Optimizing persistent homology based functions

Solving optimization tasks based on functions and losses with a topological flavor is a very active,growing field of research in data science and Topological Data Analysis, with applications in non-convexoptimization, statistics and machine learning. However, the approaches proposed in the literatureare usually anchored to a specific application and/or topological construction, and do not come withtheoretical guarantees. To address this issue, we study the differentiability of a general map associatedwith the most common topological construction, that is, the persistence map. Building on real analyticgeometry arguments, we propose a general framework that allows us to define and compute gradientsfor persistence-based functions in a very simple way. We also provide a simple, explicit and sufficientcondition for convergence of stochastic subgradient methods for such functions. This result encompassesall the constructions and applications of topological optimization in the literature. Finally, we provideassociated code, that is easy to handle and to mix with other non-topological methods and constraints, aswell as some experiments showcasing the versatility of our approach

Topological Uncertainty: Monitoring trained neural networks through persistence of activation graphs

International audienceAlthough neural networks are capable of reaching astonishing performances on a wide variety of contexts, properly training networks on complicated tasks requires expertise and can be expensive from a computational perspective. In industrial applications, data coming from an open-world setting might widely differ from the benchmark datasets on which a network was trained. Being able to monitor the presence of such variations without retraining the network is of crucial importance. In this article, we develop a method to monitor trained neural networks based on the topological properties of their activation graphs. To each new observation, we assign a Topological Uncertainty, a score that aims to assess the reliability of the predictions by investigating the whole network instead of its final layer only, as typically done by practitioners. Our approach entirely works at a post-training level and does not require any assumption on the network architecture, optimization scheme, nor the use of data augmentation or auxiliary datasets; and can be faithfully applied on a large range of network architectures and data types. We showcase experimentally the potential of Topological Uncertainty in the context of trained network selection, Out-Of-Distribution detection, and shift-detection, both on synthetic and real datasets of images and graphs

Topological Data Analysis and its usefulness for precision medicine studies

International audiencePrecision medicine allows the extraction of information from complex datasets to facilitate clinical decision-making at the individual level. Topological Data Analysis (TDA) offers promising tools that complement current analytical methods in precision medicine studies. We introduce the fundamental concepts of the TDA corpus (the simplicial complex, the Mapper graph, the persistence diagram and persistence landscape). We show how these can be used to enhance the prediction of clinical outcomes and to identify novel subpopulations of interest, particularly applied to understand remission of depression in data from the GENDEP clinical trial

A mouse ear skin model to study the dynamics of innate immune responses against the microsporidian Encephalitozoon cuniculi

Microsporidia are obligate intracellular parasites related to fungi that cause severe infections in immunocompromised individuals. Encephalitozoon cuniculi is a microsporidian species capable of infecting mammals, including human and rodents. In response to microsporidian infection, innate immune system serves as the first line of defense and allows a partial clearance of the parasite via the innate immune cells, namely macrophages, neutrophils, dendritic cells, and Natural Killer cells. According to the literature, microsporidia bypass this response in vitro by modulating the response of macrophages. In order to study host-parasites interactions in vivo, we developed a model using the mouse ear pinna in combination with an intravital imaging approach. Fluorescent E. cuniculi spores were inoculated into the skin tissue to follow for the first time in real time in an in vivo model the recruitment dynamics of EGFP + phagocytic cells in response to the parasite. The results show that parasites induce an important inflammatory recruitment of phagocytes, with alterations of their motility properties (speed, displacement length, straightness). This cellular response persists in the injection zone, with spores detected inside the phagocytes up to 72 h post-infection. Immunostainings performed on ear tissue cryosections evoke the presence of developing infectious foci from 5 days post-infection, in favor of parasite proliferation in this tissue. Overall, the newly set up mice ear pinna model will increase our understanding of the immunobiology of microsporidia and in particular, to know how they can bypass and hijack the host immune system of an immunocompetent or immunosuppressed host

RipsNet: a general architecture for fast and robust estimation of the persistent homology of point clouds

International audienceThe use of topological descriptors in modern machine learning applications, such as persistence diagrams (PDs) arising from Topological Data Analysis (TDA), has shown great potential in various domains. However, their practical use in applications is often hindered by two major limitations: the computational complexity required to compute such descriptors exactly, and their sensitivity to even low-level proportions of outliers. In this work, we propose to bypass these two burdens in a data-driven setting by entrusting the estimation of (vectorization of) PDs built on top of point clouds to a neural network architecture that we call RipsNet. Once trained on a given data set, RipsNet can estimate topological descriptors on test data very efficiently with generalization capacity. Furthermore, we prove that RipsNet is robust to input perturbations in terms of the 1-Wasserstein distance, a major improvement over the standard computation of PDs that only enjoys Hausdorff stability, yielding RipsNet to substantially outperform exactly-computed PDs in noisy settings. We showcase the use of RipsNet on both synthetic and real-world data. Our implementation will be made freely and publicly available as part of the open-source library Gudhi

Safety Concern between Autologous Fat Graft, Mesenchymal Stem Cell and Osteosarcoma Recurrence

Background: Osteosarcoma is the most common malignant primary bone tumour in young adult treated by neo adjuvant chemotherapy, surgical tumor removal and adjuvant multidrug chemotherapy. For correction of soft tissue defect consecutive to surgery and/or tumor treatment, autologous fat graft has been proposed in plastic and reconstructive surgery. Principal Findings: We report here a case of a late local recurrence of osteosarcoma which occurred 13 years after the initial pathology and 18 months after a lipofilling procedure. Because such recurrence was highly unexpected, we investigated the possible relationship of tumor growth with fat injections and with mesenchymal stem/stromal cell like cells which are largely found in fatty tissue. Results obtained in osteosarcoma pre-clinical models show that fat grafts or progenitor cells promoted tumor growth. Significance: These observations and results raise the question of whether autologous fat grafting is a safe reconstructive procedure in a known post neoplasic context

Lipolyse d'excipients lipidiques destinés à l'administration par voie orale de substances actives hydrophobes

Le Labrasol® et le Gelucire® 44/14 sont des macrogolglycérides utilisés pour l administration par voie orale des substances actives hydrophobes. Ils sont composés d acylglycérols et d esters de PEG, substrats potentiels des lipases digestives. Nous avons étudié la lipolyse in vitro de ces excipients par les lipases digestives. Nous avons mis en évidence que la lipase pancréatique humaine (HPL), principale lipase impliquée dans la lipolyse des triacylglycérols alimentaires, n était pas capable d hydrolyser ces excipients contrairement à la lipase gastrique de chien (DGL), la lipase pancréatique apparentée de type 2 (HPLRP2) et la carboxyl ester hydrolase (CEH). L étude de la spécificité des lipases digestives vis-à-vis des différents substrats contenus dans ces excipients montre que les esters de PEG sont de mauvais substrats pour la HPL et la DGL présentant une spécificité marquée pour les di- et triacylglycérols. En revanche, la HPLRP2 et la CEH hydrolysent les esters de PEG et ne sont pas spécifiques vis-à-vis des différents composés contenus dans ces excipients. Nous avons développé une méthode de simulation in vitro de la lipolyse gastro-intestinale de ces excipients prenant en compte la lipolyse gastrique puis la lipolyse duodénale. La composition des excipients lipidiques est significativement modifiée à la fin de la phase gastrique montrant l importance de la lipolyse gastrique in vivo. Nous avons aussi étudié l influence de la lipolyse gastro-intestinale du Labrasol® et du Gelucire® 44/14 sur la solubilité apparente de deux substances actives hydrophobes, le piroxicam et la cinnarizine. Il apparaît que la lipolyse gastro-intestinale de l excipient n entraîne pas de précipitation du piroxicam et permet de maintenir la cinnarizine en solution aqueuse lorsque celle-ci formulée avec le Labrasol®Labrasol® and Gelucire® 44/14 are macrogolglycerides which are used for the oral drug delivery of poorly water-soluble drugs. They are composed of acylglycerols and PEG esters potential substrates of digestive lipases. We studied the in vitro lipolysis of these excipients by digestive lipases. We showed that the human pancreatic lipase (HPL), the main lipase involved in the lipolysis of dietary triacylglycerols, was not able to hydrolyze either of these excipients contrary to dog gastric lipase (DGL), human pancreatic lipase-related protein 2 (HPLRP2), and carboxyl ester hydrolase (CEH). The study of digestive lipases specificity showed that HPL and DGL possessed specificity toward di- and triacylglycerols, whereas HPLRP2 and CEH hydrolyzed PEG esters but did not present a marked specificity. We developed an in vitro method to simulate the gastrointestinal lipolysis of these excipients. At the end of the gastric phase, the composition of both of these excipients was significantly modified underlining the importance of gastric lipolysis in vivo. We also studied the influence of excipients lipolysis on the concentration of two poorly water-soluble drugs, piroxicam and cinnarizine, in the aqueous phase. It seems that the gastrointestinal lipolysis of these excipients did not undergo piroxicam precipitation whereas it was a prerequisite to maintain cinnarizine in aqueous solution when formulated with Labrasol®.AIX-MARSEILLE2-BU Sci.Luminy (130552106) / SudocSudocFranceF

Etude de deux lipases apparentées aux lipases pancréatiques (lipase pancréatique humaine apparentée de type 2 et la lipase du plasma seminal caprin)

AIX-MARSEILLE2-BU Sci.Luminy (130552106) / SudocSudocFranceF

Etude quantitative de la sécrétion de lipase, de la lipolyse et du stockage de lipides chez Yarrowia lipolytica lors de sa croissance en présence d'huile d'olive

La sécrétion de lipase, la lipolyse extracellulaire et l absorption des acides gras (AGL) ont été étudiés chez Yarrowia lipolytica (YL) en présence d huile d olive et/ou de sucrose. Des mesures d activité lipase et d immuno-révélation ont montré que l activité lipase présente dans le milieu de culture provenait principalement de la lipase YLLIP2. L huile d olive induit la production de lipase qui est principalement associée aux cellules pendant les premières heures de cultures. YLLIP2 est ensuite libérée dans le milieu de culture avant d être totalement dégradée par les protéases. Les triglycérides (TG) sont dégradés alors que la lipase est encore attachée aux cellules. Les produits de lipolyse présents dans le milieu de culture et à l intérieur des cellules ont été quantifiés par chromatographie TLC-FID et GC. Les niveaux intracellulaires d AGL et de TG augmentent transitoirement et dépendent de la source de carbone utilisée. Une accumulation maximum de 37,8 % w/w de lipides est observée avec l huile d olive seule. Cette étude montre que la levure YL est un modèle intéressant pour étudier la lipolyse extracellulaire et l absorption des acides gras par les cellulesLipase secretion, extracellular lipolysis and fatty acid (FFA) uptake were quantified in Yarrowia lipolytica (YL) grown in the presence of olive oil and/or sucrose. Lipase assays and western blot analysis indicated that the lipase activity measured in YL cultures mainly resulted from YLLIP2 lipase. Lipase production was triggered by olive oil and YLLIP2 remained associated with the yeast cells during the first hours of culture. It was then released in the culture medium before it was totally degraded by the alkaline protease. Olive oil triglycerides (TG) were degraded when the lipase was still attached to the cell wall. The fate of lipolysis products in the culture medium and inside the yeast cell were investigated by quantitative TLC-FID and GC analysis. Intracellular levels of FFA and TG increased transiently and were dependent on the carbon sources. A maximum fat storage of 37.8% w/w was observed with olive oil alone. The present study shows that yeasts are interesting models for studying extracellular lipolysis and fat uptake by the cellAIX-MARSEILLE2-Bib.electronique (130559901) / SudocSudocFranceF

Spécificité de substrat des lipases et rôle du volet amphiphile dans la reconnaissance stéréosélective des acylglycérols

Pour identifier les mécanismes de stéréopréférence des lipases envers les acylglycérols (pro)chiraux, nous avons développé une méthode de dérivatisation des diacylglycérols chiraux, issus de l hydrolyse de triacylglycérols prochiraux, permettant de les quantifier par CLHP chirale et de déterminer l excès énantiomérique parallèlement à l évolution des produits de lipolyse. Cette méthode, validée avec des lipases possédant différentes stéréopréférences, et un modèle mathématique, estimant les constantes de spécificité et les préférences relatives de substrats, ont été utilisés pour déterminer le rôle du volet amphiphile contrôlant l accès au site actif de la lipase pancréatique humaine. L implication du volet dans la stéréosélectivité pour la position sn-1 des triacylglycérols a été démontrée et sa délétion supprime cette préférence. La synthèse d un triacylglycérol avec un acide a-éléostéarique en position sn-2 permet d étudier la spécificité des lipases pour cette position.To identify the mechanisms of stereopreference of lipases against (pro)chiral acylglycerols, we have developed a method of derivatization of chiral diacylglycerols, from the hydrolysis of prochiral triacylglycerols, to quantify by chiral HPLC and to determine the enantiomeric excess in parallel with the evolution of lipolysis products. This method, validated with lipases having different stereopreferences, and a mathematical model, to estimate the specificity constants and the relative preferences of substrates, were used to determine the role of amphiphilic lid that control the access to the active site of human pancreatic lipase. The implication of lid in the stereoselectivity for the sn-1 position of triacylglycerols has been demonstrated and its deletion removes this preference. The synthesis of a triacylglycerol with an acid a-eleostearic at sn-2 position allows studying the specificity of lipases for this position.AIX-MARSEILLE2-BU Sci.Luminy (130552106) / SudocSudocFranceF