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Minimal Kitaev chains, composed of two quantum dots (QDs) connected via a superconductor, have emerged as an attractive platform to realize Majorana bound states (MBSs). These excitations exist when the ground state is degenerate. The additional requirement of isolating the MBS wavefunctions further restricts the parameter space to discrete sweet spots. While scaling up to Kitaev chains with more than two sites has the potential to improve the stability of the MBSs, longer chains offer more features to optimize, including the MBS localization length and the excitation gap. In this work, we theoretically investigate 3-site Kitaev chains and show that there are three different types of sweet spots, obtained by maximizing distinct MBS properties: genuine 3-site sweet spots with well-localized MBSs at the ends, effective 2-site sweet spots, where the middle site acts as a barrier, and sweet spots with delocalized MBSs that overlap in the middle of the chain. These three cases feature different degrees of robustness against perturbations, with the genuine 3-site being the most stable. We analyze the energy spectrum, transport, and microwave absorption associated with these three cases, showing how to distinguish them.

The nature of dark matter, which constitutes 27% of the Universe's matter-energy content, remains one of the most challenging open questions in physics. Over the past two decades, the DAMA/LIBRA experiment has reported an annual modulation in the detection rate of $\approx$250 kg of NaI(Tl) detectors operated at the Gran Sasso Laboratory, which the collaboration interprets as evidence of the galactic dark matter detection. However, this claim has not been independently confirmed and is refuted under certain dark matter particle and halo model scenarios. Therefore, it is crucial to perform an experiment with the same target material. The ANAIS experiment uses 112.5 kg of NaI(Tl) detectors at the Canfranc Underground Laboratory and it has been collecting data since August 2017 to model-independently test the DAMA/LIBRA result. This article presents the results of the annual modulation analysis corresponding to six years of ANAIS-112 data. Our results, the most sensitive to date with the same target material, NaI(Tl), are incompatible with the DAMA/LIBRA modulation signal at a 4$\sigma$ confidence level. Such a discrepancy strongly challenges the DAMA/LIBRA dark matter interpretation and highlights the need to address systematic uncertainties affecting the comparison, particularly those related to the response of detectors to nuclear recoils, which may require further characterization of the DAMA crystals., Comment: 17 pages, 13 figures, 4 tables

We investigate the impact of limited data on training pairwise energy-based models for inverse problems aimed at identifying interaction networks. Utilizing the Gaussian model as testbed, we dissect training trajectories across the eigenbasis of the coupling matrix, exploiting the independent evolution of eigenmodes and revealing that the learning timescales are tied to the spectral decomposition of the empirical covariance matrix. We see that optimal points for early stopping arise from the interplay between these timescales and the initial conditions of training. Moreover, we show that finite data corrections can be accurately modeled through asymptotic random matrix theory calculations and provide the counterpart of generalized cross-validation in the energy based model context. Our analytical framework extends to binary-variable maximum-entropy pairwise models with minimal variations. These findings offer strategies to control overfitting in discrete-variable models through empirical shrinkage corrections, improving the management of overfitting in energy-based generative models., Comment: 23 pages, 13 figures (including appendix)

The moment of inertia and tidal deformability of idealized stars with polytropic equations of state (EOSs) are numerically calculated under both Newtonian gravity and general relativity (GR). The results explicitly confirm that the relation between the moment of inertia and tidal deformability, parameterized by the star's mass, exhibits variations of 1% to 10% for different polytropic indices in Newtonian gravity and GR, respectively. This indicates a more robust I-Love universal relation in the Newtonian framework. The theoretically derived I-Love universal relation for polytropic stars is subsequently tested against observational data for the moment of inertia and tidal deformability of the 8 planets and some moons in our solar system. The analysis reveals that the theoretical I-Love universal relation aligns well with the observational data, suggesting that it can serve as an empirical relation. Consequently, it enables the estimation of either the moment of inertia or the tidal deformability of an exoplanet if one of these quantities, along with the mass of the exoplanet, is known., Comment: 10 pages, 9 figures

Maximum entropy methods, based on the inverse Ising/Potts problem from statistical mechanics, are essential for modeling interactions between pairs of variables in data-driven problems across disciplines such as bioinformatics, ecology, and neuroscience. Despite their considerable success, these methods typically fail to capture higher-order interactions that are often essential for understanding complex systems. Conversely, modern machine learning methods capture these complex interactions, but the computational cost of interpretable frameworks makes them impractical for real-world applications. Restricted Boltzmann Machines (RBMs) provide a computationally efficient way to capture statistical correlations using hidden nodes in a bipartite neural network. In this study, we introduce a new method that maps RBMs to generalized Potts models, allowing for the extraction of interactions up to any specified order. This method utilizes large-$N$ approximations, enabled by the RBM's simple structure, to extract effective many-body couplings with minimal computational effort. Furthermore, we propose a robust framework for extracting higher-order interactions in more complex probabilistic models and a simple gauge-fixing method within the effective many-body Potts model. Our validation on synthetic datasets confirms the method's ability to recover two- and three-body interactions accurately. When applied to protein sequence data, the framework competently reconstructs protein contact maps and provides performance comparable to the best inverse Potts models. These findings confirm that RBMs are an effective and streamlined tool for exploring higher-order interactions within complex systems., Comment: 16 Pages and 5 Figures

We recently developed a Monte-Carlo method (GNC) that can simulate the dynamical evolution of a nuclear stellar cluster (NSC) with a massive black hole (MBH), where the two-body relaxations can be solved by the Fokker-Planck equations in energy and angular momentum space. Here we make a major update of GNC~ by integrating stellar potential and adiabatic invariant theory, so that we can study the self-consistent dynamics of NSCs with increasing mass of the MBH. We perform tests of the self-adaptation of cluster density due to MBH mass growth and Plummer core collapse, both finding consistent results with previous studies, the latter having a core collapse time of $\sim 17t_{\rm rh}$ by GNC, where $t_{\rm rh}$ is the time of half-mass relaxation. We use GNC~ to study the cosmological evolution of the properties of NSC and the mass of MBH assuming that the mass growth of the MBH is due to loss-cone accretion of stars (e.g., tidal disruption of stars) and stellar black holes, and compare the simulation results with the observations of NSCs in Milky-Way or near-by galaxies. Such scenario is possible to produce MBHs with mass $10^5\sim 10^7\,M_\odot$ for NSCs with stellar mass of $10^6\sim 10^9\,M_\odot$. In Milky-Way's NSC, to grow MBH up to $4\times 10^6\,M_\odot$, its size needs to be $\sim 1.7$ times more compact in early universe than the current value. MBHs with current masses $>6\times 10^{7}\,M_\odot$ seem difficult to explain by loss-cone accretion alone, and thus may require other additional accretion channels, such as gas accretion., Comment: 27 pages, 11 figures, resubmitted to ApJ after first referee's report

Hybrid superconductor-semiconductor systems have received a great deal of attention in the last few years because of their potential for quantum engineering, including novel qubits and topological devices. The proximity effect, the process by which the semiconductor inherits superconducting correlations, is an essential physical mechanism of such hybrids. Recent experiments have demonstrated the proximity effect in hole-based semiconductors, but, in contrast to electrons, the precise mechanism by which the hole bands acquire superconducting correlations remains an open question. In addition, hole spins exhibit a complex strong spin-orbit interaction, with largely anisotropic responses to electric and magnetic fields, further motivating the importance of understanding the interplay between such effects and the proximity effect. In this work, we analyze this physics with focus on germanium-based two-dimensional gases. Specifically, we develop an effective theory supported by full numerics, allowing us to extract various analytical expressions and predict different types of superconducting correlations including non-standard forms of singlet and triplet pairing mechanisms with non-trivial momentum dependence; as well as different Zeeman and Rashba spin-orbit contributions. This, together with their precise dependence on electric and magnetic fields, allows us to make specific experimental predictions, including the emergence of f-type superconductivity, Bogoliubov Fermi surfaces, and gapless regimes caused by large in-plane magnetic fields., Comment: 13 pages, 9 figures, plus Appendices

Metal halide perovskite solar cells (MHPSCs) hold great promise related to their high efficiency and low fabrication costs, but their long-term stability under environmental conditions remains a major challenge. In this study, we demonstrate an effective protection strategy to enhance the stability of MHPSCs through the incorporation of a double passivation layer based on an adamantane-based plasma polymer (ADA) at both the electron transport layer (ETL)/perovskite and perovskite/hole transport layer (HTL) interfaces. Our results show that the implemented ADA deposition technique is compatible with delicate substrates such as perovskites thin films, as their optical, morphological and optoelectronic properties are unaltered upon ADA deposition. At the same time, it provides effective protection to the perovskite material in high humidity environments. The ADA-double passivation not only reduces the formation of mobile ionic defects that cause additional recombination, but also significantly reduces humidity-induced degradation and mitigates the photocatalytic degradation caused by TiO2 under UV exposure. Stability tests performed under 100% relative humidity and continuous AM 1.5G illumination (ISOS-L-1) show that ADA dual passivated devices retained 80% of their initial efficiency after 4000 minutes, while reference samples dropped to 30%. The enhanced performance of ADA-passivated cells is attributed to protective nature of the plasma polymer layer resulting in a preservation of photocurrent and the prevention of new recombination routes. This dual passivation strategy offers a promising route to improve the environmental stability of PSCs and extend their operational lifetime.

This document compiles results obtained from the test campaign of the European Moon Rover System (EMRS) project. The test campaign, conducted at the Planetary Exploration Lab of DLR in Wessling, aimed to understand the scope of the EMRS breadboard design, its strengths, and the benefits of the modular design. The discussion of test results is based on rover traversal analyses, robustness assessments, wheel deflection analyses, and the overall transportation cost of the rover. This not only enables the comparison of locomotion modes on lunar regolith but also facilitates critical decision-making in the design of future lunar missions., Comment: 6 pages, 5 figures, conference International Conference on Space Robotics

The Majorana tetron is a prototypical topological qubit stemming from the ground state degeneracy of a superconducting island hosting four Majorana modes. This degeneracy manifests as an effective non-local spin degree of freedom, whose most paradigmatic signature is the topological Kondo effect. Degeneracies of states with different fermionic parities characterize also minimal Kitaev chains which have lately emerged as a platform to realize and study unprotected versions of Majorana modes, dubbed poor man's Majorana modes. Here, we introduce the ``poor man's Majorana tetron'', comprising four quantum dots coupled via a floating superconducting island. Its charging energy yields non-trivial correlations among the dots, although, unlike a standard tetron, it is not directly determined by the fermionic parity of the Majorana modes. The poor man's tetron displays parameter regions with a two-fold degenerate ground state with odd fermionic parity, that gives rise to an effective Anderson impurity model when coupled to external leads. We show that this system can approach a regime featuring the topological Kondo effect under a suitable tuning of experimental parameters. Therefore, the poor man's tetron is a promising device to observe the non-locality of Majorana modes and their related fractional conductance., Comment: 28 pages, 9 figures

Understanding how viral mutant spectra organize and explore genotype space is essential for unraveling the mechanisms driving evolution at the finest scale. Here we use deep-sequencing data of an amplicon in the A2 protein of the RNA bacteriophage Q$\beta$ to reconstruct genotype networks with tens of thousands of different haplotypes. The study of populations evolved under different temperature regimes uncovers generic topological features conditioned by fundamental structural motifs of genotype networks -- tetrahedrons, triangles, and squares -- that govern their local architecture. Mutant swarms display a hierarchical structure where sequences cluster around a highly connected and abundant sequence core that sustains population diversity. The immediate neighborhood of this core is comprehensively sampled, with no signs of selection, while a few mutations away sampling becomes dynamical and sparse, showing signs of purifying selection. By aggregating genotype networks from populations adapted to different temperatures, we capture the early stages of evolutionary divergence, with overlapping populations that remain connected through short mutational paths. Even at the time scale of these experiments, evolutionary pathways might be multiple, preventing the backward reconstruction of unique trajectories once mutations have been fixed. This analysis provides a detailed view of the local, fine-scale processes shaping viral quasispecies evolution and underscores the usefulness of genotype networks as an enlightening visualization of the organization of mutant swarms., Comment: 15 pages (main), 8 pages (appendixes), 4 figures (main), 6 figures (appendixes)

Majorana modes can be engineered in arrays where quantum dots (QDs) are coupled via grounded superconductors, effectively realizing an artificial Kitaev chain. Minimal Kitaev chains, composed by two QDs, can host fully-localized Majorana modes at discrete points in parameter space, known as Majorana sweet spots. Here, we extend previous works by theoretically investigating a setup with two QDs coupled via a floating superconducting island. We study the effects of the charging energy of the island and the properties of the resulting minimal Kitaev chain. We initially employ a minimal perturbative model, valid in the weak QD-island coupling regime, to derive analytic expressions for the Majorana sweet spots and the splitting of the ground state degeneracy as a function of tunable physical parameters. The conclusions from this perturbative approximation are then benchmarked using a microscopic model that explicitly describes the internal degrees of freedom of the island. Our work shows the existence of Majorana sweet spots, even when the island is not tuned at a charge-degeneracy point. In contrast to the Kitaev chains in grounded superconductors, these sweet spots involve a degeneracy between states with a well-defined number of particles., Comment: 13 pages, 9 figures

Synthetic biology is a recent area of biological engineering, whose aim is to provide cells with novel functionalities. A number of important results regarding the development of control circuits in synthetic biology have been achieved during the last decade. A differential geometry approach can be used for the analysis of said systems, which are often nonlinear. Here we demonstrate the application of such tools to analyse the structural identifiability, observability, accessibility, and controllability of several biomolecular systems. We focus on a set of synthetic circuits of current interest, which can perform several tasks, both in open loop and closed loop settings. We analyse their properties with our own methods and tools; further, we describe a new open-source implementation of the techniques., Comment: 7 pages, 1 figure, submitted to DYCOPS2025

We address the orbital distribution of stars in merging nuclear star clusters (NSCs) and the subsequent effects on supermassive black hole binary (SMBHB) evolution. We ran direct-summation $N$-body simulations with different initial conditions to do a detailed study of the resulting NSC after their progenitors had merged. Our findings reveal that prograde stars form a flattened structure, while retrograde stars have a more spherical distribution. The axial ratios of the prograde component vary based on the presence and mass ratio of the SMBHs. The fraction of prograde and retrograde stars depends on the merger orbital properties and the SMBH mass ratio. The interactions of retrograde stars with the SMBHB affect the eccentricity and separation evolution of the binary. Our analysis reveals a strong correlation between the angular momentum and eccentricity of the SMBH binary. This relationship could serve as a means to infer information about the stellar dynamics surrounding the binary. We find that prograde orbits are particularly close to the binary of SMBHs, a promising fact regarding extreme mass ratio inspiral (EMRI) production. Moreover, prograde and retrograde stars have different kinematic structures, with the prograde stars typically rotating faster than the retrograde ones. The line-of-sight velocity and velocity dispersion, as well as the velocity anisotropy of each NSC, depend on the initial merger orbital properties and SMBH mass ratios. The prograde and retrograde stars always show different behaviours. The distribution of stellar orbits and the dynamical properties of each kinematic population can potentially be used as a way to tell the properties of the parent nuclei apart, and has an important impact on expected rates of EMRIs, which will be detected by future gravitational wave observatories such as the Laser Interferometer Space Antenna (LISA). [abridged], Comment: 14 pages, 8 figures, 2 tables. Two appendices on zenodo (https://zenodo.org/records/13986686). Accepted for publication in A&A

The search for weakly interacting matter particles (WIMPs) is one of the main objectives of the High Luminosity Large Hadron Collider (HL-LHC). In this work we use Machine-Learning (ML) techniques to explore WIMP radiative decays into a Dark Matter (DM) candidate in a supersymmetric framework. The minimal supersymmetric WIMP sector includes the lightest neutralino that can provide the observed DM relic density through its co-annihilation with the second lightest neutralino and lightest chargino. Moreover, the direct DM detection cross section rates fulfill current experimental bounds and provide discovery targets for the same region of model parameters in which the radiative decay of the second lightest neutralino into a photon and the lightest neutralino is enhanced. This strongly motivates the search for radiatively decaying neutralinos which, however, suffers from strong backgrounds. We investigate the LHC reach in the search for these radiatively decaying particles by means of cut-based and ML methods and estimate its discovery potential in this well-motivated, new physics scenario., Comment: 24 pages + references, 8 figures, 3 tables, 3 appendices. Version updated with published LZ results, appendix reserved for preliminary LZ results deleted

A Josephson diode is a superconducting circuit element that enables non-reciprocal transport, allowing a dissipationless supercurrent to preferentially flow in a single direction. Existing methods for achieving the required symmetry breaking mostly rely on specifically-designed materials or carefully-engineered circuits composed of multiple Josephson junctions. Here, we demonstrate that applying a biharmonic drive to a conventional superconducting tunnel-junction induces a diode effect through harmonic mixing processes that shift the supercurrent region. We show that, in a conventional tunnel junction, unity efficiency is achievable while maintaining a large supercurrent. Moreover, the relative phase between the two driving tones determines the directionality of the diode, which can be tuned in situ., Comment: 6 pages, 3 figures

The opening of the gravitational wave window has significantly enhanced our capacity to explore the universe's most extreme and dynamic sector. In the mHz frequency range, a diverse range of compact objects, from the most massive black holes at the farthest reaches of the Universe to the lightest white dwarfs in our cosmic backyard, generate a complex and dynamic symphony of gravitational wave signals. Once recorded by gravitational wave detectors, these unique fingerprints have the potential to decipher the birth and growth of cosmic structures over a wide range of scales, from stellar binaries and stellar clusters to galaxies and large-scale structures. The TianQin space-borne gravitational wave mission is scheduled for launch in the 2030s, with an operational lifespan of five years. It will facilitate pivotal insights into the history of our universe. This document presents a concise overview of the detectable sources of TianQin, outlining their characteristics, the challenges they present, and the expected impact of the TianQin observatory on our understanding of them., Comment: TianQin Gravitational Wave Whitepaper, 72 pages, 30 figures

Studying the orbital motion of stars around Sagittarius A* in the Galactic Center provides a unique opportunity to probe the gravitational potential near the supermassive black hole at the heart of our Galaxy. Interferometric data obtained with the GRAVITY instrument at the Very Large Telescope Interferometer (VLTI) since 2016 has allowed us to achieve unprecedented precision in tracking the orbits of these stars. GRAVITY data have been key to detecting the in-plane, prograde Schwarzschild precession of the orbit of the star S2, as predicted by General Relativity. By combining astrometric and spectroscopic data from multiple stars, including S2, S29, S38, and S55 - for which we have data around their time of pericenter passage with GRAVITY - we can now strengthen the significance of this detection to an approximately $10 \sigma$ confidence level. The prograde precession of S2's orbit provides valuable insights into the potential presence of an extended mass distribution surrounding Sagittarius A*, which could consist of a dynamically relaxed stellar cusp comprised of old stars and stellar remnants, along with a possible dark matter spike. Our analysis, based on two plausible density profiles - a power-law and a Plummer profile - constrains the enclosed mass within the orbit of S2 to be consistent with zero, establishing an upper limit of approximately $1200 \, M_\odot$ with a $1 \sigma$ confidence level. This significantly improves our constraints on the mass distribution in the Galactic Center. Our upper limit is very close to the expected value from numerical simulations for a stellar cusp in the Galactic Center, leaving little room for a significant enhancement of dark matter density near Sagittarius A*., Comment: Submitted to A&A on September 17, 2024

Most complex systems can be captured by graphs or networks. Networks connect nodes (e.g.\ neurons) through edges (synapses), thus summarizing the system's structure. A popular way of interrogating graphs is community detection, which uncovers sets of geometrically related nodes. {\em Geometric communities} consist of nodes ``closer'' to each other than to others in the graph. Some network features do not depend on node proximity -- rather, on them playing similar roles (e.g.\ building bridges) even if located far apart. These features can thus escape proximity-based analyses. We lack a general framework to uncover such features. We introduce {\em topological communities}, an alternative perspective to decomposing graphs. We find clusters that describe a network as much as classical communities, yet are missed by current techniques. In our framework, each graph guides our attention to its relevant features, whether geometric or topological. Our analysis complements existing ones, and could be a default method to study networks confronted without prior knowledge. Classical community detection has bolstered our understanding of biological, neural, or social systems; yet it is only half the story. Topological communities promise deep insights on a wealth of available data. We illustrate this for the global airport network, human connectomes, and others., Comment: 34 pages, 3 main figures, 22 supporting figures

Altermagnetic superconductors offer the possibility of exploring unconventional superconductivity, including topological states and finite-momentum superconductivity, with promising applications in spintronics and quantum information. However, a direct experimental confirmation of their existence remains elusive. In this work, we propose non-magnetic impurities as probes of the interplay between altermagnetism and superconductivity. These impurities induce spin-polarized subgap states whose spatial extension reflects the magnetic order of the substrate material. Depending on whether the impurity respects the bulk symmetries or not, these states form spin-degenerate or spin-split doublets. An external magnetic field aligned with the N\'eel vector can further control the doublet splitting. We further demonstrate that coupling between impurity states leads to a position-dependent, spin-sensitive hybridization, enabling a new approach for in-situ control of atomic-size quantum devices. These findings provide unambiguous experimental signatures of altermagnetic superconductivity accessible via local measurements like scanning tunneling microscopy and open new avenues for designing tunable quantum materials., Comment: 7 + 5 pages, 5 + 3 figures

This work is a thorough and detailed study on the geometry of the unit sphere of certain Banach spaces of homogeneous polynomials in ${\mathbb{R}}^2$. Specifically, we provide a complete description of the unit spheres, identify the extreme points of the unit balls, derive explicit formulas for the corresponding polynomial norms, and describe the techniques required to tackle these questions. To enhance the comprehensiveness of this work, we complement the results and their proofs with suitable diagrams and figures. The new results presented here settle some open questions posed in the past. For the sake of completeness of this work, we briefly discuss previous known results and provide directions of research and applications of our results., Comment: 46 pages, 18 figures

Synchronization dynamics is a phenomenon of great interest in many fields of science. One of the most important fields is neuron dynamics, as synchronization in certain regions of the brain is related to some of the most common mental illnesses. In this work, we study synchronization in a small-world network of non-identical Chialvo neurons that are electrically coupled. We introduce a mismatch in one of the model parameters to construct non-identical neurons. Our study examines the effects of this parameter mismatch, the noise intensity in the stochastic model, and the coupling strength between neurons on synchronization and firing frequency. We have identified critical values of noise intensity, parameter mismatch, and rewiring probability that facilitate effective synchronization within the network. Furthermore, we observe that the balance between excitatory and inhibitory connections plays a crucial role in achieving global synchronization. Our findings offer insights into the mechanisms driving synchronization dynamics in complex neuron networks.

Two semiconducting quantum dots (QDs) coupled through a superconductor constitute a minimal realisation of a Kitaev chain with Majorana zero modes (MZMs). Such MZMs can be detected by e.g., tunneling conductance between each QD and normal leads [Dvir et al, Nature 614, 445 (2023)]. We here discuss how the seemingly trivial substitution of one of the normal leads by a superconducting (SC) one gives rise to a plethora of new effects. In particular, the coupling to the SC lead induces non-local Majorana effects upon variations of the QDs' energies. Furthermore, the lowest excitation of the chain is no longer determined by the bulk gap but rather by the energy of an emergent subgap Yu-Shiba-Rusinov (YSR) state coexisting with the MZMs. The YSR state hybridizes with the MZMs when the coupling between the SC and the QD is larger than the spin splitting, spoiling the Majorana properties, including the quantized conductance., Comment: 17 pages, 12 figures

Superconductor-semiconductor hybrid systems play a crucial role in realizing nanoscale quantum devices, including hybrid qubits, Majorana bound states, and Kitaev chains. For such hybrid devices, subgap states play a prominent role in their operation. In this work, we study such subgap states via Coulomb and tunneling spectroscopy through a superconducting island defined in a semiconductor nanowire fully coated by a superconductor. We systematically explore regimes ranging from an almost decoupled island to the open configuration. In the weak coupling regime, the experimental observations are very similar in the absence of a magnetic field and when one flux quantum is piercing the superconducting shell. Conversely, in the strong coupling regime, significant distinctions emerge between the two cases. We ascribe this different behavior to the existence of subgap states at one flux quantum, which become observable only for sufficiently strong coupling to the leads. We support our interpretation using a simple model to describe transport through the island. Our study highlights the importance of studying a broad range of tunnel couplings for understanding the rich physics of hybrid devices.

Restricted Boltzmann Machines (RBMs) are effective tools for modeling complex systems and deriving insights from data. However, training these models with highly structured data presents significant challenges due to the slow mixing characteristics of Markov Chain Monte Carlo processes. In this study, we build upon recent theoretical advancements in RBM training, to significantly reduce the computational cost of training (in very clustered datasets), evaluating and sampling in RBMs in general. The learning process is analogous to thermodynamic continuous phase transitions observed in ferromagnetic models, where new modes in the probability measure emerge in a continuous manner. Such continuous transitions are associated with the critical slowdown effect, which adversely affects the accuracy of gradient estimates, particularly during the initial stages of training with clustered data. To mitigate this issue, we propose a pre-training phase that encodes the principal components into a low-rank RBM through a convex optimization process. This approach enables efficient static Monte Carlo sampling and accurate computation of the partition function. We exploit the continuous and smooth nature of the parameter annealing trajectory to achieve reliable and computationally efficient log-likelihood estimations, enabling online assessment during the training, and propose a novel sampling strategy named parallel trajectory tempering (PTT) which outperforms previously optimized MCMC methods. Our results show that this training strategy enables RBMs to effectively address highly structured datasets that conventional methods struggle with. We also provide evidence that our log-likelihood estimation is more accurate than traditional, more computationally intensive approaches in controlled scenarios. The PTT algorithm significantly accelerates MCMC processes compared to existing and conventional methods., Comment: 31 pages, 16 figures

In this paper, we investigate the feature encoding process in a prototypical energy-based generative model, the Restricted Boltzmann Machine (RBM). We start with an analytical investigation using simplified architectures and data structures, and end with numerical analysis of real trainings on real datasets. Our study tracks the evolution of the model's weight matrix through its singular value decomposition, revealing a series of phase transitions associated to a progressive learning of the principal modes of the empirical probability distribution. The model first learns the center of mass of the modes and then progressively resolve all modes through a cascade of phase transitions. We first describe this process analytically in a controlled setup that allows us to study analytically the training dynamics. We then validate our theoretical results by training the Bernoulli-Bernoulli RBM on real data sets. By using data sets of increasing dimension, we show that learning indeed leads to sharp phase transitions in the high-dimensional limit. Moreover, we propose and test a mean-field finite-size scaling hypothesis. This shows that the first phase transition is in the same universality class of the one we studied analytically, and which is reminiscent of the mean-field paramagnetic-to-ferromagnetic phase transition., Comment: 19 pages, 6 figures, accepted to Neurips2024

We demonstrate reliable machine-learned tuning of quantum-dot-based artificial Kitaev chains to Majorana sweet spots, using the covariance matrix adaptation algorithm. We show that a loss function based on local tunnelling-spectroscopy features of a chain with two additional sensor dots added at its ends provides a reliable metric to navigate parameter space and find points where crossed Andreev reflection and elastic cotunneling between neighbouring sites balance in such a way to yield near-zero-energy modes with very high Majorana quality. We simulate tuning of two- and three-site Kitaev chains, where the loss function is found from calculating the low-energy spectrum of a model Hamiltonian that includes Coulomb interactions and finite Zeeman splitting. In both cases, the algorithm consistently converges towards high-quality sweet spots. Since tunnelling spectroscopy provides one global metric for tuning all on-site potentials simultaneously, this presents a promising way towards tuning longer Kitaev chains, which are required for achieving topological protection of the Majorana modes.

We report tunneling spectroscopy and transport measurements in superconducting Al and ferromagnetic-insulator EuS bilayers. The samples display remanent spin-splitting, roughly half the superconducting gap, and supercurrent transport above the average paramagnetic limit. We interpret this behavior as arising from the interplay between two characteristic length scales: the superconducting coherence length, $\xi$, and the magnetic domain size, $d$. By comparing experimental results to a theoretical model, we find $\xi/d \approx 10$. In this regime, spin-averaging across the micromagnetic configuration can locally suppress superconductivity, resulting in percolative supercurrent flow., Comment: 15 pages, 4+7 figures

The main purpose of this paper is to study both the underdamped and the overdamped dynamics of the nonlinear Helmholtz oscillator with a fractional order damping. For that purpose, we use the Grunwald-Letnikov fractional derivative algorithm in order to get the numerical simulations. Here, we investigate the effect of taking the fractional derivative in the dissipative term in function of the parameter a. Our main findings show that the trajectories can remain inside the well or can escape from it depending on a which plays the role of a control parameter. Besides, the parameter a is also relevant for the creation or destruction of chaotic motions. On the other hand, the study of the escape times of the particles from the well, as a result of variations of the initial conditions and the undergoing force F, is reported by the use of visualization techniques such as basins of attraction and bifurcation diagrams, showing a good agreement with previous results. Finally, the study of the escape times versus the fractional parameter a shows an exponential decay which goes to zero when a is larger than one. All the results have been carried out for weak damping where chaotic motions can take place in the non-fractional case and also for a stronger damping (overdamped case), where the influence of the fractional term plays a crucial role to enhance chaotic motions. We expect that these results can be of interest in the field of fractional calculus and its applications.

We analyze the nonlinear Helmholtz oscillator in the presence of fractional damping, a characteristic feature in several physical situations. In our specific scenario, as well as in the non-fractional case, for large enough excitation amplitudes, all initial conditions are escaping from the potential well. To address this, we incorporate the phase control technique into a parametric term, a feature commonly encountered in real-world situations. In the non-fractional case it has been shown that, a phase difference of {\phi_{OPT}} \simeq {\pi}, is the optimal value to avoid the escapes of the particles from the potential well. Here, our investigation focuses on understanding when particles escape, considering both the phase difference {\phi} and the fractional parameter {\alpha} as control parameters. Our findings unveil the robustness of phase control, as evidenced by the consistent oscillation of the optimal {\phi} value around its non-fractional counterpart when varying the fractional parameter. Additionally, our results underscore the pivotal role of the fractional parameter in governing the proportion of bounded particles, even when utilizing the optimal phase.

The Lunar Gravitational-wave Antenna (LGWA) is a proposed array of next-generation inertial sensors to monitor the response of the Moon to gravitational waves (GWs). Given the size of the Moon and the expected noise produced by the lunar seismic background, the LGWA would be able to observe GWs from about 1 mHz to 1 Hz. This would make the LGWA the missing link between space-borne detectors like LISA with peak sensitivities around a few millihertz and proposed future terrestrial detectors like Einstein Telescope or Cosmic Explorer. In this article, we provide a first comprehensive analysis of the LGWA science case including its multi-messenger aspects and lunar science with LGWA data. We also describe the scientific analyses of the Moon required to plan the LGWA mission.

We investigate the synchronization between two neurons using the stochastic version of the map-based Chialvo model. To simulate non-identical neurons, a mismatch is introduced in one of the main parameters of the model. Subsequently, the synchronization of the neurons is studied as a function of this mismatch, the noise introduced in the stochastic model, and the coupling strength between the neurons. We propose the simplest neuron network for study, as its analysis is more straightforward and does not compromise generality. Within this network, two nonidentical neuron maps are electrically coupled. In order to understand if specific behaviors affect the global behavior of the system, we consider different cases related to the behavior of the neurons (chaotic or periodic). Furthermore, we study how variations in model parameters affect the firing frequency in all cases. Additionally, we consider that the two neurons have both excitatory and inhibitory couplings. Consequently, we identify critical values of noise and mismatch for achieving satisfactory synchronization between the neurons in both cases. Finally, we conjecture that the results are of a general nature and are applicable to different neuron models.

In recent years, experimental advances have made it possible to achieve an unprecedented degree of control over the properties of subgap bound states in hybrid nanoscale superconducting structures. This research has been driven by the promise of engineering subgap states for quantum applications, which includes Majorana zero modes predicted to appear at the interface of superconductor and other materials, like topological insulators or semiconductors. In this chapter, we revise the status of the field towards the engineering of quantum devices in controllable semiconductor-superconductor heterostructures. We begin the chapter with a brief introduction about subgap states, focusing on their mathematical formulation. After introducing topological superconductivity using the Kitaev model, we discuss the advances in the search for Majorana states over the last few years, highlighting the difficulties of unambiguously distinguish these states from nontopological subgap states. In recent years, the precise engineering of bound states by a bottom-up approach using quantum dots has led to unprecedented experimental advances, including experimental demonstrations of an Andreev qubits based on a quantum dot Josephson junction and a minimal Kitaev chain based on two quantum dots coherently coupled by the bound states of an intermediate superconducting segment. These experimental advances have revitalized the field and helped to understand that, far from being a disadvantage, the presence of subgap bound states can be exploited for new qubit designs and quantum coherence experiments, including Majorana-based qubits., Comment: This is a preprint of a chapter to be published in "New Trends and Platforms for Quantum Technologies", edited by R. Aguado, R. Citro, M. Lewenstein, and M. Stern, 2024, Springer. Reproduced with permission of Springer Nature Switzerland AG. We will provide a link to the final authenticated version when available

In this paper, we study different types of phase space structures which appear in the context of relativistic chaotic scattering. By using the relativistic version of the H\'{e}non-Heiles Hamiltonian, we numerically study the topology of different kind of exit basins and compare it with the case of low velocities in which the Newtonian version of the system is valid. Specifically, we numerically study the escapes in the phase space, in the energy plane and also in the $\beta$ plane which richly characterize the dynamics of the system. In all cases, fractal structures are present, and the escaping dynamics is characterized. Besides, in every case a scaling law is numerically obtained in which the percentage of the trapped trajectories as a function of the relativistic parameter $\beta$ and the energy is obtained. Our work could be useful in the context of charged particles which eventually can be trapped in the magnetosphere, where the analysis of these structures can be relevant.

The gravitational capture of a stellar-mass object by a supermassive black hole represents a unique probe of warped spacetime. The small object, typically a stellar-mass black hole, describes a very large number of cycles before crossing the event horizon. Because of the mass difference, we call these captures extreme-mass ratio inspirals (EMRIs). Their merger event rate at the Galactic Centre is negligible, but the amount of time spent in the early inspiral is not. Early EMRIs (E-EMRIs) spend hundreds of thousands of years in band during this phase. At very early stages, the peak of the frequency will not change during an observational time. At later stages, it will change a bit and finally the EMRI explores a wide range of them when it is close to merger. We distinguish between "monocromatic" E-EMRIs, which do not change their (peak) frequency, oligochromatic E-EMRIs, which explore a short range and polychromatic ones, the EMRIs which have been discussed so far in the literature. We derive the number of E-EMRIs at the Galactic Centre, and their signal-to-noise ratios (SNR) and perform a study of parameter extraction. We show that parameters such as the spin and the mass can be extracted with an error which can be as small as $10^{-11}$ and $10^{-5}\,M_{\odot}$. There are between hundreds and thousands of E-EMRIs in their monochromatic stage at the GC, and tens in their oligochromatic phase. The SNR ranges from a minimum of $10$ (larger likelihood) to a maximum of $10^6$ (smaller likelihood). Moreover, we derive the contribution signal corresponding to the incoherent sum of continuous with two representatives masses; $10\,M_{\odot}$ and $40\,M_{\odot}$ and show that their curves will cover a significant part of LISA's sensitivity curve. Depending on their level of circularisation, they might be detected as individual sources or form a foreground population., Comment: Accepted for publication. Visit https://youtu.be/zLJ6i6TR1Nk or https://tinyurl.com/bilibili-E-EMRIs for an illustration

Silicon photonics arises as a viable solution to address the stringent resource demands of emergent technologies, such as neural networks. Within this framework, photonic memories are fundamental building blocks of photonic integrated circuits that have not yet found a standardized solution due to several trade-off among different metrics such as energy consumption, speed, footprint, or fabrication complexity, to name a few. In particular, a photonic memory exhibiting ultra-high endurance performance (> 10^6 cycles) has been elusive to date. Here, we report an ultra-high endurance silicon photonic memory using vanadium dioxide (VO_2) exhibiting a record cyclability of up to 10^7 cycles without degradation. Moreover, our memory features an ultra-compact footprint below 5 {\mu}m with potential for nanosecond and picojoule programming performance. Our silicon photonic memory could find application in emerging photonic applications demanding high number of memory updates such as photonic neural networks with in-situ training.

Hybrid organometal halide perovskites (HP) present exceptional optoelectronic properties, but their poor long-term stability is a major bottleneck for their commercialization. Herein, we present a solvent-free approach to growing single-crystal organic nanowires (ONW), nanoporous metal oxide scaffolds, and HP to form a core@multishell architecture. The synthetic procedure is carried out under mild vacuum conditions employing thermal evaporation for the metal-free phthalocyanine (H2Pc) nanowires, which will be the core, plasma-enhanced chemical vapor deposition (PECVD) for the TiO2 shell, and co-evaporation of lead iodide (PbI2) and methylammonium iodide (CH3NH3I / MAI) for the CH3NH3PbI3 (MAPbI3 / MAPI) perovskite shell. We present a detailed characterization of the nanostructures by (S)-TEM and XRD, revealing a different crystallization of the hybrid perovskite depending on the template: while the growth on H2Pc nanowires induces the typical tetragonal structure of the MAPI perovskite, a low-dimensional phase (LDP) was observed on the one-dimensional TiO2 nanotubes. Such a combination yields an unprecedentedly stable photoluminescence emission over 20 hours and over 300 hours after encapsulation in polymethyl methacrylate (PMMA) under different atmospheres including N2, air, and high moisture levels. In addition, the unique one-dimensional morphology of the system, together with the high refractive index HP, allows for a strong waveguiding effect along the nanowire length.

In this note we show that there exist a $2^\mathfrak{c}$-generated free algebra $\mathcal{S} \subset \mathbb{R}^\mathbb{R}$ of Riemann integrable functions and a free algebra $\mathcal{C} \subset \mathbb{R}^{[0,1]}$ of continuous functions, having $\mathfrak{c}$-generators, such that $r \circ c$ is not Riemann integrable for any $r \in \mathcal{S}$ and $c \in \mathcal{C}$. This result is the best possible one in terms of lineability within these families of functions and, at the same time, an improvement of a precious result (\cite[Theorem 2.7]{A}). In order to achieve our results we shall employ set theoretical tools such as the Fichtenholz-Kantorovich-Hausdorff theorem, Cantor-Smith-Volterra--type sets, and classical real analysis techniques.

The Laser Interferometer Space Antenna (LISA) is the first scientific endeavour to detect and study gravitational waves from space. LISA will survey the sky for Gravitational Waves in the 0.1 mHz to 1 Hz frequency band which will enable the study of a vast number of objects ranging from Galactic binaries and stellar mass black holes in the Milky Way, to distant massive black-hole mergers and the expansion of the Universe. This definition study report, or Red Book, presents a summary of the very large body of work that has been undertaken on the LISA mission over the LISA definition phase., Comment: 155 pages, with executive summary and table of contents