Miracle-dz/UniFAR-FTUs huggingface dataset:
Quantum supremacy in constant-time measurement-based computation: A unified architecture for sampling and verification

While quantum speed-up in solving certain decision problems by a fault-tolerant universal quantum computer has been promised, a timely research interest includes how far one can reduce the resource requirement to demonstrate a provable advantage in quantum devices without demanding quantum error correction, which is crucial for prolonging the coherence time of qubits. We propose a model device made of locally-interacting multiple qubits, designed such that simultaneous single-qubit measurements on it can output probability distributions whose average-case sampling is classically intractable, under similar assumptions as the sampling of non-interacting bosons and instantaneous quantum circuits. Notably, in contrast to these previous unitary-based realizations, our measurement-based implementation has two distinctive features. (i) Our implementation involves no adaptation of measurement bases, leading output probability distributions to be generated in constant time, independent of the system size. Thus, it could be implemented in principle without quantum error correction. (ii) Verifying the classical intractability of our sampling is done by changing the Pauli measurement bases only at certain output qubits. Our usage of random commuting quantum circuits in place of computationally universal circuits allows a unique unification of sampling and verification, so that they require the same physical resource requirements in contrast to the more demanding verification protocols seen elsewhere in the literature.
Arithmetics of homogeneous spaces over p$p$‐adic function fields

Let be the function field of a smooth projective geometrically integral curve over a finite extension of . Following the works of Harari, Scheiderer, Szamuely, Izquierdo, and Tian, we study the local–global and weak approximation problems for homogeneous spaces of with geometric stabilizers extension of a group of multiplicative type by a unipotent group. The tools used are arithmetic (local and global) duality theorems in Galois cohomology, in combination with techniques similar to those used by Harari, Szamuely, Colliot‐Thélène, Sansuc, and Skorobogatov. As a consequence, we show that any finite abelian group is a Galois group over , rediscovering the positive answer to the abelian case of the inverse Galois problem over . In the case where the curve is defined over a higher dimensional local field instead of a finite extension of , coarser results are also given.
Flexible list colorings: Maximizing the number of requests satisfied

Flexible list coloring was introduced by Dvo\v{r}\'{a}k, Norin, and Postle in 2019. Suppose $0 \leq \epsilon \leq 1$, $G$ is a graph, $L$ is a list assignment for $G$, and $r$ is a function with non-empty domain $D\subseteq V(G)$ such that $r(v) \in L(v)$ for each $v \in D$ ($r$ is called a request of $L$). The triple $(G,L,r)$ is $\epsilon$-satisfiable if there exists a proper $L$-coloring $f$ of $G$ such that $f(v) = r(v)$ for at least $\epsilon|D|$ vertices in $D$. We say $G$ is $(k, \epsilon)$-flexible if $(G,L',r')$ is $\epsilon$-satisfiable whenever $L'$ is a $k$-assignment for $G$ and $r'$ is a request of $L'$. It was shown by Dvo\v{r}\'{a}k et al. that if $d+1$ is prime, $G$ is a $d$-degenerate graph, and $r$ is a request for $G$ with domain of size $1$, then $(G,L,r)$ is $1$-satisfiable whenever $L$ is a $(d+1)$-assignment. In this paper, we extend this result to all $d$ for bipartite $d$-degenerate graphs. The literature on flexible list coloring tends to focus on showing that for a fixed graph $G$ and $k \in \mathbb{N}$ there exists an $\epsilon>0$ such that $G$ is $(k, \epsilon)$-flexible, but it is natural to try to find the largest possible $\epsilon$ for which $G$ is $(k,\epsilon)$-flexible. In this vein, we improve a result of Dvo\v{r}\'{a}k et al., by showing $d$-degenerate graphs are $(d+2, 1/2^{d+1})$-flexible. In pursuit of the largest $\epsilon$ for which a graph is $(k,\epsilon)$-flexible, we observe that a graph $G$ is not $(k, \epsilon)$-flexible for any $k$ if and only if $\epsilon>1/ \rho(G)$, where $\rho(G)$ is the Hall ratio of $G$, and we initiate the study of the list flexibility number of a graph $G$, which is the smallest $k$ such that $G$ is $(k,1/ \rho(G))$-flexible. We study relationships and connections between the list flexibility number, list chromatic number, list packing number, and degeneracy of a graph.
On the overdamping phenomenon for compressible multi-fluid systems with rough coefficients

In this paper we investigate two types of relaxation processes quantitatively in the context of small data global-in-time solutions for compressible one-velocity multi-fluid models. First, we justify the pressure-relaxation limit from a one-velocity Baer-Nunziato system to a Kapila model as the pressure-relaxation parameter tends to zero, in a uniform manner with respect to the time-relaxation parameter associated to the friction forces modeled in the equation of the velocity. This uniformity allows us to further consider the time-relaxation limit for the Kapila model. More precisely, we show that the diffusely time-rescaled solution of the Kapila system converges to the solution of a two-phase porous media type system as the time-relaxation parameter tends to zero. For both relaxation limits, we exhibit explicit convergence rates. Our proof of existence results are based on an elaborate low-frequency and high-frequency analysis via the Littlewood-Paley decomposition and it includes three main ingredients: a refined spectral analysis for the linearized problem to determine the threshold of frequencies explicitly in terms of the time-relaxation parameter, the introduction of an effective flux in the low-frequency region to overcome the loss of parameters due to the overdamping phenomenon, and the renormalized energy estimates in the high-frequency region to cancel higher-order nonlinear terms. To show the convergence rates, we discover several auxiliary unknowns that reveal better structures. In conclusion, our approach may be applied to a class of non-symmetric partially dissipative hyperbolic system with rough coefficients which do not have any time-integrability, in the context of overdamping phenomenon. It extends the latest results of Danchin and the first author [15, 16].
Detecting train driveshaft damages using accelerometer signals and Differential Convolutional Neural Networks

Railway axle maintenance is critical to avoid catastrophic failures. Nowadays, condition monitoring techniques are becoming more prominent in the industry to prevent enormous costs and damage to human lives. This paper proposes the development of a railway axle condition monitoring system based on advanced 2D-Convolutional Neural Network (CNN) architectures applied to time-frequency representations of vibration signals. For this purpose, several preprocessing steps and different types of Deep Learning (DL) and Machine Learning (ML) architectures are discussed to design an accurate classification system. The resultant system converts the railway axle vibration signals into time-frequency domain representations, i.e., spectrograms, and, thus, trains a two-dimensional CNN to classify them depending on their cracks. The results showed that the proposed approach outperforms several alternative methods tested. The CNN architecture has been tested in 3 different wheelset assemblies, achieving AUC scores of 0.93, 0.86, and 0.75 outperforming any other architecture and showing a high level of reliability when classifying 4 different levels of defects.
Improved techniques for deterministic l2 robustness

Training convolutional neural networks (CNNs) with a strict 1-Lipschitz constraint under the $l_{2}$ norm is useful for adversarial robustness, interpretable gradients and stable training. 1-Lipschitz CNNs are usually designed by enforcing each layer to have an orthogonal Jacobian matrix (for all inputs) to prevent the gradients from vanishing during backpropagation. However, their performance often significantly lags behind that of heuristic methods to enforce Lipschitz constraints where the resulting CNN is not \textit{provably} 1-Lipschitz. In this work, we reduce this gap by introducing (a) a procedure to certify robustness of 1-Lipschitz CNNs by replacing the last linear layer with a 1-hidden layer MLP that significantly improves their performance for both standard and provably robust accuracy, (b) a method to significantly reduce the training time per epoch for Skew Orthogonal Convolution (SOC) layers (>30\% reduction for deeper networks) and (c) a class of pooling layers using the mathematical property that the $l_{2}$ distance of an input to a manifold is 1-Lipschitz. Using these methods, we significantly advance the state-of-the-art for standard and provable robust accuracies on CIFAR-10 (gains of +1.79\% and +3.82\%) and similarly on CIFAR-100 (+3.78\% and +4.75\%) across all networks. Code is available at \url{https://github.com/singlasahil14/improved_l2_robustness}.
Neurodevelopmental Phenotype Prediction: A State-of-the-Art Deep Learning Model

A major challenge in medical image analysis is the automated detection of biomarkers from neuroimaging data. Traditional approaches, often based on image registration, are limited in capturing the high variability of cortical organisation across individuals. Deep learning methods have been shown to be successful in overcoming this difficulty, and some of them have even outperformed medical professionals on certain datasets. In this paper, we apply a deep neural network to analyse the cortical surface data of neonates, derived from the publicly available Developing Human Connectome Project (dHCP). Our goal is to identify neurodevelopmental biomarkers and to predict gestational age at birth based on these biomarkers. Using scans of preterm neonates acquired around the term-equivalent age, we were able to investigate the impact of preterm birth on cortical growth and maturation during late gestation. Besides reaching state-of-the-art prediction accuracy, the proposed model has much fewer parameters than the baselines, and its error stays low on both unregistered and registered cortical surfaces.
The State-of-the-art HST Astro-photometric Analysis of the Core of ω Centauri. III. The Main Sequence's Multiple Populations Galore

We take advantage of the exquisite quality of the Hubble Space Telescope 26-filter astro-photometric catalog of the core of ω Cen presented in the first paper of this series and the empirical differential-reddening correction presented in the second paper in order to distill the main sequence into its constituent populations. To this end, we restrict ourselves to the five most useful filters: the magic “trio” of F275W, F336W, and F438W, along with F606W and F814W. We develop a strategy for identifying color systems where different populations stand out most distinctly, then we isolate those populations and examine them in other filters where their subpopulations also come to light. In this way, we have identified at least 15 subpopulations, each of which has a distinctive fiducial curve through our five-dimensional photometric space. We confirm the MSa to be split into two subcomponents, and find that both the bMS and the rMS are split into three subcomponents. Moreover, we have discovered two additional MS groups: the MSd (which has three subcomponents) shares similar properties with the bMS, and the MSe (which has four subcomponents) has properties more similar to those of the rMS. We examine the fiducial curves together and use synthetic spectra to infer relative heavy-element, light-element, and helium abundances for the populations. Our findings show that the stellar populations and star formation history of ω Cen are even more complex than inferred previously. Finally, we provide as a supplement to the original catalog a list that identifies for each star which population it is most likely associated with.
Small-Angle X-Ray Scattering in Amorphous Silicon: A Computational Study

We present a computational study of small-angle X-ray scattering (SAXS) in amorphous silicon ($a$-Si) with particular emphasis on the morphology and microstructure of voids. The relationship between the scattering intensity in SAXS and the three-dimensional structure of nanoscale inhomogeneities or voids is addressed by generating ultra-large high-quality $a$-Si networks with 0.1-0.3% volume concentration of voids, as observed in experiments using SAXS and positron annihilation spectroscopy. A systematic study of the variation of the scattering intensity in the small-angle scattering region with the size, shape, number density, and the spatial distribution of the voids in the networks is presented. Our results suggest that the scattering intensity in the small-angle region is particularly sensitive to the size and the total volume-fraction of the voids, but the effect of the geometry or shape of the voids is less pronounced in the intensity profiles. A comparison of the average size of the voids obtained from the simulated values of the intensity, using the Guinier approximation and Kratky plots, with those from the spatial distribution of the atoms in the vicinity of void surfaces is presented.
The size function for cyclic cubic fields

The size function for a number field is an analogue of the dimension of the Riemann-Roch spaces of divisors on an algebraic curve. It was conjectured to attain its maximum at the trivial class of Arakelov divisors. This conjecture was proved for many number fields with unit groups of rank one. Our research confirms that the conjecture also holds for cyclic cubic fields, which have unit groups of rank two.
Anomalous ultraviolet line flux ratios in the cataclysmic variables 1RXSJ232953.9+062814, CE315, BZ UMa and EY Cyg observed with HST/STIS

Brief HST/STIS spectroscopic snapshot exposures of the cataclysmic variables 1RXSJ232953.9+062814, CE315, BZ UMa and EY Cyg reveal very large NV/CIV line flux ratios, similar to those observed in AE Aqr. Such anomalous line flux ratios have so far been observed in 10 systems, and presumably reflect a different composition of the accreted material compared to the majority of cataclysmic variables. We discuss the properties of this small sample in the context of the recent proposal by Schenker et al. (2002) that a significant fraction of the present-day population of cataclysmic variables may have passed through a phase of thermal time-scale mass transfer.
New Hamiltonians for loop quantum cosmology with arbitrary spin representations

In loop quantum cosmology, one has to make a choice of SU(2) irreducible representation in which to compute holonomies and regularize the curvature of the connection. The systematic choice made in the literature is to work in the fundamental representation, and very little is known about the physics associated with higher spin labels. This constitutes an ambiguity whose understanding, we believe, is fundamental for connecting loop quantum cosmology to full theories of quantum gravity like loop quantum gravity, its spin foam formulation, or cosmological group field theory. We take a step in this direction by providing here a new closed formula for the Hamiltonian of flat FLRW models regularized in a representation of arbitrary spin. This expression is furthermore polynomial in the basic variables which correspond to well-defined operators in the quantum theory, takes into account the so-called inverse-volume corrections, and treats in a unified way two different regularization schemes for the curvature. After studying the effective classical dynamics corresponding to single and multiple spin Hamiltonians, we study the behavior of the critical density when the number of representations is increased, and the stability of the difference equations in the quantum theory.
AN ECONOMICAL ROUTE TO ONE-WAY QUANTUM COMPUTATION

We assess the effects of a realistic intrinsic model for imperfections in cluster states by introducing noisy cluster states and characterizing their role in the one-way computational model. A suitable strategy to counter-affect these non-idealities is represented by the use of small clusters, stripped of any redundancy, which leads to the search for compact schemes for one-way quantum computation. In light of this, we quantitatively address the behavior of a simple four-qubit cluster which simulates a controlled-NOT under the influences of our model for decoherence. Our scheme can be particularly useful in an all-optical setup and the strategy we address can be directly applied in those experimental situations where small cluster states can be constucted.
Radiatively driven relativistic jets in Schwarzschild space-time

Context. Aims. We carry out a general relativistic study of radiatively driven conical fluid jets around non-rotating black holes and investigate the effects and significance of radiative acceleration, as well as radiation drag. Methods. We apply relativistic equations of motion in curved space-time around a Schwarzschild black hole for axis-symmetric one-dimensional jet in steady state, plying through the radiation field of the accretion disc. Radiative moments are computed using information of curved space-time. Slopes of physical variables at the sonic points are found using L’Hôpital’s rule and employing Runge-Kutta’s fourth order method to solve equations of motion. The analysis is carried out using the relativistic equation of state of the jet fluid. Results. The terminal speed of the jet depends on how much thermal energy is converted into jet momentum and how much radiation momentum is deposited onto the jet. Many classes of jet solutions with single sonic points, multiple sonic points, as well as those having radiation driven internal shocks are obtained. Variation of all flow variables along the jet-axis has been studied. Highly energetic electron-proton jets can be accelerated by intense radiation to terminal Lorentz factors γT ~ 3. Moderate terminal speed vT ~ 0.5 is obtained for moderately luminous discs. Lepton dominated jets may achieve γT ~ 10. Conclusions. Thermal driving of the jet itself and radiation driving by accretion disc photons produce a wide-ranging jet solutions starting from moderately strong jets to the relativistic ones. Interplay of intensity, the nature of the radiation field, and the energetics of the jet result in a variety of jet solutions. We show that radiation field is able to induce steady shocks in jets, one of the criteria to explain high-energy power-law emission observed in spectra of some of the astrophysical objects.
Asteroid Family Associations of Active Asteroids

We report on the results of a systematic search for associated asteroid families for all active asteroids known to date. We find that 10 out of 12 main-belt comets (MBCs) and five out of seven disrupted asteroids are linked with known or candidate families, rates that have ∼0.1% and ∼6% probabilities, respectively, of occurring by chance, given the overall family association rate of 37% for asteroids in the main asteroid belt. We find previously unidentified family associations between 238P/Read and the candidate Gorchakov family, 311P/PANSTARRS and the candidate Behrens family, 324P/La Sagra and the Alauda family, 354P/LINEAR and the Baptistina family, P/2013 R3-B (Catalina-PANSTARRS) and the Mandragora family, P/2015 X6 (PANSTARRS) and the Aeolia family, P/2016 G1 (PANSTARRS) and the Adeona family, and P/2016 J1-A/B (PANSTARRS) and the Theobalda family. All MBCs with family associations belong to families that contain asteroids with primitive taxonomic classifications and low average reported albedos ( ), while disrupted asteroids with family associations belong to families that contain asteroids that span wider ranges of taxonomic types and average reported albedos ( ). These findings are consistent with MBC activity being closely correlated to composition (i.e., whether an object is likely to contain ice), while disrupted asteroid activity is not as sensitive to composition. Given our results, we describe a sequence of processes by which the formation of young asteroid families could lead to the production of present-day MBCs.
Dissecting the X-Ray Emission in the Young Planetary Nebula NGC 7027

We present an analysis of a second observation of the young planetary nebula (PN) NGC 7027 by the Chandra X-ray Observatory. This latest 59.2 ks exposure with ACIS-S was acquired approximately 14 years after the initial 18.2 ks ACIS-S observation, and the improved photon statistics allow us to perform a detailed spatial and spectral analysis of the X-ray emission. Comparison with multiwavelength imaging of NGC 7027 reveals a strong anti-correlation between extinction across the nebula and the soft-band X-ray emission. Dissecting the X-ray emission into low- and high-extinction regions results in more robust characterization of the plasma spectral properties. We determine that the X-ray emitting plasma has a temperature of ∼3.6 MK, is deficient in Fe, and has an X-ray luminosity of LX ∼ 7 × 1031 erg s−1, all of which are generally consistent with the plasma properties found in PN hot bubbles. We find no evidence of evolution in the X-ray surface brightness over the 14 year baseline between CXO observations. Our analysis underscores the importance of accounting for nebular absorption of the X-ray emission in accurately determining plasma properties for hot bubbles within PNe.
Dynamically assisted nuclear fusion

We consider the prototypical deuterium-tritium fusion reaction. At intermediate initial kinetic energies (in the keV regime), a major bottle-neck of this reaction is the Coulomb barrier between the nuclei, which is overcome by tunneling. Here, we study whether the tunneling probability can be enhanced by an additional electromagnetic field, such as an x-ray free electron laser (XFEL). We find that this dynamical assistance should be feasible with present-day or near future technology.
A panoply of Schwinger-Keldysh transport

We classify all possible allowed constitutive relations of relativistic fluids in a statistical mechanical limit using the Schwinger-Keldysh effective action for hydrodynamics. We find that microscopic unitarity enforces genuinely new constraints on the allowed transport coefficients that are invisible in the classical hydrodynamic description; they are not implied by the second law or the Onsager relations. We term these conditions Schwinger-Keldysh positivity and provide explicit examples of the various allowed terms.
Chaos-Preserving Reduction of the Spin-Flip Model for VCSELs: Failure of the Adiabatic Elimination of the Spin-Population Difference

When studying the dynamics of vertical-cavity surface-emitting lasers, and their polarization properties, the spin-flip model appears to be the simplest model qualitatively reproducing all dynamical features that have been observed experimentally. Nonetheless, because of the fast time-scale of the spin-relaxation processes, the specific role and the importance of the spin-population difference—which is one of the specific feature of the spin-flip model—have been continuously questioned. In fact, the debate regarding the possible adiabatic elimination of the spin-population remains fully open. In this paper, our goal is to bring new light into this issue by demonstrating that this variable is essential to preserve the most complex dynamical features predicted by the spin-flip model, such as polarization chaos, and, therefore, needs to be conserved. To do so, we first perform a detailed analysis, focusing on the chaotic dynamics, to determine the minimal embedding dimension for the spin-flip model. As the latter confirms that a reduction of the model could be envisaged, we then consider the adiabatic elimination of the spin-population difference to highlight and explain its failure to reproduce essential dynamical features obtained in the original model.