The distribution of clusters in random graphs

AbstractGiven a random graph, we investigate the occurrence of subgraphs especially rich in edges. Specifically, given a ϵ [0,1], a set of k points in a graph G is defined to be an a-cluster of cardinality k if the induced subgraph contains at least ak2 edges, so that in the extreme case a = 1, an a-cluster is the same as a clique. We let G = G(n, p) be a random graph on n vertices with edges chosen independently with probability p. Let W denote the number of a-clusters of cardinality k in G, where k and n tend to infinity so that the expected number λ of a-clusters of cardinality k does not grow or decay too rapidly. We prove that W is asymptotically distributed as Zλ, whose distribution is Poisson with mean λ, which is the same result that Bollobás and Erdös have proved for cliques. In contrast to the situation for cliques (a = 1) however, for all a < 1 the second moment of W blows up, i.e., the expected number of neighbors of a given cluster tends to infinity. Nevertheless, the probability that there exists at least one pair of neighboring clusters tends to zero, and a Poisson approximation for W is valid

Optimal experimental design for mathematical models of haematopoiesis.

The haematopoietic system has a highly regulated and complex structure in which cells are organized to successfully create and maintain new blood cells. It is known that feedback regulation is crucial to tightly control this system, but the specific mechanisms by which control is exerted are not completely understood. In this work, we aim to uncover the underlying mechanisms in haematopoiesis by conducting perturbation experiments, where animal subjects are exposed to an external agent in order to observe the system response and evolution. We have developed a novel Bayesian hierarchical framework for optimal design of perturbation experiments and proper analysis of the data collected. We use a deterministic model that accounts for feedback and feedforward regulation on cell division rates and self-renewal probabilities. A significant obstacle is that the experimental data are not longitudinal, rather each data point corresponds to a different animal. We overcome this difficulty by modelling the unobserved cellular levels as latent variables. We then use principles of Bayesian experimental design to optimally distribute time points at which the haematopoietic cells are quantified. We evaluate our approach using synthetic and real experimental data and show that an optimal design can lead to better estimates of model parameters

Chronic locked anterior shoulder dislocation with impaction of the humeral head onto the coracoid: a case report

The glenohumeral joint is one of the most commonly dislocated joints. When dislocated, the humeral head typically moves anteriorly and medially within the soft tissues adjacent to the glenoid. We present a case of a 64-year-old female who presented with a locked anterior shoulder dislocation with impaction of the humeral head onto the coracoid. To our knowledge, this is the first reported instance of humeral head impaction onto the coracoid causing the shoulder dislocation to be irreducible by closed means. Complications of this dislocation can include humeral head deformity, pseudoparalysis, brachial plexus injury, and significant pain. Level of evidence V

Reducing the Read Noise of HAWAII-2RG Detector Systems with Improved Reference Sampling and Subtraction (IRS2)

IRS2 is a Wiener-optimal approach to using all of the reference information that Teledyne's HAWAII-2RG detector arrays provide. Using a new readout pattern, IRS2 regularly interleaves reference pixels with the normal pixels during readout. This differs from conventional clocking, in which the reference pixels are read out infrequently, and only in a few rows and columns around the outside edges of the detector array. During calibration, the data are processed in Fourier space, which is <;:lose to the noise's eigenspace. Using IRS2, we have reduced the read noise of the James Webb Space Telescope Near Infrared Spectrograph by 15% compared to conventional readout. We are attempting to achieve further gains by calibrating out recently recognized non-stationary noise that appears at the frame rate

Association between the COVID-19 pandemic and insurance-based disparities in mortality after major surgery among US adults

Importance: The COVID-19 pandemic caused significant disruptions in surgical care. Whether these disruptions disproportionately impacted economically disadvantaged individuals is unknown. Objective: To evaluate the association between the COVID-19 pandemic and mortality after major surgery among patients with Medicaid insurance or without insurance compared with patients with commercial insurance. Design, Setting, and Participants: This cross-sectional study used data from the Vizient Clinical Database for patients who underwent major surgery at hospitals in the US between January 1, 2018, and May 31, 2020. Exposures: The hospital proportion of patients with COVID-19 during the first wave of COVID-19 cases between March 1 and May 31, 2020, stratified as low (≤5.0%), medium (5.1%-10.0%), high (10.1%-25.0%), and very high (\u3e25.0%). Main Outcomes and Measures: The main outcome was inpatient mortality. The association between mortality after surgery and payer status as a function of the proportion of hospitalized patients with COVID-19 was evaluated with a quasi-experimental triple-difference approach using logistic regression. Results: Among 2 950 147 adults undergoing inpatient surgery (1 550 752 female [52.6%]) at 677 hospitals, the primary payer was Medicare (1 427 791 [48.4%]), followed by commercial insurance (1 000 068 [33.9%]), Medicaid (321 600 [10.9%]), other payer (140 959 [4.8%]), and no insurance (59 729 [2.0%]). Mortality rates increased more for patients undergoing surgery during the first wave of the pandemic in hospitals with a high COVID-19 burden (adjusted odds ratio [AOR], 1.13; 95% CI, 1.03-1.24; P = .01) and a very high COVID-19 burden (AOR, 1.38; 95% CI, 1.24-1.53; P \u3c .001) compared with patients in hospitals with a low COVID-19 burden. Overall, patients with Medicaid had 29% higher odds of death (AOR, 1.29; 95% CI, 1.22-1.36; P \u3c .001) and patients without insurance had 75% higher odds of death (AOR, 1.75; 95% CI, 1.55-1.98; P \u3c .001) compared with patients with commercial insurance. However, mortality rates for surgical patients with Medicaid insurance (AOR, 1.03; 95% CI, 0.82-1.30; P = .79) or without insurance (AOR, 0.85; 95% CI, 0.47-1.54; P = .60) did not increase more than for patients with commercial insurance in hospitals with a high COVID-19 burden compared with hospitals with a low COVID-19 burden. These findings were similar in hospitals with very high COVID-19 burdens. Conclusions and Relevance: In this cross-sectional study, the first wave of the COVID-19 pandemic was associated with a higher risk of mortality after surgery in hospitals with more than 25.0% of patients with COVID-19. However, the pandemic was not associated with greater increases in mortality among patients with no insurance or patients with Medicaid compared with patients with commercial insurance in hospitals with a very high COVID-19 burden

Principal Components Analysis of a JWST NIRSpec Detector Subsystem

We present principal component analysis (PCA) of a flight-representative James Webb Space Telescope NearInfrared Spectrograph (NIRSpec) Detector Subsystem. Although our results are specific to NIRSpec and its T - 40 K SIDECAR ASICs and 5 m cutoff H2RG detector arrays, the underlying technical approach is more general. We describe how we measured the systems response to small environmental perturbations by modulating a set of bias voltages and temperature. We used this information to compute the systems principal noise components. Together with information from the astronomical scene, we show how the zeroth principal component can be used to calibrate out the effects of small thermal and electrical instabilities to produce cosmetically cleaner images with significantly less correlated noise. Alternatively, if one were designing a new instrument, one could use a similar PCA approach to inform a set of environmental requirements (temperature stability, electrical stability, etc.) that enabled the planned instrument to meet performance requirement

The Case for Selection at CCR5-Δ32

The C-C chemokine receptor 5, 32 base-pair deletion (CCR5-Δ32) allele confers strong resistance to infection by the AIDS virus HIV. Previous studies have suggested that CCR5-Δ32 arose within the past 1,000 y and rose to its present high frequency (5%–14%) in Europe as a result of strong positive selection, perhaps by such selective agents as the bubonic plague or smallpox during the Middle Ages. This hypothesis was based on several lines of evidence, including the absence of the allele outside of Europe and long-range linkage disequilibrium at the locus. We reevaluated this evidence with the benefit of much denser genetic maps and extensive control data. We find that the pattern of genetic variation at CCR5-Δ32 does not stand out as exceptional relative to other loci across the genome. Moreover using newer genetic maps, we estimated that the CCR5-Δ32 allele is likely to have arisen more than 5,000 y ago. While such results can not rule out the possibility that some selection may have occurred at C-C chemokine receptor 5 (CCR5), they imply that the pattern of genetic variation seen atCCR5-Δ32 is consistent with neutral evolution. More broadly, the results have general implications for the design of future studies to detect the signs of positive selection in the human genome