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The presence of defects in transition metal dichalcogenides (TMDs) can lead to dramatic local changes in their properties which are of interest for a range of technologies including quantum security devices, hydrogen production, and energy storage. It is therefore essential to be able to study these materials in their native environments, including ambient conditions. Here we report single atom resolution imaging of atomic defects in MoS2, WSe2 and WS2 monolayers carried out in ambient conditions using conductive atomic force microscopy (C-AFM). By comparing measurements from a range of TMDs we use C-AFM to chemically identify the most likely atomic species for the defects observed and quantify their prevalence on each material, identifying oxygen chalcogen substitutions and transition metal substitutions as the most likely, and most common, defect types. Moreover, we demonstrate that C-AFM operated in ambient environments can resolve subtle changes in electronic structure with atomic resolution, which we apply to WSe2 monolayers doped using a nitrogen plasma, demonstrating the capability of C-AFM to resolve electronic, and chemical-specific, details at the atomic scale.

We give a simplified and self-contained proof of the following result due to Shalom, Sauer, and Gotfredsen-Kyed: two quasi-isometric simply connected nilpotent Lie groups $G$ and $H$ have isomorphic cohomology algebras. Our proof is based on considering maps which induce an ergodic measure on the space of functions from $G$ to $H$ ($\textit{ergodic maps}$), and we show that, given an ergodic quasi-isometry, one can construct an explicit isomorphism from $H^*(H)$ to $H^*(G)$. Specifically, when $\psi$ is an ergodic quasi-isometry, the pullback $\psi^*\omega$ of a differential form $\omega$ has a well-defined $\textit{amenable average}$ $\overline{\psi^*}\omega$, and we show that $\overline{\psi^*}$ is the desired isomorphism. A key observation in our proof is that quasi-isometries of nilpotent groups are coarsely volume-preserving, so the amenable average of the pullback of the volume form is always nonzero., Comment: 19 pages

We construct $d$-dimensional polyhedral chains such that the distribution of tangent planes is close to a prescribed measure on the Grassmannian and the chains are either cycles (if the prescribed measure is centered) or their boundary is the boundary of a unit $d$-cube (if the barycenter of the prescribed measure, considered as a measure on $\bigwedge^d \mathbb{R}^n$, is a simple $d$-vector). Such fillings were first proved to exist by Burago and Ivanov [Geom. funct. anal., 2004]; our work gives an explicit construction. Furthermore, in the case that the measure on the Grassmannian is supported on the set of positively oriented $d$-planes, we can construct fillings that are Lipschitz multigraphs. We apply this construction to prove that for anisotropic surface energies, ellipticity for Lipschitz multivalued functions is equivalent to polyconvexity and to show that strict polyconvexity is necessary for the atomic condition to hold.

The translation of AI-generated brain metastases (BM) segmentation into clinical practice relies heavily on diverse, high-quality annotated medical imaging datasets. The BraTS-METS 2023 challenge has gained momentum for testing and benchmarking algorithms using rigorously annotated internationally compiled real-world datasets. This study presents the results of the segmentation challenge and characterizes the challenging cases that impacted the performance of the winning algorithms. Untreated brain metastases on standard anatomic MRI sequences (T1, T2, FLAIR, T1PG) from eight contributed international datasets were annotated in stepwise method: published UNET algorithms, student, neuroradiologist, final approver neuroradiologist. Segmentations were ranked based on lesion-wise Dice and Hausdorff distance (HD95) scores. False positives (FP) and false negatives (FN) were rigorously penalized, receiving a score of 0 for Dice and a fixed penalty of 374 for HD95. Eight datasets comprising 1303 studies were annotated, with 402 studies (3076 lesions) released on Synapse as publicly available datasets to challenge competitors. Additionally, 31 studies (139 lesions) were held out for validation, and 59 studies (218 lesions) were used for testing. Segmentation accuracy was measured as rank across subjects, with the winning team achieving a LesionWise mean score of 7.9. Common errors among the leading teams included false negatives for small lesions and misregistration of masks in space.The BraTS-METS 2023 challenge successfully curated well-annotated, diverse datasets and identified common errors, facilitating the translation of BM segmentation across varied clinical environments and providing personalized volumetric reports to patients undergoing BM treatment.

We prove that in the first Heisenberg group, unlike Euclidean spaces and higher dimensional Heisenberg groups, the best possible exponent for the strong geometric lemma for intrinsic Lipschitz graphs is $4$ instead of $2$. Combined with earlier work from arXiv:2004.11447 and arXiv:2207.03013, our result completes the proof of the strong geometric lemma in Heisenberg groups. One key tool in our proof, and possibly of independent interest, is a suitable refinement of the foliated coronizations which first appeared in arXiv:2004.12522., Comment: 29 pages

Understanding the stress transfer mechanisms from a polymer matrix to two-dimensional reinforcements is essential for the preparation of high performance nanocomposites. In this study, the interfacial stress transfer from a flexible polymer substrate to monolayer and few-layer molybdenum disulfide MoS2 under tension has been investigated. Layer-dependent and strain-dependent photoluminescence (PL) spectroscopy were used to examine the stress transfer efficiency., Comment: 29 pages

We prove that the Heisenberg Riesz transform is $L_2$--unbounded on a family of intrinsic Lipschitz graphs in the first Heisenberg group $\mathbb{H}$. We construct this family by combining a method from \cite{NY2} with a stopping time argument, and we establish the $L_2$--unboundedness of the Riesz transform by introducing several new techniques to analyze singular integrals on intrinsic Lipschitz graphs. These include a formula for the Riesz transform in terms of a singular integral on a vertical plane and bounds on the flow of singular integrals that arises from a perturbation of a graph. On the way, we use our construction to show that the strong geometric lemma fails in $\mathbb{H}$ for all exponents in $[2,4)$. Our results are in stark contrast to two fundamental results in Euclidean harmonic analysis and geometric measure theory: Lipschitz graphs in $\mathbb{R}^n$ satisfy the strong geometric lemma, and the $m$--Riesz transform is $L_2$--bounded on $m$--dimensional Lipschitz graphs in $\mathbb{R}^n$ for $m\in (0,n)$.

This paper describes the use of the Murchison Widefield Array, a low-frequency radio telescope at a radio-quiet Western Australian site, as a radar receiver forming part of a continent-spanning multistatic radar network for the surveillance of space. This paper details the system geometry employed, the orbit-specific radar signal processing, and the orbit determination algorithms necessary to ensure resident space objects are detected, tracked, and propagated. Finally, the paper includes the results processed after a short collection campaign utilising several FM radio transmitters across the country, up to a maximum baseline distance of over 2500 km. The results demonstrate the Murchison Widefield Array is able to provide widefield and persistent coverage of objects in low Earth orbit.

Purpose: A core component of advancing cancer treatment research is assessing response to therapy. Doing so by hand, for example as per RECIST or RANO criteria, is tedious, time-consuming, and can miss important tumor response information; most notably, they exclude non-target lesions. We wish to assess change in a holistic fashion that includes all lesions, obtaining simple, informative, and automated assessments of tumor progression or regression. Due to often low patient enrolments in clinical trials, we wish to make response assessments with small training sets. Deep neuroevolution (DNE) can produce radiology artificial intelligence (AI) that performs well on small training sets. Here we use DNE for function approximation that predicts progression versus regression of metastatic brain disease. Methods: We analyzed 50 pairs of MRI contrast-enhanced images as our training set. Half of these pairs, separated in time, qualified as disease progression, while the other 25 images constituted regression. We trained the parameters of a relatively small CNN via mutations that consisted of random CNN weight adjustments and mutation fitness. We then incorporated the best mutations into the next generations CNN, repeating this process for approximately 50,000 generations. We applied the CNNs to our training set, as well as a separate testing set with the same class balance of 25 progression and 25 regression images. Results: DNE achieved monotonic convergence to 100% training set accuracy. DNE also converged monotonically to 100% testing set accuracy. Conclusion: DNE can accurately classify brain-metastatic disease progression versus regression. Future work will extend the input from 2D image slices to full 3D volumes, and include the category of no change. We believe that an approach such as our could ultimately provide a useful adjunct to RANO/RECIST assessment.

We prove that if a quasiconvex subset $X$ of a metric space $Y$ has finite Nagata dimension and is Lipschitz $k$-connected or admits Euclidean isoperimetric inequalities up to dimension $k$ for some $k$ then $X$ is isoperimetrically undistorted in $Y$ up to dimension $k+1$. This generalizes and strengthens a recent result of the third named author and has several consequences and applications. It yields for example that in spaces of finite Nagata dimension, Lipschitz connectedness implies Euclidean isoperimetric inequalities, and Euclidean isoperimetric inequalities imply coning inequalities. It furthermore allows us to prove an analog of the Federer-Fleming deformation theorem in spaces of finite Nagata dimension admitting Euclidean isoperimetric inequalities.