Limits on Sparse Data Acquisition: RIC Analysis of Finite Gaussian Matrices

One of the key issues in the acquisition of sparse data by means of compressed sensing (CS) is the design of the measurement matrix. Gaussian matrices have been proven to be information-theoretically optimal in terms of minimizing the required number of measurements for sparse recovery. In this paper we provide a new approach for the analysis of the restricted isometry constant (RIC) of finite dimensional Gaussian measurement matrices. The proposed method relies on the exact distributions of the extreme eigenvalues for Wishart matrices. First, we derive the probability that the restricted isometry property is satisfied for a given sufficient recovery condition on the RIC, and propose a probabilistic framework to study both the symmetric and asymmetric RICs. Then, we analyze the recovery of compressible signals in noise through the statistical characterization of stability and robustness. The presented framework determines limits on various sparse recovery algorithms for finite size problems. In particular, it provides a tight lower bound on the maximum sparsity order of the acquired data allowing signal recovery with a given target probability. Also, we derive simple approximations for the RICs based on the Tracy-Widom distribution.Comment: 11 pages, 6 figures, accepted for publication in IEEE transactions on information theor

A Review on the Structural Studies of Batteries and Host Materials by X-Ray Absorption Spectroscopy

This review highlights the use of the X-ray absorption spectroscopy (XAS) as a local structural tool for selected atoms in several host materials. The main characteristics of XAS to be element-sensitive and its applicability to all states of matter, including crystalline solids and amorphous and liquid states, permit an in-depth study of the structural properties of a large variety of materials. This includes intercalation materials where a host structure can accommodate guest species. Host guest equilibria are at the basis of a large variety of technological applications; in particular they have been used for energy storage, ion-exchange membranes, electrochromism, and analytical sensing. A selection of XAS experiments conducted in the field of batteries, mainly on cathodes, and applications in the field of metal hexacyanoferrates and double layered hydroxides are outlined

X-Ray Absorption Spectroscopy Study of Battery Materials

X-ray absorption spectroscopy (XAS) as a local structural tool for the study of the electrochemical processes in battery materials is highlighted. Due to its elemental specificity and high penetration of the X-rays in the 4–35 keV range, XAS is particularly suited for this, allowing the study of battery materials using specifically developed in situ electrochemical cells. This energy is required to dislodge one core electron from transition metal or p-group atoms, which are commonly used as redox centers in positive and negative electrode materials. In such a simple picture, the ejected photoelectron is scattered by the surrounding atoms, producing characteristic traces in the X-ray absorption spectrum. Both positive and negative electrode materials (intercalation, alloy and conversion electrodes) can be studied. The chapter starts with an introduction of the context around battery studies, followed by a short explanation of the photoelectric effect at the basis of the X-ray absorption phenomenon and to specific features of XAS. A selection of XAS experiments conducted in the field of batteries will be then outlined, also emphasizing the effects due to nanoscale dimension of the material studied. Finally, a perspectives section will summarize the specific role that this spectroscopy has played in the battery community

Emergence of a recurrent insertion in the N-terminal domain of the {SARS}-{CoV}-2 spike glycoprotein

Tracking the evolution of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) through genomic surveillance programs is undoubtedly one of the key priorities in the current pandemic situation. Although the genome of SARS-CoV-2 acquires mutations at a slower rate compared with other RNA viruses, evolutionary pressures derived from the widespread circulation of SARS-CoV-2 in the human population have progressively favored the global emergence, though natural selection, of several variants of concern that carry multiple nonsynonymous mutations in the spike glycoprotein. These are often placed in key sites within major antibody epitopes and may therefore confer resistance to neutralizing antibodies, leading to partial immune escape, or otherwise compensate infectivity deficits associated with other non-synonymous substitutions. As previously shown by other authors, several emerging variants carry recurrent deletion regions (RDRs) that display a partial overlap with antibody epitopes located in the spike N-terminal domain (NTD). Comparatively, very little attention had been directed towards spike insertion mutations prior to the emergence of the B.1.1.529 (omicron) lineage. This manuscript describes a single recurrent insertion region (RIR1) in the N-terminal domain of SARSCoV- 2 spike protein, characterized by at least 49 independent acquisitions of 1–8 additional codons between Val213 and Leu216 in different viral lineages. Even though RIR1 is unlikely to confer antibody escape, its association with two distinct formerly widespread lineages (A.2.5 and B.1.214.2), with the quickly spreading omicron and with other VOCs and VOIs warrants further investigation concerning its effects on spike structure and viral infectivity

Syndrome-Based Encoding of Compressible Sources for M2M Communication

Data originating from many devices and sensors can be modeled as sparse signals. Hence, efficient compression techniques of such data are essential to reduce bandwidth and transmission power, especially for energy constrained devices within machine to machine communication scenarios. This paper provides accurate analysis of the operational distortion-rate function (ODR) for syndrome-based source encoders of noisy sparse sources. We derive the probability density function of error due to both quantization and pre- quantization noise for a type of mixed distributed source comprising Bernoulli and an arbitrary continuous distribution, e.g., Bernoulli- uniform sources. Then, we derive the ODR for two encoding schemes based on the syndromes of Reed-Solomon (RS) and Bose, Chaudhuri, and Hocquenghem (BCH) codes. The presented analysis allows designing a quantizer such that a target average distortion is achieved. As confirmed by numerical results, the closed-form expression for ODR perfectly coincides with the simulation. Also, the performance loss compared to an entropy based encoder is tolerable

Molecular aspects of zygotic embryogenesis in sunflower (Helianthus annuus L.): correlation of positive histone marks with HaWUS expression and putative link HaWUS/HaL1L

Main conclusion The link HaWUS/HaL1L, the opposite transcriptional behavior, and the decrease/increase in positive histone marks bond to both genes suggest an inhibitory effect of WUS on HaL1L in sunflower zygotic embryos. In Arabidopsis, a group of transcription factors implicated in the earliest events of embryogenesis is the WUSCHELRELATED HOMEOBOX (WOX) protein family including WUSCHEL (WUS) and other 14 WOX protein, some of which contain a conserved WUS-box domain in addition to the homeodomain. WUS transcripts appear very early in embryogenesis, at the 16-cell embryo stage, but gradually become restricted to the center of the developing shoot apical meristem (SAM) primordium and continues to be expressed in cells of the niche/organizing center of SAM and floral meristems to maintain stem cell population. Moreover, WUS has decisive roles in the embryonic program presumably promoting the vegetative-to-embryonic transition and/or maintaining the identity of the embryonic stem cells. However, data on the direct interaction between WUS and key genes for seed development (as LEC1 and L1L) are not collected. The novelty of this report consists in the characterization of Helianthus annuus WUS (HaWUS) gene and in its analysis regarding the pattern of the methylated lysine 4 (K4) of the Histone H3 and of the acetylated histone H3 during the zygotic embryo development. Also, a parallel investigation was performed for HaL1L gene since two copies of the WUS-binding site (WUSATA), previously identified on HaL1L nucleotide sequence, were able to be bound by the HaWUS recombinant protein suggesting a not described effect of HaWUS on HaL1L transcription

Titanium activation in prussian blue based electrodes for Na-ion batteries: A synthesis and electrochemical study

Sodium titanium hexacyanoferrate (TiHCF, Na$_{0.86}$0 Ti$_{0.73 }$ [Fe(CN)$_{6}$]·3H$_{2}$O) is synthesized by a simple co-precipitation method in this study. Its crystal structure, chemical composition, and geometric/electronic structural information are investigated by X-ray powder diffraction (XRPD), microwave plasma-atomic emission spectroscopy (MP-AES), and X-ray absorption spectroscopy (XAS). The electroactivity of TiHCF as a host for Li-ion and Na-ion batteries is studied in organic electrolytes. The results demonstrate that TiHCF is a good positive electrode material for both Li-ion and Na-ion batteries. Surprisingly, however, the material shows better electrochemical performance as a Na-ion host, offering a capacity of 74 mAh g$^{-1}$ at C/20 and a 94.5% retention after 50 cycles. This is due to the activation of Ti towards the redox reaction, making TiHCF a good candidate electrode material for Na-ion batteries

Highlighting the Reversible Manganese Electroactivity in Na‐Rich Manganese Hexacyanoferrate Material for Li‐ and Na‐Ion Storage

The electroactivity of sodium‐rich manganese hexacyanoferrate (MnHCF) material constituted of only abundant elements, as insertion host for Li‐ and Na‐ions is herein comprehensively discussed. This material features high specific capacities (>130 mAh g−1) at high potentials when compared to other materials of the same class, i.e., Prussian blue analogs. The reversible electronic and structural modifications occurring during ion release/uptake, which are responsible for such high specific capacity, are revealed herein. The in‐depth electronic and structural analysis carried out combining X‐ray diffraction and X‐ray absorption spectroscopy (XAS), demonstrates that both Fe and Mn sites are involved in the electrochemical process, being the high delivered capacity the result of a reversible evolution in oxidation states of the metallic centers (Fe3+/Fe2+ and Mn2+/Mn3+). Along with the Mn2+/Mn3+ oxidation, the Mn local environment experiences a substantial yet reversible Jahn–Teller effect, being the equatorial Mn‐N distances shrunk by 10% (2.18 Å → 1.96 Å). Na‐rich MnHCF material offers slightly higher performance upon uptake and release of Na‐ions (469 Wh kg−1) than Li‐ions (457 Wh kg−1), being, however, the electronic and structural transformation independent of the adopted medium, as observed by XAS spectroscopy