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We construct an ancient solution to planar curve shortening. The solution is at all times compact and embedded. For $t\ll0$ it is approximated by the rotating Yin-Yang soliton, truncated at a finite angle $\alpha(t) = -t$, and closed off by a small copy of the Grim Reaper translating soliton., Comment: The same result was independently obtained by Charyyev, J. in arXiv:2204.05978

In this paper, we introduce a dyadic structure on convex domains of finite type via the so-called dyadic flow tents. This dyadic structure allows us to establish weighted norm estimates for the Bergman projection $P$ on such domains with respect to Muckenhoupt weights. In particular, this result gives an alternative proof of the $L^p$ boundedness of $P$. Moreover, using extrapolation, we are also able to derive weighted vector-valued estimates and weighted modular inequalities for the Bergman projection., 24 pages, 4 figures

Additional file 2: Fig. S1. Description of the study area, Haripur District, Khyber Pakhtunkhwa, Pakistan. Fig. S2. Images of some ethnoveterinary medicinal plant of District Haripur. Table S1. Relationship between Relative frequency of citation (RFC) and Use Value (UV)

Supplemental material, sj-docx-1-mdm-10.1177_0272989X211019040 for The Application of Multicriteria Decision Analysis Methods in Health Care: A Literature Review by Ilyas Khan, Liliane Pintelon and Harry Martin in Medical Decision Making

Additional file 1: File S1. Sample of questionnaire used during field survey for obtaining ethnobotanical information

Supplemental material, sj-docx-1-mdm-10.1177_0272989X211019040 for The Application of Multicriteria Decision Analysis Methods in Health Care: A Literature Review by Ilyas Khan, Liliane Pintelon and Harry Martin in Medical Decision Making

Cell-laden hydrogels are the primary building blocks for bioprinting, and, also termed bioinks, are the foundations for creating structures that can potentially recapitulate the architecture of articular cartilage. To be functional, hydrogel constructs need to unlock the regenerative capacity of encapsulated cells. The recent identification of multipotent articular cartilage-resident chondroprogenitor cells (ACPCs), which share important traits with adult stem cells, represents a new opportunity for cartilage regeneration. However, little is known about the suitability of ACPCs for tissue engineering, especially in combination with biomaterials. This study aimed to investigate the potential of ACPCs in hydrogels for cartilage regeneration and biofabrication, and to evaluate their ability for zone-specific matrix production. Gelatin methacryloyl (gelMA)-based hydrogels were used to culture ACPCs, bone marrow mesenchymal stromal cells (MSCs) and chondrocytes, and as bioinks for printing. Our data shows ACPCs outperformed chondrocytes in terms of neo-cartilage production and unlike MSCs, ACPCs had the lowest gene expression levels of hypertrophy marker collagen type X, and the highest expression of PRG4, a key factor in joint lubrication. Co-cultures of the cell types in multi-compartment hydrogels allowed generating constructs with a layered distribution of collagens and glycosaminoglycans. By combining ACPC- and MSC-laden bioinks, a bioprinted model of articular cartilage was generated, consisting of defined superficial and deep regions, each with distinct cellular and extracellular matrix composition. Taken together, these results provide important information for the use of ACPC-laden hydrogels in regenerative medicine, and pave the way to the biofabrication of 3 D constructs with multiple cell types for cartilage regeneration or in vitro tissue models. Statement of Significance Despite its limited ability to repair, articular cartilage harbors an endogenous population of progenitor cells (ACPCs), that to date, received limited attention in biomaterials and tissue engineering applications. Harnessing the potential of these cells in 3D hydrogels can open new avenues for biomaterial-based regenerative therapies, especially with advanced biofabrication technologies ( e.g. bioprinting). This study highlights the potential of ACPCs to generate neo-cartilage in a gelatin-based hydrogel and bioink. The ACPC-laden hydrogel is a suitable substrate for chondrogenesis and data shows it has a bias in directing cells towards a superficial zone phenotype. For the first time, ACPC-hydrogels are evaluated both as alternative for and in combination with chondrocytes and MSCs, using co-cultures and bioprinting for cartilage regeneration in vitro . This study provides important cues on ACPCs, indicating they represent a promising cell source for the next generation of cartilage constructs with increased biomimicry.

Let $C$ be an $m$-dimensional cone immersed in $\mathbb{R}^{n+m}$. In this paper, we show that if $F:M^m \rightarrow \mathbb{R}^{n+m}$ is a properly immersed mean curvature flow self-shrinker which is smoothly asymptotic to $C$, then it is unique and converges to $C$ with unit multiplicity. Furthermore, if $F_1$ and $F_2$ are self-expanders that both converge to $C$ smoothly asymptotically and their separation decreases faster than $\rho^{-m-1}e^{-\rho^2/4}$ in the Hausdorff metric, then the images of $F_1$ and $F_2$ coincide., Comment: 44 pages. Exposition improved, several remarks added, various arguments corrected and expanded