Combining frequency and time domain approaches to systems with multiple spike train input and output

A frequency domain approach and a time domain approach have been combined in an investigation of the behaviour of the primary and secondary endings of an isolated muscle spindle in response to the activity of two static fusimotor axons when the parent muscle is held at a fixed length and when it is subjected to random length changes. The frequency domain analysis has an associated error process which provides a measure of how well the input processes can be used to predict the output processes and is also used to specify how the interactions between the recorded processes contribute to this error. Without assuming stationarity of the input, the time domain approach uses a sequence of probability models of increasing complexity in which the number of input processes to the model is progressively increased. This feature of the time domain approach was used to identify a preferred direction of interaction between the processes underlying the generation of the activity of the primary and secondary endings. In the presence of fusimotor activity and dynamic length changes imposed on the muscle, it was shown that the activity of the primary and secondary endings carried different information about the effects of the inputs imposed on the muscle spindle. The results presented in this work emphasise that the analysis of the behaviour of complex systems benefits from a combination of frequency and time domain methods

A semi-Markov model for stroke with piecewise-constant hazards in the presence of left, right and interval censoring.

This paper presents a parametric method of fitting semi-Markov models with piecewise-constant hazards in the presence of left, right and interval censoring. We investigate transition intensities in a three-state illness-death model with no recovery. We relax the Markov assumption by adjusting the intensity for the transition from state 2 (illness) to state 3 (death) for the time spent in state 2 through a time-varying covariate. This involves the exact time of the transition from state 1 (healthy) to state 2. When the data are subject to left or interval censoring, this time is unknown. In the estimation of the likelihood, we take into account interval censoring by integrating out all possible times for the transition from state 1 to state 2. For left censoring, we use an Expectation-Maximisation inspired algorithm. A simulation study reflects the performance of the method. The proposed combination of statistical procedures provides great flexibility. We illustrate the method in an application by using data on stroke onset for the older population from the UK Medical Research Council Cognitive Function and Ageing Study

Del Pezzo surfaces with 1/3(1,1) points

We classify del Pezzo surfaces with 1/3(1,1) points in 29 qG-deformation families grouped into six unprojection cascades (this overlaps with work of Fujita and Yasutake), we tabulate their biregular invariants, we give good model constructions for surfaces in all families as degeneracy loci in rep quotient varieties and we prove that precisely 26 families admit qG-degenerations to toric surfaces. This work is part of a program to study mirror symmetry for orbifold del Pezzo surfaces.Comment: 42 pages. v2: model construction added of last remaining surface, minor corrections, minor changes to presentation, references adde

Predicting replacement of smartphones with mobile app usage

© Springer International Publishing AG 2016. To identify right customers who intend to replace the smart phone can help to perform precision marketing and thus bring significant financial gains to cell phone retailers. In this paper,we provide a study of exploiting mobile app usage for predicting users who will change the phone in the future. We first analyze the characteristics of mobile log data and develop the temporal bag-of-apps model,which can transform the raw data to the app usage vectors. We then formularize the prediction problem,present the hazard based prediction model,and derive the inference procedure. Finally,we evaluate both data model and prediction model on real-world data. The experimental results show that the temporal usage data model can effectively capture the unique characteristics of mobile log data,and the hazard based prediction model is thus much more effective than traditional classification methods. Furthermore,the hazard model is explainable,that is,it can easily show how the replacement of smart phones relate to mobile app usage over time

Physical and psychological symptoms of quality of life in the CHART randomized trial in head and neck cancer: short-term and long-term patient reported symptoms

The randomized multicentre trial of continuous hyperfractionated accelerated radiotherapy (CHART) versus conventional radiotherapy in patients with advanced head and neck cancer showed no good evidence of a difference in any of the major clinical outcomes of survival, freedom from metastases, loco-regional control and disease-free survival. Therefore an assessment of the effect of treatment on physical and psychological symptoms is vital to balance the costs and benefits of the two treatments. A total of 615 patients were asked to complete a Rotterdam Symptom Checklist and the Hospital Anxiety and Depression Scale, which cover a variety of physical and psychological symptoms, at a total of ten time points. The data consisted of short-term data (the initial 3 months) and long-term data (1 and 2 years). The short-term data was split into an exploratory data set and a confirmatory data set, and analysed using subject-specific and group-based methods. Differences were only claimed if hypotheses generated in the exploratory data set were confirmed in the confirmatory data set. The long-term data was not split into two data sets and was analysed using a group-based approach. There was evidence of significantly worse symptoms of pain at day 21 in those treated with CHART and significantly worse symptoms of cough and hoarseness at 6 weeks in those treated conventionally. There was also evidence to suggest a higher degree of decreased sexual interest at 1 year and sore muscles at 2 years in those treated with conventional radiotherapy. There is no clear indication that one regimen is superior to the other in terms of ‘quality of life’, generally the initially more severe reaction in the CHART group being offset by the longer duration of symptoms in the conventionally treated group. © 1999 Cancer Research Campaig

A doubly stochastic rainfall model with exponentially decaying pulses

We develop a doubly stochastic point process model with exponentially decaying pulses to describe the statistical properties of the rainfall intensity process. Mathematical formulation of the point process model is described along with second-order moment characteristics of the rainfall depth and aggregated processes. The derived second-order properties of the accumulated rainfall at different aggregation levels are used in model assessment. A data analysis using 15 years of sub-hourly rainfall data from England is presented. Models with fixed and variable pulse lifetime are explored. The performance of the model is compared with that of a doubly stochastic rectangular pulse model. The proposed model fits most of the empirical rainfall properties well at sub-hourly, hourly and daily aggregation levels

Serial clustering of extratropical cyclones in a multi-model ensemble of historical and future simulations

This study has investigated serial (temporal) clustering of extra-tropical cyclones simulated by 17 climate models that participated in CMIP5. Clustering was estimated by calculating the dispersion (ratio of variance to mean) of 30 December-February counts of Atlantic storm tracks passing nearby each grid point. Results from single historical simulations of 1975-2005 were compared to those from historical ERA40 reanalyses from 1958-2001 ERA40 and single future model projections of 2069-2099 under the RCP4.5 climate change scenario. Models were generally able to capture the broad features in reanalyses reported previously: underdispersion/regularity (i.e. variance less than mean) in the western core of the Atlantic storm track surrounded by overdispersion/clustering (i.e. variance greater than mean) to the north and south and over western Europe. Regression of counts onto North Atlantic Oscillation (NAO) indices revealed that much of the overdispersion in the historical reanalyses and model simulations can be accounted for by NAO variability. Future changes in dispersion were generally found to be small and not consistent across models. The overdispersion statistic, for any 30 year sample, is prone to large amounts of sampling uncertainty that obscures the climate change signal. For example, the projected increase in dispersion for storm counts near London in the CNRMCM5 model is 0.1 compared to a standard deviation of 0.25. Projected changes in the mean and variance of NAO are insufficient to create changes in overdispersion that are discernible above natural sampling variations

A generalization of the Bombieri-Pila determinant method

The so-called determinant method was developed by Bombieri and Pila in 1989 for counting integral points of bounded height on affine plane curves. In this paper we give a generalization of that method to varieties of higher dimension, yielding a proof of Heath-Brown's 'Theorem 14' by real-analytic considerations alone.Comment: 13 page

RNA Unwinding by NS3 Helicase: A Statistical Approach

The study of double-stranded RNA unwinding by helicases is a problem of basic scientific interest. One such example is provided by studies on the hepatitis C virus (HCV) NS3 helicase using single molecule mechanical experiments. HCV currently infects nearly 3% of the world population and NS3 is a protein essential for viral genome replication. The objective of this study is to model the RNA unwinding mechanism based on previously published data and study its characteristics and their dependence on force, ATP and NS3 protein concentration. In this work, RNA unwinding by NS3 helicase is hypothesized to occur in a series of discrete steps and the steps themselves occurring in accordance with an underlying point process. A point process driven change point model is employed to model the RNA unwinding mechanism. The results are in large agreement with findings in previous studies. A gamma distribution based renewal process was found to model well the point process that drives the unwinding mechanism. The analysis suggests that the periods of constant extension observed during NS3 activity can indeed be classified into pauses and subpauses and that each depend on the ATP concentration. The step size is independent of external factors and seems to have a median value of 11.37 base pairs. The steps themselves are composed of a number of substeps with an average of about 4 substeps per step and an average substep size of about 3.7 base pairs. An interesting finding pertains to the stepping velocity. Our analysis indicates that stepping velocity may be of two kinds- a low and a high velocity