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For every $n \geq 2$, let $K_k^n$ denote the hyperspace of all $k$-dimensional closed convex subsets of the Euclidean space $R^n$ endowed with the Atouch-Wets topology. Let $ K_{k,b}^n$ be the subset of $K_k^n$ consisting of all $k$-dimensional compact convex subsets. In this paper we explore the topology of $K_k^n$ and $K_{k,b}^n$ and the relation of these hyperspaces with the Grassmann manifold $G_k(n)$. We prove that both $K_k^n$ and $K_{k,b}^n$ are Hilbert cube manifolds with a fiber bundle structure over $G_k(n)$. We also show that the fiber of $K_{k,b}^n$ with respect to this fiber bundle structure is homeomorphic with $\mathbb R^{\frac{k(k+1)+2n}{2}}\times Q$, where $Q$ stands for the Hilbert cube.

This article benchmarked the ability of OpenAI's GPTs and a number of open-source LLMs to perform annotation tasks on political content. We used a novel protest event dataset comprising more than three million digital interactions and created a gold standard that includes ground-truth labels annotated by human coders about toxicity and incivility on social media. We included in our benchmark Google's Perspective algorithm, which, along with GPTs, was employed throughout their respective APIs while the open-source LLMs were deployed locally. The findings show that Perspective API using a laxer threshold, GPT-4o, and Nous Hermes 2 Mixtral outperform other LLM's zero-shot classification annotations. In addition, Nous Hermes 2 and Mistral OpenOrca, with a smaller number of parameters, are able to perform the task with high performance, being attractive options that could offer good trade-offs between performance, implementing costs and computing time. Ancillary findings using experiments setting different temperature levels show that although GPTs tend to show not only excellent computing time but also overall good levels of reliability, only open-source LLMs ensure full reproducibility in the annotation., Comment: Paper prepared for delivery at the 8th Monash-Warwick-Zurich Text-as-Data Workshop, September 16-17, 2024: 11 pages, 3 tables, 3 figures

We report the first ab initio, non-relativistic QED method that couples light and matter self-consistently beyond the electric dipole approximation and without multipolar truncations. This method is based on an extension of the Maxwell-Pauli-Kohn-Sham approach to a full minimal coupling Hamiltonian, where the space- and time-dependent vector potential is coupled to the matter system, and its back-reaction to the radiated fields is generated by the full current density. The implementation in the open-source Octopus code is designed for massively-parallel multiscale simulations considering different grid spacings for the Maxwell and matter subsystems. Here, we show the first applications of this framework to simulate renormalized Cherenkov radiation of an electronic wavepacket, magnetooptical effects with non-chiral light in non-chiral molecular systems, and renormalized plasmonic modes in a nanoplasmonic dimer. We show that in some cases the beyond-dipole effects can not be captured by a multipolar expansion Hamiltonian in the length gauge. Finally, we discuss further opportunities enabled by the framework in the field of twisted light and orbital angular momentum, inelastic light scattering and strong field physics., Comment: 31 pages, 9 figures, supporting information appended

This is an index of the contributions by the Giant Radio Array for Neutrino Detection (GRAND) Collaboration to the 10th International Workshop on Acoustic and Radio EeV Neutrino Detection Activities (ARENA 2024, University of Chicago, June 11-14, 2024). The contributions include an overview of GRAND in its present and future incarnations, methods of radio-detection that are being developed for them, and ongoing joint work between the GRAND and BEACON experiments., Comment: Note: To access the list of contributions, please follow the "HTML" link that can be found on the arXiv page

Neutrinos at ultrahigh energies can originate both from interactions of cosmic rays at their acceleration sites and through cosmic-ray interactions as they propagate through the universe. These neutrinos are expected to have a low flux which drives the need for instruments with large effective areas. Radio observations of the inclined air showers induced by tau neutrino interactions in rock can achieve this, because radio waves can propagate essentially unattenuated through the hundreds of kilometers of atmosphere. Proposed arrays for radio detection of tau neutrinos focus on either arrays of inexpensive receivers distributed over a large area, the GRAND concept, or compact phased arrays on elevated mountains, the BEACON concept, to build up a large detector area with a low trigger threshold. We present a concept that combines the advantages of these two approaches with a trigger driven by phased arrays at a moderate altitude (1 km) and sparse, high-gain outrigger receivers for reconstruction and background rejection. We show that this design has enhanced sensitivity at 100 PeV over the two prior designs with fewer required antennas and discuss the need for optimized antenna designs., Comment: ARENA2024 Conference Proceeding PoS(ARENA2024)058

In this work we explore theoretically whether a parity-violating/chiral light-matter interaction is required to capture all relevant aspects of chiral polaritonics or if a parity-conserving/achiral theory is sufficient (e.g. long-wavelength/dipole approximation). This question is non-trivial to answer, since achiral theories (Hamiltonians) still possess chiral solutions. To elucidate this fundamental theoretical question, a simple GaAs quantum ring model is coupled to an effective chiral mode of a single-handedness optical cavity in dipole approximation. The bare matter GaAs quantum ring possesses a non-degenerate ground state and a doubly degenerate first excited state. The chiral or achiral nature (superpositions) of the degenerate excited state remains undetermined for an isolated matter system. However, inside our parity-conserving description of a chiral cavity, we find that the dressed eigenstates automatically (ab-initio) attain chiral character and become energetically discriminated based on the handedness of the cavity. In contrast, the non-degenerate bare matter state (ground state) does not show an energetic discrimination inside a chiral cavity within dipole approximation. Nevertheless, our results suggest that the handedness of the cavity can still be imprinted onto these states (e.g. angular momentum and chiral current densities). Overall, above findings highlight the relevance of degenerate states in chiral polaritonics. In particularly because recent theoretical results indicate the formation of a frustrated and highly-degenerate electronic ground-state under collective strong coupling conditions, which thus might be prone to chiral symmetry breaking effects.

Time-of-flight measurements of high-energy astrophysical neutrinos can be used to probe Lorentz invariance, a pillar of modern physics. If Lorentz-invariance violation (LIV) occurs, it could cause neutrinos to slow down, with the delay scaling linearly or quadratically with their energy. We introduce non-parametric statistical methods designed to detect LIV-induced distortions in the temporal structure of a high-energy neutrino flare as it travels to Earth from a distant astrophysical source, independently of the intrinsic timing properties of the source. Our approach, illustrated using the 2014/2015 TeV-PeV neutrino flare from the blazar TXS 0506+056 detected by IceCube, finds that the LIV energy scale must exceed 10^{14} GeV (linear) or 10^9 GeV (quadratic). Our methods provide a robust means to investigate LIV by focusing solely on a neutrino flare, without relying on electromagnetic counterparts, and account for realistic energy and directional uncertainties. For completeness, we compare our limits inferred from TXS 0506+056 to the sensitivity inferred from multi-messenger detection of tentative coincidences between neutrinos and electromagnetic emission from active galactic nuclei and tidal disruption events., Comment: 16 pages, 7 figures, plus an appendix

The operation of upcoming ultra-high-energy cosmic-ray, gamma-ray, and neutrino radio-detection experiments, like the Giant Radio Array for Neutrino Detection (GRAND), poses significant computational challenges involving the production of numerous simulations of particle showers and their detection, and a high data throughput. GRANDlib is an open-source software tool designed to meet these challenges. Its primary goal is to perform end-to-end simulations of the detector operation, from the interaction of ultra-high-energy particles, through -- by interfacing with external air-shower simulations -- the ensuing particle shower development and its radio emission, to its detection by antenna arrays and its processing by data-acquisition systems. Additionally, GRANDlib manages the visualization, storage, and retrieval of experimental and simulated data. We present an overview of GRANDlib to serve as the basis of future GRAND analyses., Comment: 11 pages, 9 figures, plus appendices

We give examples of Anosov actions of $\mathbb{Z}^2$ on the $d$-torus $T^d$ that cannot be homotoped to a smooth action on $T^d\#\Sigma$, for certain exotic $d$-spheres $\Sigma$. This is deduced using work of Krannich, Kupers, and the authors that, in particular, computes the mapping class group of $T^d\#\Sigma$., Comment: 5 pages

This study proposes a simple and novel class of stretch-limiting constitutive relations for perfectly flexible elastic strings drawing from modern advances in constitutive theory for elastic bodies. We investigate strings governed by constitutive relations where stretch is a bounded, piecewise linear function of tension, extending beyond the traditional Cauchy elasticity framework. Our analysis includes explicit solutions for both catenaries and longitudinal, piecewise constant stretched motions., Comment: 13 pages, 2 figures

We performed numerical simulations of the common envelope (CE) interaction between two intermediate-mass asymptotic giant branch (AGB) stars and their low-mass companions. For the first time, formation and growth of dust in the envelope is calculated explicitly. We find that the first dust grains appear as early as $\sim$1-3 yrs after the onset of the CE, and are smaller than grains formed later. As the simulations progress, a high-opacity dusty shell forms, resulting in the CE photosphere being up to an order of magnitude larger than it would be without the inclusion of dust. At the end of the simulations, the total dust yield is $0.0082~M_{\odot}$ ($0.022~M_{\odot}$) for a CE with a $1.7~M_{\odot}$ ($3.7~M_{\odot}$) AGB star. Dust formation does not substantially lead to more mass unbinding or substantially alter the orbital evolution., Comment: 6 pages, 6 figures, contributed talk to the Proceedings IAU Symposium No. 384

We consider a Froeschl\'e map and we add a weak dissipation of the form $\lambda(\varepsilon) = 1- \varepsilon^3$, where $\varepsilon$ is the parameter of perturbation. We compute formal expansions of lower dimensional tori, both in the conservative and weakly dissipatives cases, and use them to estimate the shape of their domains of analyticity as functions of $\varepsilon$. Our results support conjectures in the literature., Comment: 16 pages, 5 Figures, 2 Tables

In this work we prove that the initial value problem (IVP) for the fifth order Korteweg-de Vries equation \begin{align*} \left. \begin{array}{rlr} u_t+\partial_x^5 u+u\partial_x u&\hspace{-2mm}=0,&\quad x\in\mathbb R,\; t>0,\\ u(x,0)&\hspace{-2mm}=u_0(x),& \end{array} \right\} \end{align*} has a unique local solution in time in the Bourgain spaces $X^{s,b}$ for appropriate values of $s$ and $b$. Besides we prove a regularity property concerning the nonlinear part of that solution. Finally, using the previous property we establish a dispersive blow-up result for global in time solutions of this IVP.

Many particles predicted by extensions of the Standard Model feature interactions with neutrinos, e.g., Majoron-like bosons $\phi$. If the mass of $\phi$ is larger than about 10 keV, they can be produced abundantly in the core of the next galactic core-collapse supernova through neutrino coalescence, and leave it with energies of around 100 MeV. Their subsequent decay to high-energy neutrinos and anti-neutrinos provides a distinctive signature at Earth. Ongoing and planned neutrino and dark matter experiments allow us to reconstruct the energy, flavor, and time of arrival of these high-energy neutrinos. For the first time, we show that these measurements can help pinpointing the mass of $\phi$ and its couplings to neutrinos of different flavor. Our results can be generalized in a straightforward manner to other hypothetical feebly interacting particles, like novel gauge bosons or heavy neutral leptons, that decay into neutrinos., Comment: 38 pages, 7 figures

This work is devoted to study the relation between regularity and decay for solutions of the two-dimensional modified Zakharov-Kuznetsov equation in the weighted Sobolev spaces $Z_{s,(r_1,r_2)}:=H^s(\R^2)\cap L^2((1+|x|^{2r_1}+|y|^{2r_2})dxdy)$.

Since neutrinos have mass differences, they could decay into one another. But their lifetimes are likely long, even when shortened by new physics, so decay likely impacts neutrinos only during long trips. This makes high-energy astrophysical neutrinos, traveling for up to billions of light-years, sensitive probes of decay. However, their sensitivity must be tempered by reality. We derive from them thorough bounds on the neutrino lifetimes accounting for critical astrophysical unknowns and the nuances of neutrino detection. Using the diffuse neutrino flux, we disfavor lifetimes $\tau \lesssim 20$-450 s $(m/{\rm eV})$, based on present IceCube data, and forecast factor-of-10 improvements by upcoming detectors. Using, for the first time, neutrinos from the active galaxy NGC 1068, extant unknowns preclude placing lifetime bounds today, but upcoming detectors could disfavor $\tau \sim 100$-5000 s $(m/{\rm eV})$., Comment: 20 pages, 6 figures, 2 tables, plus appendices

Anticipating the strategies of potential attackers is crucial for protecting critical infrastructure. We can represent the challenge of the defenders of such infrastructure as a Stackelberg security game. The defender must decide how to allocate limited resources to protect specific targets, aiming to maximize their expected utility (such as minimizing the extent of damage) and considering that attackers will respond in a way that is most advantageous to them. We present novel valid inequalities to find a Strong Stackelberg Equilibrium in both Stackelberg games and Stackelberg security games. We also consider a Stackelberg security game that aims to protect targets with a defined budget. We use branch-and-price in this game to show that our approach outperforms the standard formulation in the literature, and we conduct an extensive computational study to analyze the impact of various branch-and-price parameters on the performance of our method in different game settings.

Encompassing regions that were amongst the first inhabited by humans following the out-of-Africa expansion, hosting populations with the highest levels of archaic hominid introgression, and including Pacific islands that are the most isolated inhabited locations on the planet, Oceania has a rich, but understudied, human genomic landscape. Here we describe the first region-wide analysis of genome-wide data from population groups spanning Oceania and its surroundings, from island and peninsular southeast Asia to Papua New Guinea, east across the Pacific through Melanesia, Micronesia, and Polynesia, and west across the Indian Ocean to related island populations in the Andamans and Madagascar. In total we generate and analyze genome-wide data from 981 individuals from 92 different populations, 58 separate islands, and 30 countries, representing the most expansive study of Pacific genetics to date. In each sample we disentangle the Papuan and more recent Austronesian ancestries, which have admixed in various proportions across this region, using ancestry-specific analyses, and characterize the distinct patterns of settlement, migration, and archaic introgression separately in these two ancestries. We also focus on the patterns of clinically relevant genetic variation across Oceania--a landscape rippled with strong founder effects and island-specific genetic drift in allele frequencies--providing an atlas for the development of precision genetic health strategies in this understudied region of the world.

In this work we prove that the initial-boundary value problem (IBVP) for the fifth order Korteweg-de Vries equation \begin{align*} \left. \begin{array}{rlr} u_t+\partial_x^5 u+u\partial_x u&\hspace{-2mm}=0,&\quad x\in\mathbb R^+,\; t\in\mathbb R^+,\\ u(x,0)&\hspace{-2mm}=g(x),&\\ u(0,t)=h_1(t),\, \partial_x u(0,t)&\hspace{-2mm}=h_2(t),\,\partial_x^2 u(0,t)=h_3(t), \end{array} \right\} \end{align*} is locally well posed, when the data $g$, $h_1$, $h_2$, $h_3$ are taken in such a way that $g\in H^s(\mathbb R_x^+)$, and $h_{j+1}\in H^{\frac{s+2-j}5}(\mathbb R_t^+)$, $j=0,1,2$, $s\in [0,\frac{11}4)\setminus \{\frac12,\frac32,\frac52\}$, and satisfy the following compatibility conditions: \begin{align*} g(0)=h_1(0) \text{ if } \frac12

Nonlinear frequency conversion by optical rectification, as well as difference- and sum-frequency generation are fundamental processes for producing electromagnetic radiation at different frequencies. Here, we demonstrate that coherently excited infrared-active phonons can be used as transducers for generating nonlinear electric polarizations and magnetizations via phonon-phonon and phonon-magnon interactions, in a way similar to nonlinear optical frequency conversion. We derive analytical solutions for the time-dependent polarizations and magnetizations for the second-order response to the electric field component of an ultrashort laser pulse. These allow us to define second-order nonlinear electric and magneto-electric susceptibilities that capture the rectification, as well as the impulsive and sum-frequency excitation of coherent phonons and magnons. Our theoretical framework naturally incorporates existing mechanisms and further leads to the prediction of a hybrid magneto-opto-phononic inverse Faraday effect involving photon-phonon-magnon scattering. Our work demonstrates nonlinear phononics as a pathway to controlling the electric polarization and magnetization in solids.

We present an ultraviolet-to-infrared search for the electromagnetic (EM) counterpart to GW190425, the second-ever binary neutron star (BNS) merger discovered by the LIGO-Virgo-KAGRA Collaboration (LVK). GW190425 was more distant and had a larger localization area than GW170817, therefore we use a new tool teglon to redistribute the GW190425 localization probability in the context of galaxy catalogs within the final localization volume. We derive a 90th percentile area of 6,688 deg$^{2}$, a $\sim$1.5$\times$ improvement relative to the LIGO/Virgo map, and show how teglon provides an order of magnitude boost to the search efficiency of small ($\leq$1 deg$^{2}$) field-of-view instruments. We combine our data with all publicly reported imaging data, covering 9,078.59 deg$^2$ of unique area and 48.13% of the LIGO/Virgo-assigned localization probability, to calculate the most comprehensive kilonova, short gamma-ray burst (sGRB) afterglow, and model-independent constraints on the EM emission from a hypothetical counterpart to GW190425 to date under the assumption that no counterpart was found in these data. If the counterpart were similar to AT 2017gfo, there was a 28.4% chance that it would have been detected in the combined dataset. We are relatively insensitive to an on-axis sGRB, and rule out a generic transient with a similar peak luminosity and decline rate as AT 2017gfo to 30% confidence. Finally, across our new imaging and all publicly-reported data, we find 28 candidate optical counterparts that we cannot rule out as being associated with GW190425, finding that 4 such counterparts discovered within the localization volume and within 5 days of merger exhibit luminosities consistent with a kilonova., Comment: 41 pages, 11 figures, Submitted to ApJ

Upcoming neutrino experiments will soon search for new neutrino interactions more thoroughly than ever before, boosting the prospects of extending the Standard Model. In anticipation of this, we forecast the capability of two of the leading long-baseline neutrino oscillation experiments, DUNE and T2HK, to look for new flavor-dependent neutrino interactions with electrons, protons, and neutrons that could affect the transitions between different flavors. We interpret their sensitivity in the context of long-range neutrino interactions, mediated by a new neutral boson lighter than $10^{-10}$ eV, and sourced by the vast amount of nearby and distant matter in the Earth, Moon, Sun, Milky Way, and beyond. For the first time, we explore the sensitivity of DUNE and T2HK to a wide variety of $U(1)^\prime$ symmetries, built from combinations of lepton and baryon numbers, each of which induces new interactions that affect oscillations differently. We find ample sensitivity: in all cases, DUNE and T2HK may constrain the existence of the new interaction even if it is supremely feeble, may discover it, and, in some cases, may identify the symmetry responsible for it., Comment: 52 pages, 20 figures, 6 tables, and 5 appendices. Sensitivity results in the form of digitized files can be found at https://github.com/pragyanprasu/LRI-LBL-2024. This version has the same content as the published article in the Journal of High Energy Physics

The ongoing development of single electron, nano and atomic scale semiconductor devices would benefit greatly from a characterization tool capable of detecting single electron charging events with high spatial resolution, at low temperature. In this work, we introduce a novel Atomic Force Microscope (AFM) instrument capable of measuring critical device dimensions, surface roughness, electrical surface potential, and ultimately the energy levels of quantum dots and single electron transistors in ultra miniaturized semiconductor devices. Characterization of nanofabricated devices with this type of instrument presents a challenge: finding the device. We therefore also present a process to efficiently find a nanometre size quantum dot buried in a $10 \times 10~\text{mm}^2$ silicon sample using a combination of optical positioning, capacitive sensors and AFM topography in vacuum.

In-ice radio-detection is a promising technique to discover and characterize ultra-high-energy (UHE) neutrinos, with energies above 100 PeV, adopted by present - ARA, ARIANNA, and RNO-G - and planned - IceCube-Gen2. So far, their ability to measure neutrino flavor has remained unexplored. We show and quantify how the neutrino flavor can be measured with in-ice radio detectors using two complementary detection channels. The first channel, sensitive to $\nu_e$, identifies them via their charged-current interactions, whose radio emission is elongated in time due to the Landau-Pomeranchuk-Migdal effect. The second channel, sensitive to $\nu_\mu$ and $\nu_\tau$, identifies events made up of multiple showers generated by the muons and taus they generate. We show this in state-of-the-art forecasts geared at IceCube-Gen2, for representative choices of the UHE neutrino flux. This newfound sensitivity could allow us to infer the UHE neutrino flavor composition at their sources - and thus the neutrino production mechanism - and to probe UHE neutrino physics., Comment: Accepted in PRD (2024.05.30)

Knowledge Graphs popularity has been rapidly growing in last years. All that knowledge is available for people to query it through the many online databases on the internet. Though, it would be a great achievement if non-programmer users could access whatever information they want to know. There has been a lot of effort oriented to solve this task using natural language processing tools and creativity encouragement by way of many challenges. Our approach focuses on assuming a correct entity linking on the natural language questions and training a GPT model to create SPARQL queries from them. We managed to isolate which property of the task can be the most difficult to solve at few or zero-shot and we proposed pre-training on all entities (under CWA) to improve the performance. We obtained a 62.703% accuracy of exact SPARQL matches on testing at 3-shots, a F1 of 0.809 on the entity linking challenge and a F1 of 0.009 on the question answering challenge., Comment: 7 pages, 1 figure, 2 tables. For the implementation, see https://github.com/DiegoEmilio01/SPARQL-generation-with-entity-pre-trained-GPT-for-KG-Question-Answering

3C84 is a nearby radio source with a complex total intensity structure, showing linear polarisation and spectral patterns. A detailed investigation of the central engine region necessitates the use of VLBI above the hitherto available maximum frequency of 86GHz. Using ultrahigh resolution VLBI observations at the highest available frequency of 228GHz, we aim to directly detect compact structures and understand the physical conditions in the compact region of 3C84. We used EHT 228GHz observations and, given the limited (u,v)-coverage, applied geometric model fitting to the data. We also employed quasi-simultaneously observed, multi-frequency VLBI data for the source in order to carry out a comprehensive analysis of the core structure. We report the detection of a highly ordered, strong magnetic field around the central, SMBH of 3C84. The brightness temperature analysis suggests that the system is in equipartition. We determined a turnover frequency of $\nu_m=(113\pm4)$GHz, a corresponding synchrotron self-absorbed magnetic field of $B_{SSA}=(2.9\pm1.6)$G, and an equipartition magnetic field of $B_{eq}=(5.2\pm0.6)$G. Three components are resolved with the highest fractional polarisation detected for this object ($m_\textrm{net}=(17.0\pm3.9)$%). The positions of the components are compatible with those seen in low-frequency VLBI observations since 2017-2018. We report a steeply negative slope of the spectrum at 228GHz. We used these findings to test models of jet formation, propagation, and Faraday rotation in 3C84. The findings of our investigation into different flow geometries and black hole spins support an advection-dominated accretion flow in a magnetically arrested state around a rapidly rotating supermassive black hole as a model of the jet-launching system in the core of 3C84. However, systematic uncertainties due to the limited (u,v)-coverage, however, cannot be ignored., Comment: 15 pages, 6 figures, published in A&A

We performed numerical simulations of the common envelope (CE) interaction between thermally-pulsing asymptotic giant branch (AGB) stars of 1.7~\Msun and 3.7~\Msun, respectively, and a 0.6~\Msun compact companion. We use tabulated equations of state to take into account recombination energy. For the first time, formation and growth of dust is calculated explicitly, using a carbon dust nucleation network with a C/O abundance ratio of 2.5 (by number). The first dust grains appear within $\sim$1--3~yrs after the onset of the CE, forming an optically thick shell at $\sim$10--20~au, growing in thickness and radius to values of $\sim$400--500~au over $\sim$40~yrs, with temperatures around 400~K. Most dust is formed in unbound material, having little effect on mass ejection or orbital evolution. By the end of the simulations, the total dust yield is $\sim8.4\times10^{-3}$~\Msun and $\sim2.2\times10^{-2}$~\Msun for the CE with a 1.7~\Msun and a 3.7~\Msun AGB star, respectively, corresponding to a nucleation efficiency close to 100\%, if no dust destruction mechanism is considered. Despite comparable dust yields to single AGB stars, \textit{in CE ejections the dust forms a thousand times faster, over tens of years as opposed to tens of thousands of years}. This rapid dust formation may account for the shift in the infrared of the spectral energy distribution of some optical transients known as luminous red novae. Simulated dusty CEs support the idea that extreme carbon stars and "water fountains" may be objects observed after a CE event., Comment: 18 pages, 17 figures, 2 tables