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The efficacy of deep learning-based Computer-Aided Diagnosis (CAD) methods for skin diseases relies on analyzing multiple data modalities (i.e., clinical+dermoscopic images, and patient metadata) and addressing the challenges of multi-label classification. Current approaches tend to rely on limited multi-modal techniques and treat the multi-label problem as a multiple multi-class problem, overlooking issues related to imbalanced learning and multi-label correlation. This paper introduces the innovative Skin Lesion Classifier, utilizing a Multi-modal Multi-label TransFormer-based model (SkinM2Former). For multi-modal analysis, we introduce the Tri-Modal Cross-attention Transformer (TMCT) that fuses the three image and metadata modalities at various feature levels of a transformer encoder. For multi-label classification, we introduce a multi-head attention (MHA) module to learn multi-label correlations, complemented by an optimisation that handles multi-label and imbalanced learning problems. SkinM2Former achieves a mean average accuracy of 77.27% and a mean diagnostic accuracy of 77.85% on the public Derm7pt dataset, outperforming state-of-the-art (SOTA) methods., Comment: Accepted by WACV2025

We study the topological dynamics of the action of an acylindrically hyperbolic group on the space of its infinite index convex cocompact subgroups by conjugation. We show that, for any suitable probability measure $\mu$, random walks with respect to $\mu$ will produce elements with strong mixing properties for this action asymptotically almost surely. In particular, when the group has no finite normal subgroups this implies that the action is highly topologically transitive. Along the way, we prove technical results about convex cocompact subgroups which allow us to extend some results on random walks of Abbott and the first author.

Endometriosis is a common chronic gynecological disorder that has many characteristics, including the pouch of Douglas (POD) obliteration, which can be diagnosed using Transvaginal gynecological ultrasound (TVUS) scans and magnetic resonance imaging (MRI). TVUS and MRI are complementary non-invasive endometriosis diagnosis imaging techniques, but patients are usually not scanned using both modalities and, it is generally more challenging to detect POD obliteration from MRI than TVUS. To mitigate this classification imbalance, we propose in this paper a knowledge distillation training algorithm to improve the POD obliteration detection from MRI by leveraging the detection results from unpaired TVUS data. More specifically, our algorithm pre-trains a teacher model to detect POD obliteration from TVUS data, and it also pre-trains a student model with 3D masked auto-encoder using a large amount of unlabelled pelvic 3D MRI volumes. Next, we distill the knowledge from the teacher TVUS POD obliteration detector to train the student MRI model by minimizing a regression loss that approximates the output of the student to the teacher using unpaired TVUS and MRI data. Experimental results on our endometriosis dataset containing TVUS and MRI data demonstrate the effectiveness of our method to improve the POD detection accuracy from MRI., Comment: This paper is accepted by 2023 IEEE 20th International Symposium on Biomedical Imaging(ISBI 2023)

We show that if a right-angled Artin group $A(\Gamma)$ has a non-trivial, minimal action on a tree $T$ which is not a line, then $\Gamma$ contains a separating subgraph $\Lambda$ such that $A(\Lambda)$ stabilizes an edge in $T$.

In this paper, which is of programmatic rather than quantitative nature, we aim to further delineate and sharpen the future potential of the LISA mission in the area of fundamental physics. Given the very broad range of topics that might be relevant to LISA, we present here a sample of what we view as particularly promising directions, based in part on the current research interests of the LISA scientific community in the area of fundamental physics. We organize these directions through a "science-first" approach that allows us to classify how LISA data can inform theoretical physics in a variety of areas. For each of these theoretical physics classes, we identify the sources that are currently expected to provide the principal contribution to our knowledge, and the areas that need further development. The classification presented here should not be thought of as cast in stone, but rather as a fluid framework that is amenable to change with the flow of new insights in theoretical physics., Comment: 22 pages, 1 figure, to appear in General Relativity and Gravitation

It is known that every infinite index quasi-convex subgroup $H$ of a non-elementary hyperbolic group $G$ is a free factor in a larger quasi-convex subgroup of $G$. We give a probabilistic generalization of this result. That is, we show that when $R$ is a subgroup generated by independent random walks in $G$, then $\langle H, R\rangle\cong H\ast R$ with probability going to one as the lengths of the random walks go to infinity and this subgroup is quasi-convex in $G$. Moreover, our results hold for a large class of groups acting on hyperbolic metric spaces and subgroups with quasi-convex orbits. In particular, when $G$ is the mapping class group of a surface and $H$ is a convex cocompact subgroup we show that $\langle H, R\rangle$ is convex cocompact and isomorphic to $ H\ast R$., Comment: 31 pages, 5 figures

We construct a finitely generated group that does not satisfy the generalized Burghelea conjecture.

We prove that every countable acylindrically hyperbolic group admits a highly transitive action with finite kernel. This theorem uniformly generalizes many previously known results and allows us to answer a question of Garion and Glassner on the existence of highly transitive faithful actions of mapping class groups. It also implies that in various geometric and algebraic settings, the transitivity degree of an infinite group can only take two values, namely $1$ and $\infty$. Here by transitivity degree of a group we mean the supremum of transitivity degrees of its faithful permutation representations. Further, for any countable group $G$ admitting a highly transitive faithful action, we prove the following dichotomy: Either $G$ contains a normal subgroup isomorphic to the infinite alternating group or $G$ resembles a free product from the model theoretic point of view. We apply this theorem to obtain new results about universal theory and mixed identities of acylindrically hyperbolic groups. Finally, we discuss some open problems.

We generalize a version of small cancellation theory to the class of acylindrically hyperbolic groups. This class contains many groups which admit some natural action on a hyperbolic space, including non-elementary hyperbolic and relatively hyperbolic groups, mapping class groups, and groups of outer automorphisms of free groups. Several applications of this small cancellation theory are given, including to Frattini subgroups and Kazhdan constants, the construction of various \exotic"' quotients, and to approximating acylindrically hyperbolic groups in the topology of marked group presentations., Comment: 36 pages

Let G be a group, H a hyperbolically embedded subgroup of G, V a normed G-module, U an H-invariant submodule of V. We propose a general construction which allows to extend 1-quasi-cocycles on H with values in U to 1-quasi-cocycles on G with values in V. As an application, we show that every group G with a non-degenerate hyperbolically embedded subgroup has dim H^2_b (G, l^p(G))=\infty for p\in [1, \infty). This covers many previously known results in a uniform way. Applying our extension to quasimorphisms and using Bavard duality, we also show that hyperbolically embedded subgroups are undistorted with respect to the stable commutator length., Comment: 27 pages, 6 figures

We show that every non-decreasing function $f\colon \mathbb N\to \mathbb N$ bounded from above by $a^n$ for some $a\ge 1$ can be realized (up to a natural equivalence) as the conjugacy growth function of a finitely generated group. We also construct a finitely generated group $G$ and a subgroup $H\le G$ of index 2 such that $H$ has only 2 conjugacy classes while the conjugacy growth of $G$ is exponential. In particular, conjugacy growth is not a quasi-isometry invariant., Comment: The published version of this paper contained an inaccuracy in the proof of Corollary 5.6, which was later corrected in Corrigendum to "Conjugacy growth of finitely generated groups", Adv. Math. 294 (2016), 857-859. This version incorporates all necessary corrections

In this paper, we consider the conjugacy growth function of a group, which counts the number of conjugacy classes which intersect a ball of radius $n$ centered at the identity. We prove that in the case of virtually polycyclic groups, this function is either exponential or polynomially bounded, and is polynomially bounded exactly when the group is virtually nilpotent. The proof is fairly short, and makes use of the fact that any polycyclic group has a subgroup of finite index which can be embedded as a lattice in a Lie group, as well as exponential radical of Lie groups and Dirichlet's approximation theorem., Comment: 4 pages

In the present study, we show that ascorbic acid dose-dependently inhibited interleukin-1beta (IL-1beta)-mediated PGE2 synthesis in the human neuronal cell line, SK-N-SH. Furthermore, in combination with aspirin, ascorbic acid augmented the inhibitory effect of aspirin on PGE2 synthesis. However, ascorbic acid had no synergistic effect along with other COX inhibitors (SC-58125 and indomethacin). The inhibition of IL-1beta-mediated PGE2 synthesis by ascorbic acid was not due to the inhibition of the expression of COX-2 or microsomal prostaglandin E synthase (mPGES-1). Rather, ascorbic acid dose-dependently (0.1-100 microM) produced a significant reduction in IL-1beta-mediated production of 8-iso-prostaglandin F2alpha (8-iso-PGF2alpha), a reliable indicator of free radical formation, suggesting that the effects of ascorbic acid on COX-2-mediated PGE2 biosynthesis may be the result of the maintenance of the neuronal redox status since COX activity is known to be enhanced by oxidative stress. Our results provide in vitro evidence that the neuroprotective effects of ascorbic acid may depend, at least in part, on its ability to reduce neuronal COX-2 activity and PGE2 synthesis, owing to its antioxidant properties. Further, these experiments suggest that a combination of aspirin with ascorbic acid constitutes a novel approach to render COX-2 more sensitive to inhibition by aspirin, allowing an anti-inflammatory therapy with lower doses of aspirin, thereby avoiding the side effects of the usually high dose aspirin treatment.

Prostaglandin E2 (PGE2), is a major prostanoid produced by the activity of cyclooxygenases (COX) in response to various physiological and pathological stimuli. PGE2 exerts its effects by activating four specific E-type prostanoid receptors (EP1, EP2, EP3, and EP4). In the present study, we analyzed the expression of the PGE2 receptor EP1 (mRNA and protein) in different regions of the adult rat brain (hippocampus, hypothalamus, striatum, prefrontal cerebral cortex, parietal cortex, brain stem, and cerebellum) using reverse transcription- polymerase chain reaction, Western blotting, and immunohistochemical methods. On a regional basis, levels of EP1 mRNA were the highest in parietal cortex and cerebellum. At the protein level, we found very strong expression of EP1 in cerebellum, as revealed by Western blotting experiments. Furthermore, the present study provides for the first time evidence that the EP1 receptor is highly expressed in the cerebellum, where the Purkinje cells displayed very high immunolabeling of their perikaryon and dendrites, as observed in the immunohistochemical analysis. Results from the present study indicate that the EP1 prostanoid receptor is expressed in specific neuronal populations, which possibly determine the region-specific response to PGE2.