Let
A
be the adjacency matrix of a random
d
-regular graph on
N
vertices, and we denote its eigenvalues by
λ
1
⩾
λ
2
⋯
⩾
λ
N
. For
N
2
/
3
+
o
(
1
)
⩽
d
⩽
N
/
2
, we prove optimal rigidity estimates ...of the extreme eigenvalues of
A
, which in particular imply that
max
{
|
λ
N
|
,
λ
2
}
<
2
d
-
1
with very high probability. In the same regime of
d
, we also show that
N
2
/
3
(
λ
2
+
d
/
N
d
(
N
-
d
)
/
N
-
2
)
⟶
d
TW
1
,
where
TW
1
is the Tracy–Widom distribution for GOE; analogue results also hold for other non-trivial extreme eigenvalues.
We consider a class of sparse random matrices which includes the adjacency matrix of the Erdős–Rényi graph
G
(
N
,
p
)
. We show that if
N
ε
⩽
N
p
⩽
N
1
/
3
-
ε
then all nontrivial eigenvalues away ...from 0 have asymptotically Gaussian fluctuations. These fluctuations are governed by a single random variable, which has the interpretation of the total degree of the graph. This extends the result (Huang et al. in Ann Prob 48:916–962, 2020) on the fluctuations of the extreme eigenvalues from
N
p
⩾
N
2
/
9
+
ε
down to the optimal scale
N
p
⩾
N
ε
. The main technical achievement of our proof is a rigidity bound of accuracy
N
-
1
/
2
-
ε
(
N
p
)
-
1
/
2
for the extreme eigenvalues, which avoids the
(
N
p
)
-
1
-expansions from Erdős et al. (Ann Prob 41:2279–2375, 2013), Huang et al. (2020) and Lee and Schnelli (Prob Theor Rel Fields 171:543–616, 2018). Our result is the last missing piece, added to Erdős et al. (Commun Math Phys 314:587–640, 2012), He (Bulk eigenvalue fluctuations of sparse random matrices.
arXiv:1904.07140
), Huang et al. (2020) and Lee and Schnelli (2018), of a complete description of the eigenvalue fluctuations of sparse random matrices for
N
p
⩾
N
ε
.
We investigate to what extent the microscopic Wigner–Gaudin–Mehta–Dyson (WGMD) (or sine kernel) statistics of random matrix theory remain valid on mesoscopic scales. To that end, we compute the ...connected two-point spectral correlation function of a Wigner matrix at two mesoscopically separated points. In the mesoscopic regime, density correlations are much weaker than in the microscopic regime. Our result is an explicit formula for the two-point function. This formula implies that the WGMD statistics are valid to leading order on all mesoscopic scales, that in the real symmetric case there are subleading corrections matching precisely the WGMD statistics, while in the complex Hermitian case these subleading corrections are absent. We also uncover non-universal subleading correlations, which dominate over the universal ones beyond a certain intermediate mesoscopic scale. The proof is based on a hierarchy of Schwinger–Dyson equations for a sufficiently large class of polynomials in the entries of the Green function. The hierarchy is indexed by a tree, whose depth is controlled using stopping rules. A key ingredient in the derivation of the stopping rules is a new estimate on the density of states, which we prove to have bounded derivatives of all order on all mesoscopic scales.
Let
H
be a Hermitian random matrix whose entries
H
xy
are independent, centred random variables with variances
S
xy
=
E
|
H
xy
|
2
, where
x
,
y
∈
(
Z
/
L
Z
)
d
and
d
⩾
1
. The variance
S
xy
is ...negligible if
|
x
-
y
|
is bigger than the band width
W
. For
d
=
1
we prove that if
L
≪
W
1
+
2
7
then the eigenvectors of
H
are delocalized and that an averaged version of
|
G
xy
(
z
)
|
2
exhibits a diffusive behaviour, where
G
(
z
)
=
(
H
-
z
)
-
1
is the resolvent of
H
. This improves the previous assumption
L
≪
W
1
+
1
4
of Erdős et al. (Commun Math Phys 323:367–416,
2013
). In higher dimensions
d
⩾
2
, we obtain similar results that improve the corresponding ones from Erdős et al. (Commun Math Phys 323:367–416,
2013
). Our results hold for general variance profiles
S
xy
and distributions of the entries
H
xy
. The proof is considerably simpler and shorter than that of Erdős et al. (Ann Henri Poincaré 14:1837–1925,
2013
), Erdős et al. (Commun Math Phys 323:367–416,
2013
). It relies on a detailed Fourier space analysis combined with isotropic estimates for the fluctuating error terms. It is completely self-contained and avoids the intricate fluctuation averaging machinery from Erdős et al. (Ann Henri Poincaré 14:1837–1925,
2013
).
A complex-valued least-squares (CLS) framework is proposed in order to enhance the accuracy of the smart discrete Fourier transform (SDFT) algorithms for power system frequency estimation in the ...presence of noise and harmonic pollution. It is first established that the underlying time-series relationship among the consecutive DFT fundamental components employed by the original SDFT algorithms does not hold when noises or unexpected higher order harmonics are present, resulting in suboptimal estimation performances. To eliminate these adverse effects on the frequency estimation, the degree of the relationship breakdown is next quantified via a model mismatch error vector. The CLS technique is then employed to minimize the mean-square model deviation when the SDFT voltage modelling is suboptimal. The proposed CLS-enhanced SDFT (CLS-SDFT) methods are shown to be more accurate than the original ones in heavily noisy and harmonic-distorted environments, typical scenarios in online frequency estimation. The benefits of the SDFT framework are verified by simulations for various power system conditions, as well as for real-world measurements.
Abstract
Predicting the functional or pathogenic regulatory variants in the human non-coding genome facilitates the interpretation of disease causation. While numerous prediction methods are ...available, their performance is inconsistent or restricted to specific tasks, which raises the demand of developing comprehensive integration for those methods. Here, we compile whole genome base-wise aggregations, regBase, that incorporate largest prediction scores. Building on different assumptions of causality, we train three composite models to score functional, pathogenic and cancer driver non-coding regulatory variants respectively. We demonstrate the superior and stable performance of our models using independent benchmarks and show great success to fine-map causal regulatory variants on specific locus or at base-wise resolution. We believe that regBase database together with three composite models will be useful in different areas of human genetic studies, such as annotation-based casual variant fine-mapping, pathogenic variant discovery as well as cancer driver mutation identification. regBase is freely available at https://github.com/mulinlab/regBase.
This study aimed to characterize the lipidomic responses to community-acquired pneumonia (CAP) and provide new insight into the underlying mechanisms of pathogenesis and potential avenues for ...diagnostic and therapeutic treatments. This study was performed from January 2017 to October 2018. Lipidomic profiles were generated using ultra high-performance liquid chromatography with tandem mass spectrometry (UHPLC-MS/MS) platform. Spearman's rank correlation test and multiple linear regression analysis were applied to explore the correlation between changes in the relative abundance of lipids and clinical parameters. Kaplan-Meier methods were used to build 30-day survival curves. From the UHPLC-MS/MS results, a total of 509 and 195 lipid species were detected in the positive and negative ionization mode respectively. Positive ionization covered six lipid classes (glycerol-phospholipids, glycerolipids, sphingolipids, sterol-lipids, prenol-lipids, and fatty acid), whilst negative ionization covered three (glycerol-phospholipids, sphingolipids, fatty acid). Four lipids were selected as targets: PC (16:0_18:1), PC (18:2_20:4), PC (36:4), and PC (38:6). The relative increase of the areas under the curves for all four lipids were superior to the pneumonia severity index and CURB-65 (confusion, urea, respiratory rate, blood pressure, and age ≥65 years old) for discriminating severe CAP from CAP. Decreasing relative levels of PC (18:2_20:4), PC (38:6), and PC (36:4) were negatively related to fraction of inspiration O2; Changes in the relative abundance of PC (16:0_18:1) and PC (18:2_20:4) had significantly linear relationship with procalcitonin. Patients with an elevated level of PC (16:0_18:1) had significantly longer duration of hospital stays. As the relative abundance of PC (18:2_20:4), PC (36:4), and PC (38:6) decreased, the length of hospitalization days and 30-day mortality rate increased significantly (all log-rank p<0.05). Therefore, using the UHPLC-MS/MS platform's serum lipidomic approach can help reveal changes in lipid abundance during CAP and establish lipid profiles related to disease severity.
Breast cancer-related lymphedema (BCRL) is associated with extensive axillary dissection. Axillary lymph node dissection (ALND) based on breast lymphatics level (BLL) was proposed to minimize the ...surgical extent for node-positive breast cancer patients.
A total of 156 consecutive sentinel lymph node-positive (SLN+) or clinically node-positive (cN+) patients underwent sentinel lymph node biopsy (SLNB) with indocyanine green and methylene blue (MB). The SLNs were injected with 0.1 ml MB before removal, and a standard ALND was subsequently performed. The nodes adjacent to the blue-stained axillary lymph nodes from the breast (bALNs) were sent for pathological examination separately by resecting serial tissue every 0.5 cm away from the marginal blue-stained bALNs. Then, a pilot study comparing ALND based on BLL and standard ALND was performed.
BLL were successfully identified in 20 SLN+ (100%) and 134 cN+ (98.5%) patients. The median number of BLL was four, ranging from three to six. A horizontal line 1.0 cm away from the superior blue-stained bALN and a vertical line 1.0 cm away from the medial blue-stained bALN formed BLL II, III, and IV. All of the additional positive nodes were within 1.0 cm of the blue-stained bALNs. The minimized axillary dissection should resect upwards from the lowest BLL that contains the first confirmed negative blue-stained bALNs. In the pilot study, no patient developed axillary recurrence.
The ALND surgical procedure based on BLL could minimize the surgical extent for pathological node-positive breast cancer patients and potentially reduce the BCRL rate.
ChiCTR1800014247 .
The ST27 strain RMLUG2 contained a complete SCCmec type V, including a type mecA class C2 complex and ccrC1 complex, but in a SCCmec type VII-like order: orfX-J3-ccr-J2-mec-J1. ...the IS431 upstream ...of mecA had the opposite orientation to that downstream, in contrast with the structure of SCCmec type VII, suggesting a novel SCCmec type V variant Supplementary Figure 2C, http://links.lww.com/CM9/B273. According to SCCmec classification,4 this element is described as an SCC element, which was designated SCCRMLUG4 Supplementary Figure 2D, http://links.lww.com/CM9/B273. Giannouli et al8 reported that the accumulation of amino acid changes in FemXAB family proteins may affect cell wall synthesis, leading to atypical oxacillin responsiveness. ...we identified CC-dependent genetic variations of the 14 lug genes, indicating that the lug operon may not be conserved in the S. lugdunensis genome. ...the GenBank data may be biased because some sequences were obtained only by third-generation sequencing without assembling sequence fragments obtained by other methods.
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