Degree formula for connective K-theory

We apply the degree formula for connective $K$-theory to study rational contractions of algebraic varieties. Examples include rationally connected varieties and complete intersections.Comment: 14 page

Convolutional Neural Network for Material Decomposition in Spectral CT Scans

Spectral computed tomography acquires energy-resolved data that allows recovery of densities of constituents of an object. This can be achieved by decomposing the measured spectral projection into material projections, and passing these decomposed projections through a tomographic reconstruction algorithm, to get the volumetric mass density of each material. Material decomposition is a nonlinear inverse problem that has been traditionally solved using model-based material decomposition algorithms. However, the forward model is difficult to estimate in real prototypes. Moreover, the traditional regularizers used to stabilized inversions are not fully relevant in the projection domain.In this study, we propose a deep-learning method for material decomposition in the projection domain. We validate our methodology with numerical phantoms of human knees that are created from synchrotron CT scans. We consider four different scans for training, and one for validation. The measurements are corrupted by Poisson noise, assuming that at most 10 5 photons hit the detector. Compared to a regularized Gauss-Newton algorithm, the proposed deep-learning approach provides a compromise between noise and resolution, which reduces the computation time by a factor of 100

Diffuse optical tomography by using time-resolved single pixel camera

International audienc

Material Decomposition in Spectral CT using deep learning: A Sim2Real transfer approach

The state-of-the art for solving the nonlinear material decomposition problem in spectral computed tomography is based on variational methods, but these are computationally slow and critically depend on the particular choice of the regularization functional. Convolutional neural networks have been proposed for addressing these issues. However, learning algorithms require large amounts of experimental data sets. We propose a deep learning strategy for solving the material decomposition problem based on a U-Net architecture and a Sim2Real transfer learning approach where the knowledge that we learn from synthetic data is transferred to a real-world scenario. In order for this approach to work, synthetic data must be realistic and representative of the experimental data. For this purpose, numerical phantoms are generated from human CT volumes of the KiTS19 Challenge dataset, segmented into specific materials (soft tissue and bone). These volumes are projected into sinogram space in order to simulate photon counting data, taking into account the energy response of the scanner. We compared projection- and image-based decomposition approaches where the network is trained to decompose the materials either in the projection or in the image domain. The proposed Sim2Real transfer strategies are compared to a regularized Gauss-Newton (RGN) method on synthetic data, experimental phantom data and human thorax data

Particles dispersion in supersonic shear layers by direct numerical simulation

In experimental measurements like Laser Doppler Velocimetry, small solid or liquid particles are used to tag the flow in order to measure fluid velocity. In this case, particles are supposed to have the same behaviour as fluid particles in order to give reliability to the experimental measure. However it has been shown that noticeable errors can appear in the rms velovity measurement of supersonic jet or shear layer, even if care has been taken concerning particle seeding of the flow. The aim of this paper is to use direct numerical simulation of particle-gas flow to investigate this phenomenon

A Time-Domain Wavelet-Based Approach for Fluorescence Diffuse Optical Tomography

Purpose: In the context of fluorescence diffuse optical tomography, determining the optimal way to exploit the time-resolved information has been receiving much attention and different features of the time-resolved signals have been introduced. In this article, the authors revisit and generalize the notion of feature, considering the projection of the measurements onto some basis functions. This leads the authors to propose a novel approach based on the wavelet transform of the measurements. Methods: A comparative study between the reconstructions obtained from the proposed wavelet-based approach and the reconstructions obtained from the reference temporal moments is provided. An inhomogeneous cubic medium is considered. Reconstructions are performed from synthetic measurements assuming Poisson noise statistics. In order to provide fairly comparable reconstructions, the reconstruction scheme is associated with a particular procedure for selecting the regularization parameter. Results: In the noise-free case, the reconstruction quality is shown to be mainly driven by the number of selected features. In the presence of noise, however, the reconstruction quality depends on the type of the features. In this case, the wavelet approach is shown to outperform the moment approach. While the optimal time-resolved reconstruction quality, which is obtained considering the whole set of time samples, is recovered using only eight wavelet functions, it cannot be attained using moments. It is finally observed that the time-resolved information is of limited utility, in terms of reconstruction, when the maximum number of detected photons is lower than 105. Conclusions: The wavelet approach allows for better exploiting the time-resolved information, especially when the number of detected photons is low. However, when the number of detected photons decreases below a certain threshold, the time-resolved information itself is shown to be of limited utility

Espaces de Berkovich sur Z : \'etude locale

We investigate the local properties of Berkovich spaces over Z. Using Weierstrass theorems, we prove that the local rings of those spaces are noetherian, regular in the case of affine spaces and excellent. We also show that the structure sheaf is coherent. Our methods work over other base rings (valued fields, discrete valuation rings, rings of integers of number fields, etc.) and provide a unified treatment of complex and p-adic spaces.Comment: v3: Corrected a few mistakes. Corrected the proof of the Weierstrass division theorem 7.3 in the case where the base field is imperfect and trivially value

Boundary value problems for second order linear difference equations: application to the computation of the inverse of generalized Jacobi matrices

We have named generalized Jacobi matrices to those that are practically tridiagonal, except for the two final entries and the two first entries of its first andits last row respectively. This class of matrices encompasses both standard Jacobiand periodic Jacobi matrices that appear in many contexts in pure and appliedmathematics. Therefore, the study of the inverse of these matrices becomes ofspecific interest. However, explicit formulas for inverses are known only in a fewcases, in particular when the coefficients of the diagonal entries are subjected tosome restrictions.We will show that the inverse of generalized Jacobi matrices can be raisedin terms of the resolution of a boundary value problem associated with a secondorder linear difference equation. In fact, recent advances in the study of lineardifference equations, allow us to compute the solution of this kind of boundaryvalue problems. So, the conditions that ensure the uniqueness of the solution ofthe boundary value problem leads to the invertibility conditions for the matrix,whereas that solutions for suitable problems provide explicitly the entries of theinverse matrix.Peer ReviewedPostprint (author's final draft

Multiple-view time-resolved diffuse optical tomography based on structured illumination and compressive detection

A time-resolved Diffuse Optical Tomography system based on multiple view acquisition, pulsed structured light illumination and detection with spatial compression is proposed. Reconstructions on heterogeneous tissue mimicking phantoms are presented

Limits on WWgamma and WWZ Couplings from W Boson Pair Production

The results of a search for W boson pair production in pbar-p collisions at sqrt{s}=1.8 TeV with subsequent decay to emu, ee, and mumu channels are presented. Five candidate events are observed with an expected background of 3.1+-0.4 events for an integrated luminosity of approximately 97 pb^{-1}. Limits on the anomalous couplings are obtained from a maximum likelihood fit of the E_T spectra of the leptons in the candidate events. Assuming identical WWgamma and WWZ couplings, the 95 % C.L. limits are -0.62<Delta_kappa<0.77 (lambda = 0) and -0.53<lambda<0.56 (Delta_kappa = 0) for a form factor scale Lambda = 1.5 TeV.Comment: 10 pages, 1 figure, submitted to Physical Review