Well posedness and Maximum Entropy Approximation for the Dynamics of Quantitative Traits

We study the Fokker-Planck equation derived in the large system limit of the Markovian process describing the dynamics of quantitative traits. The Fokker-Planck equation is posed on a bounded domain and its transport and diffusion coefficients vanish on the domain's boundary. We first argue that, despite this degeneracy, the standard no-flux boundary condition is valid. We derive the weak formulation of the problem and prove the existence and uniqueness of its solutions by constructing the corresponding contraction semigroup on a suitable function space. Then, we prove that for the parameter regime with high enough mutation rate the problem exhibits a positive spectral gap, which implies exponential convergence to equilibrium. Next, we provide a simple derivation of the so-called Dynamic Maximum Entropy (DynMaxEnt) method for approximation of moments of the Fokker-Planck solution, which can be interpreted as a nonlinear Galerkin approximation. The limited applicability of the DynMaxEnt method inspires us to introduce its modified version that is valid for the whole range of admissible parameters. Finally, we present several numerical experiments to demonstrate the performance of both the original and modified DynMaxEnt methods. We observe that in the parameter regimes where both methods are valid, the modified one exhibits slightly better approximation properties compared to the original one.Comment: 28 pages, 4 tables, 5 figure

High-Speed Signal and Power Distribution of a Digital Tracking Calorimeter for Proton Computed Tomography

Masteroppgave i fysikkPHYS399MAMN-PHY

Probabilistic models of individual and collective animal behavior

Recent developments in automated tracking allow uninterrupted, high-resolution recording of animal trajectories, sometimes coupled with the identification of stereotyped changes of body pose or other behaviors of interest. Analysis and interpretation of such data represents a challenge: the timing of animal behaviors may be stochastic and modulated by kinematic variables, by the interaction with the environment or with the conspecifics within the animal group, and dependent on internal cognitive or behavioral state of the individual. Existing models for collective motion typically fail to incorporate the discrete, stochastic, and internal-state-dependent aspects of behavior, while models focusing on individual animal behavior typically ignore the spatial aspects of the problem. Here we propose a probabilistic modeling framework to address this gap. Each animal can switch stochastically between different behavioral states, with each state resulting in a possibly different law of motion through space. Switching rates for behavioral transitions can depend in a very general way, which we seek to identify from data, on the effects of the environment as well as the interaction between the animals. We represent the switching dynamics as a Generalized Linear Model and show that: (i) forward simulation of multiple interacting animals is possible using a variant of the Gillespie's Stochastic Simulation Algorithm; (ii) formulated properly, the maximum likelihood inference of switching rate functions is tractably solvable by gradient descent; (iii) model selection can be used to identify factors that modulate behavioral state switching and to appropriately adjust model complexity to data. To illustrate our framework, we apply it to two synthetic models of animal motion and to real zebrafish tracking data.Comment: 26 pages, 11 figure

Topics in Applied Stochastic Dynamics.

Randomness in natural systems come from various sources, for example from the discrete nature of the underlying dynamical process when viewed on a small scale. In this thesis we study the effect of stochasticity on the dynamics in three applications, each with different sources and effects of randomness. In the first application we study the Hodgkin-Huxley model of the neuron with a random ion channel mechanism via numerical simulation. Randomness affects the nonlinear mechanism of a neuron’s firing behavior by spike induction as well as by spike suppression. The sensitivity to different types of channel noise is explored and robustness of the dynamical properties is studied using two distinct stochastic models. In the second application we compare and contrast the effectiveness of mixing of a passive scalar by stirring using different notions of mixing efficiency. We explore the non-commutativity of the limits of large Peclet numbers and large spatial scale separation between the flow and sources and sinks, and propose and examine a conceptual approach that captures some compat- ible features of the different models and measures of mixing. In the last application we design a stochastic dynamical system that mimics the properties of so-called ho- mogeneous Rayleigh-Benard convection and show that arbitrary small noise changes the dynamical properties of the model. The system’s properties are further exam- ined using the first exit time problem. The three applications show that randomness of small magnitude may play important and counterintuitive roles in determinig a system’s properties.Ph.D.Applied and Interdisciplinary MathematicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/64775/1/kbodova_1.pd

Busulfan/Fludarabine- or Treosulfan/Fludarabine-Based Conditioning Regimen for Patients with Wiskott-Aldrich Syndrome – an EBMT Inborn Errors Working Party and Scetide Study

Introduction Excellent survival rates have been reported after allogeneic haematopoietic stem cell transplantation (HSCT) for Wiskott-Aldrich syndrome (WAS) patients. Recipient age >5 years in MUD HSCT as well as MMFD as donor were negative predictors for outcome. However, the vast majority of HSCTs in previously published studies were performed with (oral) busulfan/cyclophosphamide-based conditioning and in the early 2000 years or before. Objectives To compare OS and EFS after HSCT with either busulfan/fludarabine (BuFlu) ± thiotepa (TT) or treosulfan/fludarabine (TreoFlu) ± TT as recommended for primary immunodeficiencies since 2005 by the inborn errors working party (IEWP) of EBMT and ESID. Methods We performed a retrospective analysis via the EBMT and SCETIDE registries of WAS patients transplanted between 20006 and 2016 with these two regimens. At the time of this interim analysis, 174 patients were included, 92 (53%) with BuFlu±TT and 82 (47%) with TreoFlu±TT conditioning, with a median age of 1.6 years (0.2-30) at HSCT and a median follow-up of 32.9 months (1.5-128.9). Donors were MSD in 30, other MRD in 5, MUD (9/10 or 10/10) in 105, MMUD ( Results Two year overall survival (OS) of the entire cohort was 88.6% (95% c.i. 83.5%-93.6%). There was no significant difference in OS between BuFlu±TT or TreoFlu±TT conditioning (2-year OS 88.1% vs. 89.5%; p=0.7). Patients aged >5 years had a worse OS as compared to those 5 years or younger at HSCT (74.9% vs. 90.8%; p=0.005). The type of donor had no influence on OS: 96.4% for MSD/MFD, 86.8% for MUD/MMUD and 87.7% for MMFD (p=0.4). The rate of complete (≥90%) donor chimerism at last follow-up or before a secondary procedure (if a patient had one) was 41/42 (98%) in the BuFlu±TT group and 21/35 (60%) in the TreoFlu±TT group (p=0.0001). Twenty-six patients required a second procedure: stem cell boost in 4, donor lymphocyte infusion in 9, 2nd HSCT in 15 and splenectomy in 1. The 2-year cumulative incidence (CI) of second procedures was higher at 33.9% in the TreoFlu±TT versus 12.8% in the BuFlu±TT group (p=0.017), and 2-year EFS (events: second procedure or death) was 61.4% in the TreoFlu±TT and 75.0% in the BuFlu±TT group (p=0.2). Grade II-IV acute GVHD had the same incidence in both groups (24.4% vs. 26.3%; p=0.849) and chronic GVHD of any grade was borderline more frequent in the TreoFlu±TT group (17.2% vs 6.7%; p=0.054). Conclusion HSCT with either BuFlu±TT or TreoFlu±TT conditioning reliably cures almost 90% of patients with WAS regardless of donor type. Age >5 years at HSCT remains a negative risk factor. More patients were mixed chimeras and required second procedures after TreoFlu±TT than after BuFlu±TT conditioning. These data confirm the feasibility and efficacy of the regimens currently recommended by the IEWP

Uncertainty-aware spot rejection rate as quality metric for proton therapy using a digital tracking calorimeter

Objective. Proton therapy is highly sensitive to range uncertainties due to the nature of the dose deposition of charged particles. To ensure treatment quality, range verification methods can be used to verify that the individual spots in a pencil beam scanning treatment fraction match the treatment plan. This study introduces a novel metric for proton therapy quality control based on uncertainties in range verification of individual spots. Approach. We employ uncertainty-aware deep neural networks to predict the Bragg peak depth in an anthropomorphic phantom based on secondary charged particle detection in a silicon pixel telescope designed for proton computed tomography. The subsequently predicted Bragg peak positions, along with their uncertainties, are compared to the treatment plan, rejecting spots which are predicted to be outside the 95% confidence interval. The such-produced spot rejection rate presents a metric for the quality of the treatment fraction. Main results. The introduced spot rejection rate metric is shown to be well-defined for range predictors with well-calibrated uncertainties. Using this method, treatment errors in the form of lateral shifts can be detected down to 1 mm after around 1400 treated spots with spot intensities of 1 × 107 protons. The range verification model used in this metric predicts the Bragg peak depth to a mean absolute error of 1.107 ± 0.015 mm. Significance. Uncertainty-aware machine learning has potential applications in proton therapy quality control. This work presents the foundation for future developments in this area.publishedVersio

Performance of the electromagnetic and hadronic prototype segments of the ALICE Forward Calorimeter

We present the performance of a full-length prototype of the ALICE Forward Calorimeter (FoCal). The detector is composed of a silicon-tungsten electromagnetic sampling calorimeter with longitudinal and transverse segmentation (FoCal-E) of about 20$X_0$ and a hadronic copper-scintillating-fiber calorimeter (FoCal-H) of about 5$\lambda_{\rm int}$. The data were taken between 2021 and 2023 at the CERN PS and SPS beam lines with hadron (electron) beams up to energies of 350 (300) GeV. Regarding FoCal-E, we report a comprehensive analysis of its response to minimum ionizing particles across all pad layers. The longitudinal shower profile of electromagnetic showers is measured with a layer-wise segmentation of 1$X_0$. As a projection to the performance of the final detector in electromagnetic showers, we demonstrate linearity in the full energy range, and show that the energy resolution fulfills the requirements for the physics needs. Additionally, the performance to separate two-showers events was studied by quantifying the transverse shower width. Regarding FoCal-H, we report a detailed analysis of the response to hadron beams between 60 and 350 GeV. The results are compared to simulations obtained with a Geant4 model of the test beam setup, which in particular for FoCal-E are in good agreement with the data. The energy resolution of FoCal-E was found to be lower than 3% at energies larger than 100 GeV. The response of FoCal-H to hadron beams was found to be linear, albeit with a significant intercept that is about factor 2 larger than in simulations. Its resolution, which is non-Gaussian and generally larger than in simulations, was quantified using the FWHM, and decreases from about 16% at 100 GeV to about 11% at 350 GeV. The discrepancy to simulations, which is particularly evident at low hadron energies, needs to be further investigated.Comment: 55 pages (without acronyms), 45 captioned figure

f0(980) production in inelastic pp collisions at s = 5.02 TeV

The measurement of the production of f0(980) in inelastic pp collisions at sqrt(s) = 5.02 TeV is presented. This is the first reported measurement of inclusive f0(980) yield at LHC energies. The production is measured at midrapidity, |y| pi+pi- hadronic decay channel using the ALICE detector. The pT-differential yields are compared to those of pions, protons and ϕ mesons as well as to predictions from the HERWIG 7.2 QCD-inspired Monte Carlo event generator and calculations from a coalescence model that uses the AMPT model as an input. The ratio of the pT-integrated yield of f0(980) relative to pions is compared to measurements in e+e- and pp collisions at lower energies and predictions from statistical hadronisation models and HERWIG 7.2. A mild collision energy dependence of the f0(980) to pion production is observed in pp collisions from SPS to LHC energies. All considered models underpredict the pT-integrated 2f0(980)/(pi+ + pi-) ratio. The prediction from the canonical statistical hadronisation model assuming a zero total strangeness content of f0(980) is consistent with the data within 1.9σ and is the closest to the data. The results provide an essential reference for future measurements of the particle yield and nuclear modification in p–Pb and Pb–Pb collisions, which have been proposed to be instrumental to probe the elusive nature and quark composition of the f0(980) scalar meson