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1. Sampling Multiple Edges Efficiently

   Eden, T.; Mossel, S.; Rubinfeld, R. (January 2021, Random)

   We present a sublinear time algorithm that allows one to sample multiple edges from a distribution that is pointwise ϵ-close to the uniform distribution, in an amortized-efficient fashion. We consider the adjacency list query model, where access to a graph G is given via degree and neighbor queries. The problem of sampling a single edge in this model has been raised by Eden and Rosenbaum (SOSA 18). Let n and m denote the number of vertices and edges of G, respectively. Eden and Rosenbaum provided upper and lower bounds of Θ∗(n/ √ m) for sampling a single edge in general graphs (where O ∗(·) suppresses poly(1/ϵ) and poly(log n) dependencies). We ask whether the query complexity lower bound for sampling a single edge can be circumvented when multiple samples are required. That is, can we get an improved amortized per-sample cost if we allow a preprocessing phase? We answer in the affirmative. We present an algorithm that, if one knows the number of required samples q in advance, has an overall cost that is sublinear in q, namely, O∗(√ q · (n/ √ m)), which is strictly preferable to O∗(q · (n/ √ m)) cost resulting from q invocations of the algorithm by Eden and Rosenbaum. Subsequent to a preliminary version of this work, Tětek and Thorup (arXiv, preprint) proved that this bound is essentially optimal. 

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2. Calculating QCD Phase Diagram Trajectories of Nuclear Collisions using a Semi-analytical Model

   https://doi.org/10.1051/epjconf/202327601012  

   Mendenhall, Todd; Lin, Zi-Wei (January 2023, EPJ Web of Conferences)

   Kim, Y.; Moon, D.H. (Ed.)

   At low to moderate collision energies where the parton formation time τ F is not small compared to the nuclear crossing time, the finite nuclear thickness significantly affects the energy density ϵ( t ) and net conserved-charge densities such as the net-baryon density n B ( t ) produced in heavy ion collisions. As a result, at low to moderate energies the trajectory in the QCD phase diagram is also affected by the finite nuclear thickness. Here, we first discuss our semi-analytical model and its results on ϵ( f ), n R ( t ), n Q ( t ), and n s ( t ) in central Au+Au collisions. We then compare the T ( t ), μ B ( t ), μ Q ( t ), and μ S ( t ) extracted with the ideal gas equation of state (EoS) with quantum statistics to those extracted with a lattice QCD-based EoS. We also compare the T -μ B trajectories with the RHIC chemical freezeout data. Finally, we discuss the effect of transverse flow on the trajectories. 

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3. Characterization of Gas-Phase Native(-Like) Proteins Using Structures for Lossless Ion Manipulations

   https://doi.org/10.26434/chemrxiv-2025-xnx1z-v2  

   Lee, Jung; Gandhi, Viraj; Harrilal, Christopher; Parvate, Amar; Bhotika, Harsh; Thibert, Stephanie; Ives, Ashley; Zhang, Xin; Schenter, Gregory; Larriba-Andaluz, Carlos; et al (June 2025, Chem Arxiv)

   High resolution mobility-based ion separations in Structures for Lossless Ion Manipulations (SLIM) have been useful for ion mobility separations for a variety of molecular classes in the gas phase. Here, we present multi-pass SLIM separations for gas-phase proteins in their near-native state exhibiting charge state dependent arrival time distributions using carbonic anhydrase (29 kDa), alcohol dehydrogenase (148 kDa), and apo-transferrin (79 kDa). For the selected charge states of each protein species, we investigate the conformational space using molecular dynamic simulations and calculated the collision cross section (CCS) values using IMoS. The measured CCS values obtained from the SLIM arrival time distributions (ATDs) agreed within ~6% difference when compared to the calculated CCS values. The experimental CCS values were obtained from calibration curves for the arrival times of Agilent Tune Mix ions. For multi-pass separations, the ATDs were converted to CCS values by deconvoluting the multi-pass arrival times into accurate single-pass values amenable to the single-pass calibration curves. Mass spectra of carbonic anhydrase (CA) showed three different charge states (z = 9+ to 11+). Their corresponding mobility peaks were baseline-separated using 8-m single-pass separations. Single-pass analysis of alcohol dehydrogenase (ADH) exhibit three predominant charge states (z = 23+ to 25+) with mobility overlap between adjacent charge states. The mobility peak resolution for ADH improved with multi-pass separations (up to 24-m path length). In addition, CCS distributions obtained for charge states z = 16+ to 18+ of apo-transferrin reveal a transition from a compact unimodal form (z = 18+ and 19+) to broader multi-modal CCS distributions for z = 16+. For apo-transferrin, 40-m multi-pass separations were performed allowing for complete isolation of the selected mobility range corresponding to z = 17+ leading to selective isolation of a narrow arrival time window. The extended mobility separations provided minimal alterations to the structure of the proteins, and the experimentally derived CCS values showed minimal change as a function of separation time or number of passes. Mobility-based ion separations for native-like proteins, using SLIM, open opportunities for native-IMS applications as well as other manipulations enabled by SLIM like mobility selective isolation and collection. 

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4. Sequence modeling of higher-order wave modes of binary black hole mergers

   Tiki, Victoria; Pham, Kiet; Huerta, EA (September 2024, ArXiv)

   Higher-order gravitational wave modes from quasi-circular, spinning, non-precessing binary black hole mergers encode key information about these systems' nonlinear dynamics. We model these waveforms using transformer architectures, targeting the evolution from late inspiral through ringdown. Our data is derived from the \texttt{NRHybSur3dq8} surrogate model, which includes spherical harmonic modes up to ℓ≤4 (excluding (4,0), (4,±1) and including (5,5) modes). These waveforms span mass ratios q≤8, spin components sz1,2∈[−0.8,0.8], and inclination angles θ∈[0,π]. The model processes input data over the time interval t∈[−5000M,−100M) and generates predictions for the plus and cross polarizations, (h+,h×), over the interval t∈[−100M,130M]. Utilizing 16 NVIDIA A100 GPUs on the Delta supercomputer, we trained the transformer model in 15 hours on over 14 million samples. The model's performance was evaluated on a test dataset of 840,000 samples, achieving mean and median overlap scores of 0.996 and 0.997, respectively, relative to the surrogate-based ground truth signals. We further benchmark the model on numerical relativity waveforms from the SXS catalog, finding that it generalizes well to out-of-distribution systems, capable of reproducing the dynamics of systems with mass ratios up to q=15 and spin magnitudes up to 0.998, with a median overlap of 0.969 across 521 NR waveforms and up to 0.998 in face-on/off configurations. These results demonstrate that transformer-based models can capture the nonlinear dynamics of binary black hole mergers with high accuracy, even outside the surrogate training domain, enabling fast sequence modeling of higher-order wave modes. 

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5. Leptogenesis during an era of early SU(2) confinement

   https://doi.org/10.1103/nmpt-fwz6  

   Bhalla-Ladd, India; Ginnett, Izzy; Tait, Tim_M P (October 2025, Physical Review D)

   We explore leptogenesis during a cosmological epoch during which the electroweak $\mathrm{SU}(2{)}_L$force is confined. During weak confinement, there is only one conserved nonanomalous global charge, $r$, which is a linear combination of lepton-number, baryon-number, and hypercharge. The inclusion of heavy Majorana neutrinos leads to an $r$-charge and $CP$-violating interaction with a composite scalar, $\mathrm{\Phi }$, and composite fermions, $\mathrm{\Psi }$, allowing for the generation of an $r$-charge asymmetry, which translates into a baryon asymmetry post $\mathrm{SU}(2{)}_L$deconfinement. Determining the resulting baryon asymmetry as a function of the model parameters, we find that the predicted baryon-asymmetry can match observations for a wide swath of parameter space: a weak confinement scale ${\mathrm{\Lambda }}_W\sim {10}^{11}–{10}^{14}\mathrm{GeV}$, the sum of the Standard Model Yukawa couplings $\sum Y_{i\alpha }{Y}_{i\alpha }^{*}\sim {10}^{-2}-{10}^0$, $m_{\mathrm{\Phi }}/m_{\mathrm{\Psi }}\sim 0-0.5$, and a $\mathrm{\Phi }-\mathrm{\Psi }-\mathrm{\Psi }$coupling $\left|g\right|\sim 1$with complex phase ${\theta }_g\sim \pi /4$. While leptogenesis under the assumption of a standard cosmology relies on the complex phase of the neutrino Yukawa couplings, the asymmetry generated in this novel background cosmology primarily depends on a strong phase from $\mathrm{SU}(2{)}_L$confinement, ${\theta }_g$, and favors negligible $CP$-violation in the right-handed neutrino decays. 

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