Let A be an $n \times n$ symmetric matrix with $(A_{i,j})_{i\leqslant j}$ independent and identically distributed according to a subgaussian distribution. We show that

$$ \begin{align*}\mathbb{P}(\sigma_{\min}(A) \leqslant \varepsilon n^{-1/2} ) \leqslant C \varepsilon + e^{-cn},\end{align*} $$

where $\sigma _{\min }(A)$ denotes the least singular value of A and the constants $C,c>0 $ depend only on the distribution of the entries of A. This result confirms the folklore conjecture on the lower tail of the least singular value of such matrices and is best possible up to the dependence of the constants on the distribution of $A_{i,j}$. Along the way, we prove that the probability that A has a repeated eigenvalue is $e^{-\Omega (n)}$, thus confirming a conjecture of Nguyen, Tao and Vu [Probab. Theory Relat. Fields 167 (2017), 777–816].

Déjà vu and involuntary autobiographical memories (IAMs) are differentiated by a number of factors including metacognition. In contrast to IAMs, déjà vu activates regions associated with self-awareness including the right dorsolateral prefrontal cortex.

Social robots have limited social competences. This leads us to view them as depictions of social agents rather than actual social agents. However, people also have limited social competences. We argue that all social interaction involves the depiction of social roles and that they originate in, and are defined by, their function in accounting for failures of social competence.

Group Name: DHHS Epi

Background: The inoculation with SARS-CoV-2 vaccine at long-term care facilities (LTCFs) in Nebraska began on December 28, 2020, as part of the Centers for Disease Control and Prevention (CDC) Pharmacy Partnership for Long-Term Care Program.1 As of February 5, 2021, 159 skilled nursing facilities (SNFs) had completed their first vaccine clinic, and 7,271 residents and 6,768 staff had received the first dose of the 2-dose series. Surveillance data before vaccination (December 21–27, 2020) and after the first vaccination dose (January 25–31, 2021) indicate that the weekly SARS-CoV-2 positivity rate at SNFs decreased from 1.18% to 0.42% for residents and 0.54% to 0.11% for staff.2,3,4 In this study, we examined the perceived decrease in new transmission initiated by the first dose of vaccine at SNFs. Methods: We analyzed the data with separate logistic regressions for residents and staff. We included 145 SNFs that completed their first vaccine clinic, and we used the Federal and Pharmacy Partnership database for the number of residents and staff that received the first dose of vaccine at the first vaccine clinic. We followed the SNFs for 21 days after the first vaccine clinic from December 28, 2020, through February 5, 2021, for any first-time SARS-CoV-2–positive cases. The National Healthcare Safety Network (NHSN) database was used to collect the information on the number of residents present at the facility on the day of the first vaccine clinic, if available, or days before in the same week as the first vaccine clinic. The staff count for each facility was extracted from Nebraska Licensure for LTCFs. We collected new case information from the state surveillance, the NHSN, and the Test-Nebraska platform. Results: The mean resident vaccine coverage was 80% and the median staff vaccine coverage was 43%. We found a reverse association between staff vaccine coverage and new positive staff cases. For each percentage increase in staff vaccine coverage, the odds of having a new staff positive case 7 days and 14 days after the first vaccine clinic decrease by 26% and 48%, respectively. No association between coverage and new resident transmission was detected. Possible confounding exists when infected residents might have tested positive 7–14 days after the first vaccine clinic who were not affected by the vaccine. Conclusions: Although we observed the association between lower case count with increased facility-level vaccine coverage, we would need to wait for the administration of the second dose of vaccine before assessing the level of association between coverage and new transmission. Further initiatives are warranted to increase the suboptimal vaccine coverage for staff.

Funding: No

Disclosures: None

Background: Chlorhexidine bathing reduces bacterial skin colonization and prevents infections in specific patient populations. As chlorhexidine use becomes more widespread, concerns about bacterial tolerance to chlorhexidine have increased; however, testing for chlorhexidine minimum inhibitory concentrations (MICs) is challenging. We adapted a broth microdilution (BMD) method to determine whether chlorhexidine MICs changed over time among 4 important healthcare-associated pathogens. Methods: Antibiotic-resistant bacterial isolates (Staphylococcus aureus from 2005 to 2019 and Escherichia coli, Klebsiella pneumoniae, and Enterobacter cloacae complex from 2011 to 2019) were collected through Emerging Infections Program surveillance in 2 sites (Georgia and Tennessee) or through public health reporting in 1 site (Orange County, California). A convenience sample of isolates were collected from facilities with varying amounts of chlorhexidine use. We performed BMD testing using laboratory-developed panels with chlorhexidine digluconate concentrations ranging from 0.125 to 64 μg/mL. After successfully establishing reproducibility with quality control organisms, 3 laboratories performed MIC testing. For each organism, epidemiological cutoff values (ECVs) were established using ECOFFinder. Results: Among 538 isolates tested (129 S. aureus, 158 E. coli, 142 K. pneumoniae, and 109 E. cloacae complex), S. aureus, E. coli, K. pneumoniae, and E. cloacae complex ECVs were 8, 4, 64, and 64 µg/mL, respectively (Table 1). Moreover, 14 isolates had an MIC above the ECV (12 E. coli and 2 E. cloacae complex). The MIC50 of each species is reported over time (Table 2). Conclusions: Using an adapted BMD method, we found that chlorhexidine MICs did not increase over time among a limited sample of S. aureus, E. coli, K. pneumoniae, and E. cloacae complex isolates. Although these results are reassuring, continued surveillance for elevated chlorhexidine MICs in isolates from patients with well-characterized chlorhexidine exposure is needed as chlorhexidine use increases.

Funding: None

Disclosures: None

Modes of debris entrainment and subsequent transfer in seven “normal” and five surge-type glaciers in Svalbard (76–79° N) are outlined in the context of the structural evolution of a glacier as the ice deforms during flow. Three main modes of entrainment and transfer are inferred from structural and sedimentological observations: (i) The incorporation of angular rockfall material within the stratified sequence of snow/firn/superimposed ice. This debris takes an englacial path through the glacier, becoming folded. At the margins and at the boundaries of flow units the stratified ice including debris is strongly folded, so that near the snout the debris emerges at the surface on the hinges and limbs of the folds, producing medial moraines which merge towards the snout. The resulting lines of debris are transmitted to the proglacial area in the form of regular trains of angular debris. (ii) Incorporation of debris of both supraglacial and basal character within longitudinal foliation. This is particularly evident at the surface of the glacier at the margins or at flow unit boundaries. It can be sometimes demonstrated that foliation is a product of strong folding, since it usually has an axial planar relationship with folded stratification. Foliation-parallel debris thus represents a more advanced stage of deformation than in (i). Although the presence of basal debris is problematic, it is proposed that this material is tightly folded ice derived from the bed in the manner of disharmonie folding. The readily deformed subglacial sediment or bedrock surface represents the plane of décollement. (iii) Thrusting, whereby debris-rich basal ice (including regelation ice) and subglacial sediments are uplifted into an englacial position, sometimes emerging at the ice surface. This material is much more variable in character than that derived from rockfalls, and reflects the substrate lithologies; diamicton with striated clasts and sandy gravels are the most common facies represented. Thrusting is a dynamic process, and in polythermal glaciers is probably linked mainly to the transition from sliding to frozen bed conditions. It is not therefore a solely ice-marginal or proglacial process.

Empirical evidence from dialogue, both corpus and experimental, highlights the importance of interaction in language use – and this raises some questions for Christiansen & Chater's (C&C's) proposals. We endorse C&C's call for an integrated framework but argue that their emphasis on local, individual production and comprehension makes it difficult to accommodate the ubiquitous, interactive, and defeasible processes of clarification and repair in conversation.