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We present a state-of-the-art prediction for cross sections of neutrino deep inelastic scattering (DIS) from nucleon at high neutrino energies, $E_{\nu }$, up to 1000 EeV ( ${10}^{12}\mathrm{GeV}$). Our calculations are based on the latest CT18 NNLO parton distribution functions (PDFs) and their associated uncertainties. To make predictions for the highest energies, we extrapolate the PDFs to small $x$according to several procedures and assumptions, thus affecting the uncertainties at ultrahigh $E_{\nu }$; we quantify the uncertainties corresponding to these choices. Similarly, we quantify the uncertainties introduced by the nuclear corrections that are required to evaluate neutrino-nuclear cross sections for the neutrino observatories. These results can be applied to currently running astrophysical neutrino observatories, such as IceCube and KM3NeT, as well as various future experiments that have been proposed. 

Abstract We study the dependence of the transverse mass distribution of charged leptons and the missing energy on parton distributions (PDFs) adapted toWboson mass measurements at the CDF and ATLAS experiments. We compare the shape variations of the distribution induced by different PDFs and find that the spread of predictions from different PDF sets can be significantly larger than the PDF uncertainty predicted by a specific PDF set. We suggest analyzing the experimental data using up-to-date PDFs to gain a better understanding of the PDF uncertainties inWboson mass measurements. We also perform a series of Lagrange multiplier scans to identify the constraints on the transverse mass distribution imposed by individual data sets in the CT18 global analysis. In the case of the CDF measurement, the distribution is mostly sensitive tod-quark PDFs in the intermediatexregion, which are largely constrained by DIS and Drell-Yan data on deuteron targets and Tevatron lepton charge asymmetry data. 

Abstract In this paper, we prove a tight minimum degree condition in general graphs for the existence of paths between two given endpoints whose lengths form a long arithmetic progression with common difference one or two. This allows us to obtain a number of exact and optimal results on cycle lengths in graphs of given minimum degree, connectivity or chromatic number. More precisely, we prove the following statements by a unified approach: 1. Every graph $$G$$ with minimum degree at least $k+1$ contains cycles of all even lengths modulo $$k$$; in addition, if $$G$$ is $$2$$-connected and non-bipartite, then it contains cycles of all lengths modulo $$k$$. 2. For all $$k\geq 3$$, every $$k$$-connected graph contains a cycle of length zero modulo $$k$$. 3. Every $$3$$-connected non-bipartite graph with minimum degree at least $k+1$ contains $$k$$ cycles of consecutive lengths. 4. Every graph with chromatic number at least $k+2$ contains $$k$$ cycles of consecutive lengths. The 1st statement is a conjecture of Thomassen, the 2nd is a conjecture of Dean, the 3rd is a tight answer to a question of Bondy and Vince, and the 4th is a conjecture of Sudakov and Verstraëte. All of the above results are best possible. 

We review progress in the global QCD analysis by the CTEQ-TEA group since the publication of CT18 parton distribution functions (PDFs) in the proton. Specifically, we discuss comparisons of CT18 NNLO predictions with the LHC 13 TeV measurements as well as with the FNAL SeaQuest and BNL STAR data on lepton pair production. The specialized CT18X PDFs approximating saturation effects are compared with the CT18sx PDFs obtained using NLL/NLO small-$$x$$ resummation. Short summaries are presented for the special CT18 parton distributions with fitted charm and with lattice QCD inputs. A recent comparative analysis of the impact of deuteron nuclear effects on the parton distributions by the CTEQ-JLab and CTEQ-TEA groups is summarized. 

Breathing biomarkers, such as breathing rate, fractional inspiratory time, and inhalation-exhalation ratio, are vital for monitoring the user's health and well-being. Accurate estimation of such biomarkers requires breathing phase detection, i.e., inhalation and exhalation. However, traditional breathing phase monitoring relies on uncomfortable equipment, e.g., chestbands. Smartphone acoustic sensors have shown promising results for passive breathing monitoring during sleep or guided breathing. However, detecting breathing phases using acoustic data can be challenging for various reasons. One of the major obstacles is the complexity of annotating breathing sounds due to inaudible parts in regular breathing and background noises. This paper assesses the potential of using smartphone acoustic sensors for passive unguided breathing phase monitoring in a natural environment. We address the annotation challenges by developing a novel variant of the teacher-student training method for transferring knowledge from an inertial sensor to an acoustic sensor, eliminating the need for manual breathing sound annotation by fusing signal processing with deep learning techniques. We train and evaluate our model on the breathing data collected from 131 subjects, including healthy individuals and respiratory patients. Experimental results show that our model can detect breathing phases with 77.33% accuracy using acoustic sensors. We further present an example use-case of breathing phase-detection by first estimating the biomarkers from the estimated breathing phases and then using these biomarkers for pulmonary patient detection. Using the detected breathing phases, we can estimate fractional inspiratory time with 92.08% accuracy, the inhalation-exhalation ratio with 86.76% accuracy, and the breathing rate with 91.74% accuracy. Moreover, we can distinguish respiratory patients from healthy individuals with up to 76% accuracy. This paper is the first to show the feasibility of detecting regular breathing phases towards passively monitoring respiratory health and well-being using acoustic data captured by a smartphone. 

Abstract Sulfur belongs among H₂O, CO₂, and Cl as one of the key volatiles in Earth’s chemical cycles. High oxygen fugacity, sulfur concentration, and δ³⁴S values in volcanic arc rocks have been attributed to significant sulfate addition by slab fluids. However, sulfur speciation, flux, and isotope composition in slab-dehydrated fluids remain unclear. Here, we use high-pressure rocks and enclosed veins to provide direct constraints on subduction zone sulfur recycling for a typical oceanic lithosphere. Textural and thermodynamic evidence indicates the predominance of reduced sulfur species in slab fluids; those derived from metasediments, altered oceanic crust, and serpentinite have δ³⁴S values of approximately −8‰, −1‰, and +8‰, respectively. Mass-balance calculations demonstrate that 6.4% (up to 20% maximum) of total subducted sulfur is released between 30–230 km depth, and the predominant sulfur loss takes place at 70–100 km with a net δ³⁴S composition of −2.5 ± 3‰. We conclude that modest slab-to-wedge sulfur transport occurs, but that slab-derived fluids provide negligible sulfate to oxidize the sub-arc mantle and cannot deliver³⁴S-enriched sulfur to produce the positive δ³⁴S signature in arc settings. Most sulfur has negative δ³⁴S and is subducted into the deep mantle, which could cause a long-term increase in the δ³⁴S of Earth surface reservoirs.