Hyper-bag-graphs and their applications: Modeling, Analyzing and Visualizing Complex Networks of Co-occurrences

Obtaining insights in the tremendous amount of data in which the Big Data era has brought us, requires to develop specific tools, that are not only summaries of data through classical charts and tables, but that allow full navigation and browsing of a dataset. The proper modeling of databases can enable such navigation and we propose in this Thesis a methodology to achieve the browsing of an information space, through its different facets. To achieve the modeling of such an information space, co-occurrences of data instances are built referring to a common reference type. Historically, the co-occurrences were seen as pairwise relationships and developed as such. The move to hypergraphs enables the possibility to take into account the multi-adicity of the relationships, and to have a representation through the incident graph that simplifies deeply its 2-section. Nonetheless, representing large hypergraphs calls for a coarsening of the information by having insights on important vertices and hyperedges. One classical way to achieve it is to use a diffusion process over the network. Achieving it using an incident matrix is feasible but brings us to a pitfall, as it brings us back to a pairwise relationship. Making proper diffusion requires a tensor approach. This is well known for uniform hypergraphs, where all the hyperedges have same cardinality, but still very challenging for general hypergraphs. After redefining the concept of adjacency in general hypergraphs, we propose a first e-adjacency tensor, that involves a Hypergraph Uniformisation Process and a Polynomial Homogenization Process. This is achieved by uniformisation of the original hypergraph by decomposing it into layers—each of them containing a uniform hypergraph—and filling each layer with additional special vertices and merging them together. This process requires to have as many additional vertices as the number of layers. In order to reduce the number of special vertices, we need to have the possibility of re- peating a vertex when filling, which is not possible with hyperedges as they are sets. We need multisets. It, therefore, requires a new mathematical structure, that we have intro- duced and called hyper-bag-graph—hb-graph for short—, which is a family of multisets of a given universe. Co-occurrences can also have repetitions or individual weighting of their vertices inside a given co-occurrence and hb-graphs fit to handle it. Hence, we introduce a hb-graph framework for co-occurrence networks. We then work on diffusion on such structures, using, in a first step, a matrix approach. Aggregating the ranking of vertices and hb- edges of this diffusion on each of the facet of the information space is achieved by using a multi-diffusion scheme. Since different facets might have different focus of interest, we introduce a biased diffusion that enables a tuning on the point of emphasis on the feature we are interested in. Finally, coming back to e-adjacency tensor, we propose three e-adjacency tensors of hb- graphs, that are based on different ways of filling the hb-edges. The m-uniformisation that is achieved is evaluated and compared to the ones achieved by hb-edge splitting, concluding that any m-uniformisation process has an influence on the exchange-based diffusion that we propose. Hence, we conclude that diffusion using the tensor approach must be done in an informed manner to account for this diffusion change. We finally discuss different possible of achieving it and present a new Laplacian that can help to achieve it

Ovarian metastases of ileal neuroendocrine tumor

International audienceA 55-year-old, menopausal woman with history of breast carcinoma was referred for recurrent abdominal pain without diarrhea. Physical examination, routine biological investigation, and serum CA15-3 were normal. Abdominal contrast-enhanced computed tomography (CT) found a 15-mm ileal hyper-vascularized lesion with mild intestinal dilation and a mesenteric mass of about 20 mm. Both ovaries were moderately enlarged without radiological overt signs of malignancy. CT findings were consistent with ileal neuroendocrine tumor (ileal-NET) with mesenteric invasion. Serum value of chromogranin A was normal. 18F-Fluorodihydroxyphenylalanine (18F-FDOPA) positron emission tomography (PET)/CT was added to the preoperative work-up 1and distinctly identified the primary ileal-NET with the mesenteric involvement. Moreover, intense and pathological 18F-FDOPA uptake was shown in both ovaries and 1 peritoneal nodule of a few millimeters in the Douglas space (Fig 1, A), suggesting ovarian metastases with peritoneal carcinomatosis. Surgical exploration found the primary tumor and the mesenteric lesion that were removed by a 20-cm ileal resection and mesenteric lymphadenectomy. Intervention was completed by bilateral salpingo-oophorectomy, omentectomy, and multiple peritoneal biopsies (Fig 1, B). Postoperative course was uneventful, and pathology confirmed a 20-mm, well-differentiated grade-2 ileal-NET (Ki-67: 4%) with mesenteric invasion, ovarian bilateral spread, and pelvic peritoneal metastases as small as a few millimeters in size (pT4N2M1, UICC 2016)

Weyl connection and non-abelian gauge field

In graphs, the concept of adjacency is clearly defined: it is a pairwise relationship between vertices. Adjacency in hypergraphs has to integrate hyperedge multi-adicity: the concept of adjacency needs to be defined properly by introducing two new concepts: k-adjacency – k vertices are in the same hyperedge – and e-adjacency – vertices of a given hyperedge are e-adjacent. In order to build a new e-adjacency tensor that is interpretable in terms of hypergraph uniformisation, we designed two processes: the first is a hypergraph uniformisation process (HUP) and the second is a polynomial homogeneisation process (PHP). The PHP allows the construction of the e-adjacency tensor while the HUP ensures that the PHP keeps interpretability. This tensor is symmetric and can be fully described by the number of hyperedges; its order is the range of the hypergraph, while extra dimensions allow to capture additional hypergraph structural information including the maximum level of k-adjacency of each hyperedge. Some results on spectral analysis are discussed

A bicentric retrospective study of the correlation of EAU BCR risk groups with 18^{18}F-PSMA-1007 PET/CT detection in prostate cancer biochemical recurrence

International audienceThe European Association of Urology (EAU) has proposed a risk stratification for patients harboring biochemical recurrence (BCR) after radical prostatectomy: ISUP  12 months for low risk, and ISUP ≥ 4 or PSAdt ≤ 12 months for high risk. This dual-center retrospective study aims to investigate the correlation between the EAU risk stratification for BCR following radical prostatectomy and the detection rate of lesions using $^{18}$F-PSMA-1007 PET/CT. Among the 71 included patients (58 high-risk, 13 low-risk), with a median PSA level of 1.43 ng/ml, PET/CT demonstrated a significantly higher positivity in the high-risk group compared to the low-risk group (72.4% vs. 38.0%, p = 0.026). Analysis of recurrence sites revealed a similar proportion of pelvic-confined disease in both groups (24.1% vs. 23.1%, p = 0.935), but a significantly higher incidence of metastatic disease in the high-risk group (51.7% vs. 15.4%, p = 0.017), with detailed findings indicating an increased prevalence of bone metastases in the high-risk BCR group (37.8% vs. 7.7%, p = 0.048). Therefore, PSMA PET/CT offers valuable insights for treatment decisions, aligning with the evolving landscape of prostate cancer management

Nuclear medicine imaging for bone metastases assessment: what else besides bone scintigraphy in the era of personalized medicine?

International audienceAccurate detection and reliable assessment of therapeutic responses in bone metastases are imperative for guiding treatment decisions, preserving quality of life, and ultimately enhancing overall survival. Nuclear imaging has historically played a pivotal role in this realm, offering a diverse range of radiotracers and imaging modalities. While the conventional bone scan using 99mTc marked bisphosphonates has remained widely utilized, its diagnostic performance is hindered by certain limitations. Positron emission tomography, particularly when coupled with computed tomography, provides improved spatial resolution and diagnostic performance with various pathology-specific radiotracers. This review aims to evaluate the performance of different nuclear imaging modalities in clinical practice for detecting and monitoring the therapeutic responses in bone metastases of diverse origins, addressing their limitations and implications for image interpretation.</jats:p

Hybrdi PEDOT-metal nanoparticles - New substitutes for PEDOT:PSS in electrochromic layers - Towards improved performance

Hybrid organic-inorganic nanocomposites of poly(3,4-ethylenedioxythiophene) (PEDOT) and silver or gold {PEDOT-metal (PEDOT-M) nano-objects (M = Ag, Au) (particle diameter down to 60 nm)} were prepared by a one-pot oxidative aqueous dispersion polymerization using ammonium persulfate as an oxidant and the corresponding metal salts as co-oxidant (HAuCl4 and AgNO3) in the presence of pyrrole-modified-poly(N-vinylpyrrolidone-co-vinyl alcohol) (PVP-co-PVAL-mod-Py) stabilizer. The hydrophilic character of such a stabilizer enhances the polymer layer through hydrophilic interactions, which leads to a smooth surface with high wetting properties for subsequent electropolymerizations. PEDOT-M is more conducting than the commercially available PEDOT:PSS, in which the PSS acts as an insulating agent (electrical conductivities up to 1.25 S cm-1). These nanocomposites were used to replace PEDOT:PSS as anchoring layer for further EDOT monomer polymerization, providing an improvement of the electrochromic properties of PEDOT in terms of not only contrast ratio and coloration efficiency but also switching time response

Cutting-edge imaging of cardiac metastases from neuroendocrine tumors: Lesson from a case series

With the increasing availability of high-performance medical imaging for the management of patients with neuroendocrine tumors (NETs), a progressive growth of asymptomatic and incidentally detected cardiac metastases (CMs) has been observed in the recent years. In clinical practice, CMs of NENs are often incidentally detected by whole-bod