On the minimum number of inversions to make a digraph kk-(arc-)strong

The {\it inversion} of a set $X$ of vertices in a digraph $D$ consists of reversing the direction of all arcs of $D\langle X\rangle$. We study $sinv'_k(D)$ (resp. $sinv_k(D)$) which is the minimum number of inversions needed to transform $D$ into a $k$-arc-strong (resp. $k$-strong) digraph and sinv'_k(n) = \max\{sinv'_k(D) \mid D~\mbox{is a 2k$-edge-connected digraph of order$n}\}. We show : $(i): \frac{1}{2} \log (n - k+1) \leq sinv'_k(n) \leq \log n + 4k -3$ ; $(ii):$ for any fixed positive integers $k$ and $t$, deciding whether a given oriented graph $\vec{G}$ satisfies $sinv'_k(\vec{G}) \leq t$ (resp. $sinv_k(\vec{G}) \leq t$) is NP-complete ; $(iii):$ if $T$ is a tournament of order at least $2k+1$, then $sinv'_k(T) \leq sinv_k(T) \leq 2k$, and $sinv'_k(T) \leq \frac{4}{3}k+o(k)$; $(iv):\frac{1}{2}\log(2k+1) \leq sinv'_k(T) \leq sinv_k(T)$ for some tournament $T$ of order $2k+1$; $(v):$ if $T$ is a tournament of order at least $19k-2$ (resp. $11k-2$), then $sinv'_k(T) \leq sinv_k(T) \leq 1$ (resp. $sinv_k(T) \leq 3$); $(vi):$ for every $\epsilon>0$, there exists $C$ such that $sinv'_k(T) \leq sinv_k(T) \leq C$ for every tournament $T$ on at least $2k+1 + \epsilon k$ vertices

Maximum Independent Set when excluding an induced minor: K1+tK2K_1 + tK_2 and tC3⊎C4tC_3 \uplus C_4

Dallard, Milani\v{c}, and \v{S}torgel [arXiv '22] ask if for every class excluding a fixed planar graph $H$ as an induced minor, Maximum Independent Set can be solved in polynomial time, and show that this is indeed the case when $H$ is any planar complete bipartite graph, or the 5-vertex clique minus one edge, or minus two disjoint edges. A positive answer would constitute a far-reaching generalization of the state-of-the-art, when we currently do not know if a polynomial-time algorithm exists when $H$ is the 7-vertex path. Relaxing tractability to the existence of a quasipolynomial-time algorithm, we know substantially more. Indeed, quasipolynomial-time algorithms were recently obtained for the $t$-vertex cycle, $C_t$ [Gartland et al., STOC '21] and the disjoint union of $t$ triangles, $tC_3$ [Bonamy et al., SODA '23]. We give, for every integer $t$, a polynomial-time algorithm running in $n^{O(t^5)}$ when $H$ is the friendship graph $K_1 + tK_2$ ($t$ disjoint edges plus a vertex fully adjacent to them), and a quasipolynomial-time algorithm running in $n^{O(t^2 \log n)+t^{O(1)}}$ when $H$ is $tC_3 \uplus C_4$ (the disjoint union of $t$ triangles and a 4-vertex cycle). The former extends a classical result on graphs excluding $tK_2$ as an induced subgraph [Alekseev, DAM '07], while the latter extends Bonamy et al.'s result.Comment: 15 pages, 2 figure

Small But Unwieldy

We show that for any natural number $s$, there is a constant $\gamma$ and a subgraph-closed class having, for any natural $n$, at most $\gamma^n$ graphs on $n$ vertices up to isomorphism, but no adjacency labeling scheme with labels of size at most $s \log n$. In other words, for every $s$, there is a small (even tiny) monotone class without universal graphs of size $n^s$. Prior to this result, it was not excluded that every small class has an almost linear universal graph, or equivalently a labeling scheme with labels of size $(1+o(1))\log n$. The existence of such a labeling scheme, a scaled-down version of the recently disproved Implicit Graph Conjecture, was repeatedly raised [Gavoille and Labourel, ESA '07; Dujmovi\'{c} et al., JACM '21; Bonamy et al., SIDMA '22; Bonnet et al., Comb. Theory '22]. Furthermore, our small monotone classes have unbounded twin-width, thus simultaneously disprove the already-refuted Small conjecture; but this time with a self-contained proof, not relying on elaborate group-theoretic constructions.Comment: 24 pages, 1 figure, shortened abstrac

A tamed family of triangle-free graphs with unbounded chromatic number

We construct a hereditary class of triangle-free graphs with unbounded chromatic number, in which every non-trivial graph either contains a pair of non-adjacent twins or has an edgeless vertex cutset of size at most two. This answers in the negative a question of Chudnovsky, Penev, Scott, and Trotignon. The class is the hereditary closure of a family of (triangle-free) twincut graphs $G_1, G_2, \ldots$ such that $G_k$ has chromatic number $k$. We also show that every twincut graph is edge-critical

Imaging of Vascular Aphasia

Brain imaging is essential for the diagnosis of acute stroke and vascular aphasia. Magnetic resonance imaging (MRI) is the modality of choice for the etiological diagnosis of aphasia, the assessment of its severity, and the prediction of recovery. Diffusion weighted imaging is used to detect, localize, and quantify the extension of the irreversibly injured brain tissue called ischemic core. Perfusion weighted imaging (from MRI or CT) is useful to assess the extension of hypoperfused but salvageable tissue called penumbra. Functional imaging (positron emission tomography (PET), functional MRI (fMRI)) may help predicting recovery and is useful for the understanding of language networks and individual variability. This chapter is meant to review the state of the art of morphological and functional imaging of vascular aphasia and to illustrate the MRI profiles of different aphasic syndromes

How can we combat multicenter variability in MR radiomics? Validation of a correction procedure

International audienc

New insights into the genetic etiology of Alzheimer's disease and related dementias

Characterization of the genetic landscape of Alzheimer's disease (AD) and related dementias (ADD) provides a unique opportunity for a better understanding of the associated pathophysiological processes. We performed a two-stage genome-wide association study totaling 111,326 clinically diagnosed/'proxy' AD cases and 677,663 controls. We found 75 risk loci, of which 42 were new at the time of analysis. Pathway enrichment analyses confirmed the involvement of amyloid/tau pathways and highlighted microglia implication. Gene prioritization in the new loci identified 31 genes that were suggestive of new genetically associated processes, including the tumor necrosis factor alpha pathway through the linear ubiquitin chain assembly complex. We also built a new genetic risk score associated with the risk of future AD/dementia or progression from mild cognitive impairment to AD/dementia. The improvement in prediction led to a 1.6- to 1.9-fold increase in AD risk from the lowest to the highest decile, in addition to effects of age and the APOE ε4 allele

Multiancestry analysis of the HLA locus in Alzheimer’s and Parkinson’s diseases uncovers a shared adaptive immune response mediated by HLA-DRB1*04 subtypes

Across multiancestry groups, we analyzed Human Leukocyte Antigen (HLA) associations in over 176,000 individuals with Parkinson’s disease (PD) and Alzheimer’s disease (AD) versus controls. We demonstrate that the two diseases share the same protective association at the HLA locus. HLA-specific fine-mapping showed that hierarchical protective effects of HLA-DRB1*04 subtypes best accounted for the association, strongest with HLA-DRB1*04:04 and HLA-DRB1*04:07, and intermediary with HLA-DRB1*04:01 and HLA-DRB1*04:03. The same signal was associated with decreased neurofibrillary tangles in postmortem brains and was associated with reduced tau levels in cerebrospinal fluid and to a lower extent with increased Aβ42. Protective HLA-DRB1*04 subtypes strongly bound the aggregation-prone tau PHF6 sequence, however only when acetylated at a lysine (K311), a common posttranslational modification central to tau aggregation. An HLA-DRB1*04-mediated adaptive immune response decreases PD and AD risks, potentially by acting against tau, offering the possibility of therapeutic avenues

Analyse des perturbations orbitales d'un satellite autour de Mars / Orbital perturbations analysis of a spacecraft around Mars

Mars est entourée d'une atmosphère ténue, composée à 95% de dioxyde de carbone (CO2). Au cours d'une année martienne, des transferts de masse (jusqu'à 30% du CO2 atmosphérique) entre l'atmosphère et les calottes polaires produisent des variations temporelles à très grande longueur d'onde du champ de gravité, notamment des harmoniques zonaux de son développement en harmoniques sphériques (de fait les coefficients "composites" de degré 2 et 3). D'un autre côté, le potentiel gravitationnel du Soleil induit des déformations, dites de marée, du volume martien. Ces déformations produisent un potentiel perturbateur en tout point extérieur à la planète, proportionnel à son nombre de Love de degré 2 k2. k2 traduit la réponse élastique de la planète au potentiel solaire et permet de caractériser physiquement le noyau de Mars (sa nature, solide ou liquide, et son rayon). Une manière de quantifier les transferts de la masse atmosphérique et l'état du noyau est de déterminer les perturbations inhérentes sur le mouvement d'un satellite artificiel. Le cycle saisonnier du CO2 et l'état du noyau impliquent aussi des variations de la rotation de Mars. Une autre manière de quantifier les transferts de la masse atmosphérique et l'état du noyau est donc d'observer leurs effets sur la rotation. Des simulations d'observations de trajectographie de satellites (comme celles de Mars Global Surveyor, MGS, Odyssey, MODY) et/ou de la position d'un réseau de stations à la surface de Mars (comme dans l'expérience NEIGE) nous ont permis de voir s'il est possible de restituer précisément les variations des harmoniques zonaux de gravité de bas degré et/ou la rotation. Avec les observations réelles de trajectographie des missions américaines MGS et MODY, on a restitué les variations des harmoniques zonaux de gravité de bas degré et k2.(PHYS 3)--UCL, 200