Weak Galilean invariance as a selection principle for coarse-grained diffusive models

Galilean invariance is a cornerstone of classical mechanics. It states that for closed systems the equations of motion of the microscopic degrees of freedom do not change under Galilean transformations to different inertial frames. However, the description of real world systems usually requires coarse-grained models integrating complex microscopic interactions indistinguishably as friction and stochastic forces, which intrinsically violate Galilean invariance. By studying the coarse-graining procedure in different frames, we show that alternative rules -- denoted as "weak Galilean invariance" -- need to be satisfied by these stochastic models. Our results highlight that diffusive models in general can not be chosen arbitrarily based on the agreement with data alone but have to satisfy weak Galilean invariance for physical consistency

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

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

Loopy Lévy flights enhance tracer diffusion in active suspensions.

7 pages, 3 figuresBrownian motion is widely used as a model of diffusion in equilibrium media throughout the physical, chemical and biological sciences. However, many real-world systems are intrinsically out of equilibrium owing to energy-dissipating active processes underlying their mechanical and dynamical features1. The diffusion process followed by a passive tracer in prototypical active media, such as suspensions of active colloids or swimming microorganisms2, differs considerably from Brownian motion, as revealed by a greatly enhanced diffusion coefficient3-10 and non-Gaussian statistics of the tracer displacements6,9,10. Although these characteristic features have been extensively observed experimentally, there is so far no comprehensive theory explaining how they emerge from the microscopic dynamics of the system. Here we develop a theoretical framework to model the hydrodynamic interactions between the tracer and the active swimmers, which shows that the tracer follows a non-Markovian coloured Poisson process that accounts for all empirical observations. The theory predicts a long-lived Lévy flight regime11 of the loopy tracer motion with a non-monotonic crossover between two different power-law exponents. The duration of this regime can be tuned by the swimmer density, suggesting that the optimal foraging strategy of swimming microorganisms might depend crucially on their density in order to exploit the Lévy flights of nutrients12. Our framework can be applied to address important theoretical questions, such as the thermodynamics of active systems13, and practical ones, such as the interaction of swimming microorganisms with nutrients and other small particles14 (for example, degraded plastic) and the design of artificial nanoscale machines15

Successful salvage therapy for refractory primary cutaneous gamma-delta T-cell lymphoma with a combination of brentuximab vedotin and gemcitabine.

Primary cutaneous gamma-delta T-cell lymphoma (PCGD-TCL) is a very rare lymphoma with an aggressive clinical course and a dismal outcome. The prognosis is linked to a pronounced resistance to chemotherapy and radiotherapy. No standard treatment approach is defined due to the low frequency of the disease and lack of prospective studies. CD30 is expressed in almost half of the cases of PCGD-TCL, which offers a potential therapeutic option. We report the successful treatment of a 68-year-old man who suffered PCGD-TCL with a combination of Brentuximab Vedotin and Gemcitabine after the failure of two lines of previous chemotherapy. CD30 expression was only partial. The treatment was very well tolerated and allowed the patient to benefit from allogeneic hematopoietic stem cell transplantation

Spectral Properties of Stochastic Processes Possessing Finite Propagation Velocity.

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

PTLD Burkitt Lymphoma in a Patient with Remote Lymphomatoid Granulomatosis.

Posttransplant lymphoproliferative disorder (PTLD) is a potentially fatal complication of solid organ transplantation. The majority of PTLD is of B-cell origin, and 90% are associated with the Epstein-Barr virus (EBV). Lymphomatoid granulomatosis (LG) is a rare, EBV-associated systemic angiodestructive lymphoproliferative disorder, which has rarely been described in patients with renal transplantation. We report the case of a patient with renal transplantation for SLE, who presented, 9 months after renal transplantation, an EBV-associated LG limited to the intracranial structures that recovered completely after adjustment of her immunosuppressive treatment. Nine years later, she developed a second PTLD disorder with central nervous system initial manifestation. Workup revealed an EBV-positive PTLD Burkitt lymphoma, widely disseminated in most organs. In summary, the reported patient presented two lymphoproliferative disorders (LG and Burkitt's lymphoma), both with initial neurological manifestation, at 9 years interval. With careful reduction of the immunosuppression after the first manifestation and with the use of chemotherapy combined with radiotherapy after the second manifestation, our patient showed complete disappearance of neurologic symptoms and she is clinically well with good kidney function. No recurrence has been observed by radiological imaging until now

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

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

Occurrence of malignant neoplasia in patients with primary hyperparathyroidism

Introduction The association between primary hyperparathyroidism (1HPT) and cancer is debated. The present study was aimed to investigate the occurrence of neoplasia in 1HPT. Patients and methods All consecutive patients (n = 1750) referred to our \u201cOsteoporosis and Metabolic Disease\u201d outpatients clinic for osteoporosis or hypercalcemia were eligible for the study. The exclusion criteria were: the finding of osteoporosis and/or altered calcium-phosphorous metabolism in the context of investigations for malignancy, the presence of diseases known to influence the cancer risk and the heavy smoking habit. Eventually, 1606 patients (1407 females, 199 males) were enrolled. In all patients calcium-phosphorous metabolism, PTH and vitamin D levels were measured and the occurrence of cancer during the 10 years prior the study inclusion was recorded. Results One-hundred-sixty-three patients had 1HPT while 1443 had not. Patients with and without 1HPT were comparable for age and gender. In 1HPT patients the occurrence of all, breast, kidney and skin cancer was significantly higher (21.5%, 12.2%, 2.5%, 1.8%, respectively) than in patients without 1HPT (12.4%, 6.9%, 0.3%, 0.3%, p < 0.05 for all comparisons). The 1HPT presence was significantly associated with the occurrence of all neoplasia and of breast, skin and kidney neoplasia (odds ratio, 95% confidence interval, p value: 1.93, 1.27\u20132.92, 0.002; 1.93, 1.11\u20133.35, 0.002; 9.18, 2.16\u201338.8, 0.003; 8.23, 1.71\u201339.5, 0.008, respectively), after adjusting for age, gender (as appropriate), smoking habit and vitamin D levels. Conclusion During the 10 years prior the diagnosis of 1HPT, the occurrence of all, breast, skin and kidney neoplasia is increased