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Return words are a classical tool for studying shift spaces with low factor complexity. In recent years, their projection inside groups have attracted some attention, for instance in the context of dendric shift spaces, of generation of pseudorandom numbers (through the welldoc property), and of profinite invariants of shift spaces. Aiming at unifying disparate works, we introduce a notion of stability for subgroups generated by return words. Within this framework, we revisit several existing results and generalize some of them. We also study general aspects of stability, such as decidability or closure under certain operations.

We experimentally show that the Inelastic Cooper-Pair Tunneling Amplifier (ICTA), implementing a DC-powered parametric amplification scheme, can achieve gain and noise performance similar to that of Josephson parametric amplifiers. Using experimental data and simulations, we show that the ICTA has near-quantum-limited noise as long as the integral voltage bias noise divided by the superconducting flux quantum is below the amplification bandwidth. We observe a gain of 20 dB with noise below 1.7 times the quantum limit when the full width at half maximum of the integral voltage noise, expressed as frequency, is 5.6 MHz., Comment: 14 pages, 5 figures

Dendric shift spaces simultaneously generalize codings of regular interval exchanges and episturmian shift spaces, themselves both generalizations of Sturmian words. One of the key properties enforced by dendricity is the Return Theorem. In this paper, we prove its converse, providing the following natural algebraic perspective on dendricity: A minimal shift space is dendric if and only if every set of return words is a basis of the free group over the alphabet., Comment: 7 pages

The Cryogenic Underground Observatory for Rare Events (CUORE) is a detector array comprised by 988 5$\;$cm$\times$5$\;$cm$\times$5$\;$cm TeO$_2$ crystals held below 20 mK, primarily searching for neutrinoless double-beta decay in $^{130}$Te. Unprecedented in size amongst cryogenic calorimetric experiments, CUORE provides a promising setting for the study of exotic through-going particles. Using the first tonne-year of CUORE's exposure, we perform a search for hypothesized fractionally charged particles (FCPs), which are well-motivated by various Standard Model extensions and would have suppressed interactions with matter. No excess of FCP candidate tracks is observed over background, setting leading limits on the underground FCP flux with charges between $e/24-e/5$ at 90\% confidence level. Using the low background environment and segmented geometry of CUORE, we establish the sensitivity of tonne-scale sub-Kelvin detectors to diverse signatures of new physics., Comment: 7 pages, 5 figures

We present the model we developed to reconstruct the CUORE radioactive background based on the analysis of an experimental exposure of 1038.4 kg yr. The data reconstruction relies on a simultaneous Bayesian fit applied to energy spectra over a broad energy range. The high granularity of the CUORE detector, together with the large exposure and extended stable operations, allow for an in-depth exploration of both spatial and time dependence of backgrounds. We achieve high sensitivity to both bulk and surface activities of the materials of the setup, detecting levels as low as 10 nBq kg$^{-1}$ and 0.1 nBq cm$^{-2}$, respectively. We compare the contamination levels we extract from the background model with prior radio-assay data, which informs future background risk mitigation strategies. The results of this background model play a crucial role in constructing the background budget for the CUPID experiment as it will exploit the same CUORE infrastructure.

Nuclear quadrupolar resonance (NQR) spectroscopy reveals chemical bonding patterns in materials and molecules through the unique coupling between nuclear spins and local fields. However, traditional NQR techniques require macroscopic ensembles of nuclei to yield a detectable signal, which precludes the study of individual molecules and obscures molecule-to-molecule variations due to local perturbations or deformations. Optically active electronic spin qubits, such as the nitrogen-vacancy (NV) center in diamond, facilitate the detection and control of individual nuclei through their local magnetic couplings. Here, we use NV centers to perform NQR spectroscopy on their associated nitrogen-14 ($^{14}$N) nuclei at room temperature. In mapping the nuclear quadrupolar Hamiltonian, we resolve minute variations between individual nuclei. The measurements further reveal correlations between the parameters in the NV center's electronic spin Hamiltonian and the $^{14}$N quadropolar Hamiltonian, as well as a previously unreported Hamiltonian term that results from symmetry breaking. We further design pulse sequences to initialize, readout, and control the quantum evolution of the $^{14}$N nuclear state using the nuclear quadrupolar Hamiltonian., Comment: 15 pages, 10 figures

The current experiments searching for neutrinoless double-$\beta$ ($0\nu\beta\beta$) decay also collect large statistics of Standard Model allowed two-neutrino double-$\beta$ ($2\nu\beta\beta$) decay events. These can be used to search for Beyond Standard Model (BSM) physics via $2\nu\beta\beta$ decay spectral distortions. $^{100}$Mo has a natural advantage due to its relatively short half-life, allowing higher $2\nu\beta\beta$ decay statistics at equal exposures compared to the other isotopes. We demonstrate the potential of the dual read-out bolometric technique exploiting a $^{100}$Mo exposure of 1.47 kg $\times$ y, acquired in the CUPID-Mo experiment at the Modane underground laboratory (France). We set limits on $0\nu\beta\beta$ decays with the emission of one or more Majorons, on $2\nu\beta\beta$ decay with Lorentz violation, and $2\nu\beta\beta$ decay with a sterile neutrino emission. In this analysis, we investigate the systematic uncertainty induced by modeling the $2\nu\beta\beta$ decay spectral shape parameterized through an improved model, an effect never considered before. This work motivates searches for BSM processes in the upcoming CUPID experiment, which will collect the largest amount of $2\nu\beta\beta$ decay events among the next-generation experiments.

This paper studies obstructions to preservation of return sets by episturmian morphisms. We show, by way of an explicit construction, that infinitely many obstructions exist. This generalizes and improves an earlier result about Sturmian morphisms.

First-break picking is an essential step in seismic data processing. First arrivals should be picked by an expert. This is a time-consuming procedure and subjective to a certain degree, leading to different results for different operators. In this study, we used a U-Net architecture with residual blocks to perform automatic first-break picking based on deep learning. Focusing on the effects of weight initialization on this process, we conduct this research by using the weights of a pretrained network that is used for object detection on the ImageNet dataset. The efficiency of the proposed method is tested on two real datasets. For both datasets, we pick manually the first breaks for less than 10% of the seismic shots. The pretrained network is fine-tuned on the picked shots and the rest of the shots are automatically picked by the neural network. It is shown that this strategy allows to reduce the size of the training set, requiring fine tuning with only a few picked shots per survey. Using random weights and more training epochs can lead to a lower training loss, but such a strategy leads to overfitting as the test error is higher than the one of the pretrained network. We also assess the possibility of using a general dataset by training a network with data from three different projects that are acquired with different equipment and at different locations. This study shows that if the general dataset is created carefully it can lead to more accurate first-break picking, otherwise the general dataset can decrease the accuracy. Focusing on near-surface geophysics, we perform traveltime tomography and compare the inverted velocity models based on different first-break picking methodologies. The results of the inversion show that the first breaks obtained by the pretrained network lead to a velocity model that is closer to the one obtained from the inversion of expert-picked first breaks.

The matter-antimatter asymmetry underlines the incompleteness of the current understanding of particle physics. Neutrinoless double-beta ($0\nu \beta\beta$) decay may help explain this asymmetry, while unveiling the Majorana nature of the neutrino. The CUORE experiment searches for $0\nu \beta\beta$ decay of $^{130}$Te using a tonne-scale cryogenic calorimeter operated at milli-kelvin temperatures. We report no evidence for $0\nu \beta\beta$ decay and place a lower limit on the half-life of T$_{1/2}$ $>$ 3.8 $\times$ 10$^{25}$ years (90% C.I.) with over 2 tonne$\cdot$year TeO$_2$ exposure. The tools and techniques developed for this result and the 5 year stable operation of nearly 1000 detectors demonstrate the infrastructure for a next-generation experiment capable of searching for $0\nu \beta\beta$ decay across multiple isotopes.

The density of a rational language can be understood as the frequency of some "pattern" in the shift space, for example a pattern like "words with an even number of a given letter." We study the density of group languages, i.e. rational languages recognized by morphisms onto finite groups, inside shift spaces. We show that the density with respect to any given ergodic measure on a shift space exists for every group language, because it can be computed by using any ergodic lift of the given measure to some skew product between the shift space and the recognizing group. We then further study densities in shifts of finite type (with a suitable notion of irreducibility), and then in minimal shifts. In the latter case, we obtain a closed formula for the density under the condition that the skew product has minimal closed invariant subsets which are ergodic under the product of the original measure and the uniform probability measure on the group. The formula is derived in part from a characterization of minimal closed invariant subsets for skew products relying on notions of cocycles and coboundaries. In the case where the whole skew product is ergodic under the product measure, then the density is just the cardinality of the subset of the group which defines the language divided by the cardinality of the group. Moreover, we provide sufficient conditions for the skew product to have minimal closed invariant subsets that are ergodic under the product measure. Finally, we investigate the link between minimal closed invariant subsets, return words and bifix codes., Comment: Significant additions to the paper

Prions are misfolded proteins that transmit their structural arrangement to neighboring proteins. In biological systems, prion dynamics can produce a variety of complex functional outcomes. Yet, an understanding of prionic causes has been hampered by the fact that few computational models exist that allow for experimental design, hypothesis testing, and control. Here, we identify essential prionic properties and present a biologically inspired model of prions using simple mechanical structures capable of undergoing complex conformational change. We demonstrate the utility of our approach by designing a prototypical mechanical prion and validating its properties experimentally. Our work provides a design framework for harnessing and manipulating prionic properties in natural and artificial systems., Comment: Added supplements, 25 pages, 11 figures

Si and its oxides have been extensively explored in theoretical research due to their technological and industrial importance. Simultaneously describing interatomic interactions within both Si and SiO$_2$ without the use of \textit{ab initio} methods is considered challenging, given the charge transfers involved. Herein, this challenge is overcome by developing a unified machine learning interatomic potentials describing the Si/ SiO$_2$/ O system, based on the moment tensor potential (MTP) framework. This MTP is trained using a comprehensive database generated using density functional theory simulations, encompassing a wide range of crystal structures, point defects, extended defects, and disordered structure. Extensive testing of the MTP is performed, indicating it can describe static and dynamic features of very diverse Si, O, and SiO$_2$ atomic structures with a degree of fidelity approaching that of DFT

The future Habitable Worlds Observatory aims to characterize the atmospheres of rocky exoplanets around solar-type stars. The vector vortex coronagraph (VVC) is a main candidate to reach the required contrast of $10^{-10}$. However, the VVC requires polarization filtering and every observing band requires a different VVC. The triple-grating vector vortex coronagraph (tgVVC) aims to mitigate these limitations by combining multiple gratings that minimize the polarization leakage over a large spectral bandwidth. In this paper, we present laboratory results of a tgVVC prototype using the In-Air Coronagraphic Testbed (IACT) facility at NASA's Jet Propulsion Laboratory and the Space Coronagraph Optical Bench (SCoOB) at the University of Arizona Space Astrophysics Lab (UASAL). We study the coronagraphic performance with polarization filtering at 633 nm and reach a similar average contrast of $2 \times 10^{-8}$ between 3-18 $\lambda/D$ at the IACT, and $6 \times 10^{-8}$ between 3-14 $\lambda/D$ at SCoOB. We explore the limitations of the tgVVC by comparing the testbed results. We report on other manufacturing errors and ways to mitigate their impact., Comment: 9 pages, 5 figures, SPIE Optics + Photonics - Techniques and Instrumentation for Detection of Exoplanets XI

The Coronagraph Instrument of the Nancy Grace Roman Space Telescope (Roman Coronagraph) will be capable of both total intensity and polarization measurements of circumstellar disks. The polarimetric performance is impacted by polarization effects introduced by all mirrors before the Wollaston prisms. In this paper, we aim to characterize these effects for the Roman Coronagraph in bands 1 and 4 using the FALCO and PROPER packages. We simulate the effect of polarization aberrations that impact the polarimetric contrast and the instrumental polarization effects to study the polarimetric accuracy. We include spacecraft rolls, but leave out systematic camera noise. We find that polarimetric differential imaging (PDI) improves the contrast by a factor of six. The PDI contrast of $\sim 8 \times 10^{-11}$ is limited by polarized speckles from instrumental polarization effects and polarization aberrations. By injecting polarized companions with at various contrast levels and demodulating their polarimetric signal, we recover their source Stokes vector within 2%., Comment: 16 pages, 16 figures, SPIE Optics + Photonics - Techniques and Instrumentation for Detection of Exoplanets XI

Neutrinoless double beta decay ($0\nu\beta\beta$) is a yet unobserved nuclear process which would demonstrate Lepton Number violation, a clear evidence of beyond Standard Model physics. The process two neutrino double beta decay ($2\nu\beta\beta)$ is allowed by the Standard Model and has been measured in numerous experiments. In this letter, we report a measurement of $2\nu\beta\beta$ decay half-life of $^{100}$Mo to the ground state of $^{100}$Ru of $(7.07~\pm~0.02~\text{(stat.)}~\pm~0.11~\text{(syst.)})~\times~10^{18}$~yr by the CUPID-Mo experiment. With a relative precision of $\pm~1.6$ \% this is the most precise measurement to date of a $2\nu\beta\beta$ decay rate in $^{100}$Mo. In addition, we constrain higher-order corrections to the spectral shape which provides complementary nuclear structure information. We report a novel measurement of the shape factor $\xi_{3,1}=0.45~\pm 0.03~\text{(stat.)} \ \pm 0.05 \ \text{(syst.)}$, which is compared to theoretical predictions for different nuclear models. We also extract the first value for the effective axial vector coupling constant obtained from a spectral shape study of $2\nu\beta\beta$ decay., Comment: 8 pages, 5 figures

Intrinsically motivated exploration has proven useful for reinforcement learning, even without additional extrinsic rewards. When the environment is naturally represented as a graph, how to guide exploration best remains an open question. In this work, we propose a novel approach for exploring graph-structured data motivated by two theories of human curiosity: the information gap theory and the compression progress theory. The theories view curiosity as an intrinsic motivation to optimize for topological features of subgraphs induced by nodes visited in the environment. We use these proposed features as rewards for graph neural-network-based reinforcement learning. On multiple classes of synthetically generated graphs, we find that trained agents generalize to longer exploratory walks and larger environments than are seen during training. Our method computes more efficiently than the greedy evaluation of the relevant topological properties. The proposed intrinsic motivations bear particular relevance for recommender systems. We demonstrate that next-node recommendations considering curiosity are more predictive of human choices than PageRank centrality in several real-world graph environments., Comment: 15 pages, 5 figures in main text, and 18 pages, 9 figures in supplement