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1. High-resolution Spectroscopy of SN 2023ixf’s First Week: Engulfing the Asymmetric Circumstellar Material

   https://doi.org/10.3847/1538-4357/acf366  

   Smith, Nathan ; Pearson, Jeniveve ; Sand, David J. ; Ilyin, Ilya ; Bostroem, K. Azalee ; Hosseinzadeh, Griffin ; Shrestha, Manisha ( October 2023 , The Astrophysical Journal)

   We present a series of high-resolution echelle spectra of SN 2023ixf in M101, obtained nightly during the first week or so after discovery using PEPSI on the Large Binocular Telescope. NaiD absorption in these spectra indicates a host reddening ofE(B−V) = 0.031 mag and a systemic velocity of +7 km s⁻¹relative to the average redshift of M101. Dramatic changes are seen in the strength and shape of strong emission lines emitted by circumstellar material (CSM), including Heiiλ4686, Civλλ5801,5811, Hα, and Nivλλ7109,7123. In general, these narrow lines broaden to become intermediate-width lines before disappearing from the spectrum within a few days, indicating a limited extent to the dense CSM of around 20–30 au (or ≲10^14.7cm). Hαpersists in the spectrum for about a week as an intermediate-width emission line with P Cyg absorption at 700–1300 km s⁻¹arising in the post-shock shell of swept-up CSM. Early narrow emission lines are blueshifted and indicate an expansion speed in the pre-shock CSM of about 115 km s⁻¹, but with even broader emission in higher-ionization lines. This is faster than the normal winds of red supergiants, suggesting some mode of eruptive mass loss from the progenitor or radiative acceleration of the CSM. A lack of narrow blueshifted absorption suggests that most of the CSM is not along our line of sight. This and several other clues indicate that the CSM of SN 2023ixf is significantly aspherical. We find that CSM lines disappear after a few days because the asymmetric CSM is engulfed by the supernova photosphere.

    

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2. Large deviation principles for lacunary sums

   https://doi.org/10.1090/tran/8788  

   Aistleitner, Christoph ; Gantert, Nina ; Kabluchko, Zakhar ; Prochno, Joscha ; Ramanan, Kavita ( October 2022 , Transactions of the American Mathematical Society)

   Let (ak)k∈N be an increasing sequence of positive integers satisfying the Hadamard gap condition a_{k+1}/a_k > q > 1 for all k ∈ N, and let S_n(ω) = \sum_{k=1}^n cos(2πa_kω), n ∈ N, ω ∈ [0, 1]. Then S_n is called a lacunary trigonometric sum, and can be viewed as a random variable defined on the probability space Ω = [0, 1] endowed with Lebesgue measure. Lacunary sums are known to exhibit several properties that are typical for sums of independent random variables. For example, a central limit theorem for (S_n)_{n∈N} has been obtained by Salem and Zygmund, while a law of the iterated logarithm is due to Erdős and Gál. In this paper we study large deviation principles for lacunary sums. Specifically, under the large gap condition ak+1/ak → ∞, we prove that the sequence (Sn/n)n∈N does indeed satisfy a large deviation principle with speed n and the same rate function I􏰡 as for sums of independent random variables with the arcsine distribution. On the other hand, we show that the large deviation principle may fail to hold when we only assume the Hadamard gap condition. However, we show that in the special case when ak = qk for some q ∈ {2, 3, . . .}, (S_n/n)_{n∈N} satisfies a large deviation principle (with speed n) and a rate function I_q that is different from I, and describe an algorithm to compute an arbitrary number of terms in the Taylor expansion of Iq . In addition, we also prove that Iq converges pointwise to I as q → ∞. Furthermore, we construct a random perturbation (a_k)_{k∈N} of the sequence (2^k)_{k∈N} for which a_{k+1}/a_k → 2 as k → ∞, but for which at the same time (S_n/n)n∈N satisfies a large deviation principle with the same rate function I as in the independent case, which is surprisingly different from the rate function I_2 one might naïvely expect. We relate this fact to the number of solutions of certain Diophantine equations. Together, these results show that large deviation principles for lacunary trigonometric sums are very sensitive to the arithmetic properties of the sequence (a_k)_{k∈N}. This is particularly noteworthy since no such arithmetic effects are visible in the central limit theorem or in the law of the iterated logarithm for lacunary trigonometric sums. Our proofs use a combination of tools from probability theory, harmonic analysis, and dynamical systems. 

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3. Lower Bounds Against Sparse Symmetric Functions of ACC Circuits: Expanding the Reach of #SAT Algorithms

   https://doi.org/10.1007/s00224-022-10106-8  

   Vyas, Nikhil ; Williams, R. Ryan ( November 2022 , Theory of Computing Systems)

   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$\mathsf {Quasi}\text {-}\mathsf {NP} = \mathsf {NTIME}[n^{(\log n)^{O(1)}}]$$\mathrm{Quasi}-\mathrm{NP}=\mathrm{NTIME}\left[n^{{\left(\log n\right)}^{O\left(1\right)}}\right]$and other complexity classes do not have small circuits (in the worst case and/or on average) from various circuit classes$\mathcal { C}$$C$, by showing that$\mathcal { C}$$C$admits non-trivial satisfiability and/or#SAT algorithms which beat exhaustive search by a minor amount. In this paper, we present a new strong lower bound consequence of having a non-trivial#SAT algorithm for a circuit class${\mathcal C}$$C$. Say that a symmetric Boolean functionf(x₁,…,x_n) issparseif it outputs 1 onO(1) values of${\sum }_{i} x_{i}$${\sum }_i{x}_i$. We show that for every sparsef, and for all “typical”$\mathcal { C}$$C$, faster#SAT algorithms for$\mathcal { C}$$C$circuits imply lower bounds against the circuit class$f \circ \mathcal { C}$$f\circ C$, which may bestrongerthan$\mathcal { C}$$C$itself. In particular:

   #SAT algorithms forn^k-size$\mathcal { C}$$C$-circuits running in 2ⁿ/n^ktime (for allk) implyNEXPdoes not have$(f \circ \mathcal { C})$$(f\circ C)$-circuits of polynomial size.

   #SAT algorithms for$2^{n^{{\varepsilon }}}$$2^{n^{\epsilon }}$-size$\mathcal { C}$$C$-circuits running in$2^{n-n^{{\varepsilon }}}$$2^{n-n^{\epsilon }}$time (for someε> 0) implyQuasi-NPdoes not have$(f \circ \mathcal { C})$$(f\circ C)$-circuits of polynomial size.

   Applying#SAT algorithms from the literature, one immediate corollary of our results is thatQuasi-NPdoes not haveEMAJ∘ACC⁰∘THRcircuits of polynomial size, whereEMAJis the “exact majority” function, improving previous lower bounds againstACC⁰[Williams JACM’14] andACC⁰∘THR[Williams STOC’14], [Murray-Williams STOC’18]. This is the first nontrivial lower bound against such a circuit class.

    

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4. [C ii] Spectral Mapping of the Galactic Wind and Starbursting Disk of M82 with SOFIA

   https://doi.org/10.3847/1538-4357/acff6e  

   Levy, Rebecca C. ; Bolatto, Alberto D. ; Tarantino, Elizabeth ; Leroy, Adam K. ; Armus, Lee ; Emig, Kimberly L. ; Herrera-Camus, Rodrigo ; Marrone, Daniel P. ; Mills, Elisabeth ; Ricken, Oliver ; et al ( November 2023 , The Astrophysical Journal)

   M82 is an archetypal starburst galaxy in the local Universe. The central burst of star formation, thought to be triggered by M82's interaction with other members in the M81 group, is driving a multiphase galaxy-scale wind away from the plane of the disk that has been studied across the electromagnetic spectrum. Here, we present new velocity-resolved observations of the [Cii] 158μm line in the central disk and the southern outflow of M82 using the upGREAT instrument on board SOFIA. We also report the first detections of velocity-resolved (ΔV= 10 km s⁻¹) [Cii] emission in the outflow of M82 at projected distances of ≈1–2 kpc south of the galaxy center. We compare the [Cii] line profiles to observations of CO and Hiand find that likely the majority (>55%) of the [Cii] emission in the outflow is associated with the neutral atomic medium. We find that the fraction of [Cii] actually outflowing from M82 is small compared to the bulk gas outside the midplane (which may be in a halo or tidal streamers), which has important implications for observations of [Cii] outflows at higher redshift. Finally, by comparing the observed ratio of the [Cii] and CO intensities to models of photodissociation regions, we estimate that the far-ultraviolet (FUV) radiation field in the disk is ∼10^3.5G₀, in agreement with previous estimates. In the outflow, however, the FUV radiation field is 2–3 orders of magnitudes lower, which may explain the high fraction of [Cii] arising from the neutral medium in the wind.

    

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5. The Reactivity of Ambident Nucleophiles: Marcus Theory or Hard and Soft Acids and Bases Principle?

   https://doi.org/10.1002/jcc.26052  

   Wang, Yi‐Gui ; Barnes, Ericka C. ; Kaya, Savaș ; Sharma, Vinit ( August 2019 , Journal of Computational Chemistry)

   The model reactions CH₃X + (NH—CH=O)M ➔ CH₃—NH—NH═O or NH═CH—O—CH₃ + MX (M = none, Li, Na, K, Ag, Cu; X = F, Cl, Br) are investigated to demonstrate the feasibility of Marcus theory and the hard and soft acids and bases (HSAB) principle in predicting the reactivity of ambident nucleophiles. The delocalization indices (DI) are defined in the framework of the quantum theory of atoms in molecules (QT‐AIM), and are used as the scale of softness in the HSAB principle. To react with the ambident nucleophile NH═CH—O⁻, the carbocation H₃C⁺from CH₃X (F, Cl, Br) is actually a borderline acid according to the DI values of the forming C…N and C…O bonds in the transition states (between 0.25 and 0.49), while the counter ions are divided into three groups according to the DI values of weak interactions involving M (M…X, M…N, and M…O): group I (M = none, and Me₄N) basically show zero DI values; group II species (M = Li, Na, and K) have noticeable DI values but the magnitudes are usually less than 0.15; and group III species (M = Ag and Cu(I)) have significant DI values (0.30–0.61). On a relative basis, H₃C⁺is a soft acid with respect to group I and group II counter ions, and a hard acid with respect to group III counter ions. Therefore, N‐regioselectivity is found in the presence of group I and group II counter ions (M = Me₄N, Li, Na, K), while O‐regioselectivity is observed in the presence of the group III counter ions (M = Ag, and Cu(I)). The hardness of atoms, groups, and molecules is also calculated with new functions that depend on ionization potential (I) and electron affinity (A) and use the atomic charges obtained from localization indices (LI), so that the regioselectivity is explained by the atomic hardness of reactive nitrogen atoms in the transition states according to the maximum hardness principle (MHP). The exact Marcus equation is derived from the simple harmonic potential energy parabola, so that the concepts of activation free energy, intrinsic activation barrier, and reaction energy are completely connected. The required intrinsic activation barriers can be either estimated fromab initiocalculations on reactant, transition state, and product of the model reactions, or calculated from identity reactions. The counter ions stabilize the reactant through bridging N‐ and O‐site of reactant of identity reactions, so that the intrinsic barriers for the salts are higher than those for free ambident anions, which is explained by the increased reorganization parameter Δr. The proper application of Marcus theory should quantitatively consider all three terms of Marcus equation, and reliably represent the results with potential energy parabolas for reactants and all products. For the model reactions, both Marcus theory and HSAB principle/MHP principle predict the N‐regioselectivity when M = none, Me₄N, Li, Na, K, and the O‐regioselectivity when M = Ag and Cu(I). © 2019 Wiley Periodicals, Inc.

    

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