An (n, k) maximum distance separable (MDS) code can be used to store data in n storage nodes, such that the system can tolerate the failure of any (n−k) storage nodes. Recently, MDS codes have been constructed which satisfy an additional optimal repair property as follows: the failure of a single storage node can be repaired by downloading a fraction of 1/(n − k) of the data stored in every surviving storage node. In previous constructions satisfying this optimal repair property, the size of the code is polynomial in k for the highredundancy regime of k/n ≤ 1/2, but the codes have an exponential size (w.r.t. k) for the practically important lowredundancy regime of k/n > 1/2. In this paper, we construct a class of polynomial size codes in this low redundancy regime.

Strain sensors based on a porous CNT/PDMS nanocomposite can detect a collection of human body motions and actuation of soft robotics.

Near-infrared (NIR) fluorophores absorbing maximally in the region beyond 800 nm, i.e., deep-NIR spectral region, are actively sought for biomedical applications. Ideal dyes are bright, nontoxic, photostable, biocompatible, and easily derivatized to introduce functionalities (e.g., for bioconjugation or aqueous solubility). The rational design of such fluorophores remains a major challenge. Silicon-substituted rhodamines have been successful for bioimaging applications in the red spectral region. The longer-wavelength silicon-substituted congeners for the deep-NIR spectral region are unknown to date. We successfully prepared four silicon-substituted bis-benzannulated rhodamine dyes (ESi5a–ESi5d), with an efficient five-step cascade on a gram-scale. Because of the extensive overlapping of their HOMO–LUMO orbitals, ESi5a–ESi5d are highly absorbing (λabs ≈ 865 nm and ε > 105 cm–1 M–1). By restraining both the rotational freedom via annulation and the vibrational freedom via silicon-imparted strain, the fluorochromic scaffold of ESi5 is highly rigid, resulting in an unusually long fluorescence lifetime (τ > 700 ps in CH2Cl2) and a high fluorescence quantum yield (ϕ = 0.14 in CH2Cl2). Their half-lives toward photobleaching are 2 orders of magnitude longer than the current standard (ICG in serum). They are stable in the presence of biorelevant concentration of nucleophiles or reactive oxygen species. They are minimally toxic and readily metabolized. Upon tail vein injection of ESi5a (as an example), the vasculature of a nude mouse was imaged with a high signal-to-background ratio. ESi5 dyes have broad potentials for bioimaging in the deep-NIR spectral region.

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