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Free, publiclyaccessible full text available July 1, 2024

Abstract We continue the program of proving circuit lower bounds via circuit satisfiability algorithms. So far, this program has yielded several concrete results, proving that functions in
and other complexity classes do not have small circuits (in the worst case and/or on average) from various circuit classes$\mathsf {Quasi}\text {}\mathsf {NP} = \mathsf {NTIME}[n^{(\log n)^{O(1)}}]$ $\mathrm{Quasi}\mathrm{NP}=\mathrm{NTIME}\left[{n}^{{\left(\mathrm{log}n\right)}^{O\left(1\right)}}\right]$ , by showing that$\mathcal { C}$ $C$ admits nontrivial satisfiability and/or$\mathcal { C}$ $C$# SAT algorithms which beat exhaustive search by a minor amount. In this paper, we present a new strong lower bound consequence of having a nontrivial# SAT algorithm for a circuit class . Say that a symmetric Boolean function${\mathcal C}$ $C$f (x _{1},…,x _{n}) issparse if it outputs 1 onO (1) values of . We show that for every sparse${\sum }_{i} x_{i}$ ${\sum}_{i}{x}_{i}$f , and for all “typical” , faster$\mathcal { C}$ $C$# SAT algorithms for circuits imply lower bounds against the circuit class$\mathcal { C}$ $C$ , which may be$f \circ \mathcal { C}$ $f\circ C$stronger than itself. In particular:$\mathcal { C}$ $C$# SAT algorithms forn ^{k}size circuits running in 2^{n}/$\mathcal { C}$ $C$n ^{k}time (for allk ) implyN E X P does not have circuits of polynomial size.$(f \circ \mathcal { C})$ $(f\circ C)$# SAT algorithms for size$2^{n^{{\varepsilon }}}$ ${2}^{{n}^{\epsilon}}$ circuits running in$\mathcal { C}$ $C$ time (for some$2^{nn^{{\varepsilon }}}$ ${2}^{n{n}^{\epsilon}}$ε > 0) implyQ u a s i N P does not have circuits of polynomial size.$(f \circ \mathcal { C})$ $(f\circ C)$Applying
# SAT algorithms from the literature, one immediate corollary of our results is thatQ u a s i N P does not haveE M A J ∘A C C ^{0}∘T H R circuits of polynomial size, whereE M A J is the “exact majority” function, improving previous lower bounds againstA C C ^{0}[Williams JACM’14] andA C C ^{0}∘T H R [Williams STOC’14], [MurrayWilliams STOC’18]. This is the first nontrivial lower bound against such a circuit class. 
ABSTRACT We present early spectral observations of the very slow Galactic nova Gaia22alz, over its gradual rise to peak brightness that lasted 180 d. During the first 50 d, when the nova was only 3–4 mag above its normal brightness, the spectra showed narrow (FWHM ≈ 400 km s−1) emission lines of H Balmer, He i, He ii, and C iv but no P Cygni absorption. A few weeks later, the highexcitation He ii and C iv lines disappeared, and P Cygni profiles of Balmer, He i, and eventually Fe ii lines emerged, yielding a spectrum typical of classical novae before peak. We propose that the early (first 50 d) spectra of Gaia22alz, particularly the emission lines with no P Cygni profiles, are produced in the white dwarf’s optically thin envelope or accretion disc, reprocessing ultraviolet and potentially Xray emission from the white dwarf after a dramatic increase in the rate of thermonuclear reactions, during a phase known as the ‘early Xray/UV flash’. If true, this would be one of the rare times that the optical signature of the early Xray/UV flash has been detected. While this phase might last only a few hours in other novae and thus be easily missed, it was possible to detect in Gaia22alz due to its very slow and gradual rise and thanks to the efficiency of new allsky surveys in detecting transients on their rise. We also consider alternative scenarios that could explain the early spectral features of Gaia22alz and its gradual rise.

Naor, Seffi ; Buchbinder, Niv (Ed.)

Abstract Progressive cementation and sealing of faultlocalized fractures impact crustal mass transport and the recovery of fault strength following slip events. We use discrete fracture network (DFN) models to examine how fracture sealing during endmember cementation mechanisms (i.e., reaction versus transportedlimited cementation) influences the partitioning of fluid flow through time. DfnWorks was used to generate randomized fracture networks parameterized with fracture orientation data compiled from field studies. Singlephase flow simulations were performed for each network over a series of timesteps, and network parameters were modified to reflect progressive fracture sealing consistent with either reaction or transportlimited crystal growth. Results show that when fracture cementation is reactionlimited, fluid flow becomes progressively channelized into a smaller number of fractures with larger apertures. When fracture cementation is transportlimited, fluid flow experiences progressive dechannelization, becoming more homogeneously distributed throughout the fracture network. These behaviors are observed regardless of the DFN parameterization, suggesting that the effect is an intrinsic component of all fracture networks subjected to the endmember cementation mechanisms. These results have firstorder implications for the spatial distribution of fluid flow in fractured rocks and recovery of permeability and strength during fault/fracture healing in the immediate aftermath of fault slip.