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1. The spectrum of marginally-deformed $$ \mathcal{N} $$ = 2 CFTs with AdS4 S-fold duals of type IIB

   https://doi.org/10.1007/JHEP12(2021)214  

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

   A bstract A holographic duality was recently established between an $$ \mathcal{N} $$ N = 4 non-geometric AdS 4 solution of type IIB supergravity in the so-called S-fold class, and a three- dimensional conformal field theory (CFT) defined as a limit of $$ \mathcal{N} $$ N = 4 super-Yang-Mills at an interface. Using gauged supergravity, the $$ \mathcal{N} $$ N = 2 conformal manifold (CM) of this CFT has been assessed to be two-dimensional. Here, we holographically characterise the large- N operator spectrum of the marginally-deformed CFT. We do this by, firstly, providing the algebraic structure of the complete Kaluza-Klein (KK) spectrum on the associated two-parameter family of AdS4 solutions. And, secondly, by computing the $$ \mathcal{N} $$ N = 2 super-multiplet dimensions at the first few KK levels on a lattice in the CM, using new exceptional field theory techniques. Our KK analysis also allows us to establish that, at least at large N , this $$ \mathcal{N} $$ N = 2 CM is topologically a non-compact cylindrical Riemann surface bounded on only one side. 

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2. 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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3. Weak and strong solutions for a fluid‐poroelastic‐structure interaction via a semigroup approach

   https://doi.org/10.1002/mma.10533  

   Avalos, George; Gurvich, Elena; Webster, Justin_T (October 2024, Mathematical Methods in the Applied Sciences)

   A filtration system comprising a Biot poroelastic solid coupled to an incompressible Stokes free‐flow is considered in 3D. Across the flat 2D interface, the Beavers‐Joseph‐Saffman coupling conditions are taken. In the inertial, linear, and non‐degenerate case, the hyperbolic‐parabolic coupled problem is posed through a dynamics operator on a chosen energy space, adapted from Stokes‐Lamé coupled dynamics. A semigroup approach is utilized to circumvent issues associated to mismatched trace regularities at the interface. The generation of a strongly continuous semigroup for the dynamics operator is obtained via a non‐standard maximality argument. The latter employs a mixed‐variational formulation in order to invoke the Babuška‐Brezzi theorem. The Lumer‐Philips theorem then yields semigroup generation, and thereby, strong and generalized solutions are obtained. For the linear dynamics, density obtains the existence of weak solutions; we extend to the case where the Biot compressibility of constituents degenerates. Thus, for the inertial linear Biot‐Stokes filtration system, we provide a clear elucidation of strong solutions and a construction of weak solutions, as well as their regularity through associated estimates. 

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4. High- χ , low- N micelles from partially perfluorinated block polymers

   https://doi.org/10.1039/d2sm00513a  

   Williams, Eric R.; van den Bergh, Wessel; Stefik, Morgan (October 2022, Soft Matter)

   Kinetically trapped (“persistent”) micelles enable emerging applications requiring a constant core diameter. Preserving a χN barrier to chain exchange with low- N requires a commensurately higher χ core–solvent for micelle persistence. Low- N , high- χ micelles containing fluorophobic interactions were studied using poly(ethylene oxide- b -perfluorooctyl acrylate)s (O 45 F X , x = 8, 11) in methanolic solutions. DLS analysis of micelles revealed chain exchange only for O 45 F 8 while SAXS analysis suggested elongated core block conformations commensurate with the contour lengths. Micelle chain exchange from solution perturbations were examined by characterizing their behavior as templates for inorganic materials via SAXS and SEM. In contrast to the F 8 analog, the larger χN barrier for the O 45 F 11 enabled persistent micelle behavior in both thin films and bulk samples despite the low T g micelle core. Careful measures of micelle core diameters and pore sizes revealed that the nanoparticle distribution extended through the corona and 0.52 ± 0.15 nm into the core–corona interface, highlighting thermodynamics favoring both locations simultaneously. 

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5. Learning Proximal Operators to Discover Multiple Optima

   Li, Lingxiao; Aigerman, Noam; Kim, Vladimir; Li, Jiajin; Greenewald, Kristjan; Yurochkin, Mikhail; Solomon, Justin (May 2023, International Conference on Learning Representations)

   Finding multiple solutions of non-convex optimization problems is a ubiquitous yet challenging task. Most past algorithms either apply single-solution optimization methods from multiple random initial guesses or search in the vicinity of found solutions using ad hoc heuristics. We present an end-to-end method to learn the proximal operator of a family of training problems so that multiple local minima can be quickly obtained from initial guesses by iterating the learned operator, emulating the proximal-point algorithm that has fast convergence. The learned proximal operator can be further generalized to recover multiple optima for unseen problems at test time, enabling applications such as object detection. The key ingredient in our formulation is a proximal regularization term, which elevates the convexity of our training loss: by applying recent theoretical results, we show that for weakly-convex objectives with Lipschitz gradients, training of the proximal operator converges globally with a practical degree of over-parameterization. We further present an exhaustive benchmark for multi-solution optimization to demonstrate the effectiveness of our method. 

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