Periodic Splines and Gaussian Processes for the Resolution of Linear Inverse Problems

This paper deals with the resolution of inverse problems in a periodic setting or, in other terms, the reconstruction of periodic continuous-domain signals from their noisy measurements. We focus on two reconstruction paradigms: variational and statistical. In the variational approach, the reconstructed signal is solution to an optimization problem that establishes a tradeoff between fidelity to the data and smoothness conditions via a quadratic regularization associated to a linear operator. In the statistical approach, the signal is modeled as a stationary random process defined from a Gaussian white noise and a whitening operator; one then looks for the optimal estimator in the mean-square sense. We give a generic form of the reconstructed signals for both approaches, allowing for a rigorous comparison of the two.We fully characterize the conditions under which the two formulations yield the same solution, which is a periodic spline in the case of sampling measurements. We also show that this equivalence between the two approaches remains valid on simulations for a broad class of problems. This extends the practical range of applicability of the variational method

Exclusion processes: short range correlations induced by adhesion and contact interactions

We analyze the out-of-equilibrium behavior of exclusion processes where agents interact with their nearest neighbors, and we study the short-range correlations which develop because of the exclusion and other contact interactions. The form of interactions we focus on, including adhesion and contact-preserving interactions, is especially relevant for migration processes of living cells. We show the local agent density and nearest-neighbor two-point correlations resulting from simulations on two dimensional lattices in the transient regime where agents invade an initially empty space from a source and in the stationary regime between a source and a sink. We compare the results of simulations with the corresponding quantities derived from the master equation of the exclusion processes, and in both cases, we show that, during the invasion of space by agents, a wave of correlations travels with velocity v(t) ~ t^(-1/2). The relative placement of this wave to the agent density front and the time dependence of its height may be used to discriminate between different forms of contact interactions or to quantitatively estimate the intensity of interactions. We discuss, in the stationary density profile between a full and an empty reservoir of agents, the presence of a discontinuity close to the empty reservoir. Then, we develop a method for deriving approximate hydrodynamic limits of the processes. From the resulting systems of partial differential equations, we recover the self-similar behavior of the agent density and correlations during space invasion

Automatic quantification of the microvascular density on whole slide images, applied to paediatric brain tumours

Angiogenesis is a key phenomenon for tumour progression, diagnosis and treatment in brain tumours and more generally in oncology. Presently, its precise, direct quantitative assessment can only be done on whole tissue sections immunostained to reveal vascular endothelial cells. But this is a tremendous task for the pathologist and a challenge for the computer since digitised whole tissue sections, whole slide images (WSI), contain typically around ten gigapixels. We define and implement an algorithm that determines automatically, on a WSI at objective magnification $40\times$, the regions of tissue, the regions without blur and the regions of large puddles of red blood cells, and constructs the mask of blur-free, significant tissue on the WSI. Then it calibrates automatically the optical density ratios of the immunostaining of the vessel walls and of the counterstaining, performs a colour deconvolution inside the regions of blur-free tissue, and finds the vessel walls inside these regions by selecting, on the image resulting from the colour deconvolution, zones which satisfy a double-threshold criterion. A mask of vessel wall regions on the WSI is produced. The density of microvessels is finally computed as the fraction of the area of significant tissue which is occupied by vessel walls. We apply this algorithm to a set of 186 WSI of paediatric brain tumours from World Health Organisation grades I to IV. The segmentations are of very good quality although the set of slides is very heterogeneous. The computation time is of the order of a fraction of an hour for each WSI on a modest computer. The computed microvascular density is found to be robust and strongly correlates with the tumour grade. This method requires no training and can easily be applied to other tumour types and other stainings

HAGE, a cancer/testis antigen expressed at the protein level in a variety of cancers

The search for novel tumour antigens that are either uniquely expressed or over-expressed in a wide variety of tumours is still ongoing. Because of their expression in a broad spectrum of cancers and limited expression in normal tissues, cancer/testis antigens are considered to be potentially reliable targets for immunotherapy of cancer in general. The helicase antigen HAGE has been identified as a cancer/testis antigen. However, little is known about its expression in normal and cancer tissues. Using a newly developed antibody against HAGE, specific staining of its expression by immunohistochemistry was validated and optimised on murine tumours transfected to express the HAGE protein. The antibody was subsequently used to determine HAGE expression in normal human and cancer tissue microarrays. HAGE protein expression was confirmed in 75% (12/16) of carcinomas as compared to normal tissues, which either did not express HAGE at all or expressed HAGE at very low levels with the exception of testis. Interestingly, discrepancies were also found between mRNA analysis by real time quantitative PCR (RT-qPCR) and protein analysis by immunohistochemistry, emphasising the need to validate the expression of cancer/testis antigens at the protein level prior to the development of new vaccine strategies. HAGE is therefore proposed to be a valid candidate for designing a broad spectrum vaccine against cancer

Head and neck: Salivary gland tumors: an overview

Review on Head and neck: Salivary gland tumors: an overview, with data on clinics, and the genes involved

Head and Neck: Paraganglioma: an overview

Review on Head and Neck paragangliomas, with data on clinics, and the genes involved