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.

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.

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.

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 GW 5.8 10 -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; GW f 3.4 10 -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 GW f 3.9 10 -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 datadriven 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 2 than can be achieved with individually resolved mergers alone.

Abstract 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. KEY WORDS: Generalized cross-validationKnot positionPiecewise linearRegression analysis

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.

Abstract Principles compenents (PC) are often interpreted by looking at the loading for each variable. Variable with a small-magnitude loading are ignored and given PC is then approximated by the linear combination involving only the remaining variable. It is argued that this procedure is potentially misleading in various respects. Examples are given alternatives are suggested.

Abstract. Glacier-wide mass balance has been measured for more than sixty years and is widely used as an indicator of climate change and to assess the glacier contribution to runoff and sea level rise. Until recently, comprehensive uncertainty assessments have rarely been carried out and mass balance data have often been applied using rough error estimation or without consideration of errors. In this study, we propose a framework for reanalysing glacier mass balance series that includes conceptual and statistical toolsets for assessment of random and systematic errors, as well as for validation and calibration (if necessary) of the glaciological with the geodetic balance results. We demonstrate the usefulness and limitations of the proposed scheme, drawing on an analysis that comprises over 50 recording periods for a dozen glaciers, and we make recommendations to investigators and users of glacier mass balance data. Reanalysing glacier mass balance series needs to become a standard procedure for every monitoring programme to improve data quality, including reliable uncertainty estimates.

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.

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.

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.

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.

Estimates of genetic components are important for our understanding of how individual characteristics are transferred between generations. We show that the level of heritability varies between 0.12 and 0.68 in six morphological traits in house sparrows (Passer domesticus L.) in northern Norway. Positive and negative genetic correlations were present among traits, suggesting evolutionary constraints on the evolution of some of these characters. A sexual difference in the amount of heritable genetic variation was found in tarsus length, wing length, bill depth and body condition index, with generally higher heritability in females. In addition, the structure of the genetic variance-covariance matrix for the traits differed between the sexes. Genetic correlations between males and females for the morphological traits were however large and not significantly different from one, indicating that sex-specific responses to selection will be influenced by intersexual differences in selection differentials. Despite this, some traits had heritability above 0.1 in females, even after conditioning on the additive genetic covariance between sexes and the additive genetic variances in males. Moreover, a meta-analysis indicated that higher heritability in females than in males may be common in birds. Thus, this indicates sexual differences in the genetic architecture of birds. Consequently, as in house sparrows, the evolutionary responses to selection will often be larger in females than males. Hence, our results suggest that sex-specific additive genetic variances and covariances, although ignored in most studies, should be included when making predictions of evolutionary changes from standard quantitative genetic models.

Summary In this paper it is to be shown that F isher's non‐randomizing exact test for 2 × 2‐tables, which is a conditional test, can by simple means be changed into an unconditional test using raised levels of significance; not seldom, especially for not too large samples, the level of significance can be doubled. This leads in many cases to a considerable increase of power of the test. A table with raised levels has been prepared up to sample sizes of 50 and a rule of thumb, which can be used if this table is not available, has been developEd.

Abstract This study investigates the implementation of environmental management accounting in translating environmental management strategy into organizational performance. Further, the study identifies the influence of institutional pressures on environmental management strategy and environmental management accounting to provide a better description of the impact of the institutional environment on corporate environmental practices. The data were collected from 144 business entities in Sri Lanka using a web‐based survey and analyzed using partial least squares structural equation modeling. We found statistically significant evidence to state that the environmental management strategy is positively associated with the environmental and economic performance of organizations, whereas environmental management accounting mediates this relationship. Further, a firm's institutional environment positively affects both environmental management strategies and environmental management accounting. This study emphasizes that the organizational information systems such as environmental management accounting are useful in providing information on environmental costs and monitoring environmental and financial performance when implementing environmental management strategies in the pursuit of corporate sustainable development.