P-splines with derivative based penalties and tensor product smoothing of unevenly distributed data

The P-splines of Eilers and Marx (1996) combine a B-spline basis with a discrete quadratic penalty on the basis coefficients, to produce a reduced rank spline like smoother. P-splines have three properties that make them very popular as reduced rank smoothers: i) the basis and the penalty are sparse, enabling efficient computation, especially for Bayesian stochastic simulation; ii) it is possible to flexibly `mix-and-match' the order of B-spline basis and penalty, rather than the order of penalty controlling the order of the basis as in spline smoothing; iii) it is very easy to set up the B-spline basis functions and penalties. The discrete penalties are somewhat less interpretable in terms of function shape than the traditional derivative based spline penalties, but tend towards penalties proportional to traditional spline penalties in the limit of large basis size. However part of the point of P-splines is not to use a large basis size. In addition the spline basis functions arise from solving functional optimization problems involving derivative based penalties, so moving to discrete penalties for smoothing may not always be desirable. The purpose of this note is to point out that the three properties of basis-penalty sparsity, mix-and-match penalization and ease of setup are readily obtainable with B-splines subject to derivative based penalization. The penalty setup typically requires a few lines of code, rather than the two lines typically required for P-splines, but this one off disadvantage seems to be the only one associated with using derivative based penalties. As an example application, it is shown how basis-penalty sparsity enables efficient computation with tensor product smoothers of scattered data

Forecasting Player Behavioral Data and Simulating in-Game Events

Understanding player behavior is fundamental in game data science. Video games evolve as players interact with the game, so being able to foresee player experience would help to ensure a successful game development. In particular, game developers need to evaluate beforehand the impact of in-game events. Simulation optimization of these events is crucial to increase player engagement and maximize monetization. We present an experimental analysis of several methods to forecast game-related variables, with two main aims: to obtain accurate predictions of in-app purchases and playtime in an operational production environment, and to perform simulations of in-game events in order to maximize sales and playtime. Our ultimate purpose is to take a step towards the data-driven development of games. The results suggest that, even though the performance of traditional approaches such as ARIMA is still better, the outcomes of state-of-the-art techniques like deep learning are promising. Deep learning comes up as a well-suited general model that could be used to forecast a variety of time series with different dynamic behaviors

Two dimensional smoothing via an optimised Whittaker smoother

Background In many applications where moderate to large datasets are used, plotting relationships between pairs of variables can be problematic. A large number of observations will produce a scatter-plot which is difficult to investigate due to a high concentration of points on a simple graph. In this article we review the Whittaker smoother for enhancing scatter-plots and smoothing data in two dimensions. To optimise the behaviour of the smoother an algorithm is introduced, which is easy to programme and computationally efficient. Results The methods are illustrated using a simple dataset and simulations in two dimensions. Additionally, a noisy mammography is analysed. When smoothing scatterplots the Whittaker smoother is a valuable tool that produces enhanced images that are not distorted by the large number of points. The methods is also useful for sharpening patterns or removing noise in distorted images. Conclusion The Whittaker smoother can be a valuable tool in producing better visualisations of big data or filter distorted images. The suggested optimisation method is easy to programme and can be applied with low computational cost

Dynamical density delay maps: simple, new method for visualising the behaviour of complex systems

Background. Physiologic signals, such as cardiac interbeat intervals, exhibit complex fluctuations. However, capturing important dynamical properties, including nonstationarities may not be feasible from conventional time series graphical representations. Methods. We introduce a simple-to-implement visualisation method, termed dynamical density delay mapping (``D3-Map'' technique) that provides an animated representation of a system's dynamics. The method is based on a generalization of conventional two-dimensional (2D) Poincar� plots, which are scatter plots where each data point, x(n), in a time series is plotted against the adjacent one, x(n+1). First, we divide the original time series, x(n) (n=1,..., N), into a sequence of segments (windows). Next, for each segment, a three-dimensional (3D) Poincar� surface plot of x(n), x(n+1), hx(n),x(n+1) is generated, in which the third dimension, h, represents the relative frequency of occurrence of each (x(n),x(n+1)) point. This 3D Poincar\'e surface is then chromatised by mapping the relative frequency h values onto a colour scheme. We also generate a colourised 2D contour plot from each time series segment using the same colourmap scheme as for the 3D Poincar\'e surface. Finally, the original time series graph, the colourised 3D Poincar\'e surface plot, and its projection as a colourised 2D contour map for each segment, are animated to create the full ``D3-Map.'' Results. We first exemplify the D3-Map method using the cardiac interbeat interval time series from a healthy subject during sleeping hours. The animations uncover complex dynamical changes, such as transitions between states, and the relative amount of time the system spends in each state. We also illustrate the utility of the method in detecting hidden temporal patterns in the heart rate dynamics of a patient with atrial fibrillation. The videos, as well as the source code, are made publicly available. Conclusions. Animations based on density delay maps provide a new way of visualising dynamical properties of complex systems not apparent in time series graphs or standard Poincar\'e plot representations. Trainees in a variety of fields may find the animations useful as illustrations of fundamental but challenging concepts, such as nonstationarity and multistability. For investigators, the method may facilitate data exploration

Applied immuno-epidemiological research: an approach for integrating existing knowledge into the statistical analysis of multiple immune markers.

BACKGROUND: Immunologists often measure several correlated immunological markers, such as concentrations of different cytokines produced by different immune cells and/or measured under different conditions, to draw insights from complex immunological mechanisms. Although there have been recent methodological efforts to improve the statistical analysis of immunological data, a framework is still needed for the simultaneous analysis of multiple, often correlated, immune markers. This framework would allow the immunologists' hypotheses about the underlying biological mechanisms to be integrated. RESULTS: We present an analytical approach for statistical analysis of correlated immune markers, such as those commonly collected in modern immuno-epidemiological studies. We demonstrate i) how to deal with interdependencies among multiple measurements of the same immune marker, ii) how to analyse association patterns among different markers, iii) how to aggregate different measures and/or markers to immunological summary scores, iv) how to model the inter-relationships among these scores, and v) how to use these scores in epidemiological association analyses. We illustrate the application of our approach to multiple cytokine measurements from 818 children enrolled in a large immuno-epidemiological study (SCAALA Salvador), which aimed to quantify the major immunological mechanisms underlying atopic diseases or asthma. We demonstrate how to aggregate systematically the information captured in multiple cytokine measurements to immunological summary scores aimed at reflecting the presumed underlying immunological mechanisms (Th1/Th2 balance and immune regulatory network). We show how these aggregated immune scores can be used as predictors in regression models with outcomes of immunological studies (e.g. specific IgE) and compare the results to those obtained by a traditional multivariate regression approach. CONCLUSION: The proposed analytical approach may be especially useful to quantify complex immune responses in immuno-epidemiological studies, where investigators examine the relationship among epidemiological patterns, immune response, and disease outcomes

Attainment rate as a surrogate indicator of the intervertebral neutral zone length in lateral bending: An in vitro proof of concept study

Background Lumbar segmental instability is often considered to be a cause of chronic low back pain. However, defining its measurement has been largely limited to laboratory studies. These have characterised segmental stability as the intrinsic resistance of spine specimens to initial bending moments by quantifying the dynamic neutral zone. However these measurements have been impossible to obtain in vivo without invasive procedures, preventing the assessment of intervertebral stability in patients. Quantitative fluoroscopy (QF), measures the initial velocity of the attainment of intervertebral rotational motion in patients, which may to some extent be representative of the dynamic neutral zone. This study sought to explore the possible relationship between the dynamic neutral zone and intervertebral rotational attainment rate as measured with (QF) in an in vitro preparation. The purpose was to find out if further work into this concept is worth pursuing. Method This study used passive recumbent QF in a multi-segmental porcine model. This assessed the intrinsic intervertebral responses to a minimal coronal plane bending moment as measured with a digital force guage. Bending moments about each intervertebral joint were calculated and correlated with the rate at which global motion was attained at each intervertebral segment in the first 10° of global motion where the intervertebral joint was rotating. Results Unlike previous studies of single segment specimens, a neutral zone was found to exist during lateral bending. The initial attainment rates for left and right lateral flexion were comparable to previously published in vivo values for healthy controls. Substantial and highly significant levels of correlation between initial attainment rate and neutral zone were found for left (Rho = 0.75, P = 0.0002) and combined left-right bending (Rho = 0.72, P = 0.0001) and moderate ones for right alone (Rho = 0.55, P = 0.0012). Conclusions This study found good correlation between the initial intervertebral attainment rate and the dynamic neutral zone, thereby opening the possibility to detect segmental instability from clinical studies. However the results must be treated with caution. Further studies with multiple specimens and adding sagittal plane motion are warranted

Colorectal Cancer Prognosis Following Obesity Surgery in a Population-Based Cohort Study

Background: Obesity surgery involves mechanical and physiological changes of the gastrointestinal tract that might promote colorectal cancer progression. Thus, we hypothesised that obesity surgery is associated with poorer prognosis in patients with colorectal cancer. Methods: This nationwide population-based cohort study included all patients with an obesity diagnosis who subsequently developed colorectal cancer in Sweden from 1980 to 2012. The exposure was obesity surgery, and the main and secondary outcomes were disease-specific mortality and all-cause mortality, respectively. Cox proportional hazard survival models were used to calculate hazard ratios (HRs) with 95% confidence intervals (CIs), adjusted for sex, age, calendar year and education level. Results: The exposed and unexposed cohort included 131 obesity surgery and 1332 non-obesity surgery patients with colorectal cancer. There was a statistically significant increased rate of colorectal cancer deaths following obesity surgery (disease-specific HR 1.50, 95% CI 1.00–2.19). When analysed separately, the mortality rate was more than threefold increased in rectal cancer patients with prior obesity surgery (disease-specific HR 3.70, 95% CI 2.00–6.90), while no increased mortality rate was found in colon cancer patients (disease-specific HR 1.10, 85% CI 0.67–1.70). Conclusion: This population-based study among obese individuals found a poorer prognosis in colorectal cancer following obesity surgery, which was primarily driven by the higher mortality rate in rectal cancer

Prothymosin alpha: a ubiquitous polypeptide with potential use in cancer diagnosis and therapy

The thymus is a central lymphoid organ with crucial role in generating T cells and maintaining homeostasis of the immune system. More than 30 peptides, initially referred to as “thymic hormones,” are produced by this gland. Although the majority of them have not been proven to be thymus-speciWc, thymic peptides comprise an eVective group of regulators, mediating important immune functions. Thymosin fraction Wve (TFV) was the Wrst thymic extract shown to stimulate lymphocyte proliferation and diVerentiation. Subsequent fractionation of TFV led to the isolation and characterization of a series of immunoactive peptides/polypeptides, members of the thymosin family. Extensive research on prothymosin (proT) and thymosin 1 (T1) showed that they are of clinical signiWcance and potential medical use. They may serve as molecular markers for cancer prognosis and/or as therapeutic agents for treating immunodeWciencies, autoimmune diseases and malignancies. Although the molecular mechanisms underlying their eVect are yet not fully elucidated proT and T1 could be considered as candidates for cancer immunotherapy. In this review, we will focus in principle on the eventual clinical utility of proT, both as a tumor biomarker and in triggering anticancer immune responses. Considering the experience acquired via the use of T1 to treat cancer patients, we will also discuss potential approaches for the future introduction of proT into the clinical setting

Analysis of Overlapped and Noisy Hydrogen/Deuterium Exchange Mass Spectra

This document is the Accepted Manuscript version of a Published Work that appeared in final form in the Journal of the American Chemical Society, copyright © American Chemical Society after peer review and technical editing by the publisher. To access the final edited and published work see http://doi.org/10.1007/s13361-013-0727-5.Noisy and overlapped mass spectrometry data hinders the sequence coverage that can be obtained from Hydrogen Deuterium exchange analysis, and places a limit on the complexity of the samples that can be studied by this technique. Advances in instrumentation have addressed these limits, but as the complexity of the biological samples under investigation increases, these problems are reencountered. Here we describe the use of binomial distribution fitting with asymmetric linear squares regression for calculating the accurate deuterium content for mass envelopes of low signal or that contain significant overlap. The approach is demonstrated with a test data set of HIV Env gp140 wherein inclusion of the new analysis regime resulted in obtaining exchange data for 42 additional peptides, improving the sequence coverage by 11%. At the same time, the precision of deuterium uptake measurements was improved for nearly every peptide examined. The improved processing algorithms also provide an efficient method for deconvolution of bimodal mass envelopes and EX1 kinetic signatures. All these functions and visualization tools have been implemented in the new version of the freely available software, HX-Express v2