Miracle-dz/UniFAR-FTUs huggingface dataset:
Quantum critical scaling of fidelity in BCS-like model

We study scaling of the ground-state fidelity in neighborhoods of quantum critical points in a model of interacting spinful fermions—a BCS-like model. Due to the exact diagonalizability of the model, in one and higher dimensions, scaling of the ground-state fidelity can be analyzed numerically with great accuracy, not only for small systems but also for macroscopic ones, together with the crossover region between them. Additionally, in the one-dimensional case we have been able to derive a number of analytical formulas for fidelity and show that they accurately fit our numerical results; these results are reported in the paper. Besides regular critical points and their neighborhoods, where well-known scaling laws are obeyed, there is the multicritical point and critical points in its proximity where anomalous scaling behavior is found. We also consider scaling of fidelity in neighborhoods of critical points where fidelity oscillates strongly as the system size or the chemical potential is varied. Our results for a one-dimensional version of a BCS-like model are compared with those obtained recently by Rams and Damski in similar studies of a quantum spin chain—an anisotropic XY model in a transverse magnetic field.
Characterizing X-ray binary long-term variability

Long-term (‘superorbital’) periods or modulations have been detected in a wide variety of both low- and high-mass X-ray binaries at X-ray and optical wavelengths. A variety of mechanisms have been proposed to account for the variability properties, such as precessing and/or warped accretion discs, amongst others. The All Sky Monitor onboard the Rossi X-ray Timing Explorer provides the most extensive (? 15 years) and sensitive X-ray archive for studying such behaviour. It is also clear that such variations can be intermittent and/or a function of X-ray spectral state. Consequently, we use a time-dependent dynamic power spectrum method to examine how these modulations vary with time in 25 X-ray binaries for which superorbital periodicities have been previously reported. Our aim is to characterize these periodicities in a completely systematic way. Some (such as Her X-1 and LMC X-4) are remarkably stable, but others show a range of properties, from even longer variability time-scales to quite chaotic behaviour
Rotatable random sequences in local fields

An infinite sequence of real random variables $(\xi_1, \xi_2, \dots)$ is said to be rotatable if every finite subsequence $(\xi_1, \dots, \xi_n)$ has a spherically symmetric distribution. A celebrated theorem of Freedman states that $(\xi_1, \xi_2, \dots)$ is rotatable if and only if $\xi_j = \tau \eta_j$ for all $j$, where $(\eta_1, \eta_2, \dots)$ is a sequence of independent standard Gaussian random variables and $\tau$ is an independent nonnegative random variable. Freedman's theorem is equivalent to a classical result of Schoenberg which says that a continuous function $\phi : \mathbb{R}_+ \to \mathbb{C}$ with $\phi(0) = 1$ is completely monotone if and only if $\phi_n: \mathbb{R}^n \to \mathbb{R}$ given by $\phi_n(x_1, \ldots, x_n) = \phi(x_1^2 + \cdots + x_n^2)$ is nonnegative definite for all $n \in \mathbb{N}$. We establish the analogue of Freedman's theorem for sequences of random variables taking values in local fields using probabilistic methods and then use it to establish a local field analogue of Schoenberg's result. Along the way, we obtain a local field counterpart of an observation variously attributed to Maxwell, Poincare, and Borel which says that if $(\zeta_1, \ldots, \zeta_n)$ is uniformly distributed on the sphere of radius $\sqrt{n}$ in $\mathbb{R}^n$, then, for fixed $k \in \mathbb{N}$, the distribution of $(\zeta_1, \ldots, \zeta_k)$ converges to that of a vector of $k$ independent standard Gaussian random variables as $n \to \infty$.
Particle Acceleration during Magnetic Reconnection in a Low-beta Pair Plasma

Plasma energization through magnetic reconnection in the magnetically-dominated regime featured by low plasma beta ($\beta = 8 \pi nkT_0/B^2 \ll 1$) and/or high magnetization ($\sigma = B^2/(4 \pi nmc^2) \gg 1$) is important in a series of astrophysical systems such as solar flares, pulsar wind nebula, and relativistic jets from black holes, etc. In this paper, we review the recent progress on kinetic simulations of this process and further discuss plasma dynamics and particle acceleration in a low-$\beta$ reconnection layer that consists of electron-positron pairs. We also examine the effect of different initial thermal temperatures on the resulting particle energy spectra. While earlier papers have concluded that the spectral index is smaller for higher $\sigma$, our simulations show that the spectral index approaches $p=1$ for sufficiently low plasma $\beta$, even if $\sigma \sim 1$. Since this predicted spectral index in the idealized limit is harder than most observations, it is important to consider effects that can lead to a softer spectrum such as open boundary simulations. We also remark that the effects of 3D reconnection physics and turbulence on reconnection need to be addressed in the future.
ANISOTROPY OF TeV COSMIC RAYS AND OUTER HELIOSPHERIC BOUNDARIES

Cosmic rays in the energy range from about tens of GeV to several hundreds of TeV are observed on Earth, with an energy-dependent anisotropy of order 0.01%–0.1% and a consistent topology that appears to significantly change at higher energy. The nearest and most recent galactic cosmic-ray sources might stochastically dominate the observation and possibly explain a change in orientation of the anisotropy as a function of energy. However, the diffusion approximation is not able to explain its non-dipolar structure and, in particular, the significant contribution of small angular scale features. Particle propagation within the mean free path in the local interstellar medium might have a major role in determining the properties of galactic cosmic rays, such as their arrival distribution. In particular, scattering on perturbations induced in the local interstellar magnetic field by the heliosphere wake may cause a re-distribution of anisotropic cosmic rays below about 100 TeV toward the direction of the elongated heliotail and of the local interstellar magnetic field in the outer heliosphere. Such scattering processes are considered responsible for the observed TeV cosmic-ray global anisotropy and its fine angular structure.
Legendrian Submanifolds in $R^{2n+1}$ and Contact Homology

Contact homology for Legendrian submanifolds in standard contact $(2n+1)$-space is rigorously defined using moduli spaces of holomorphic disks with Lagrangian boundary conditions in complex $n$-space. It provides new invariants of Legendrian isotopy. Using these invariants the theory of Legendrian isotopy is shown to be very rich. For example, infinite families of pairwise non-isotopic Legendrian $n$-spheres and $n$-tori, which are indistinguishable by means of previously known invariants, are constructed. In a sense, the definition of contact homology presented in this paper is a high dimensional analog of the work of Chekanov and others on Legendrian 1-knots in 3-space.
ToDD: Topological Compound Fingerprinting in Computer-Aided Drug Discovery

In computer-aided drug discovery (CADD), virtual screening (VS) is used for identifying the drug candidates that are most likely to bind to a molecular target in a large library of compounds. Most VS methods to date have focused on using canonical compound representations (e.g., SMILES strings, Morgan fingerprints) or generating alternative fingerprints of the compounds by training progressively more complex variational autoencoders (VAEs) and graph neural networks (GNNs). Although VAEs and GNNs led to significant improvements in VS performance, these methods suffer from reduced performance when scaling to large virtual compound datasets. The performance of these methods has shown only incremental improvements in the past few years. To address this problem, we developed a novel method using multiparameter persistence (MP) homology that produces topological fingerprints of the compounds as multidimensional vectors. Our primary contribution is framing the VS process as a new topology-based graph ranking problem by partitioning a compound into chemical substructures informed by the periodic properties of its atoms and extracting their persistent homology features at multiple resolution levels. We show that the margin loss fine-tuning of pretrained Triplet networks attains highly competitive results in differentiating between compounds in the embedding space and ranking their likelihood of becoming effective drug candidates. We further establish theoretical guarantees for the stability properties of our proposed MP signatures, and demonstrate that our models, enhanced by the MP signatures, outperform state-of-the-art methods on benchmark datasets by a wide and highly statistically significant margin (e.g., 93% gain for Cleves-Jain and 54% gain for DUD-E Diverse dataset).
A half-century of global collaboration in science and the “Shrinking World”

Abstract Recent decades have witnessed a dramatic shift in the cross-border collaboration mode of researchers, with countries increasingly cooperating and competing with one another. It is crucial for leaders in academia and policy to understand the full extent of international research collaboration, their country’s position within it, and its evolution over time. However, evidence for such world-scale dynamism is still scarce. This paper provides unique evidence of how international collaboration clusters have formed and evolved over the past 50 years across various scientific publications, using data from OpenAlex, a large-scale open bibliometrics platform launched in 2022. I first examine how the global presence of top-tier countries has changed in 15 natural science disciplines over time, as measured by publication volumes and international collaboration rates. Notably, I observe that the United States and China have been rapidly moving closer together for decades but began moving apart after 2019. I then perform a hierarchical clustering to analyze and visualize the international collaboration clusters for each discipline and period. Finally, I provide quantitative evidence of a “Shrinking World” of research collaboration at a global scale over the past half-century. My results provide valuable insights into the big picture of past, present, and future international collaboration.
Formation and evolution of blue compact dwarfs: the origin of their steep rotation curves

The origin of the observed steep rotation curves of blue compact dwarf galaxies (BCDs) remains largely unexplained by theoretical models of BCD formation. We therefore investigate the rotation curves in BCDs formed from mergers between gas-rich dwarf irregular galaxies based on the results of numerical simulations for BCD formation. The principal results are as follows. The dark matter of merging dwarf irregulars undergoes a central concentration so that the central density can become up to six times higher than those of the initial dwarf irregulars. However, the more compact dark matter halo alone can not reproduce the gradient differences observed between dwarf irregulars and BCDs. We provide further support that the central concentration of gas due to rapid gas-transfer to the central regions of dwarf--dwarf mergers is responsible for the observed difference in rotation curve gradients. The BCDs with central gas concentration formed from merging can thus show steeply rising rotation curves in their central regions. Such gas concentration is also responsible for central starbursts of BCDs and the high central surface brightness and is consistent with previous BCD studies. We discuss the relationship between rotational velocity gradient and surface brightness, the dependence of BCD rotation curves on star formation threshold density, progenitor initial profile, interaction type and merger mass ratio, as well as potential evolutionary links between dwarf irregulars, BCDs and compact dwarf irregulars.
Confinement of Brownian polymers under geometric area tilts

We consider tightness for families of non-colliding Brownian bridges above a hard wall, which are subject to geometrically growing self-potentials of tilted area type. The model is introduced in order to mimic level lines of $2+1$ discrete Solid-On-Solid random interfaces above a hard wall.
University of Birmingham Production of charged pions, kaons and protons at large transverse momenta in pp and Pb–Pb collisions atsNN = 2.76 TeV

Transverse momentum spectra of π ± , K ± and p ( ¯ p ) up to p T = 20 GeV / c at mid-rapidity in pp, peripheral (60–80%) and central (0–5%) Pb–Pb collisions at √ s NN = 2 . 76 TeV have been measured using the ALICE detector at the Large Hadron Collider. The proton-to-pion and the kaon-to-pion ratios both show a distinct peak at p T ≈ 3 GeV / c in central Pb–Pb collisions. Below the peak, p T < 3 GeV / c , both ratios are in good agreement with hydrodynamical calculations, suggesting that the peak itself is dominantly the result of radial ﬂow rather than anomalous hadronization processes. For p T > 10 GeV / c particle ratios in pp and Pb–Pb collisions are in agreement and the nuclear modiﬁcation factors for π ± , K ± and p ( ¯ p ) indicate that, within the systematic and statistical uncertainties, the suppression is the same. This suggests that the chemical composition of leading particles from jets in the medium is similar to that of vacuum jets.
The velocity field in MOND cosmology

The recently developed code for N-body/hydrodynamics simulations in Modified Newtonian Dynamics (MOND), known as RAyMOND, is used to investigate the consequences of MOND on structure formation in a cosmological context, with a particular focus on the velocity field. This preliminary study investigates the results obtained with the two formulations of MOND implemented in RAyMOND, as well as considering the effects of changing the choice of MOND interpolation function, and the cosmological evolution of the MOND acceleration scale. The simulations are contrived such that structure forms in a background cosmology that is similar to $\Lambda$CDM, but with a significantly lower matter content. Given this, and the fact that a fully consistent MOND cosmology is still lacking, we compare our results with a standard $\Lambda$CDM simulation, rather than observations. As well as demonstrating the effectiveness of using RAyMOND for cosmological simulations, it is shown that a significant enhancement of the velocity field is likely an unavoidable consequence of the gravitational modification implemented in MOND, and may represent a clear observational signature of such a modification. It is further suggested that such a signal may be clearest in intermediate density regions such as cluster outskirts and filaments.
Fast Algorithms for $\ell_p$-Regression

The $\ell_p$-norm regression problem is a classic problem in optimization with wide ranging applications in machine learning and theoretical computer science. The goal is to compute $x^{\star} =\arg\min_{Ax=b}\|x\|_p^p$, where $x^{\star}\in \mathbb{R}^n, A\in \mathbb{R}^{d\times n},b \in \mathbb{R}^d$ and $d\leq n$. Efficient high-accuracy algorithms for the problem have been challenging both in theory and practice and the state of the art algorithms require $poly(p)\cdot n^{\frac{1}{2}-\frac{1}{p}}$ linear system solves for $p\geq 2$. In this paper, we provide new algorithms for $\ell_p$-regression (and a more general formulation of the problem) that obtain a high-accuracy solution in $O(p n^{\frac{(p-2)}{(3p-2)}})$ linear system solves. We further propose a new inverse maintenance procedure that speeds-up our algorithm to $\widetilde{O}(n^{\omega})$ total runtime, where $O(n^{\omega})$ denotes the running time for multiplying $n \times n$ matrices. Additionally, we give the first Iteratively Reweighted Least Squares (IRLS) algorithm that is guaranteed to converge to an optimum in a few iterations. Our IRLS algorithm has shown exceptional practical performance, beating the currently available implementations in MATLAB/CVX by 10-50x.
Central Star Formation in Early-type Galaxy I Zw 81 in the Bootes Void

The origin of star formation in customarily passively evolving early-type massive galaxies is poorly understood. We present a case study of a massive galaxy, I Zw 81, inside the Bootes void. The void galaxy is known to host active galactic nuclei (AGN). Our detailed 2D decomposition of the surface brightness distribution in the Canada France Hawaii Telescope (CFHT) g and r bands revealed multiple structural components such as a nuclear point source, a bar, a ring, and an inner exponential disk followed by an outer low surface brightness disk. I Zw 81 turns out to be a disk-dominated galaxy with lenticular morphology. The modeling of the multiwavelength spectral energy distribution shows that the galaxy is star-forming (SF), and belongs to the blue cloud. We find that the optical (g−r) color of the bar is bluer than the disks, and the far- and near-ultraviolet emission inside the galaxy observed with Imaging Telescope onboard AstroSat is concentrated in the central few kpc region enclosing the bar. The strong bar might be playing a pivotal role in driving the gas inflow and causing SF activity in tandem with the minor merger-like interactions as evident from the deep CFHT data. The low-luminosity AGN is insufficient to quench the central SF. The results are peculiar from the standpoint of a massive barred lenticular galaxy.
An Exploration of Degeneracy in Abelian Varieties of Fermat Type

The term degenerate is used to describe abelian varieties whose Hodge rings contain exceptional cycles -- Hodge cycles that are not generated by divisor classes. We can see the effect of the exceptional cycles on the structure of an abelian variety through its Mumford-Tate group, Hodge group, and Sato-Tate group. In this article we examine degeneracy through these different but related lenses. We specialize to a family of abelian varieties of Fermat type, namely Jacobians of hyperelliptic curves of the form $y^2=x^m-1$. We prove that the Jacobian of the curve is degenerate whenever $m$ is an odd, composite integer. We explore the various forms of degeneracy for several examples, each illustrating different phenomena that can occur.
COSMIC-RAY ACCELERATION EFFICIENCY VERSUS TEMPERATURE EQUILIBRATION: THE CASE OF SNR 0509-67.5

We study the 0509-67.5 supernova remnant in the Large Magellanic Cloud with the VLT/FORS2 spectrograph. We detect a broad component in the Hα emission with an FWHM of 2680 ± 70 km s−1 and 3900 ± 800 km s−1 for the southwest (SW) and northeast (NE) shocks, respectively. For the SW, the proton temperature appears to be too low for the shock velocity, which we attribute to a cosmic-ray pressure behind the shock front of at least 20% of the total pressure. For the NE, the post-shock proton temperature and the shock velocity are compatible, only if the plasma behind the shock front has a degree of thermal equilibrium of over 20%, which is at odds with current models for temperature equilibration behind fast shocks, which do not accelerate cosmic rays. If we assume the electron temperature to be less than 10% of the proton temperature, we find a post-shock cosmic-ray pressure of at least 7%.
Designing the Architecture of a Convolutional Neural Network Automatically for Diabetic Retinopathy Diagnosis

Diabetic retinopathy (DR) is a leading cause of blindness in middle-aged diabetic patients. Regular screening for DR using fundus imaging aids in detecting complications and delays the progression of the disease. Because manual screening takes time and is subjective, deep learning has been used to help graders. Pre-trained or brute force CNN models are used in existing DR grading CNN-based approaches that are not suited to fundus image complexity. To solve this problem, we present a method for automatically customizing CNN models based on fundus image lesions. It uses k-medoid clustering, principal component analysis (PCA), and inter-class and intra-class variations to determine the CNN model’s depth and width. The designed models are lightweight, adapted to the internal structures of fundus images, and encode the discriminative patterns of DR lesions. The technique is validated on a local dataset from King Saud University Medical City, Saudi Arabia, and two challenging Kaggle datasets: EyePACS and APTOS2019. The auto-designed models outperform well-known pre-trained CNN models such as ResNet152, DenseNet121, and ResNeSt50, as well as Google’s AutoML and Auto-Keras models based on neural architecture search (NAS). The proposed method outperforms current CNN-based DR screening methods. The proposed method can be used in various clinical settings to screen for DR and refer patients to ophthalmologists for further evaluation and treatment.
Thermodynamic entropy of a many-body energy eigenstate

It is argued that a typical many-body energy eigenstate has a well-defined thermodynamic entropy and that individual eigenstates possess thermodynamic characteristics analogous to those of generic isolated systems. We examine large systems with eigenstate energies equivalent to finite temperatures. When quasi-static evolution of a system is adiabatic (in the quantum mechanical sense), two coupled subsystems can transfer heat from one subsystem to another and yet remain in an energy eigenstate. To explicitly construct the entropy from the wave function, degrees of freedom are divided into two unequal parts. It is argued that the entanglement entropy between these two subsystems is the thermodynamic entropy per degree of freedom for the smaller subsystem. This is done by tracing over the larger subsystem to obtain a density matrix and calculating the diagonal and off-diagonal contributions to the entanglement entropy.
Structural classification of boron nitride twisted bilayers and ab initio investigation of their stacking-dependent electronic structure

Since the discovery of superconductive twisted bilayer graphene which initiated the field of twistronics, moiré systems have not ceased to exhibit fascinating properties. We demonstrate that in boron nitride twisted bilayers, for a given moiré periodicity, there are five different stackings which preserve the monolayer hexagonal symmetry (i.e. the invariance upon rotations of 120°) and not only two as always discussed in literature. We introduce some definitions and a nomenclature that identify unambiguously the twist angle and the stacking sequence of any hexagonal bilayer with order-3 rotation symmetry. Moreover, we employ density functional theory to study the evolution of the band structure as a function of the twist angle for each of the five stacking sequences of boron nitride bilayers. We show that the gap is indirect at any angle and in any stacking, and identify features that are conserved within the same stacking sequence irrespective of the angle of twist.
LoCuSS: A Herschel view of obscured star formation in Abell 1835

We present Herschel/PACS, MMT/Hectospec and XMM-Newton observations of Abell 1835, one of the brightest X-ray clusters on the sky, and the host of a strong cool core. Even though Abell 1835 has a prototypically “relaxed” X-ray morphology and no signs of ongoing merger activity in strong- and weak-lensing mass maps, it has a complex velocity distribution, suggesting that it is still accreting significant amounts of mass in the form of smaller satellite systems. Indeed, we find strong dynamical segregation of starforming dusty galaxies from the optically selected cluster population. Most Herschel sources are found close to the virial radius of the cluster, and almost a third appear to be embedded within a filament feeding the cluster from the SW. We find that the most luminous infrared galaxies are likely involved in galaxy-galaxy interactions that may have triggered the current phase of star formation.