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1. Peeling from a liquid

   https://doi.org/10.1039/D3SM00487B  

   Kumar, Deepak; Zhou, Nuoya; Brau, Fabian; Menon, Narayanan; Davidovitch, Benny (October 2023, Soft Matter)

   We establish the existence of a cusp in the curvature of a solid sheet at its contact with a liquid subphase. 

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2. Learning a manifold from a teacher’s demonstrations

   Wang, P.; Givchi, A.; Shafto, P. (January 2020, NeurIPS workshop: TDA and beyond)

   null (Ed.)
3. QCD challenges from pp to A–A collisions

   https://doi.org/10.1140/epja/s10050-020-00270-1  

   Adolfsson, J.; Andronic, A.; Bierlich, C.; Bozek, P.; Chakraborty, S.; Christiansen, P.; Chinellato, D. D.; Fries, R. J.; Gustafson, G.; van Hees, H.; et al (November 2020, The European Physical Journal A)

   null (Ed.)

   Abstract This paper is a write-up of the ideas that were presented, developed and discussed at the third International Workshop on QCD Challenges from pp to A–A, which took place in August 2019 in Lund, Sweden (Workshop link: https://indico.lucas.lu.se/event/1214/ ). The goal of the workshop was to focus on some of the open questions in the field and try to come up with concrete suggestions for how to make progress on both the experimental and theoretical sides. The paper gives a brief introduction to each topic and then summarizes the primary results. 

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4. Determining a local Hamiltonian from a single eigenstate

   https://doi.org/10.22331/q-2019-07-08-159  

   Qi, Xiao-Liang; Ranard, Daniel (July 2019, Quantum)

   null (Ed.)

   We ask whether the knowledge of a single eigenstate of a local Hamiltonian is sufficient to uniquely determine the Hamiltonian. We present evidence that the answer is ``yes" for generic local Hamiltonians, given either the ground state or an excited eigenstate. In fact, knowing only the two-point equal-time correlation functions of local observables with respect to the eigenstate should generically be sufficient to exactly recover the Hamiltonian for finite-size systems, with numerical algorithms that run in a time that is polynomial in the system size. We also investigate the large-system limit, the sensitivity of the reconstruction to error, and the case when correlation functions are only known for observables on a fixed sub-region. Numerical demonstrations support the results for finite one-dimensional spin chains (though caution must be taken when extrapolating to infinite-size systems in higher dimensions). For the purpose of our analysis, we define the `` k -correlation spectrum" of a state, which reveals properties of local correlations in the state and may be of independent interest. 

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5. CUTTING A PART FROM MANY MEASURES

   https://doi.org/10.1017/fms.2019.33  

   BLAGOJEVIĆ, PAVLE V.; PALIĆ, NEVENA; SOBERÓN, PABLO; ZIEGLER, GÜNTER M. (January 2019, Forum of Mathematics, Sigma)

   Holmsen, Kynčl and Valculescu recently conjectured that if a finite set $$X$$ with $$\ell n$$ points in $$\mathbb{R}^{d}$$ that is colored by $$m$$ different colors can be partitioned into $$n$$ subsets of $$\ell$$ points each, such that each subset contains points of at least $$d$$ different colors, then there exists such a partition of $$X$$ with the additional property that the convex hulls of the $$n$$ subsets are pairwise disjoint. We prove a continuous analogue of this conjecture, generalized so that each subset contains points of at least $$c$$ different colors, where we also allow $$c$$ to be greater than $$d$$ . Furthermore, we give lower bounds on the fraction of the points each of the subsets contains from $$c$$ different colors. For example, when $$n\geqslant 2$$ , $$d\geqslant 2$$ , $$c\geqslant d$$ with $$m\geqslant n(c-d)+d$$ are integers, and $$\unicode[STIX]{x1D707}_{1},\ldots ,\unicode[STIX]{x1D707}_{m}$$ are $$m$$ positive finite absolutely continuous measures on $$\mathbb{R}^{d}$$ , we prove that there exists a partition of $$\mathbb{R}^{d}$$ into $$n$$ convex pieces which equiparts the measures $$\unicode[STIX]{x1D707}_{1},\ldots ,\unicode[STIX]{x1D707}_{d-1}$$ , and in addition every piece of the partition has positive measure with respect to at least $$c$$ of the measures $$\unicode[STIX]{x1D707}_{1},\ldots ,\unicode[STIX]{x1D707}_{m}$$ . 

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