Obstructions for Matroids of Path-Width at most k and Graphs of Linear Rank-Width at most k

International audienceEvery minor-closed class of matroids of bounded branch-width can be characterized by a minimal list of excluded minors, but unlike graphs, this list could be infinite in general. However, for each fixed finite field $\mathbb F$, the list contains only finitely many $\mathbb F$-representable matroids, due to the well-quasi-ordering of $\mathbb F$-representable matroids of bounded branch-width under taking matroid minors [J. F. Geelen, A. M. H. Gerards, and G. Whittle (2002)]. But this proof is non-constructive and does not provide any algorithm for computing these $\mathbb F$-representable excluded minors in general. We consider the class of matroids of path-width at most $k$ for fixed $k$. We prove that for a finite field $\mathbb F$, every $\mathbb F$-representable excluded minor for the class of matroids of path-width at most~$k$ has at most $2^{|\mathbb{F}|^{O(k^2)}}$ elements. We can therefore compute, for any integer $k$ and a fixed finite field $\mathbb F$, the set of $\mathbb F$-representable excluded minors for the class of matroids of path-width $k$, and this gives as a corollary a polynomial-time algorithm for checking whether the path-width of an $\mathbb F$-represented matroid is at most $k$. We also prove that every excluded pivot-minor for the class of graphs having linear rank-width at most $k$ has at most $2^{2^{O(k^2)}}$ vertices, which also results in a similar algorithmic consequence for linear rank-width of graphs

Mitochondrial function contributes to oxysterol-induced osteogenic differentiation in mouse embryonic stem cells

AbstractOxysterols, oxidized derivatives of cholesterol, are biologically active molecules. Specific oxysterols have potent osteogenic properties that act on osteoprogenitor cells. However, the molecular mechanisms underlying these osteoinductive effects on embryonic stem cells (ESCs) are unknown. This study investigated the effect of an oxysterol combination of 22(S)-hydroxycholesterol and 20(S)-hydroxycholesterol (SS) on osteogenic differentiation of ESCs and the alterations to mitochondrial activity during differentiation. Osteogenic differentiation was assessed by alkaline phosphatase (ALP) activity, matrix mineralization, mRNA expression of osteogenic factors, runt-related transcription factor 2, osterix, and osteocalcin, and protein levels of collagen type IA (COLIA) and osteopontin (OPN). Treatment of cells with SS increased osteoinductive activity compared to the control group. Intracellular reactive oxygen species production, intracellular ATP content, mitochondrial membrane potential, mitochondrial mass, mitochondrial DNA copy number, and mRNA expression of peroxisome proliferator-activated receptor-γ coactivators 1α and β, transcription factors involved in mitochondrial biogenesis, were significantly increased during osteogenesis, indicating upregulation of mitochondrial activity. Oxysterol combinations also increased protein levels of mitochondrial respiratory complexes I–V. We also found that SS treatment increased hedgehog signaling target genes, Smo and Gli1 expression. Inhibition of Hh signaling by cyclopamine suppressed mitochondrial biogenesis and ESC osteogenesis. Subsequently, oxysterol-induced Wnt/β-catenin pathways were inhibited by repression of Hh signaling and mitochondrial biogenesis. Transfection of β-catenin specific siRNA decreased the protein levels of COLIA and OPN, as well as ALP activity. Collectively, these data suggest that lipid-based oxysterols enhance differentiation of ESCs toward the osteogenic lineage by regulating mitochondrial activity, canonical Hh/Gli, and Wnt/β-catenin signaling

Refining Generative Process with Discriminator Guidance in Score-based Diffusion Models

The proposed method, Discriminator Guidance, aims to improve sample generation of pre-trained diffusion models. The approach introduces a discriminator that gives explicit supervision to a denoising sample path whether it is realistic or not. Unlike GANs, our approach does not require joint training of score and discriminator networks. Instead, we train the discriminator after score training, making discriminator training stable and fast to converge. In sample generation, we add an auxiliary term to the pre-trained score to deceive the discriminator. This term corrects the model score to the data score at the optimal discriminator, which implies that the discriminator helps better score estimation in a complementary way. Using our algorithm, we achive state-of-the-art results on ImageNet 256x256 with FID 1.83 and recall 0.64, similar to the validation data's FID (1.68) and recall (0.66). We release the code at https://github.com/alsdudrla10/DG.Comment: International Conference on Machine Learning (ICML23

Electroactive Artificial Muscles Based on Functionally Antagonistic Core–Shell Polymer Electrolyte Derived from PS-b-PSS Block Copolymer

Electroactive ionic soft actuators, a type of artificial muscles containing a polymer electrolyte membrane sandwiched between two electrodes, have been intensively investigated owing to their potential applications to bioinspired soft robotics, wearable electronics, and active biomedical devices. However, the design and synthesis of an efficient polymer electrolyte suitable for ion migration have been major challenges in developing high-performance ionic soft actuators. Herein, a highly bendable ionic soft actuator based on an unprecedented block copolymer is reported, i.e., polystyrene-b-poly(1-ethyl-3-methylimidazolium-4-styrenesulfonate) (PS-b-PSS-EMIm), with a functionally antagonistic core–shell architecture that is specifically designed as an ionic exchangeable polymer electrolyte. The corresponding actuator shows exceptionally good actuation performance, with a high displacement of 8.22 mm at an ultralow voltage of 0.5 V, a fast rise time of 5 s, and excellent durability over 14 000 cycles. It is envisaged that the development of this high-performance ionic soft actuator could contribute to the progress toward the realization of the aforementioned applications. Furthermore, the procedure described herein can also be applied for developing novel polymer electrolytes related to solid-state lithium batteries and fuel cells

Fatigue Prediction of the Discharge Pipe in Reciprocating Compressor

In this paper, a fatigue prediction of the line discharge tube for reciprocating compressor being installed in a refrigerator was studied. The tube usually gets plenty of the repeated loads caused by the start and stop motion of a reciprocating compressor. There are two representative methods to predict the fatigue stress. At first the stress-life can be applied to the problem which takes a lot of repeated stress within the elastic strain range. Second is the strain-life method which can be used when it comes to the problem of a small repeated stress in the plastic strain range. This paper presents the stress-life method how the design parameters of a discharge pipe relate to the fatigue prediction and analyzes the co-relation between them

A Novel sLRP6E1E2 Inhibits Canonical Wnt Signaling, Epithelial-to-Mesenchymal Transition, and Induces Mitochondria-Dependent Apoptosis in Lung Cancer

Aberrant activation of the Wnt pathway contributes to human cancer progression. Antagonists that interfere with Wnt ligand/receptor interactions can be useful in cancer treatments. In this study, we evaluated the therapeutic potential of a soluble Wnt receptor decoy in cancer gene therapy. We designed a Wnt antagonist sLRP6E1E2, and generated a replication-incompetent adenovirus (Ad), dE1-k35/sLRP6E1E2, and a replication-competent oncolytic Ad, RdB-k35/sLRP6E1E2, both expressing sLRP6E1E2. sLRP6E1E2 prevented Wnt-mediated stabilization of cytoplasmic β-catenin, decreased Wnt/β-catenin signaling and cell proliferation via the mitogen-activated protein kinase, and phosphatidylinositol 3-kinase pathways. sLRP6E1E2 induced apoptosis, cytochrome c release, and increased cleavage of PARP and caspase-3. sLRP6E1E2 suppressed growth of the human lung tumor xenograft, and reduced motility and invasion of cancer cells. In addition, sLRP6E1E2 upregulated expression of epithelial marker genes, while sLRP6E1E2 downregulated mesenchymal marker genes. Taken together, sLRP6E1E2, by inhibiting interaction between Wnt and its receptor, suppressed Wnt-induced cell proliferation and epithelial-to-mesenchymal transition