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1. Free fermions revisited

   https://doi.org/10.1142/S0219498826502695  

   Milas, Antun; Penn, Michael (June 2025, Journal of Algebra and Its Applications)

   Free fermion vertex superalgebras are discussed from the point of view of Urod vertex algebras [T. Arakawa, T. Creutzig and B. Feigin, Urod algebras and translation of [Formula: see text]-algebras, Forum Mathematics Sigma, Vol. 10 (Cambridge University Press, 2022) and M. Bershtein, B. Feigin and A. Litvinov, Coupling of two conformal field theories and Nakajima–Yoshioka blow-up equations, preprint (2013), arXiv:1310.7281]. We present all finite decompositions of the [Formula: see text]-fermion vertex algebra via Virasoro and [Formula: see text] superconformal vertex algebras. We also present decompositions of higher rank fermion algebras using affine [Formula: see text]-algebras, and a conjecture on the existence of the “square root” of the [Formula: see text] fermion algebra. 

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2. On the Maximum F‐Free Induced Subgraphs in Kt‐Free Graphs

   https://doi.org/10.1002/rsa.21273  

   Balogh, József; Chen, Ce; Luo, Haoran (January 2025, Random Structures & Algorithms)

   ABSTRACT For graphs and , let be the minimum possible size of a maximum ‐free induced subgraph in an ‐vertex ‐free graph. This notion generalizes the Ramsey function and the Erdős–Rogers function. Establishing a container lemma for the ‐free subgraphs, we give a general upper bound on , assuming the existence of certain locally dense ‐free graphs. In particular, we prove that for every graph with , where , we have For the cases where is a complete multipartite graph, letting , we prove that We also make an observation which improves the bounds of by a polylogarithmic factor. 

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3. Gas‐free initiation for free‐radical frontal polymerization through charge transfer complexes

   https://doi.org/10.1002/pol.20240335  

   Gary, Daniel P; Al_Mahmud, Md Abdullah; Dawson, Madison G; Pojman, John A (September 2024, Journal of Polymer Science)

   Abstract Frontal polymerization is a process in which a localized reaction zone propagates through the coupling of thermal transport and the Arrhenius kinetics of exothermic polymerization. Most initiators that have been used produce volatile by‐products, which create bubbles and voids. Tetraalkyl ammonium persulfates have been used but these require synthesis and do not have long shelf lives. A charge transfer complex (CTC) composed of an iodonium salt, and a phosphine compound has been identified as a gas‐free initiator for free‐radical thermal frontal polymerization. This CTC has 4‐(dimethylamino)phenyldiphenly phophine (DMAPDP) as the donor and p‐(octyloxyphenyl)phenyliodonium hexafluoroantimonate as the acceptor (IOC‐8). The CTC was tested with several acrylates, and all were found to support bubble‐free fronts. We determined the CTC mole ratio for some monomers at which the front velocity reaches a plateau. 

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4. Scale-free behavioral dynamics directly linked with scale-free cortical dynamics

   https://doi.org/10.7554/eLife.79950  

   Jones, Sabrina A; Barfield, Jacob H; Norman, V Kindler; Shew, Woodrow L (January 2023, eLife)

   Naturally occurring body movements and collective neural activity both exhibit complex dynamics, often with scale-free, fractal spatiotemporal structure. Scale-free dynamics of both brain and behavior are important because each is associated with functional benefits to the organism. Despite their similarities, scale-free brain activity and scale-free behavior have been studied separately, without a unified explanation. Here, we show that scale-free dynamics of mouse behavior and neurons in the visual cortex are strongly related. Surprisingly, the scale-free neural activity is limited to specific subsets of neurons, and these scale-free subsets exhibit stochastic winner-take-all competition with other neural subsets. This observation is inconsistent with prevailing theories of scale-free dynamics in neural systems, which stem from the criticality hypothesis. We develop a computational model which incorporates known cell-type-specific circuit structure, explaining our findings with a new type of critical dynamics. Our results establish neural underpinnings of scale-free behavior and clear behavioral relevance of scale-free neural activity. 

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5. Free-energy orbital-free density functional theory: recent developments, perspective, and outlook

   https://doi.org/10.1088/2516-1075/adadd4  

   Karasiev, Valentin_V; Hilleke, Katerina_P; Trickey, Samuel_B (January 2025, Electronic Structure)

   Abstract By summarizing the constraint-based development of orbital-free free-energy density functional approximations, we provide a perspective on progress over the last 15 years, the limitations of existing functionals, and the challenges awaiting resolution. We outline the chronology of the development of non-interacting and exchange-correlation free-energy orbital-free functionals and summarize the theoretical basis of existing local density approximation (LDA), second-order approximation, generalized gradient approximation (GGA), and meta-GGAs. We discuss limitations and challenges such as problems with thermodynamic derivatives, free-energy nonadditivity and the closely related issue of all-electron versus valence-only local pseudo-potential performance. 

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