Branching Feller diffusion for cell division with parasite infection

We describe the evolution of the quantity of parasites in a population of cells which divide in continuous-time. The quantity of parasites in a cell follows a Feller diffusion, which is splitted randomly between the two daughter cells when a division occurs. The cell division rate may depend on the quantity of parasites inside the cell and we are interested in the cases of constant or monotone division rate. We first determine the asymptotic behavior of the quantity of parasites in a cell line, which follows a Feller diffusion with multiplicative jumps. We then consider the evolution of the infection of the cell population and give criteria to determine whether the proportion of infected cells goes to zero (recovery) or if a positive proportion of cells becomes largely infected (proliferation of parasites inside the cells)

Limit theorems for Markov processes indexed by continuous time Galton--Watson trees

We study the evolution of a particle system whose genealogy is given by a supercritical continuous time Galton--Watson tree. The particles move independently according to a Markov process and when a branching event occurs, the offspring locations depend on the position of the mother and the number of offspring. We prove a law of large numbers for the empirical measure of individuals alive at time t. This relies on a probabilistic interpretation of its intensity by mean of an auxiliary process. The latter has the same generator as the Markov process along the branches plus additional jumps, associated with branching events of accelerated rate and biased distribution. This comes from the fact that choosing an individual uniformly at time t favors lineages with more branching events and larger offspring number. The central limit theorem is considered on a special case. Several examples are developed, including applications to splitting diffusions, cellular aging, branching L\'{e}vy processes.Comment: Published in at http://dx.doi.org/10.1214/10-AAP757 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Checkpoint inhibitors and the gut

Checkpoint inhibitors have revolutionized treatments in modern oncology, including many conditions previously relegated to palliative therapies only. However, emerging recognition of checkpoint inhibitor-related adverse events has complicated the status of checkpoint inhibitor-related therapies. This review article discusses gastrointestinal adverse events as a result of checkpoint inhibitor therapy, as well as limitations of current guidelines, thus providing recommendations for guideline revision and future study direction

Nonparametric estimation of the fragmentation kernel based on a PDE stationary distribution approximation

We consider a stochastic individual-based model in continuous time to describe a size-structured population for cell divisions. This model is motivated by the detection of cellular aging in biology. We address here the problem of nonparametric estimation of the kernel ruling the divisions based on the eigenvalue problem related to the asymptotic behavior in large population. This inverse problem involves a multiplicative deconvolution operator. Using Fourier technics we derive a nonparametric estimator whose consistency is studied. The main difficulty comes from the non-standard equations connecting the Fourier transforms of the kernel and the parameters of the model. A numerical study is carried out and we pay special attention to the derivation of bandwidths by using resampling

Integer Complexity Generalizations in Various Rings

In this paper, we investigate generalizations of the Mahler-Popkens complexity of integers. Specifically, we generalize to $k$-th roots of unity, polynomials over the naturals, and the integers mod $m$. In cyclotomic rings, we establish upper and lower bounds for integer complexity, investigate the complexity of roots of unity using cyclotomic polynomials, and introduce a concept of "minimality.'' In polynomials over the naturals, we establish bounds on the sizes of complexity classes and establish a trivial but useful upper bound. In the integers mod $m$, we introduce the concepts of "inefficiency'', "resilience'', and "modified complexity.'' In hopes of improving the upper bound on the complexity of the most complex element mod $m$, we also use graphs to visualize complexity in these finite rings.Comment: 44 pages, 11 figures, Research Lab from PROMY

A comprehensive model of the optical spectra of carbon nanotubes on substrate by polarized microscopy

Polarized optical microscopy and spectroscopy are progressively becoming key methods for the high-throughput characterization of individual carbon nanotubes (CNTs) and other one-dimensional nanostructures, on substrate and in devices. The optical response of CNTs on substrate in cross polarization experiments is usually limited by the polarization conservation of the optical elements in the experimental setup. We developed a theoretical model taking into account the depolarization by the setup and the optical response of the substrate. We show that proper modelization of the experimental data requires to take into account both non-coherent and coherent light depolarization by the optical elements. We also show how the nanotube signal can be decoupled from the complex reflection factor of the anti-reflection substrate which is commonly used to enhance the optical contrast. Finally, we describe an experimental protocol to extract the depolarization parameters and the complex nanotube susceptibility, and how it can improve the chirality assignment of individual carbon nanotubes in complex cases.Comment: 10 pages, 7 Figures, submitted to PRB. A supplementary information completes this pape

Defective phagocytic corpse processing results in neurodegeneration and can be rescued by TORC1 activation

This work was supported by NIH Grants R01 GM094452 (K.M.) and F31 GM099425 (J.I.E.), BU Alzheimer's Disease Core Center NIH Grant P30 AG13846, Boston University Undergraduate Research Opportunities Program grants (J.A.T., V.S.), and NIH Grant R01 AG044113 to M.B.F. We thank the Bloomington Stock Center, TRiP at Harvard Medical School, the Kyoto Drosophila Genetic Resource Center, Estee Kurant, Eric Baehrecke, Marc Freeman, and Mary Logan for fly strains. We thank Todd Blute for assistance with electron microscopy and the Developmental Studies Hybridoma Bank for antibodies. (R01 GM094452 - NIH; F31 GM099425 - NIH; R01 AG044113 - NIH; P30 AG13846 - BU Alzheimer's Disease Core Center NIH Grant; Boston University Undergraduate Research Opportunities Program)https://www.jneurosci.org/content/36/11/3170.longPublished versionPublished versio