singleton-type bound (we call a locally repairable code optimal if it achieves the Singleton-type bound). In the breakthrough work of [14], several classes of optimal locally repairable codes were constructed via subcodes of Reed-Solomon codes. Thus, the lengths of the codes given in [14] are upper bounded by the code alphabet size q.Recently, it was proved through extension of construction in [14] that length of q-ary optimal locally repairable codes can be q + 1 in [7]. Surprisingly, [2] presented a few examples of q-ary optimal locally repairable codes of small distance and locality with code length achieving roughly q 2 . Very recently, it was further shown in [8] that there exist q-ary optimal locally repairable codes with length bigger than q + 1 and distance propositional to n. Thus, it becomes an interesting and challenging problem to construct new families of q-ary optimal locally repairable codes of length bigger than q + 1.In this paper, we construct a class of optimal locally repairable codes of distance 3 and 4 with unbounded length (i.e., length of the codes is independent of the code alphabet size). Our technique is through cyclic codes with particular generator and parity-check polynomials that are carefully chosen.

A locally repairable code (LRC) with locality r allows for the recovery of any erased codeword symbol using only r other codeword symbols. A Singleton-type bound dictates the best possible trade-off between the dimension and distance of LRCs -an LRC attaining this trade-off is deemed optimal. Such optimal LRCs have been constructed over alphabets growing linearly in the block length. Unlike the classical Singleton bound, however, it was not known if such a linear growth in the alphabet size is necessary, or for that matter even if the alphabet needs to grow at all with the block length. Indeed, for small code distances 3, 4, arbitrarily long optimal LRCs were known over fixed alphabets.Here, we prove that for distances d 5, the code length n of an optimal LRC over an alphabet of size q must be at most roughly O(dq 3 ). For the case d = 5, our upper bound is O(q 2 ). We complement these bounds by showing the existence of optimal LRCs of length Ω d,r (q 1+1/⌊(d−3)/2⌋ ) when d r + 2. These bounds match when d = 5, thus pinning down n = Θ(q 2 ) as the asymptotically largest length of an optimal LRC for this case.