Adaptive Damping Design of PMSG Integrated Power System with Virtual Synchronous Generator Control by Jun Deng, Jianbo Wang, Shupeng Li, Haijing Zhang, Shutao Peng, Tong Wang

“…The active power of PMSG is selected as the variable parameter vector to establish a polytopic linear variable parameter system model. Then, based on the hybrid H₂/H_∞ control method, each vertex state feedback matrix is solved by linear matrix inequality, and a subsynchronous oscillation adaptive damping controller with polytope is obtained. …”
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Eradication Conditions of Infected Cell Populations in the 7-Order HIV Model with Viral Mutations and Related Results by Konstantin E. Starkov, Anatoly N. Kanatnikov

“…We compute ultimate upper bounds for all model variables that define a polytope containing the attracting set. The theoretical possibility of eradicating HIV-infected populations has been investigated in the case of a therapy aimed only at eliminating wild-type HIV particles. …”
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Immunogenicity evaluation of the HIV-1 Tat containing polyepitope DNA vaccine adjuvanted with CpG-ODNs in mice by Ehsan Jazaeri, Atiyeh Mahdavi, Asghar Abdoli

“…Materials and Methods: Herein, we comparatively investigated the immunogenic potency of the HIV-1 polytope DNA vaccine containing CpG oligodeoxynucleotides (CpG-ODNs) in BALB/c mice. …”
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A broadly protective vaccine against cutaneous human papillomaviruses by Filipe Colaco Mariz, Kathrin Balz, Manuela Dittrich, Yueru Zhang, Fan Yang, Xueer Zhao, Angelo Bolchi, Simone Ottonello, Martin Müller

“…By applying a modular polytope-based approach, in this work, we explored different vaccine candidates based on selected, tandemly arranged cHPV-L2 epitopes fused to thioredoxin (Trx) as a scaffold protein. …”
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Pricing Equilibria and Graphical Valuations by Candogan, Utku Ozan, Ozdaglar, Asuman, Parrilo, Pablo A.

“…Interestingly, by exploiting a novel connection between the existence of a pricing equilibrium and the partitioning polytope associated with the underlying graph, we also establish that for simple (series-parallel) value graphs, a pricing equilibrium with anonymous graphical pricing rule exists if and only if a Walrasian equilibrium exists. …”
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Reconfiguration of satisfying assignments and subset sums: Easy to find, hard to connect by Demaine, Erik D

“…• Given two points in {0,1}n contained in a polytope P specified by a constant number of linear inequalities, is there a path in the n-hypercube connecting the two points and contained in P? …”
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Approximate inference in graphical models using LP relaxations by Sontag, David Alexander

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Structure of optimal martingale transport plans in general dimensions by Ghoussoub, N, Kim, Y, Lim, T

“…In some cases, πx is supported on the vertices of a k(x)-dimensional polytope, such as when the target measure is discrete. …”

Learning via automaton minimization and matrix factorization by Marusic, I

“…We first tackle a variant of the problem, restricted NMF, which has applications in topic modelling and a geometric interpretation as the nested polytope problem. Lastly we show that NMF is polynomial-time reducible to automaton minimization, and then use our results on NMF to answer old open problems on minimizing labelled Markov chains and probabilistic automata.…”

A Reduced-Order Robust Wide-Area Damping Control for Wind-PV-Thermal-Bundled Power System Considering Operational Uncertainties and Communication Resilience by Zhen Wang, Rehan Sadiq, Deqiang Gan

“…At first, the uncertainties are characterized in the form of polytope vertices, where each vertex represents a linearized model corresponding to a distinct operating condition. …”
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Reduction of Low Frequency Oscillations Using an Enhanced Power System Stabilizer via Linear Parameter Varying Approach by Vahid Nazari, Mohammad Hossein Mousavi, Hassan Moradi CheshmehBeigi

“…To guarantee the flexibility of the stabilizer with respect to the aforementioned issues, the power system polytopic representation is used. In order to apply the new method, the nonlinear equations of the system at each operating point, located in a polytope, are parametrically linearized by scheduling variables. …”
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Costly circuits, submodular schedules and approximate Carathéodory Theorems by Bojja Venkatakrishnan, Shaileshh, Viswanath, Pramod, Alizadeh Attar, Mohammadreza

“…Seen alternatively, the algorithm provides a fast and approximate solution toward a constructive version of Carathéodory’s Theorem for the Birkhoff polytope. The algorithm also has strong connections to submodular optimization, achieves a performance at least half that of the optimal schedule and strictly outperforms the state of the art in a variety of traffic demand settings. …”
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Comparing elliptic and toric hypersurface Calabi-Yau threefolds at large Hodge numbers by Huang, Yu-Chien, Taylor IV, Washington

“…There is a close correspondence between the structure of “tops” in the toric polytope construction and Tate form tunings of Weierstrass models for elliptic fibrations. …”
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Reconfiguration of Satisfying Assignments and Subset Sums: Easy to Find, Hard to Connect by Cardinal, Jean, Demaine, Erik D., Eppstein, David, Hearn, Robert A., Winslow, Andrew

“…Given two points in {0,1}n contained in a polytope P specified by a constant number of linear inequalities, is there a path in the n-hypercube connecting the two points and contained in P? …”
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A Generalized Fault Coverage Model for Linear Time-Invariant Systems by Dominguez-Garcia, A. D., Schindall, Joel E., Kassakian, John G.

“…These performance requirements constrain the system trajectories to some region of the state-space defined by a symmetrical polytope. When a fault occurs, the state-transition matrix, and the input matrix might be altered; and then, it is guaranteed the system survives the fault if all possible post-fault trajectories are fully contained in the region of the state-space defined by the performance requirements. …”
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Power and limitations of convex formulations via linear and semidefinite programming lifts by Fawzi, Hamza

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Anisotropic geometry-conforming d-simplicial meshing via isometric embeddings by Caplan, Philip Claude, Haimes, Robert, Darmofal, David L, Galbraith, Marshall C.

“…In particular, we compute restricted Voronoi simplices using exact arithmetic and use data structures based on convex polytope theory. Finally, since adaptive solvers require geometry-conforming meshes, we offer a Steiner vertex insertion algorithm for ensuring the extracted dual Delaunay triangulation is homeomorphic to the input geometries. …”
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Dispersion of mass and the complexity of geometric problems by Rademacher, Luis Alexis

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Exchangeable equilibria by Stein, Noah D. (Noah Daniel)

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Algorithms and hardness results for the jump number problem, the joint replenishment problem, and the optimal clustering of frequency-constrained maintenance jobs by Telha Cornejo, Claudio (Claudio A.)

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