502 research outputs found

    Gaucher Disease and Myelofibrosis: A Combined Disease or a Misdiagnosis?

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    Background: Gaucher disease (GD) and primary myelofibrosis (PMF) share similar clinical and laboratory features, such as cytopenia, hepatosplenomegaly, and marrow fibrosis, often resulting in a misdiagnosis. Case Report: We report here the case of a young woman with hepatosplenomegaly, leukopenia, and thrombocytopenia. Based on bone marrow (BM) findings and on liver biopsy showing extramedullary hematopoiesis, an initial diagnosis of PMF was formulated. The patient refused stem cell transplantation from an HLA-identical sibling. Low-dose melphalan was given, without any improvement. Two years later, a BM evaluation showed Gaucher cells. Low glucocerebrosidase and high chitotriosidase levels were indicative for GD. Molecular analysis revealed N370S/complex I mutations. Enzyme replacement therapy with imiglucerase was commenced, resulting in clinical and hematological improvements. Due to an unexpected and persistent organomegaly, PMF combined with GD were suspected. JAK2V617F, JAK2 exon 12, MPL, calreticulin, and exon 9 mutations were negative, and BM examination showed no marrow fibrosis. PMF was excluded. Twenty years after starting treatment, the peripheral cell count and liver size were normal, whereas splenomegaly persisted. Conclusion: In order to avoid a misdiagnosis, a diagnostic algorithm for patients with hepatosplenomegaly combined with cytopenia is suggested

    Extended Poisson-Kac Theory: A Unifying Framework for Stochastic Processes

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    Stochastic processes play a key role for modeling a huge variety of transport problems out of equilibrium, with manifold applications throughout the natural and social sciences. To formulate models of stochastic dynamics the conventional approach consists in superimposing random fluctuations on a suitable deterministic evolution. These fluctuations are sampled from probability distributions that are prescribed a priori, most commonly as Gaussian or L\'evy. While these distributions are motivated by (generalised) central limit theorems they are nevertheless \textit{unbounded}, meaning that arbitrarily large fluctuations can be obtained with finite probability. This property implies the violation of fundamental physical principles such as special relativity and may yield divergencies for basic physical quantities like energy. Here we solve the fundamental problem of unbounded random fluctuations by constructing a comprehensive theoretical framework of stochastic processes possessing physically realistic finite propagation velocity. Our approach is motivated by the theory of L\'evy walks, which we embed into an extension of conventional Poisson-Kac processes. The resulting extended theory employs generalised transition rates to model subtle microscopic dynamics, which reproduces non-trivial spatio-temporal correlations on macroscopic scales. It thus enables the modelling of many different kinds of dynamical features, as we demonstrate by three physically and biologically motivated examples. The corresponding stochastic models capture the whole spectrum of diffusive dynamics from normal to anomalous diffusion, including the striking `Brownian yet non Gaussian' diffusion, and more sophisticated phenomena such as senescence. Extended Poisson-Kac theory can therefore be used to model a wide range of finite velocity dynamical phenomena that are observed experimentally.Comment: 26 pages, 5 figure

    Spectral Properties of Stochastic Processes Possessing Finite Propagation Velocity.

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    This article investigates the spectral structure of the evolution operators associated with the statistical description of stochastic processes possessing finite propagation velocity. Generalized Poisson-Kac processes and Lévy walks are explicitly considered as paradigmatic examples of regular and anomalous dynamics. A generic spectral feature of these processes is the lower boundedness of the real part of the eigenvalue spectrum that corresponds to an upper limit of the spectral dispersion curve, physically expressing the relaxation rate of a disturbance as a function of the wave vector. We also analyze Generalized Poisson-Kac processes possessing a continuum of stochastic states parametrized with respect to the velocity. In this case, there is a critical value for the wave vector, above which the point spectrum ceases to exist, and the relaxation dynamics becomes controlled by the essential part of the spectrum. This model can be extended to the quantum case, and in fact, it represents a simple and clear example of a sub-quantum dynamics with hidden variables

    Age representation of Levy walks: partial density waves, relaxation and first passage time statistics

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    Lévy walks (LWs) define a fundamental class of finite velocity stochastic processes that can be introduced as a special case of continuous time random walks. Alternatively, there is a hyperbolic representation of them in terms of partial probability density waves. Using the latter framework we explore the impact of aging on LWs, which can be viewed as a specific initial preparation of the particle ensemble with respect to an age distribution. We show that the hyperbolic age formulation is suitable for a simple integral representation in terms of linear Volterra equations for any initial preparation. On this basis relaxation properties, i.e. the convergence towards equilibrium of a generic thermodynamic function dependent on the spatial particle distribution, and first passage time statistics in bounded domains are studied by connecting the latter problem with solute release kinetics. We find that even normal diffusive LWs, where the long-term mean square displacement increases linearly with time, may display anomalous relaxation properties such as stretched exponential decay. We then discuss the impact of aging on the first passage time statistics of LWs by developing the corresponding Volterra integral representation. As a further natural generalization the concept of LWs with wearing is introduced to account for mobility losses

    A renormalisation approach to excitable reaction-diffusion waves in fractal media

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    Of fundamental importance to wave propagation in a wide range of physical phenomena is the structural geometry of the supporting medium. Recently, there have been several investigations on wave propagation in fractal media. We present here a renormalization approach to the study of reaction-diffusion (RD) wave propagation on finitely ramified fractal structures. In particular we will study a Rinzel-Keller (RK) type model, supporting travelling waves on a Sierpinski gasket (SG), lattice

    Long-term bone outcomes in Italian patients with Gaucher disease type 1 or type 3 treated with imiglucerase: A sub-study from the International Collaborative Gaucher Group (ICGG) Gaucher Registry

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    Background: Gaucher disease (GD) is a lysosomal storage disorder. We evaluated the “real-world” effectiveness of first-line imiglucerase on long-term bone outcomes in Italian patients in the International Collaborative Gaucher Group (ICGG) Gaucher Registry. Methods: Patients treated with imiglucerase for ≥2 years and with bone assessments at baseline and during follow-up were selected. Data on bone pain, bone crises, marrow infiltration, avascular necrosis, infarction, lytic lesions, Erlenmeyer flask deformity, bone fractures, mineral density, and imiglucerase dosage were evaluated. Results: Data on bone manifestations were available for 73 of 229 patients (31.9 %). Bone crises frequency decreased significantly from baseline to the most recent follow-up (p < 0.001), with some improvement observed in bone pain prevalence. Bone pain and bone crises prevalence decreased significantly from baseline at 2 to <4 and 4 to <6 years (all p < 0.05). A low median (25th, 75th percentile) baseline imiglucerase dosage was identified in patients reporting bone pain or bone crises (15.0 [13.7, 30.0] and 22.8 [17.5, 36.0] U/kg once every 2 weeks, respectively). Conclusion: Our study suggests that the management of GD in Italy, with regards to imiglucerase dosage, is suboptimal and confirms the need for clinicians to monitor and correctly treat bone disease according to best practice guidelines

    Time fractional Schrodinger equation

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    The Schrodinger equation is considered with the first order time derivative changed to a Caputo fractional derivative, the time fractional Schrodinger equation. The resulting Hamiltonian is found to be non-Hermitian and non-local in time. The resulting wave functions are thus not invariant under time reversal. The time fractional Schrodinger equation is solved for a free particle and for a potential well. Probability and the resulting energy levels are found to increase over time to a limiting value depending on the order of the time derivative. New identities for the Mittag-Leffler function are also found and presented in an appendix.Comment: 23 page
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