Department of Mathematical Sciences

BACKGROUND: Recently, two centers have independently developed a risk score for predicting postoperative nausea and vomiting (PONV). This study investigated (1) whether risk scores are valid across centers and (2) whether risk scores based on logistic regression coefficients can be simplified without loss of discriminating power. METHODS: Adult patients from two centers (Oulu, Finland: n = 520, and Wuerzburg, Germany: n = 2202) received inhalational anesthesia (without antiemetic prophylaxis) for various types of surgery. PONV was defined as nausea or vomiting within 24 h of surgery. Risk scores to estimate the probability of PONV were obtained by fitting logistic regression models. Simplified risk scores were constructed based on the number of risk factors that were found significant in the logistic regression analyses. Original and simplified scores were cross-validated. A combined data set was created to estimate a potential center effect and to construct a final risk score. The discriminating power of each score was assessed using the area under the receiver operating characteristic curves. RESULTS: Risk scores derived from one center were able to predict PONV from the other center (area under the curve = 0.65-0.75). Simplification did not essentially weaken the discriminating power (area under the curve = 0.63-0.73). No center effect could be detected in a combined data set (odds ratio = 1.06, 95% confidence interval = 0.71-1.59). The final score consisted of four predictors: female gender, history of motion sickness (MS) or PONV, nonsmoking, and the use of postoperative opioids. If none, one, two, three, or four of these risk factors were present, the incidences of PONV were 10%, 21%, 39%, 61% and 79%. CONCLUSIONS: The risk scores derived from one center proved valid in the other and could be simplified without significant loss of discriminating power. Therefore, it appears that this risk score has broad applicability in predicting PONV in adult patients undergoing inhalational anesthesia for various types of surgery. For patients with at least two out of these four identified predictors a prophylactic antiemetic strategy should be considered.

This paper analyses multivariate high frequency financial data using realized covariation. We provide a new asymptotic distribution theory for standard methods such as regression, correlation analysis, and covariance. It will be based on a fixed interval of time (e.g., a day or week), allowing the number of high frequency returns during this period to go to infinity. Our analysis allows us to study how high frequency correlations, regressions, and covariances change through time. In particular we provide confidence intervals for each of these quantities.

Although mRNA decay rates are a key determinant of the steady-state concentration for any given mRNA species, relatively little is known, on a population level, about what factors influence turnover rates and how these rates are integrated into cellular decisions. We decided to measure mRNA decay rates in two human cell lines with high-density oligonucleotide arrays that enable the measurement of decay rates simultaneously for thousands of mRNA species. Using existing annotation and the Gene Ontology hierarchy of biological processes, we assign mRNAs to functional classes at various levels of resolution and compare the decay rate statistics between these classes. The results show statistically significant organizational principles in the variation of decay rates among functional classes. In particular, transcription factor mRNAs have increased average decay rates compared with other transcripts and are enriched in "fast-decaying" mRNAs with half-lives <2 h. In contrast, we find that mRNAs for biosynthetic proteins have decreased average decay rates and are deficient in fast-decaying mRNAs. Our analysis of data from a previously published study of Saccharomyces cerevisiae mRNA decay shows the same functional organization of decay rates, implying that it is a general organizational scheme for eukaryotes. Additionally, we investigated the dependence of decay rates on sequence composition, that is, the presence or absence of short mRNA motifs in various regions of the mRNA transcript. Our analysis recovers the positive correlation of mRNA decay with known AU-rich mRNA motifs, but we also uncover further short mRNA motifs that show statistically significant correlation with decay. However, we also note that none of these motifs are strong predictors of mRNA decay rate, indicating that the regulation of mRNA decay is more complex and may involve the cooperative binding of several RNA-binding proteins at different sites.

The projection of age-stratified cancer incidence and mortality rates is of great interest due to demographic changes, but also therapeutical and diagnostic developments. Bayesian age-period-cohort (APC) models are well suited for the analysis of such data, but are not yet used in routine practice of epidemiologists. Reasons may include that Bayesian APC models have been criticized to produce too wide prediction intervals. Furthermore, the fitting of Bayesian APC models is usually done using Markov chain Monte Carlo (MCMC), which introduces complex convergence concerns and may be subject to additional technical problems. In this paper we address both concerns, developing efficient MCMC-free software for routine use in epidemiological applications. We apply Bayesian APC models to annual lung cancer data for females in five different countries, previously analyzed in the literature. To assess the predictive quality, we omit the observations from the last 10 years and compare the projections with the actual observed data based on the absolute error and the continuous ranked probability score. Further, we assess calibration of the one-step-ahead predictive distributions. In our application, the probabilistic forecasts obtained by the Bayesian APC model are well calibrated and not too wide. A comparison to projections obtained by a generalized Lee-Carter model is also given. The methodology is implemented in the user-friendly R-package BAPC using integrated nested Laplace approximations.

The objective of this study is to investigate and compare the results of three data mining approaches, the support vector machines (SVM), decision tree (DT), and Naïve Bayes (NB) models for spatial prediction of landslide hazards in the Hoa Binh province (Vietnam). First, a landslide inventory map showing the locations of 118 landslides was constructed from various sources. The landslide inventory was then randomly partitioned into 70% for training the models and 30% for the model validation. Second, ten landslide conditioning factors were selected (i.e., slope angle, slope aspect, relief amplitude, lithology, soil type, land use, distance to roads, distance to rivers, distance to faults, and rainfall). Using these factors, landslide susceptibility indexes were calculated using SVM, DT, and NB models. Finally, landslide locations that were not used in the training phase were used to validate and compare the landslide susceptibility maps. The validation results show that the models derived using SVM have the highest prediction capability. The model derived using DT has the lowest prediction capability. Compared to the logistic regression model, the prediction capability of the SVM models is slightly better. The prediction capability of the DT and NB models is lower.

We report results of a search for an isotropic gravitational-wave background (GWB) using data from Advanced LIGO's and Advanced Virgo's third observing run (O3) combined with upper limits from the earlier O1 and O2 runs. Unlike in previous observing runs in the advanced detector era, we include Virgo in the search for the GWB. The results of the search are consistent with uncorrelated noise, and therefore we place upper limits on the strength of the GWB. We find that the dimensionless energy density ${\mathrm{\ensuremath{\Omega}}}_{\mathrm{GW}}\ensuremath{\le}5.8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}$ at the 95% credible level for a flat (frequency-independent) GWB, using a prior which is uniform in the log of the strength of the GWB, with 99% of the sensitivity coming from the band 20--76.6 Hz; ${\mathrm{\ensuremath{\Omega}}}_{\mathrm{GW}}(f)\ensuremath{\le}3.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}$ at 25 Hz for a power-law GWB with a spectral index of $2/3$ (consistent with expectations for compact binary coalescences), in the band 20--90.6 Hz; and ${\mathrm{\ensuremath{\Omega}}}_{\mathrm{GW}}(f)\ensuremath{\le}3.9\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$ at 25 Hz for a spectral index of 3, in the band 20--291.6 Hz. These upper limits improve over our previous results by a factor of 6.0 for a flat GWB, 8.8 for a spectral index of $2/3$, and 13.1 for a spectral index of 3. We also search for a GWB arising from scalar and vector modes, which are predicted by alternative theories of gravity; we do not find evidence of these, and place upper limits on the strength of GWBs with these polarizations. We demonstrate that there is no evidence of correlated noise of magnetic origin by performing a Bayesian analysis that allows for the presence of both a GWB and an effective magnetic background arising from geophysical Schumann resonances. We compare our upper limits to a fiducial model for the GWB from the merger of compact binaries, updating the model to use the most recent data-driven population inference from the systems detected during O3a. Finally, we combine our results with observations of individual mergers and show that, at design sensitivity, this joint approach may yield stronger constraints on the merger rate of binary black holes at $z\ensuremath{\gtrsim}2$ than can be achieved with individually resolved mergers alone.

A simple method is presented for fitting regression models that are nonlinear in the explanatory variables. Despite its simplicity—or perhaps because of it—the method has some powerful characteristics that cause it to be competitive with and often superior to more sophisticated techniques, especially for small data sets in the presence of high noise.

BACKGROUND: The high incidence of and mortality from colorectal cancer (160,000 new cases and 60,000 deaths in the United States each year) are compelling public health concerns. Following the evolution of effective surgery for this disease since the 1960s, the focus has been on improving methods of detection and integrating them into effective screening programs. PURPOSE: This was the first study to evaluate the effectiveness, in a setting of comprehensive medical examinations, of using the fecal occult blood test in conjunction with sigmoidoscopy, rather than sigmoidoscopy alone, to screen for colorectal cancer. Our end points were extent of compliance with fecal occult blood test and sigmoidoscopy, numbers of cancers detected, and mortality rate. METHODS: From 1975 through 1979, a total of 21,756 patients (aged 40 and older) who presented at the Preventive Medicine Institute-Strang Clinic for routine medical examinations were enrolled by calendar period into study and control groups. Study patients were offered annually both rigid sigmoidoscopy examinations and fecal occult blood tests requiring two stool specimens per day for 3 days, while control patients were offered only annual sigmoidoscopy. The majority of fecal occult blood test cards were not rehydrated before assay. Patients with positive tests were referred for double-contrast barium enema and colonoscopy. Two distinct trials were carried out. Trial I was primarily a demonstration of feasibility of using the fecal occult blood test as a supplemental screening method. Of the 9277 participants, 7168 (77%) were assigned to the study group and offered the fecal occult blood test. In trial II, approximately half of the 12,479 patients were assigned to each group. Patients in both trials had follow-up through 1984. RESULTS: Compliance with the fecal occult blood test was initially high in both trials, but diminished such that only 56% of study patients in trial I and 20% of those in trial II returned for second tests. On the initial (prevalence) screen, a substantial number of early-stage cancers were detected by the fecal occult blood test, primarily in trial II. In trial II, survival probability was significantly greater (P < .001) in the study group than in the controls (70% versus 48%), and colorectal cancer mortality was lower (0.36 versus 0.63) with borderline significance (P = .053, one-sided). CONCLUSIONS AND IMPLICATIONS: The screening of average-risk individuals (aged 50 and older) for colorectal cancer through use of the fecal occult blood test in conjunction with sigmoidoscopy can increase the likelihood of early detection of this disease. This practice, coupled with prompt diagnostic work-up following positive tests, will result in treatment of earlier stage cancers and increased survival after treatment.

Abstract In this paper, we explore quadrature methods for highly oscillatory integrals. Generalizing the method of stationary phase, we expand such integrals into asymptotic series in inverse powers of the frequency. The outcome is two families of methods, one based on a truncation of the asymptotic series and the other extending an approach implicit in the work of Filon (Filon 1928 Proc. R. Soc. Edinb.49, 38–47). Both kinds of methods approximate the integral as a linear combination of function values and derivatives, with coefficients that may depend on frequency. We determine asymptotic properties of these methods, proving, perhaps counterintuitively, that their performance drastically improves as frequency grows. The paper is accompanied by numerical results that demonstrate the potential of this set of ideas.

It is possible to specify a model for interest rates in various ways, by giving the dynamics of the spot rate or of the forward rates, for example. A less well–developed approach is to specify the law of the state–price density process directly. In abstract, the state–price density process is a positive supermartingale, and the theory of Markov processes provides a rich framework for the generation of examples of such things. We show how this can be done, and provide simple examples (some familiar, some new) where prices of derivatives can be computed very easily. One benefit of the potential approach is that it becomes very easy to model the yield curve in many countries at once, together with the exchange rates between them.

Abstract Topological photonics emerged as a novel route to engineer the flow of light. Topologically protected photonic edge modes, which are supported at the perimeters of topologically nontrivial insulating bulk structures, are of particular interest as they may enable low‐loss optical waveguides immune to structural disorder. Very recently, there has been a sharp rise of interest in introducing gain materials into such topological photonic structures, primarily aiming at revolutionizing semiconductor lasers with the aid of physical mechanisms existing in topological physics. Examples of remarkable realizations are topological lasers with unidirectional light output under time‐reversal symmetry breaking and topologically protected polariton and micro/nanocavity lasers. Moreover, the introduction of gain and loss provides a fascinating playground to explore novel topological phases, which are in close relevance to non‐Hermitian and parity‐time symmetric quantum physics and are, in general, difficult to access using fermionic condensed matter systems. Here, we review the cutting‐edge research on active topological photonics, in which optical gain plays a pivotal role. We discuss recent realizations of topological lasers of various kinds, together with the underlying physics explaining the emergence of topological edge modes. In such demonstrations, the optical modes of the topological lasers are determined by the dielectric structures and support lasing oscillation with the help of optical gain. We also address recent research on topological photonic systems in which gain and loss, themselves, essentially influence topological properties of the bulk systems. We believe that active topological photonics provides powerful means to advance micro/nanophotonics systems for diverse applications and topological physics, itself, as well.

In this paper we explore the potential of multilevel models for meta-analysis of trials with binary outcomes for both summary data, such as log-odds ratios, and individual patient data. Conventional fixed effect and random effects models are put into a multilevel model framework, which provides maximum likelihood or restricted maximum likelihood estimation. To exemplify the methods, we use the results from 22 trials to prevent respiratory tract infections; we also make comparisons with a second example data set comprising fewer trials. Within summary data methods, confidence intervals for the overall treatment effect and for the between-trial variance may be derived from likelihood based methods or a parametric bootstrap as well as from Wald methods; the bootstrap intervals are preferred because they relax the assumptions required by the other two methods. When modelling individual patient data, a bias corrected bootstrap may be used to provide unbiased estimation and correctly located confidence intervals; this method is particularly valuable for the between-trial variance. The trial effects may be modelled as either fixed or random within individual data models, and we discuss the corresponding assumptions and implications. If random trial effects are used, the covariance between these and the random treatment effects should be included; the resulting model is equivalent to a bivariate approach to meta-analysis. Having implemented these techniques, the flexibility of multilevel modelling may be exploited in facilitating extensions to standard meta-analysis methods.

We show that the Camassa–Holm equation ut − uxxt + 3uux − 2uxuxx − uuxxx = 0 possesses a global continuous semigroup of weak conservative solutions for initial data u|t=0 in H1. The result is obtained by introducing a coordinate transformation into Lagrangian coordinates. To characterize conservative solutions it is necessary to include the energy density given by the positive Radon measure μ with . The total energy is preserved by the solution.

Abstract This research investigates the heat and mass transfer in 3-D MHD radiative flow of water based hybrid nanofluid over an extending sheet by employing the strength of numerical computing based Lobatto IIIA method. Nanoparticles of aluminum oxide (Al 2 O 3 ) and silver (Ag) are being used with water (H 2 O) as base fluid. By considering the heat transfer phenomenon due to thermal radiation effects. The physical flow problem is then modeled into set of PDEs, which are then transmuted into equivalent set of nonlinear ODEs by utilizing the appropriate similarity transformations. The system of ODEs is solved by the computational strength of Lobatto IIIA method to get the various graphical and numerical results for analyzing the impact of various physical constraints on velocity and thermal profiles. Additionally, the heat transfers and skin friction analysis for the fluid flow dynamics is also investigated. The relative errors up to the accuracy level of 1e-15, established the worth and reliability of the computational technique. It is observed that heat transfer rate increases with the increase in magnetic effect, Biot number and rotation parameter.

Abstract Individual variation in susceptibility and exposure is subject to selection by natural infection, accelerating the acquisition of immunity, and reducing herd immunity thresholds and epidemic final sizes. This is a manifestation of a wider population phenomenon known as “frailty variation”. Despite theoretical understanding, public health policies continue to be guided by mathematical models that leave out considerable variation and as a result inflate projected disease burdens and overestimate the impact of interventions. Here we focus on trajectories of the coronavirus disease (COVID-19) pandemic in England and Scotland until November 2021. We fit models to series of daily deaths and infer relevant epidemiological parameters, including coefficients of variation and effects of non-pharmaceutical interventions which we find in agreement with independent empirical estimates based on contact surveys. Our estimates are robust to whether the analysed data series encompass one or two pandemic waves and enable projections compatible with subsequent dynamics. We conclude that vaccination programmes may have contributed modestly to the acquisition of herd immunity in populations with high levels of pre-existing naturally acquired immunity, while being critical to protect vulnerable individuals from severe outcomes as the virus becomes endemic. Graphical Abstract Highlights Variation in susceptibility/exposure responds to selection by natural infection Selection on susceptibility/exposure flattens epidemic curves Models with incomplete heterogeneity overestimate intervention impacts Individual variation lowered the natural herd immunity threshold for SARS-CoV-2

OBJECTIVES: (1) To quantify lethality of firearms relative to other suicide methods, (2) to quantify the extent to which suicide mortality may be reduced by limiting access to firearms. METHODS: Data on suicides and hospitalised para-suicides that occurred in the state of Illinois from 1990 to 1997 were combined. Total number of episodes for each suicide method was estimated as the sum of the number of suicides and the number of para-suicides for that method. Gender and suicide method were used as proxies for intention to die, and estimated lethality of suicide methods within method-gender groups (for example, male firearm users). Logistic regression was used to quantify the lethality of firearms relative to other suicide methods. Excess mortality associated with the use of firearms was estimated by conservatively assuming that in the absence of firearms the next most lethal suicide method would be used. RESULTS: From January 1990 to December 1997, among individuals 10 years or older in the state of Illinois, there were 37,352 hospital admissions for para-suicide and 10,287 completed suicides. Firearms are the most lethal suicide method. Episodes involving firearms are 2.6 times (95% CI 2.1 to 3.1) more lethal than those involving suffocation-the second most lethal suicide method. Preventing access to firearms can reduce the proportion of fatal firearms related suicides by 32% among minors, and 6.5% among adults. CONCLUSIONS: Limiting access to firearms is a potentially effective means of reducing suicide mortality.

(1986). Cleft comodule algebras for a bialgebra. Communications in Algebra: Vol. 14, No. 5, pp. 801-817.

Scattering factors for twenty-three atoms have been calculated from Hartree and Hartree-Fock radial wave functions.The results are compared with James & Brinclley's values and with those recently obtained by other authors.

Color codes are topological stabilizer codes with unusual transversality properties. Here I show that their group of transversal gates is optimal and only depends on the spatial dimension, not the local geometry. I also introduce a generalized, subsystem version of color codes. In 3D they allow the transversal implementation of a universal set of gates by gauge fixing, while error-dectecting measurements involve only four or six qubits.

t Dr. E. T. Goodwin has pointed out to the author that there is a strong connection between the idea of the Samelson inverse and a result ([22] p. 675, eq. ( 53)) of Lanczos.-' (* -Vwhere xr is the complex conjugate of xT.The point x with respect to the unit sphere in w-space.t.