Asymptotic Chow Semistability Implies Ding Polystability for Gorenstein Toric Fano Varieties by Naoto Yotsutani

“…</i><b>71</b> (2019), 495–524.) and specifying the symmetry of the associated polytopes as well.…”
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Mixed volumes of hypersimplices, root systems and shifted young tableaux by Croitoru, Dorian (Dorian Eugen)

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Structure-function analysis of the presumptive Arabidopsis auxin permease AUX1. by Swarup, R, Kargul, J, Marchant, A, Zadik, D, Rahman, A, Mills, R, Yemm, A, May, S, Williams, L, Millner, P, Tsurumi, S, Moore, I, Napier, R, Kerr, I, Bennett, M

“…We were able to demonstrate in conjunction with helix prediction programs that AUX1 represents a polytopic membrane protein composed of 11 transmembrane spanning domains. …”

The ER membrane protein complex promotes biogenesis of sterol-related enzymes maintaining cholesterol homeostasis by Volkmar, N, Thezenas, M, Louie, S, Juszkiewicz, S, Nomura, D, Hegde, R, Kessler, B, Christianson, J

“…Insertion of the weakly hydrophobic tail-anchor (TA) of SQS into the ER membrane by the EMC ensures sufficient flux through the sterol biosynthetic pathway while biogenesis of polytopic SOAT1 promoted by the EMC provides cells with the ability to store free cholesterol as inert cholesteryl esters. …”

Automatic verification of concurrent stochastic systems by Kwiatkowska, M, Parker, D, Norman, G, Santos, G

“…For zerosum properties it requires solving matrix games via linear programming, and for equilibria-based properties we find social welfare or social cost Nash equilibria of bimatrix games via the method of labelled polytopes through an SMT encoding. We implement this approach in PRISM-games, which required extending the tool’s modelling language for CSGs, and apply it to case studies from domains including robotics, computer security and computer networks, explicitly demonstrating the benefits of both CSGs and equilibria-based properties.…”

Hierarchical Lateral Control Scheme for Autonomous Vehicle with Uneven Time Delays Induced by Vision Sensors by Qi Liu, Yahui Liu, Congzhi Liu, Baiming Chen, Wenhao Zhang, Liang Li, Xuewu Ji

“…Secondly, the state space of the system is augmented to describe such uncertainties with polytopic inclusions, which is controlled by an H&infin;-based LQR controller with a low cost of online computation. …”
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Phylogenetic analysis of promoter regions of human Dolichol kinase (DOLK) and orthologous genes using bioinformatics tools by Farooqi Nadia, Rahman Ataur, Ali Yasir, Ali Kishwar, Khan Muhammad Ezaz Hasan, Jones David Aaron, Abdelkarim Mouadh, Ullah Farman, Jalil Fazal

“…The Dolichol kinase (DOLK) gene encodes the polytopic DOLK protein associated with the endoplasmic reticulum (ER) N-glycosylation pathway catalyzing the final step in the biosynthesis of dolichol phosphate. …”
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Substrate recognition mechanism of the endoplasmic reticulum-associated ubiquitin ligase Doa10 by Kevin Wu, Samuel Itskanov, Diane L. Lynch, Yuanyuan Chen, Aasha Turner, James C. Gumbart, Eunyong Park

“…Abstract Doa10 (MARCHF6 in metazoans) is a large polytopic membrane-embedded E3 ubiquitin ligase in the endoplasmic reticulum (ER) that plays an important role in quality control of cytosolic and ER proteins. …”
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Arrangements of equal minors in the positive Grassmannian by Farber, Miriam, Postnikov, Alexander

“…We show that arrangements of equal minors of largest value are in bijection with sorted sets, which earlier appeared in the context of alcoved polytopes and Gröbner bases. Maximal arrangements of this form correspond to simplices of the alcoved triangulation of the hypersimplex; and the number of such arrangements equals the Eulerian number. …”
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Shapes and recession cones in mixed-integer convex representability by Zadik, Ilias, Lubin, Miles, Vielma, Juan Pablo

“…Second, we provide an example of an MICP-R set which is the countably infinite union of polytopes all of which have different shapes (no pair is combinatorially equivalent, which implies they are not affine transformations of each other). …”
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Modern Trends in Structural and Solid Mechanics. by Challamel, Noël, editor 600936, Kaplunov, Julius, editor 642013, Takewaki, Izuru, editor 372742

Causal structures from entropic information: geometry and novel scenarios by Rafael Chaves, Lukas Luft, David Gross

“…Many of our results are based on a geometric observation: Bell polytopes for two-outcome measurements can be naturally imbedded into the convex cone of attainable marginal entropies. …”
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Landau discriminants by Sebastian Mizera, Simon Telen

“…In order to study degenerate limits of Landau equations and bounds on the degree of the Landau discriminant, we introduce Landau polytopes and study their facet structure. Finally, we provide an efficient numerical algorithm for the computation of the number of master integrals based on the connection to algebraic statistics. …”
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Pareto task inference analysis reveals cellular trade-offs in diffuse large B-Cell lymphoma transcriptomic data by Jonatan Blais, Julie Jeukens

“…The Pareto optimality theory has been proposed as a framework allowing to identify such trade-offs in biological data from its prediction that it would lead to the presence of specific geometrical patterns (polytopes) in, e.g., gene expression space, with vertices representing specialized phenotypes. …”
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Glycoconjugate pathway connections revealed by sequence similarity network analysis of the monotopic phosphoglycosyl transferases by O’Toole, Katherine H, Imperiali, Barbara, Allen, Karen N

“…Additionally, unexpected fusions of the monoPGT with members of the polytopic PGT superfamily were discovered, implying a possible evolutionary link through the shared polyprenol phosphate substrate. …”
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Analysis and design of networked control systems by Saba Salehi

“…Uncertainties of the networked control system will be characterized by polytopic uncertain parameters using Jordan canonical form. …”
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Multiplicative robust and stochastic MPC with application to wind turbine control by Evans, M

“…The uncertainty in the predicted future states and inputs is bounded by polytopes. The computational cost of running the controller is reduced by calculating matrices offline that provide a means to construct outer approximations to robust constraints to be applied online. …”

Novel epididymis-specific mRNAs downregulated by HE6/Gpr64 receptor gene disruption. by Davies, B, Behnen, M, Cappallo-Obermann, H, Spiess, A, Theuring, F, Kirchhoff, C

“…The cloned cDNA sequences predicted hydrophobic polytopic membrane proteins containing the DUF716 motif. …”

Causal inference with instruments and other supplementary variables. by Ramsahai, R

“…Using an approach based on convex polytopes, bounds are computed here in terms of the pairwise (A,B) and (A,C) distributions, in direct analogy to the classic use but without the linearity assumption. …”

Central limit model checking by Bortolussi, L, Cardelli, L, Kwiatkowska, M, Laurenti, L

“…We then develop efficient and scalable approximate model checking algorithms on the resulting Gaussian process, where we restrict the target regions for probabilistic reachability to convex polytopes. This allows us to derive an abstraction in terms of a time-inhomogeneous discrete-time Markov chain (DTMC), whose dimension is independent of the number of species, on which model checking is performed. …”