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1. 2d $$ \mathcal{N} $$ = (0, 1) gauge theories and Spin(7) orientifolds

   https://doi.org/10.1007/JHEP03(2022)150  

   Franco, Sebastián; Mininno, Alessandro; Uranga, Ángel M.; Yu, Xingyang (March 2022, Journal of High Energy Physics)

   A bstract We initiate the geometric engineering of 2d $$ \mathcal{N} $$ N = (0 , 1) gauge theories on D1-branes probing singularities. To do so, we introduce a new class of backgrounds obtained as quotients of Calabi-Yau 4-folds by a combination of an anti-holomorphic involution leading to a Spin(7) cone and worldsheet parity. We refer to such constructions as Spin(7) orientifolds . Spin(7) orientifolds explicitly realize the perspective on 2d $$ \mathcal{N} $$ N = (0 , 1) theories as real slices of $$ \mathcal{N} $$ N = (0 , 2) ones. Remarkably, this projection is geometrically realized as Joyce’s construction of Spin(7) manifolds via quotients of Calabi-Yau 4-folds by anti-holomorphic involutions. We illustrate this construction in numerous examples with both orbifold and non-orbifold parent singularities, discuss the role of the choice of vector structure in the orientifold quotient, and study partial resolutions. 

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2. Conditions for obtaining positronium Bose–Einstein condensation in a micron-sized cavity

   https://doi.org/10.1140/epjd/s10053-022-00427-1  

   Asaro, Marcus X.; Herrera, Steven; Fuentes-Garcia, Melina; Cecchini, Gabriel G.; Membreno, Erick E.; Greaves, Rod G.; Mills, Allen P. (June 2022, The European Physical Journal D)

   Abstract The quest for making a triplet positronium (Ps) Bose–Einstein condensate confined in a micron-sized cavity in a material such as porous silica faces at least three interrelated problems: (1) About $$10^7$$ 10 7 spin polarized Ps atoms must be injected into a small cavity within a porous solid material without vaporizing it. (2) It is known that Ps atoms confined in 30–100 nm diameter cavities in porous silica do not remain in the gas phase, but become stuck to the cavity walls at room temperature (Cooper et al., Phys. Rev. B 97:205302, 2018). (3) Cooling a gas of Ps atoms to cryogenic temperatures by energy exchange with the walls would be a very slow process (Saito and Hyodo, in: Surko, Gianturco (eds) New Directions in Antimatter Chemistry and Physics, Springer Dordrecht, Netherlands, 2001) because of the relatively low collision rate with the walls and the large mismatch between the masses of the Ps and the wall atoms. A possible solution of these difficulties is presented, based on cooling the implanted positrons in an isotopically pure diamond single crystal target, subsequent saturating of the wall Ps coverage so that a substantial portion of the Ps will be in the gaseous state, and thermalizing the gas-phase Ps via collisions with the low effective mass wall Ps. A design process for the target material is outlined as well, including preliminary results in porous cavity fabrication using focused ion beam milling. Graphical abstract 

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3. Supersymmetric spectroscopy on AdS4 × S7 and AdS4 × S6

   https://doi.org/10.1007/JHEP07(2021)094  

   Cesàro, Mattia; Larios, Gabriel; Varela, Oscar (July 2021, Journal of High Energy Physics)

   A bstract New techniques based on Exceptional Field Theory have recently allowed for the calculation of the Kaluza-Klein spectra of certain AdS 4 solutions of D = 11 and massive IIA supergravity. These are the solutions that consistently uplift on S 7 and S 6 from vacua of maximal four-dimensional supergravity with SO(8) and ISO(7) gaugings. In this paper, we provide an algorithmic procedure to compute the complete Kaluza-Klein spectrum of five such AdS 4 solutions, all of them $$ \mathcal{N} $$ N = 1, and give the first few Kaluza-Klein levels. These solutions preserve SO(3) and U(1) × U(1) internal symmetry in D = 11, and U(1) (two of them) and no continuous symmetry in type IIA. Together with previously discussed cases, our results exhaust the Kaluza-Klein spectra of known supersymmetric AdS 4 solutions in D = 11 and type IIA in the relevant class. 

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4. Toward Optimal Radio Colorings of Hypercubes via SAT-solving

   https://doi.org/10.29007/qrmp  

   Subercaseaux, Bernardo; Heule, Marijn (June 2023, EasyChair)

   Radio 2-colorings of graphs are a generalization of vertex colorings motivated by the problem of assigning frequency channels in radio networks. In a radio 2-coloring of a graph, vertices are assigned integer colors so that the color of two vertices u and v differ by at least 2 if u and v are neighbors, and by at least 1 if u and v have a common neighbor. Our work improves the best-known bounds for optimal radio 2-colorings of small hypercube graphs, a combinatorial problem that has received significant attention in the past. We do so by using automated reasoning techniques such as symmetry breaking and Cube and Conquer, obtaining that for n = 7 and n = 8, the coding-theory upper bounds of Whittlesey et al. (1995) are not tight. Moreover, we prove the answer for n = 7 to be either 12 or 13, thus making a substantial step towards answering an open problem by Knuth (2015). Finally, we include several combinatorial observations that might be useful for further progress, while also arguing that fully determining the answer for n = 7 will require new techniques. 

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5. LES: Locally Exploitative Sampling for Robot Path Planning

   https://doi.org/10.1109/ICRA48891.2023.10160279  

   Joshi, Sagar Suhas; Hutchinson, Seth; Tsiotras, Panagiotis (May 2023, IEEE)

   Sampling-based algorithms solve the path planning problem by generating random samples in the search space and incrementally growing a connectivity graph or a tree. Conventionally, the sampling strategy used in these algorithms is biased towards exploration to acquire information about the search-space. In contrast, this work proposes an optimization-based procedure that generates new samples so as to improve the cost-to-come value of vertices in a given neighborhood. The application of the proposed algorithm adds an exploitative bias to sampling and results in a faster convergence1 to the optimal solution compared to other state-of-the-art sampling techniques. This is demonstrated using benchmarking experiments performed for 7 DOF Panda and 14 DOF Baxter robots. 

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