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1. A constant N2H+ (1-0)-to-HCN (1-0) ratio on kiloparsec scales

   https://doi.org/10.1051/0004-6361/202347050  

   Jiménez-Donaire, M. J.; Usero, A.; Bešlić, I.; Tafalla, M.; Chacón-Tanarro, A.; Salomé, Q.; Eibensteiner, C.; García-Rodríguez, A.; Hacar, A.; Barnes, A. T.; et al (August 2023, Astronomy & Astrophysics)

   Nitrogen hydrides such as NH3 and N2H+ are widely used by Galactic observers to trace the cold dense regions of the interstellar medium. In external galaxies, because of limited sensitivity, HCN has become the most common tracer of dense gas over large parts of galaxies. We provide the first systematic measurements of N2H+ (1-0) across different environments of an external spiral galaxy, NGC 6946. We find a strong correlation (r > 0.98, p < 0.01) between the HCN (1-0) and N2H+ (1-0) intensities across the inner ∼8 kpc of the galaxy, at kiloparsec scales. This correlation is equally strong between the ratios N2H+ (1-0)/CO (1-0) and HCN (1-0)/CO (1-0), tracers of dense gas fractions (fdense). We measure an average intensity ratio of N2H+ (1-0)/HCN (1-0) = 0.15 ± 0.02 over our set of five IRAM-30m pointings. These trends are further supported by existing measurements for Galactic and extragalactic sources. This narrow distribution in the average ratio suggests that the observed systematic trends found in kiloparsec-scale extragalactic studies of fdense and the efficiency of dense gas (SFEdense) would not change if we employed N2H+ (1-0) as a more direct tracer of dense gas. At kiloparsec scales our results indicate that the HCN (1-0) emission can be used to predict the expected N2H+ (1-0) over those regions. Our results suggest that, even if HCN (1-0) and N2H+ (1-0) trace different density regimes within molecular clouds, subcloud differences average out at kiloparsec scales, yielding the two tracers proportional to each other. 

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2. On Robust Fractional 0-1 Programming

   https://doi.org/10.1287/ijoo.2019.0025  

   Mehmanchi, Erfan; Gillen, Colin P.; Gómez, Andrés; Prokopyev, Oleg A. (January 2020, INFORMS Journal on Optimization)

   We study single- and multiple-ratio robust fractional 0-1 programming problems (RFPs). In particular, this work considers RFPs under a wide range of disjoint and joint uncertainty sets, where the former implies separate uncertainty sets for each numerator and denominator and the latter accounts for different forms of interrelatedness between them. We first demonstrate that unlike the deterministic case, a single-ratio RFP is nondeterministic polynomial-time hard under general polyhedral uncertainty sets. However, if the uncertainty sets are imbued with a certain structure, variants of the well-known budgeted uncertainty, the disjoint and joint single-ratio RFPs are polynomially solvable when the deterministic counterpart is. We also propose mixed-integer linear programming (MILP) formulations for multiple-ratio RFPs. We conduct extensive computational experiments using test instances based on real and synthetic data sets to evaluate the performance of our MILP reformulations as well as to compare the disjoint and joint uncertainty sets. Finally, we demonstrate the value of the robust approach by examining the robust solution in a deterministic setting and vice versa. 

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3. Fractional 0–1 programming and submodularity

   https://doi.org/10.1007/s10898-022-01131-5  

   Han, Shaoning; Gómez, Andrés; Prokopyev, Oleg A. (January 2022, Journal of Global Optimization)
4. Expansion of random 0/1 polytopes

   https://doi.org/10.1002/rsa.21184  

   Leroux, Brett; Rademacher, Luis (March 2024, Random Structures & Algorithms)

   Abstract A conjecture of Milena Mihail and Umesh Vazirani (Proc. 24th Annu. ACM Symp. Theory Comput., ACM, Victoria, BC, 1992, pp. 26–38.) states that the edge expansion of the graph of every polytope is at least one. Any lower bound on the edge expansion gives an upper bound for the mixing time of a random walk on the graph of the polytope. Such random walks are important because they can be used to generate an element from a set of combinatorial objects uniformly at random. A weaker form of the conjecture of Mihail and Vazirani says that the edge expansion of the graph of a polytope in is greater than one over some polynomial function of . This weaker version of the conjecture would suffice for all applications. Our main result is that the edge expansion of the graph of arandompolytope in is at least with high probability. 

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5. $${\mathbb A}^{0|1}$$-Torsors, Quotients by Free $${\mathbb A}^{0|1}$$-Actions, and Embeddings into $$\Pi $$-Projective Spaces and Super-Grassmannians G(1|1, n|n)

   https://doi.org/10.1007/s00220-023-04769-8  

   Polishchuk, Alexander (September 2023, Communications in Mathematical Physics)