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Few primitives are as intertwined with the foundations of cryptography as Oblivious Transfer (OT). Not surprisingly, with the advent of the use of quantum resources in information processing, OT played a central role in establishing new possibilities (and defining impossibilities) pertaining to the use of these novel assets. A major research path is minimizing the required assumptions to achieve OT, and studying their consequences. Regarding its computation, it is impossible to construct unconditionally-secure OT without extra assumptions; and, regarding communication complexity, achieving 1-shot (and even non-interactive) OT has proved to be an elusive task, widely known to be impossible classically. Moreover, this has strong consequencesfor realizing round-optimal secure computation, in particular 1-shot 2-Party Computation (2PC). In this work, three main contributions are evidenced by leveraging quantum resources: 1. Unconditionally-secure 2-message non-interactive OT protocol constructed in the Noisy-Quantum-Storage Model. 2. 1-shot OT in the Noisy-Quantum-Storage Model -- proving that this construction is possible assuming the existence of one-way functions and sequential functions. 3. 1-shot 2PC protocol compiled from a semi-honest 1-shot OT to semi-honest 1-shot Yao's Garbled Circuits protocol., Comment: 32 pages, 2 figures

What does a black hole look like? In 1+3 spacetime dimensions, the optical appearance of a black hole is a bidimensional region in the observer's sky often called the black hole shadow, as supported by the EHT observations. In higher dimensions this question is more subtle and observational setup dependent. Previous studies considered the shadows of higher dimensional black holes to remain bidimensional. We argue that the latter should be regarded as a tomography of a higher dimensional structure, the hypershadow, which would be the structure "seen" by higher dimensional observers. As a case study we consider the cohomogeneity-one Myers-Perry black hole in 1+4 dimensions, and compute its tridimensional hypershadow., Comment: 23 pages, 5 figures

Star formation in the central molecular zone (CMZ) is suppressed with respect to that of the Galactic disk, and this is likely related to its high turbulent environment. This turbulence impedes the potential detection of prestellar cores. We present the temperature, density, and spatial structure of the CMZ molecular cloud G+0.693-0.027, which has been proposed to host a prestellar cluster in the Sgr B2 region. We analysed multiple HC$_{3}$N rotational transitions that were observed with the IRAM 30m, APEX, Yebes 40m, and GBT radio telescopes, together with SMA+APEX spatially resolved maps. The spectral shape of HC$_{3}$N lines shows three velocity components: a broad component with a line width of 23 km s$^{-1}$ (C1), and two narrow components with line widths of 7.2 and 8.8 km s$^{-1}$ (C2 and C3). This suggests that a fraction of the molecular gas in this cloud is undergoing turbulence dissipation. From a non-local thermodynamic equilibrium analysis we have found H$_{2}$ densities of 2$\times$10$^{4}$ cm$^{-3}$, 5$\times$10$^{4}$ cm$^{-3}$, and 4$\times$10$^{5}$ cm$^{-3}$ and kinetic temperatures of 140 K, 30 K, and 80 K for C1, C2, and C3, respectively. The spatially resolved maps confirm that the colder and high-density condensations C2 and C3, which peak in the 70-85 km s$^{-1}$ velocity range, are embedded in a more diffuse and warmer gas (C1). The larger-scale structure of the Sgr B2 region shows a hole at 40-50 km s$^{-1}$ that is likely due to a small cloud that shocked the Sgr B2 region and is spatially related with a massive cloud at 60-80 km s$^{-1}$. We propose that the impacting small cloud sequentially triggered the formation of Sgr B2(M), (N), and (S) and the condensations in G+0.693-0.027 during its passage. Based on the analysis of the masses of the two condensations and on the virial parameters, C2 might expand, while C3 might further fragment or collapse., Comment: 21 pages, 16 figures, 5 tables, 4 appendix - Accepted for publication in A&A

Sulphur-bearing species play crucial roles in interstellar chemistry, yet their precise characterisation remains challenging. Here, we present laboratory experiments aimed at extending the high-resolution spectroscopy of protonated carbonyl sulphide (HOCS$^+$), a recently detected molecular ion in space. Using a frequency-modulated free-space absorption spectrometer, we detected rotational transitions of HOCS$^+$ in an extended negative glow discharge with a mixture of H$_2$ and OCS, extending the high-resolution rotational characterisation of the cation well into the millimetre wave region (200-370 GHz). Comparisons with prior measurements and quantum chemical calculations revealed an overall agreement in the spectroscopic parameters. With the new spectroscopic dataset in hand, we re-investigated the observations of HOCS$^+$ towards G+0.693-0.027, which were initially based solely on K$_a$ = 0 lines contaminated by HNC$^{34}$S. This re-investigation enabled the detection of weak K$_a$ = 0 transitions, free from HNC$^{34}$S contamination. Our high-resolution spectroscopic characterisation also provides valuable insights for future millimetre and submillimetre astronomical observations of these species in different interstellar environments. In particular, the new high-resolution catalogue will facilitate the search for this cation in cold dark clouds, where very narrow line widths are typically observed., Comment: 9 pages, 3 figures, and 3 tables. Accepted for publication in Astronomy & Astrophysics

In this paper we consider proper orthogonal decomposition (POD) methods that do not include difference quotients (DQs) of snapshots in the data set. The inclusion of DQs have been shown in the literature to be a key element in obtaining error bounds that do not degrade with the number of snapshots. More recently, the inclusion of DQs has allowed to obtain pointwise (as opposed to averaged) error bounds that decay with the same convergence rate (in terms of the POD singular values) as averaged ones. In the present paper, for POD methods not including DQs in their data set, we obtain error bounds that do not degrade with the number of snapshots if the function from where the snapshots are taken has certain degree of smoothness. Moreover, the rate of convergence is as close as that of methods including DQs as the smoothness of the function providing the snapshots allows. We do this by obtaining discrete counterparts of Agmon and interpolation inequalities in Sobolev spaces. Numerical experiments validating these estimates are also presented., Comment: 23 pages, 2 figures

We report the first detection of the metal-bearing molecules sodium sulfide (NaS) and magnesium sulfide (MgS) and the tentative detection of calcium monoxide (CaO) in the interstellar medium (ISM) towards the Galactic Center molecular cloud G+0.693-0.027. The derived column densities are (5.0+-1.1) x 10$^{10}$ cm$^{-2}$, (6.0+-0.6) x $^{10}$ cm$^{-2}$, and (2.0+-0.5) x $^{10}$ cm$^{-2}$, respectively. This translates into fractional abundances with respect to H$_2$ of (3.7+-1.0) x $10^{-13}$, (4.4+-0.8) x $10^{-13}$, and (1.5+-0.4) x $10^{-13}$, respectively. We have also searched for other Na-, Mg- and Ca-bearing species towards this source but none of them have been detected and thus we provide upper limits for their abundances. We discuss the possible chemical routes involved in the formation of these molecules containing metals under interstellar conditions. Finally, we compare the ratio between sulfur-bearing and oxygen-bearing molecules with and without metals, finding that metal-bearing sulfur molecules are much more abundant than metal-bearing oxygen ones, in contrast with the general trend found in the ratios between other non metal- oxygen- and sulfur-bearing molecules. This further strengthen the idea that sulfur may be little depleted in G+0.693-0.027 as a result of the low velocity shocks present in this source sputtering large amounts of material from dust grains., Comment: 18 pages, 7 tables and 7 figures, final version accepted by ApJ

With the fast and unstoppable evolution of robotics and artificial intelligence, effective autonomous navigation in real-world scenarios has become one of the most pressing challenges in the literature. However, demanding requirements, such as real-time operation, energy and computational efficiency, robustness, and reliability, make most current solutions unsuitable for real-world challenges. Thus, researchers are forced to seek innovative approaches, such as bio-inspired solutions. Indeed, animals have the intrinsic ability to efficiently perceive, understand, and navigate their unstructured surroundings. To do so, they exploit self-motion cues, proprioception, and visual flow in a cognitive process to map their environment and locate themselves within it. Computational neuroscientists aim to answer ''how'' and ''why'' such cognitive processes occur in the brain, to design novel neuromorphic sensors and methods that imitate biological processing. This survey aims to comprehensively review the application of brain-inspired strategies to autonomous navigation, considering: neuromorphic perception and asynchronous event processing, energy-efficient and adaptive learning, or the imitation of the working principles of brain areas that play a crucial role in navigation such as the hippocampus or the entorhinal cortex., Comment: 35 pages, 6 figures, journal article

Methods to find the solution state for optimization problems encoded into Ising Hamiltonians are a very active area of current research. In this work we compare the quantum approximate optimization algorithm (QAOA) with multi-stage quantum walks (MSQW). Both can be used as variational quantum algorithms, where the control parameters are optimized classically. A fair comparison requires both quantum and classical resources to be assessed. Alternatively, parameters can be chosen heuristically, as we do in this work, providing a simpler setting for comparisons. Using both numerical and analytical methods, we obtain evidence that MSQW outperforms QAOA, using equivalent resources. We also show numerically for random spin glass ground state problems that MSQW performs well even for few stages and heuristic parameters, with no classical optimization., Comment: 19 pages, 6 figures, minor update in v2 to correct author name

Functional data analysis has become a tool of interest in applied areas such as economics, medicine, and chemistry. Among the techniques developed in recent literature, functional semiparametric regression stands out for its balance between flexible modelling and output interpretation. Despite the large variety of research papers dealing with scalar-on-function (SoF) semiparametric models, there is a notable gap in software tools for their implementation. This article introduces the R package \texttt{fsemipar}, tailored for these models. \texttt{fsemipar} not only estimates functional single-index models using kernel smoothing techniques but also estimates and selects relevant scalar variables in semi-functional models with multivariate linear components. A standout feature is its ability to identify impact points of a curve on the response, even in models with multiple functional covariates, and to integrate both continuous and pointwise effects of functional predictors within a single model. In addition, it allows the use of location-adaptive estimators based on the $k$-nearest-neighbours approach for all the semiparametric models included. Its flexible interface empowers users to customise a wide range of input parameters and includes the standard S3 methods for prediction, statistical analysis, and estimate visualization (\texttt{predict}, \texttt{summary}, \texttt{print}, and \texttt{plot}), enhancing clear result interpretation. Throughout the article, we illustrate the functionalities and the practicality of \texttt{fsemipar} using two chemometric datasets., Comment: 41 pages, 7 figures, 11 tables

The aim of this note is to construct a neural network for which the linear finite element approximation of a simple one dimensional boundary value problem is a minimum of the cost function to find out if the neural network is able to reproduce the finite element approximation. The deepest goal is to shed some light on the problems one encounters when trying to use neural networks to approximate partial differential equations

Multiphoton indistinguishability is a central resource for quantum enhancement in sensing and computation. Developing and certifying large scale photonic devices requires reliable and accurate characterization of this resource, preferably using methods that are robust against experimental errors. Here, we propose a set of methods for the characterization of multiphoton indistinguishability, based on measurements of bunching and photon number variance. Our methods are robust in a semi-device independent way, in the sense of being effective even when the interferometers are incorrectly dialled. We demonstrate the effectiveness of this approach using an advanced photonic platform comprising a quantum-dot single-photon source and a universal fully-programmable integrated photonic processor. Our results show the practical usefulness of our methods, providing robust certification tools that can be scaled up to larger systems., Comment: 19 pages + 10 figures

Self-supervised contrastive learning has emerged as one of the most successful deep learning paradigms. In this regard, it has seen extensive use in image registration and, more recently, in the particular field of medical image registration. In this work, we propose to test and extend and improve a state-of-the-art framework for color fundus image registration, ConKeD. Using the ConKeD framework we test multiple loss functions, adapting them to the framework and the application domain. Furthermore, we evaluate our models using the standarized benchmark dataset FIRE as well as several datasets that have never been used before for color fundus registration, for which we are releasing the pairing data as well as a standardized evaluation approach. Our work demonstrates state-of-the-art performance across all datasets and metrics demonstrating several advantages over current SOTA color fundus registration methods

The quantum central limit theorem derived by Cushen and Hudson provides the foundations for understanding how subsystems of large bosonic systems evolving unitarily do reach equilibrium. It finds important applications in the context of quantum interferometry, for example, with photons. A practical feature of current photonic experiments, however, is that photons carry their own internal degrees of freedom pertaining to, e.g., the polarization or spatiotemporal mode they occupy, which makes them partially distinguishable. The ensuing deviation from ideal indistinguishability is well known to have observable consequences, for example in relation with boson bunching, but an understanding of its role in bosonic equilibration phenomena is still missing. Here, we generalize the Cushen-Hudson quantum central limit theorem to encompass scenarios with partial distinguishability, implying an asymptotic convergence of the subsystem's reduced state towards a multimode Gaussian state defined over the internal degrees of freedom. While these asymptotic internal states may not be directly accessible, we show that particle number distributions carry important signatures of distinguishability, which may be used to diagnose experimental imperfections in large boson sampling experiments., Comment: 8+2 pages, 2 figures

Superconducting RF cavities are used in particle accelerators to provide energy to the particle beam. Such cavities are mostly fabricated in niobium and often operated in superfluid helium. One of their limits of operation is the appearance of a local quench, initiated by a local field enhancement due to a defect, which leads to a normal conducting transition of the cavity. Localizing the quench area can be achieved with temperature mapping systems. Another method is the use of second sound wave propagation in superfluid helium. Measuring the time of propagation of these waves from quench location to special sensors, called Oscillating Superleak Transducers (OSTs), and using their well-known velocity should allow trilateration. However, most of experimental measurements on cavities show "premature signals", i.e. the second sound signals arrive earlier on the OSTs than expected. This paper presents several quench experiments on cavities equipped with OSTs and temperature mapping quench detection systems. Two hypotheses can explain the observed premature signals. The first one assesses faster propagation in helium. An experimental setup has been developed for testing this hypothesis, where second sound is created by a localized heater in a controlled environment up to 4.3 kW/cm2 and 2.8 J. Premature signals could not be verified in this setup. A second hypothesis based on a simple model including several processes in niobium and second sound propagation in helium is discussed. The model improves significantly the prediction of the times of arrival of the second sound waves. The overall study shows that the processes in niobium play a prominent role in the second sound detection for superconducting cavities., Comment: 12 pages, 22 images

The spin-orbit splitting between neutron 1$p$ orbitals at $^{33}$Si has been deduced using the single-neutron-adding ($d$,$p$) reaction in inverse kinematics with a beam of $^{32}$Si, a long-lived radioisotope. Reaction products were analyzed by the newly implemented SOLARIS spectrometer at the reaccelerated-beam facility at the National Superconducting Cyclotron Laboratory. The measurements show reasonable agreement with shell-model calculations that incorporate modern cross-shell interactions, but they contradict the prediction of proton density depletion based on relativistic mean-field theory. The evolution of the neutron 1$p$-shell orbitals is systematically studied using the present and existing data in the isotonic chains of $N=17$, 19, and 21. In each case, a smooth decrease in the separation of the $1p_{3/2}$-$1p_{1/2}$ orbitals is seen as the respective $p$-orbitals approach zero binding, suggesting that the finite nuclear potential strongly influences the evolution of nuclear structure in this region., Comment: 10 pages, 5 figures

We report the first detection in the interstellar medium of $N$-cyanomethanimine (H$_2$CNCN), the stable dimer of HCN of highest energy, and the most complex organic molecule identified in space containing the prebiotically relevant NCN backbone. We have identified a plethora of $a$-type rotational transitions with 3 $\leq J_\text{up} \leq$ 11 and $K_\text{a} \leq$ 2 that belong to this species towards the Galactic Center G+0.693-0.027 molecular cloud, the only interstellar source showing the three cyanomethanimine isomers (including the $Z$- and $E$- isomers of $C$-cyanomethanimine, HNCHCN). We have derived a total column density for H$_2$CNCN of (2.9$\, \pm \,$0.1)$\times$10$^{12}$ cm$^{-2}$, which translates into a total molecular abundance with respect to H$_2$ of (2.1$\, \pm \,$0.3)$\times$10$^{-11}$. We have also revisited the previous detection of $E$- and $Z$-HNCHCN, and found a total $C/N$-cyanomethanimine abundance ratio of 31.8$\, \pm \,$1.8 and a $Z/E$-HNCHCN ratio of 4.5$\, \pm \,$0.2. While the latter can be explained on the basis of thermodynamic equilibrium, chemical kinetics are more likely responsible for the observed $C/N$-cyanomethanimine abundance ratio, where the gas-phase reaction between methanimine (CH$_2$NH) and the cyanogen radical (CN) arises as the primary formation route., Comment: 22 pages, 8 figures, 3 tables, 2 appendix - Accepted for publication in The Astrophysical Journal

We present the first detection in space of thionylimide (HNSO) toward the Galactic Center molecular cloud G+0.693-0.027, thanks to the superb sensitivity of an ultradeep molecular line survey carried out with the Yebes 40$\,$m and IRAM 30$\,$m telescopes. This molecule is the first species detected in the interstellar medium containing, simultaneously, N, S and O. We have identified numerous $K$$_a$ = 0, 1 and 2 transitions belonging to HNSO covering from $J$$_{\rm up}$ = 2 to $J$$_{\rm up}$ = 10, including several completely unblended features. We derive a molecular column density of $N$ = (8 $\pm$ 1)$\times$10$^{13}$ cm$^{-2}$, yielding a fractional abundance relative to H$_2$ of $\sim$6$\times$10$^{-10}$, which is about $\sim$37 and $\sim$4.8 times less abundant than SO and SO2, respectively. Although there are still many unknowns in the interstellar chemistry of NSO-bearing molecules, we propose that HNSO is likely formed through the reaction of the NSO radical and atomic H on the surface of icy grains, with alternative routes also deserving exploration. Finally, HNSO appears as a promising link between N- , S- and O- interstellar chemistry and its discovery paves the route to the detection of a new family of molecules in space., Comment: Forthcoming paper in The Astrophysical Journal Letters (in press)

Quantum theory is traditionally formulated using complex numbers. This imaginarity of quantum theory has been quantified as a resource with applications in discrimination tasks, pseudorandomness generation, and quantum metrology. Here we propose witnesses for imaginarity that are basis-independent, relying on measurements of unitary-invariant properties of sets of states. For 3 pure states, we completely characterize the invariant values attainable by quantum theory, and give a partial characterization for 4 pure states. We show that simple pairwise overlap measurements suffice to witness imaginarity of sets of 4 states, but not for sets of 3. Our witnesses are experimentally friendly, opening up a new path for measuring and using imaginarity as a resource., Comment: 4+6 pages, 1 figure

This paper studies discretization of time-dependent partial differential equations (PDEs) by proper orthogonal decomposition reduced order models (POD-ROMs). Most of the analysis in the literature has been performed on fully-discrete methods using first order methods in time, typically the implicit Euler time integrator. Our aim is to show which kind of error bounds can be obtained using any time integrator, both in the full order model (FOM), applied to compute the snapshots, and in the POD-ROM method. To this end, we analyze in this paper the continuous-in-time case for both the FOM and POD-ROM methods, although the POD basis is obtained from snapshots taken at a discrete (i.e., not continuous) set times. Two cases for the set of snapshots are considered: The case in which the snapshots are based on first order divided differences in time and the case in which they are based on temporal derivatives. Optimal pointwise-in-time error bounds {between the FOM and the POD-ROM solutions} are proved for the $L^2(\Omega)$ norm of the error for a semilinear reaction-diffusion model problem. The dependency of the errors on the distance in time between two consecutive snapshots and on the tail of the POD eigenvalues is tracked. Our detailed analysis allows to show that, in some situations, a small number of snapshots in a given time interval might be sufficient to accurately approximate the solution in the full interval. Numerical studies support the error analysis.

We present the first detection in space of O-protonated carbonyl sulfide (\ch{HOCS+}), in the midst of an ultradeep molecular line survey toward the G+0.693-0.027 molecular cloud. From the observation of all $K$$_a$ = 0 transitions ranging from $J$$_{lo}$ = 2 to $J$$_{lo}$ = 13 of \ch{HOCS+} covered by our survey, we derive a column density of $N$ = (9 $\pm$ 2)$\times$10$^{12}$ cm$^{-2}$, translating into a fractional abundance relative to H$_2$ of $\sim$7$\times$10$^{-11}$. Conversely, the S-protonated \ch{HSCO+} isomer remains undetected, and we derive an upper limit to its abundance with respect to H$_2$ of $\leq$3$\times$10$^{-11}$, a factor of $\geq$2.3 less abundant than \ch{HOCS+}. We obtain a \ch{HOCS+}/OCS ratio of $\sim$2.5$\times$10$^{-3}$, in good agreement with the prediction of astrochemical models. These models show that one of the main chemical routes to the interstellar formation of \ch{HOCS+} is likely the protonation of OCS, which appears to be more efficient at the oxygen end. Also, we find that high values of cosmic-ray ionisation rates (10$^{-15}$-10$^{-14}$ s$^{-1}$) are needed to reproduce the observed abundance of \ch{HOCS+}. In addition, we compare the O/S ratio across different interstellar environments. G+0.693-0.027 appears as the source with the lowest O/S ratio. We find a \ch{HOCO+}/\ch{HOCS+} ratio of $\sim$31, in accordance with other O/S molecular pairs detected toward this region and also close to the O/S solar value ($\sim$37). This fact indicates that S is not significantly depleted within this cloud due to the action of large-scale shocks, unlike in other sources where S-bearing species remain trapped on icy dust grains., Comment: Forthcoming paper in The Astrophysical Journal (in press)

This paper focuses on a semiparametric regression model in which the response variable is explained by the sum of two components. One of them is parametric (linear), the corresponding explanatory variable is measured with additive error and its dimension is finite ($p$). The other component models, in a nonparametric way, the effect of a functional variable (infinite dimension) on the response. $k$-NN based estimators are proposed for each component, and some asymptotic results are obtained. A simulation study illustrates the behaviour of such estimators for finite sample sizes, while an application to real data shows the usefulness of our proposal., Comment: 23 pages, 2 figures, 3 tables