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In this note, we generalise the concept of topo-isomorphic extensions and define finite topomorphic extensions as topological dynamical systems whose factor map to the maximal equicontinuous factor is measure-theoretically at most $m$-to-one for some $m\in\mathbb{N}$. We further define multivariate versions of mean equicontinuity, complementing the notion of multivariate mean sensitivity introduced by Li, Ye and Yu, and then show that any $m$-to-one topomorphic extension is mean $(m+1)$-equicontinuous. This falls in line with the well-known result, due to Downarowicz and Glasner, that strictly ergodic systems are isomorphic extensions if and only if they are mean equicontinuous. While in the multivariate case we can only conjecture that the converse direction also holds, the result provides an indication that multivariate equicontinuity properties are strongly related to finite extension structures. For minimal systems, an Auslander-Yorke type dichotomy between multivariate mean equicontinuity and sensitivity is shown as well.

In this paper, we develop the semiclassical analysis of the lowest dimensional simply connected nilpotent Lie group of step 3, called the Engel group and denoted by ${\mathbb E}$, in the continuity of the works for groups of step 2 realized and exhibiting new features specific to groups of higher step. We are interested in the propagation of the semiclassical measures associated to solutions of the Schr\"odinger equation for the canonical subLaplacian $\Delta_{\mathbb E}$ and at different time-scales $\tau$. In particular, for $\tau=1$ we recover a quantum-classical correspondence where we observe the fundamental role of abnormal extremal lifts of the Engel group and are able to discuss the speed of the propagation of the singularities. Furthermore, in order to understand the dispersive nature of the subLaplcian, we are led to develop a second-microlocal analysis on particular cones in our phase space. This is done by relating the quasi-contact structure of the group ${\mathbb E}$ to its semiclassical analysis via harmonic analysis. As a consequence, we are able to prove obstruction to local smoothness-type estimates and Strichartz estimates for the Engel subLaplacian.

The NANOGrav 15-year data provides compelling evidence for a stochastic gravitational-wave (GW) background at nanohertz frequencies. The simplest model-independent approach to characterizing the frequency spectrum of this signal consists in a simple power-law fit involving two parameters: an amplitude A and a spectral index \gamma. In this paper, we consider the next logical step beyond this minimal spectral model, allowing for a running (i.e., logarithmic frequency dependence) of the spectral index, \gamma_run(f) = \gamma + \beta \ln(f/f_ref). We fit this running-power-law (RPL) model to the NANOGrav 15-year data and perform a Bayesian model comparison with the minimal constant-power-law (CPL) model, which results in a 95% credible interval for the parameter \beta consistent with no running, \beta \in [-0.80,2.96], and an inconclusive Bayes factor, B(RPL vs. CPL) = 0.69 +- 0.01. We thus conclude that, at present, the minimal CPL model still suffices to adequately describe the NANOGrav signal; however, future data sets may well lead to a measurement of nonzero \beta. Finally, we interpret the RPL model as a description of primordial GWs generated during cosmic inflation, which allows us to combine our results with upper limits from big-bang nucleosynthesis, the cosmic microwave background, and LIGO-Virgo-KAGRA., Comment: 17 pages, 4 figures, 2 tables

We present a characterization of the Hamiltonians that generate optimal-speed unitary time evolution and the associated dynamical trajectory, where the initial states are either pure states or quasi-pure quantum states. We construct the manifold of pure states as an orbit under the conjugation action of the Lie group $\SU(n)$ on the manifold of one-dimensional orthogonal projectors, obtaining an isometry with the flag manifold $\SU(n)/\textnormal{S}(\textnormal{U}(1)\times \textnormal{U}(n-1 ))$. From this construction, we show that Hamiltonians generating optimal-speed time evolution are fully characterized by equigeodesic vectors of $\SU(n)/\textnormal{S}(\textnormal{U}(1)\times \textnormal{U}(n-1))$. We later extend that result to quasi-pure quantum states., Comment: 14 pages

Resampling is a common technique applied in digital signal processing. Based on the Fast Fourier Transformation (FFT), we apply an optimization called here the LMN method to achieve fast and robust re-sampling. In addition to performance comparisons with some other popular methods, we illustrate the effectiveness of this LMN method in a particle physics experiment: re-sampling of waveforms from Liquid Argon Time Projection Chambers., Comment: 24 pages, 11 figures, to be submitted to JINST

In this paper, combining the Rashevsky-Chow-Sussmann (orbit) theorem with the Ambrose-Singer theorem, we introduce the notion of controllable principal connections on principal $G$-bundles. Using this concept, under a mild assumption of compactness, we estimate the Gromov-Hausdorff distance between principal $G$-bundles and certain reductive homogeneous $G$-spaces. In addition, we prove that every reduction of the structure group $G$ to a closed connected subgroup gives rise to a sequence of Riemannian metrics on the total space for which the underlying sequence of metric spaces converges, in the Gromov-Housdorff topology, to a normal reductive homogeneous $G$-space. This last finding allows one to detect the presence of certain reductive homogeneous $G$-spaces in the Gromov-Housdorff closure of the moduli space of Riemannian metrics of the total space of the bundle through topological invariants provided by obstruction theory., Comment: 13 pages, Comments are welcome

We explore the bound neutrons decay into invisible particles (e.g., $n\rightarrow 3 \nu$ or $nn \rightarrow 2 \nu$) in the JUNO liquid scintillator detector. The invisible decay includes two decay modes: $ n \rightarrow { inv} $ and $ nn \rightarrow { inv} $. The invisible decays of $s$-shell neutrons in $^{12}{\rm C}$ will leave a highly excited residual nucleus. Subsequently, some de-excitation modes of the excited residual nuclei can produce a time- and space-correlated triple coincidence signal in the JUNO detector. Based on a full Monte Carlo simulation informed with the latest available data, we estimate all backgrounds, including inverse beta decay events of the reactor antineutrino $\bar{\nu}_e$, natural radioactivity, cosmogenic isotopes and neutral current interactions of atmospheric neutrinos. Pulse shape discrimination and multivariate analysis techniques are employed to further suppress backgrounds. With two years of exposure, JUNO is expected to give an order of magnitude improvement compared to the current best limits. After 10 years of data taking, the JUNO expected sensitivities at a 90% confidence level are $\tau/B( n \rightarrow { inv} ) > 5.0 \times 10^{31} \, {\rm yr}$ and $\tau/B( nn \rightarrow { inv} ) > 1.4 \times 10^{32} \, {\rm yr}$., Comment: 28 pages, 7 figures, 4 tables

We construct 1-parameter families of well-known solutions to the Yamabe problem defined on Aloff-Wallach Spaces to determine bifurcation instants for these homogeneous spaces by examining changes in the Morse index of these metrics as the parameter varies over the positive real numbers. A bifurcation point for such families is an accumulation point of other solutions to the Yamabe problem, while a local rigidity point is an isolated solution of this problem, i.e., it is not a bifurcation point.

The internal total-energy of the black-body is a physical quantity of paramount importance in the development of modern physics. Accordingly, together with a brief historical development, we report and comment last breaking news (2018-2024) concerning the definition and properties of this quantity. The first comment concerns with the inclusion of the Casimir energy that avoids the vacuum catastrophe implied by he presence of zero-point energy, thus leading to further quantum contributions associated with boundary effects. The second comment concerns with a semi-classical simulation of a one dimensional black-body whose results suggest a possible reconsideration on the role of classical physics on the quantum black-body., Comment: 5 pages, no figures

In arXiv:2404.19088, we initiated a program linking birational invariants with smooth ones and offering new interpretations of classical invariants, such as the Kervaire-Milnor invariants. Here, we rely on the profound geometric reasoning provided by Lupercio and Uribe in the early 00s to establish a connection between Chen-Ruan cohomology and several $G$-birational invariants introduced in the pioneering works Kontsevich, Kresch, Pestun, Tschinkel, along with presenting applications. Combined with the theory of atoms by Katzarkov, Kontsevich, Pantev, and Yu, the proposal in this paper program will lead to a theory of equivariant atoms., Comment: a) Clarified what kind of group actions we are considering. b) Recalled birationality for Deligne-Mumford (DM) stacks and explained how they still contain information on finite group actions. c) Explained the role of gerbes in twisting Chen-Ruan cohomology and presented details on how they can be useful in obstructing birational types of certain DM stacks. 32 pages. 1 Appendix

As more distributed energy resources become part of the demand-side infrastructure, it is important to quantify the energy flexibility they provide on a community scale, particularly to understand the impact of geographic, climatic, and occupant behavioral differences on their effectiveness, as well as identify the best control strategies to accelerate their real-world adoption. CityLearn provides an environment for benchmarking simple and advanced distributed energy resource control algorithms including rule-based, model-predictive, and reinforcement learning control. CityLearn v2 presented here extends CityLearn v1 by providing a simulation environment that leverages the End-Use Load Profiles for the U.S. Building Stock dataset to create virtual grid-interactive communities for resilient, multi-agent distributed energy resources and objective control with dynamic occupant feedback. This work details the v2 environment design and provides application examples that utilize reinforcement learning to manage battery energy storage system charging/discharging cycles, vehicle-to-grid control, and thermal comfort during heat pump power modulation.

S. Donaldson disproved the smooth $\mathrm{h}$-cobordism conjecture in dimension $4$ by studying invariants coming from the moduli space of connections on $\mathrm{SO}(3)$-bundles over smooth $4$-dimension manifolds $X$. In this paper, we reverse his point of view in dimension $8$. Namely, we consider fibrations coming from diffeomorphisms classes of homotopy Hopf manifolds $\Sigma^7\times\mathrm{S}^1$, i.e., $\Sigma^7$ is a homotopy sphere, seeing the bases as moduli spaces for additional structures. Our overarching objective is to establish a correspondence between the smooth invariants of Kervaire--Milnor and categorical invariants. One interprets pairwise non-diffeomorphic smooth structures on $\Sigma^7\times\mathrm{S}^1$ in terms of non-rationality. This paper's contributions are diverse, each carrying its significance. We believe profound connections exist between the themes addressed, which connect hypersurface singularity theory, Homological Mirror Symmetry, Topological Modular forms ($\mathrm{tmf}$), and Spherical T-duality., Comment: 71 pages, 2 appendixes. Comments are welcome

In the field of 3D Human Pose Estimation (HPE), accurately estimating human pose, especially in scenarios with occlusions, is a significant challenge. This work identifies and addresses a gap in the current state of the art in 3D HPE concerning the scarcity of data and strategies for handling occlusions. We introduce our novel BlendMimic3D dataset, designed to mimic real-world situations where occlusions occur for seamless integration in 3D HPE algorithms. Additionally, we propose a 3D pose refinement block, employing a Graph Convolutional Network (GCN) to enhance pose representation through a graph model. This GCN block acts as a plug-and-play solution, adaptable to various 3D HPE frameworks without requiring retraining them. By training the GCN with occluded data from BlendMimic3D, we demonstrate significant improvements in resolving occluded poses, with comparable results for non-occluded ones. Project web page is available at https://blendmimic3d.github.io/BlendMimic3D/., Comment: Accepted at 6th Workshop and Competition on Affective Behavior Analysis in-the-wild - CVPR 2024 Workshop

In this paper, we aim to explore the interplay between neutrinos and quantum gravity, illustrating some proposals about the use of these particles as probes for the supposed quantized structure of spacetime. The residual signatures of a more fundamental theory of quantum gravity can manifest themselves modifying the free particle dispersion relations and the connected velocity. In neutrino sector these supposed effects can modify the time of flight for astrophysical particles with different energies and can affect the usual neutrino oscillation pattern introducing species depending perturbations. We will highlight how perturbations caused by non-standard interactions in the solar neutrino sector can mimic the presumed quantum gravity effects. In fact, the mathematical formulation of non-standard interactions is equivalent to that of CPT-odd perturbations. We will, therefore, emphasize the need to identify the nature of different contributions in order to disentangle them in the search for quantum gravity effects. As a final point we will discuss the possibility to detect in the neutrino sector decoherence effects caused by the quantum gravity supposed perturbations. By reviewing current experimental constraints and observations, we seek to shed light on the intricate relationship between neutrinos and quantum gravity, and discuss the challenges and future directions in this fascinating field of research., Comment: 37 pages, 3 figures

Solid-state cooling devices offer compact, quiet, reliable and environmentally friendly solutions that currently rely primarily on the thermoelectric (TE) effect. Despite more than two centuries of research, classical thermoelectric coolers suffer from low efficiency which hampers wider application. In this study, the less researched Anomalous Ettingshausen effect (AEE), a transverse thermoelectric phenomenon, is presented as a new approach for on-chip cooling. This effect can be boosted in materials with non-trivial band topologies as demonstrated in the Heusler alloy $\text{Co}_2\text{MnGa}$. Enabled by the high quality of our material, in situ scanning thermal microscopy experiments reveal a record-breaking anomalous Ettingshausen coefficient of $-2.1$~mV in $\mu$m-sized on-chip cooling devices at room temperature. A significant 44\% of the effect is contributed by the intrinsic topological properties, in particular the Berry curvature of $\text{Co}_2\text{MnGa}$, emphasising the unique potential of magnetic Weyl semimetals for high-performance spot cooling in nanostructures.

Since the advent of new pairwise non-diffeomorphic structures on smooth manifolds, it has been questioned whether two topologically identical manifolds could admit different geometries. Not surprisingly, physicists have wondered whether a smooth structure assumption different from some classical known models could produce different physical meanings. In this paper, we inaugurate a very computational manner to produce physical models on classical and exotic spheres that can be built equivariantly, such as the classical Gromoll--Meyer exotic spheres. As first applications, we produce Lorentzian metrics on homeomorphic but not diffeomorphic manifolds that enjoy the same physical properties, such as geodesic completeness, positive Ricci curvature, and compatible time orientation. These constructions can be pulled back to higher models, such as exotic ten spheres bounding spin manifolds, to be approached in forthcoming papers., Comment: Accepted paper. To appear in Differential Geometry and its Applications

The disposal and recycling of electronic waste (e-waste) is a global challenge. The disassembly of components is a crucial step towards an efficient recycling process, avoiding the destructive methods. Although most disassembly work is still done manually due to the diversity and complexity of components, there is a growing interest in developing automated methods to improve efficiency and reduce labor costs. This study aims to robotize the desoldering process and extracting components from printed circuit boards (PCBs), with the goal of automating the process as much as possible. The proposed strategy consists of several phases, including the controlled contact of the robotic tool with the PCB components. A specific tool was developed to apply a controlled force against the PCB component, removing it from the board. The results demonstrate that it is feasible to remove the PCB components with a high success rate (approximately 100% for the bigger PCB components)., Comment: Sixth Iberian Robotics Conference, Robot 2023

We report an extensive high-sensitivity search for axion dark matter above 1\,GHz at the Center for Axion and Precision Physics Research (CAPP). The cavity resonant search, exploiting the coupling between axions and photons, explored the frequency (mass) range of 1.025\,GHz (4.24\,$\mu$eV) to 1.185\,GHz (4.91\,$\mu$eV). We have introduced a number of innovations in this field, demonstrating the practical approach of optimizing all the relevant parameters of axion haloscopes, extending presently available technology. The CAPP 12\,T magnet with an aperture of 320\,mm made of Nb$_3$Sn and NbTi superconductors surrounding a 37-liter ultralight-weight copper cavity is expected to convert DFSZ axions into approximately $10^2$ microwave photons per second. A powerful dilution refrigerator, capable of keeping the core system below 40\,mK, combined with quantum-noise limited readout electronics, achieved a total system noise of about 200\,mK or below, which corresponds to a background of roughly $4\times 10^3$ photons per second within the axion bandwidth. The combination of all those improvements provides unprecedented search performance, imposing the most stringent exclusion limits on axion--photon coupling in this frequency range to date. These results also suggest an experimental capability suitable for highly-sensitive searches for axion dark matter above 1\,GHz., Comment: A detailed axion dark matter article with 27 pages, 22 figures

Conditions data is the subset of non-event data that is necessary to process event data. It poses a unique set of challenges, namely a heterogeneous structure and high access rates by distributed computing. The HSF Conditions Databases activity is a forum for cross-experiment discussions inviting as broad a participation as possible. It grew out of the HSF Community White Paper work to study conditions data access, where experts from ATLAS, Belle II, and CMS converged on a common language and proposed a schema that represents best practice. Following discussions with a broader community, including NP as well as HEP experiments, a core set of use cases, functionality and behaviour was defined with the aim to describe a core conditions database API. This paper will describe the reference implementation of both the conditions database service and the client which together encapsulate HSF best practice conditions data handling. Django was chosen for the service implementation, which uses an ORM instead of the direct use of SQL for all but one method. The simple relational database schema to organise conditions data is implemented in PostgreSQL. The task of storing conditions data payloads themselves is outsourced to any POSIX-compliant filesystem, allowing for transparent relocation and redundancy. Crucially this design provides a clear separation between retrieving the metadata describing which conditions data are needed for a data processing job, and retrieving the actual payloads from storage. The service deployment using Helm on OKD will be described together with scaling tests and operations experience from the sPHENIX experiment running more than 25k cores at BNL.

Large Language Models (LLMs) are increasingly bringing advances to Natural Language Processing. However, low-resource languages, those lacking extensive prominence in datasets for various NLP tasks, or where existing datasets are not as substantial, such as Portuguese, already obtain several benefits from LLMs, but not to the same extent. LLMs trained on multilingual datasets normally struggle to respond to prompts in Portuguese satisfactorily, presenting, for example, code switching in their responses. This work proposes a fine-tuned LLaMA 2-based model for Portuguese prompts named Bode in two versions: 7B and 13B. We evaluate the performance of this model in classification tasks using the zero-shot approach with in-context learning, and compare it with other LLMs. Our main contribution is to bring an LLM with satisfactory results in the Portuguese language, as well as to provide a model that is free for research or commercial purposes., Comment: 10 pages, 3 figures

In Si/SiGe heterostructures, the low-lying excited valley state seriously limit operability and scalability of electron spin qubits. For characterizing and understanding the local variations in valley splitting, fast probing methods with high spatial and energy resolution are lacking. Leveraging the spatial control granted by conveyor-mode spin-coherent electron shuttling, we introduce a method for two-dimensional mapping of the local valley splitting by detecting magnetic field dependent anticrossings of ground and excited valley states using entangled electron spin-pairs as a probe. The method has sub-{\mu}eV energy accuracy and a nanometer lateral resolution. The histogram of valley splittings spanning a large area of 210 nm by 18 nm matches well with statistics obtained by the established but time-consuming magnetospectroscopy method. For the specific heterostructure, we find a nearly Gaussian distribution of valley splittings and a correlation length similar to the quantum dot size. Our mapping method may become a valuable tool for engineering Si/SiGe heterostructures for scalable quantum computing., Comment: 17 pages, 11 Figures

In this work, we systematically derive explicit expressions for the Poincar\'e Group generators on arbitrary-rank tensors and spinor-tensors in $D=3+1$ and $D=2+1$ spacetimes, thus generalizing previous works in the literature for the groups $ISO(3,1)$ and $ISO(2,1)$. From the Casimir eigenvalue equations, we demonstrate in a model-independent way the Fierz-Pauli constraints for massive particles for spins $\mathfrak{s}=5/2$, 3, and 4 in $D=3+1$ and helicities $\alpha=5/2$, 3, and 4 in $D=2+1$ dimensions. We also comment on the demonstration of the Fierz-Pauli constraints for the general case of arbitrary spin (helicity)., Comment: 27 pages

Due to a result by Glasner and Downarowicz, it is known that a minimal system is mean equicontinuous if and only if it is an isomorphic extension of its maximal equicontinuous factor. The majority of known examples of this type are almost automorphic, that is, the factor map to the maximal equicontinuous factor is almost one-to-one. The only cases of isomorphic extensions which are not almost automorphic are again due to Glasner and Downarowicz, who in the same article provide a construction of such systems in a rather general topological setting. Here, we use the Anosov-Katok method in order to provide an alternative route to such examples and to show that these may be realised as smooth skew product diffeomorphisms of the two-torus with an irrational rotation on the base. Moreover - and more importantly - a modification of the construction allows to ensure that lifts of these diffeomorphism to finite covering spaces provide novel examples of finite-to-one topomorphic extensions of irrational rotations. These are still strictly ergodic and share the same dynamical eigenvalues as the original system, but show an additional singular continuous component of the dynamical spectrum.

In this paper we present an extension of Landauer paradigm, conductance is transmission, to the case of macroscopic classical conductors making use of a description of conductance and resistance based on the application of the fluctuation dissipation (FD) theorem. The main result is summarized in the expressions below for conductance $G$ and resistance $R$ at thermodynamic equilibrium, with the usual meaning of symbols. $G$ is given in terms of the variance of total carrier number fluctuations between two ideal transparent contacts in an open system described by a grand canonical ensemble as $$ G =\frac{e^2 \overline{v_x'^2} \tau}{L^2 K_BT} \overline{\delta N^2} %= \frac{e^2 \sqrt{\overline{v_x'^2}} \Gamma }{L K_BT} \overline{\delta %N^2} %= \frac{e^2 \overline{N} \Gamma } {Lm\sqrt{\overline{v_x'^2}}} \ \ \ \ $$ By contrast $R$ is given in terms of the variance of carrier drift-velocity fluctuations due to the instantaneous carrier specular reflection at the internal contact interfaces of a closed system described by a canonical ensemble as $$ R= \frac{(m L)^2}{e^2 K_BT \tau} \overline{\delta v_d^2} %= \frac {Lm\sqrt{\overline{v_x'^2}}} {e^2 \overline{N} \Gamma } $$ The FD approach gives evidence of the duality property of conductance related to transmission and resistance related to reflection. Remarkably, the expressions above are shown to recover the quantum Landauer paradigm in the limit of zero temperature for a one-dimensional conductor.