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Olivier Dubois

Publications and source records attributed to Olivier Dubois.

4 recordsLinked to original sources

Label-free subcellular 3D imaging of oocytes and embryos via reflection matrix microscopy

Non-invasive morphological assessment is the cornerstone of oocyte and embryo selection in assisted reproductive technology, yet clinical practice remains limited by two-dimensional, qualitative microscopy. While three-dimensional (3D) fluorescence imaging provides cellular insights, its inherent phototoxicity precludes routine clinical use. Conversely, existing label-free modalities fail to resolve subcellular structures in thick specimens due to two distinct physical barriers: large-scale refractive index heterogeneities, such as the cumulus cells surrounding oocytes, that induce severe aberrations; and short-scale fluctuations, primarily from cytoplasmic lipids, that generate a multiple scattering ``fog''. Here, we report an ultra-fast Reflection Matrix Imaging (RMI) platform designed to overcome these depth and resolution limits. By capturing the back-scattered electromagnetic field for a set of plane-wave illuminations at multiple wavelengths, we record a multi-spectral reflection matrix. From this matrix, we leverage digital adaptive focusing algorithms to computationally compensate for sample-induced aberrations while realigning forward multiple scattering trajectories with the single-scattering contribution. This approach enables label-free 3D visualization of oocytes and blastocysts with an unprecedented subcellular resolution of 300 nm throughout the entire specimen volume. We demonstrate the reliable identification of germinal vesicles and nuclear status in stages previously inaccessible to conventional optics, including imaging through dense cumulus cells. Our method provides a powerful, non-invasive tool for objective grading across all pre-implantation stages, potentially transforming decision-making in clinical IVF.

physics.optics↗

Second moment method for a family of boolean CSP

The estimation of phase transitions in random boolean Constraint Satisfaction Problems (CSP) is based on two fundamental tools: the first and second moment methods. While the first moment method on the number of solutions permits to compute upper bounds on any boolean CSP, the second moment method used for computing lower bounds proves to be more tricky and in most cases gives only the trivial lower bound 0. In this paper, we define a subclass of boolean CSP covering the monotone versions of many known NP-Complete boolean CSPs. We give a method for computing non trivial lower bounds for any member of this subclass. This is achieved thanks to an application of the second moment method to some selected solutions called characteristic solutions that depend on the boolean CSP considered. We apply this method with a finer analysis to establish that the threshold $r_{k}$ (ratio : #constrains/#variables) of monotone 1-in-k-SAT is $\log k/k\leq r_{k}\leq\log^{2}k/k$.

cs.DM↗

Typical random 3-SAT formulae and the satisfiability threshold

We present a new structural (or syntatic) approach for estimating the satisfiability threshold of random 3-SAT formulae. We show its efficiency in obtaining a jump from the previous upper bounds, lowering them to 4.506. The method combines well with other techniques, and also applies to other problems, such as the 3-colourability of random graphs.

cs.DM↗

Approximating the satisfiability threshold for random k-XOR-formulas

In this paper we study random linear systems with $k$ variables per equation over the finite field GF(2), or equivalently $k$-XOR-CNF formulas. In a previous paper Creignou and Daudé proved that the phase transition for the consistency (satisfiability) of such systems (formulas) exhibits a sharp threshold. Here we prove that the phase transition occurs as the number of equations (clauses) is proportional to the number of variables. For any $k\ge 3$ we establish first estimates for the critical ratio. For $k=3$ we get 0.93 as an upper bound, 0.89 as a lower bound, whereas experiments suggest that the critical ratio is approximately 0.92.

cs.DM↗