Rayleigh-Ritz majorization error bounds of the mixed type

The absolute change in the Rayleigh quotient (RQ) for a Hermitian matrix with respect to vectors is bounded in terms of the norms of the residual vectors and the angle between vectors in [\doi{10.1137/120884468}]. We substitute multidimensional subspaces for the vectors and derive new bounds of absolute changes of eigenvalues of the matrix RQ in terms of singular values of residual matrices and principal angles between subspaces, using majorization. We show how our results relate to bounds for eigenvalues after discarding off-diagonal blocks or additive perturbations.Comment: 20 pages, 1 figure. Accepted to SIAM Journal on Matrix Analysis and Application

Explicit model predictive control accuracy analysis

Model Predictive Control (MPC) can efficiently control constrained systems in real-time applications. MPC feedback law for a linear system with linear inequality constraints can be explicitly computed off-line, which results in an off-line partition of the state space into non-overlapped convex regions, with affine control laws associated to each region of the partition. An actual implementation of this explicit MPC in low cost micro-controllers requires the data to be "quantized", i.e. represented with a small number of memory bits. An aggressive quantization decreases the number of bits and the controller manufacturing costs, and may increase the speed of the controller, but reduces accuracy of the control input computation. We derive upper bounds for the absolute error in the control depending on the number of quantization bits and system parameters. The bounds can be used to determine how many quantization bits are needed in order to guarantee a specific level of accuracy in the control input.Comment: 6 pages, 7 figures. Accepted to IEEE CDC 201

Angles between subspaces and their tangents

Principal angles between subspaces (PABS) (also called canonical angles) serve as a classical tool in mathematics, statistics, and applications, e.g., data mining. Traditionally, PABS are introduced via their cosines. The cosines and sines of PABS are commonly defined using the singular value decomposition. We utilize the same idea for the tangents, i.e., explicitly construct matrices, such that their singular values are equal to the tangents of PABS, using several approaches: orthonormal and non-orthonormal bases for subspaces, as well as projectors. Such a construction has applications, e.g., in analysis of convergence of subspace iterations for eigenvalue problems.Comment: 15 pages, 1 figure, 2 tables. Accepted to Journal of Numerical Mathematic

Bounds for the Rayleigh quotient and the spectrum of self-adjoint operators

The absolute change in the Rayleigh quotient (RQ) is bounded in this paper in terms of the norm of the residual and the change in the vector. If $x$ is an eigenvector of a self-adjoint bounded operator $A$ in a Hilbert space, then the RQ of the vector $x$, denoted by $\rho(x)$, is an exact eigenvalue of $A$. In this case, the absolute change of the RQ $|\rho(x)-\rho(y)|$ becomes the absolute error in an eigenvalue $\rho(x)$ of $A$ approximated by the RQ $\rho(y)$ on a given vector $y.$ There are three traditional kinds of bounds of the eigenvalue error: a priori bounds via the angle between vectors $x$ and $y$; a posteriori bounds via the norm of the residual $Ay-\rho(y)y$ of vector $y$; mixed type bounds using both the angle and the norm of the residual. We propose a unifying approach to prove known bounds of the spectrum, analyze their sharpness, and derive new sharper bounds. The proof approach is based on novel RQ vector perturbation identities.Comment: 13 page

Characterization of a Novel blaKLUC Variant With Reduced β-Lactam Resistance From an IncA/C Group Plasmid in a Clinical Klebsiella pneumoniae Isolate

Similar to other CTX-M family enzymes, KLUC is a recently identified and emerging determinant of cefotaxime resistance that has been recovered from at least three Enterobacteriaceae species, including Kluyvera cryocrescens, Escherichia coli, and Enterobacter cloacae. Whether this extended-spectrum β-lactamase (ESBL) has been disseminated among commonly isolated Enterobacteriaceae is worthy of further investigation. In this study, we screened 739 nosocomial Enterobacteriaceae isolates (240 Klebsiella pneumoniae and 499 E. coli strains) and found that one K. pneumoniae and four E. coli isolates harbored the blaKLUC gene. Three blaKLUC determinants isolated from E. coli were entirely identical to a blaKLUC-3 gene previously recovered in the same hospital. PFGE of four blaKLUC-harboring E. coli strains showed that prevalence of these determinants was most likely mediated by horizontal gene transfer but not clonal dissemination. However, the variant isolated from K. pneumoniae belonged to a novel member of the KLUC enzyme group. This newly identified enzyme (KLUC-5) has an amino acid substitution compared with previously identified KLUC-1 (G18S) and KLUC-3 (G240D). Antimicrobial susceptibility tests showed that KLUC-5 significantly reduced resistance activity to almost all the selected antimicrobials compared to previously identified KLUC-3. Site-directed mutagenesis showed that blaKLUC-5-D240G and blaKLUC-5-S18G significantly enhanced the MIC against its best substrate. Conjugation and S1-PFGE indicated that blaKLUC-5 was located on a transferable plasmid, which was further decoded by single-molecule, real-time sequencing. Comparative genome analysis showed that its backbone exhibited genetic homology to the IncA/C incompatibility group plasmids. A transposable element, ISEcp1, was detected 256-bp upstream of the blaKLUC-5 gene; this location was inconsistent with the previously identified blaKLUC-1 but congruent with the variants recovered from E. coli in the same hospital. These data provide evidence of the increasingly emerging KLUC group of ESBLs in China

Multiplexed Quantum Dot Labeling of Activated c-Met Signaling in Castration-Resistant Human Prostate Cancer

The potential application of multiplexed quantum dot labeling (MQDL) for cancer detection and prognosis and monitoring therapeutic responses has attracted the interests of bioengineers, pathologists and cancer biologists. Many published studies claim that MQDL is effective for cancer biomarker detection and useful in cancer diagnosis and prognosis, these studies have not been standardized against quantitative biochemical and molecular determinations. In the present study, we used a molecularly characterized human prostate cancer cell model exhibiting activated c-Met signaling with epithelial to mesenchymal transition (EMT) and lethal metastatic progression to bone and soft tissues as the gold standard, and compared the c-Met cell signaling network in this model, in clinical human prostate cancer tissue specimens and in a castration-resistant human prostate cancer xenograft model. We observed c-Met signaling network activation, manifested by increased phosphorylated c-Met in all three. The downstream survival signaling network was mediated by NF-κB and Mcl-1 and EMT was driven by receptor activator of NF-κB ligand (RANKL), at the single cell level in clinical prostate cancer specimens and the xenograft model. Results were confirmed by real-time RT-PCR and western blots in a human prostate cancer cell model. MQDL is a powerful tool for assessing biomarker expression and it offers molecular insights into cancer progression at both the cell and tissue level with high degree of sensitivity

Effect of different modalities of artificial intelligence rehabilitation techniques on patients with upper limb dysfunction after stroke—A network meta-analysis of randomized controlled trials

BackgroundThis study aimed to observe the effects of six different types of AI rehabilitation techniques (RR, IR, RT, RT + VR, VR and BCI) on upper limb shoulder-elbow and wrist motor function, overall upper limb function (grip, grasp, pinch and gross motor) and daily living ability in subjects with stroke. Direct and indirect comparisons were drawn to conclude which AI rehabilitation techniques were most effective in improving the above functions.MethodsFrom establishment to 5 September 2022, we systematically searched PubMed, EMBASE, the Cochrane Library, Web of Science, CNKI, VIP and Wanfang. Only randomized controlled trials (RCTs) that met the inclusion criteria were included. The risk of bias in studies was evaluated using the Cochrane Collaborative Risk of Bias Assessment Tool. A cumulative ranking analysis by SUCRA was performed to compare the effectiveness of different AI rehabilitation techniques for patients with stroke and upper limb dysfunction.ResultsWe included 101 publications involving 4,702 subjects. According to the results of the SUCRA curves, RT + VR (SUCRA = 84.8%, 74.1%, 99.6%) was most effective in improving FMA-UE-Distal, FMA-UE-Proximal and ARAT function for subjects with upper limb dysfunction and stroke, respectively. IR (SUCRA = 70.5%) ranked highest in improving FMA-UE-Total with upper limb motor function amongst subjects with stroke. The BCI (SUCRA = 73.6%) also had the most significant advantage in improving their MBI daily living ability.ConclusionsThe network meta-analysis (NMA) results and SUCRA rankings suggest RT + VR appears to have a greater advantage compared with other interventions in improving upper limb motor function amongst subjects with stroke in FMA-UE-Proximal and FMA-UE-Distal and ARAT. Similarly, IR had shown the most significant advantage over other interventions in improving the FMA-UE-Total upper limb motor function score of subjects with stroke. The BCI also had the most significant advantage in improving their MBI daily living ability. Future studies should consider and report on key patient characteristics, such as stroke severity, degree of upper limb impairment, and treatment intensity/frequency and duration.Systematic review registrationwww.crd.york.ac.uk/prospero/#recordDetail, identifier: CRD42022337776

Characterization and Function of the 1-Deoxy-D-xylose-5-Phosphate Synthase (DXS) Gene Related to Terpenoid Synthesis in Pinus massoniana

In the methyl-D-erythritol-4-phosphate (MEP) pathway, 1-deoxy-D-xylose-5-phosphate synthase (DXS) is considered the key enzyme for the biosynthesis of terpenoids. In this study, PmDXS (MK970590) was isolated from Pinus massoniana. Bioinformatics analysis revealed homology of MK970590 with DXS proteins from other species. Relative expression analysis suggested that PmDXS expression was higher in roots than in other plant parts, and the treatment of P. massoniana seedlings with mechanical injury via 15% polyethylene glycol 6000, 10 mM H2O2, 50 μM ethephon (ETH), 10 mM methyl jasmonate (MeJA), and 1 mM salicylic acid (SA) resulted in an increased expression of PmDXS. pET28a-PmDXS was expressed in Escherichia coli TransB (DE3) cells, and stress analysis showed that the recombinant protein was involved in resistance to NaCl and drought stresses. The subcellular localization of PmDXS was in the chloroplast. We also cloned a full-length 1024 bp PmDXS promoter. GUS expression was observed in Nicotiana benthamiana roots, stems, and leaves. PmDXS overexpression significantly increased carotenoid, chlorophyll a, and chlorophyll b contents and DXS enzyme activity, suggesting that DXS is important in isoprenoid biosynthesis. This study provides a theoretical basis for molecular breeding for terpene synthesis regulation and resistance

Properties of Concrete Prepared with Recycled Aggregates Treated by Bio-Deposition Adding Oxygen Release Compound

Recycled aggregates have high water absorption and crushing index. In order to improve the properties of recycled aggregates in concrete production, various treatments were used to modify the aggregates. In recent years, bio-deposition as a new treatment method of recycled aggregates was environmentally friendly. An improved method of bio-deposition was implemented to modify the properties of recycled mortar aggregates (RMA). O-bio-deposition is based on aerobic bacteria induced CaCO3 precipitation by respiration by varying the distance between the RMA and the bottom of the container and by adding an oxygen release compound to the culture solution that contains bacteria to promote the induction of CaCO3. First, the physical properties, including water absorption, crushing value, and apparent density, of the coarse RMA under different treatment methods were determined, and an o-bio-deposition treatment method was obtained. The fine RMA was treated and compared with the untreated RMA. Concretes were then prepared from the treated coarse RMA, and compressive strength and slump were determined. In addition, the effect of the o-bio-deposition treatment on the RMA surface and the micro-cracks of concretes were observed by scanning electron microscopy (SEM). It was found that the water absorption and crushing index of the coarse RMA treated by o-bio-deposition were reduced by 40.38 and 19.76% compared with untreated RMA, respectively. Regarding the concrete, the slump and the compressive strength (28 d) of concrete were increased by 115% and 25.3%, respectively compared with the untreated concrete