Miracle-dz/UniFAR-FTUs huggingface dataset:
Following the Ground States of Full‐RSB Spherical Spin Glasses

We focus on spherical spin glasses whose Parisi distribution has support of the form [0, q]. For such models we construct paths from the origin to the sphere that consistently remain close to the ground‐state energy on the sphere of corresponding radius. The construction uses a greedy strategy, which always follows a direction corresponding to the most negative eigenvalues of the Hessian of the Hamiltonian. For finite mixtures ξ(x) it provides an algorithm of time complexity O(Ndeg(ξ)) to find w.h. p. points with the ground‐state energy, up to a small error.
MAGNETIC FIELDS IN COSMOLOGICAL SIMULATIONS OF DISK GALAXIES

Observationally, magnetic fields reach equipartition with thermal energy and cosmic rays in the interstellar medium of disk galaxies such as the Milky Way. However, thus far cosmological simulations of the formation and evolution of galaxies have usually neglected magnetic fields. We employ the moving-mesh code Arepo to follow for the first time the formation and evolution of a Milky Way–like disk galaxy in its full cosmological context while taking into account magnetic fields. We find that a prescribed tiny magnetic seed field grows exponentially by a small-scale dynamo until it saturates around z = 4 with a magnetic energy of about 10% of the kinetic energy in the center of the galaxy's main progenitor halo. By z = 2, a well-defined gaseous disk forms in which the magnetic field is further amplified by differential rotation, until it saturates at an average field strength of ∼6 μG in the disk plane. In this phase, the magnetic field is transformed from a chaotic small-scale field to an ordered large-scale field coherent on scales comparable to the disk radius. The final magnetic field strength, its radial profile, and the stellar structure of the disk compare well with observational data. A minor merger temporarily increases the magnetic field strength by about a factor of two, before it quickly decays back to its saturation value. Our results are highly insensitive to the initial seed field strength and suggest that the large-scale magnetic field in spiral galaxies can be explained as a result of the cosmic structure formation process.
Slow-walking inflation

We propose a new model of slow-roll inflation in string cosmology, based on warped throat supergravity solutions displaying `walking' dynamics, i.e. the coupling constant of the dual gauge theory slowly varies over a range of energy scales. The features of the throat geometry are sourced by a rich field content, given by the dilaton and RR and NS fluxes. By considering the motion of a D3-brane probe in this geometry, we are able to analytically calculate the brane potential in a physically interesting regime. This potential has an inflection point: in its proximity we realize a model of inflation lasting sixty e-foldings, and whose robust predictions are in agreement with current observations. We are also able to interpret some of the most interesting aspects of this scenario in terms of the properties of the QFT dual theory.
From homogeneous metric spaces to Lie groups

We study connected, locally compact metric spaces with transitive isometry groups. For all ε ∈ R, each such space is (1, ε)-quasi-isometric to a Lie group equipped with a left-invariant metric. Further, every metric Lie group is (1, C)-quasi-isometric to a solvable Lie group, and every simply connected metric Lie group is (1, C)-quasi-isometrically homeomorphic to a solvable-bycompact metric Lie group. While any contractible Lie group may be made isometric to a solvable group, only those that are solvable and of type (R) may be made isometric to a nilpotent Lie group, in which case the nilpotent group is the nilshadow of the group. Finally, we give a complete metric characterisation of metric Lie groups for which there exists an automorphic dilation. These coincide with the metric spaces that are locally compact, connected, homogeneous, and admit a metric dilation.
Sharp one-sided curvature estimates for mean curvature flow and applications

We prove a sharp pinching estimate for immersed mean convex solutions of mean curvature flow which unifies and improves all previously known pinching estimates, including the umbilic estimate of Huisken, the convexity estimates of Huisken--Sinestrari and the cylindrical estimate of Huisken--Sinestrari. Namely, we show that the curvature of the solution pinches onto the convex cone generated by the curvatures of any shrinking cylinder solutions admitted by the initial data. For example, if the initial data is $(m+1)$-convex, then the curvature of the solution pinches onto the convex hull of the curvatures of the shrinking cylinders $\mathbb{R}^m\times S^{n-m}_{\sqrt{2(n-m)(1-t)}}$, $t<1$. In particular, this yields a sharp estimate for the largest principal curvature, which we use to obtain a new proof of a sharp estimate for the inscribed curvature for embedded solutions. Making use of a recent idea of Huisken--Sinestrari, we then obtain a series of sharp estimates for ancient solutions. In particular, we obtain a convexity estimate for ancient solutions which allows us to improve recent characterizations of the shrinking sphere due to Huisken--Sinestrari and Haslhofer--Hershkovitz.
Molecular and biometric data on Carabus (Macrothorax) morbillosus Fabricius, 1792 (Coleoptera, Carabidae) from Mid Mediterranean areas

﻿Abstract The present study was carried out using molecular and biometric data of Carabus (Macrothorax) morbillosus from mid-Mediterranean areas to determine additional information on basal relationships among its representative subspecies. To this aim, two different kinds of approach were employed, including a morphometric analysis of four morphological parameters (i.e., elytra length, elytra width, pronotum length, pronotum width) of 128 specimens, and a Bayesian genetic analysis of 44 cytochrome oxidase subunit I (COI) partial sequences (i.e., 38 examined for the first time and six retrieved from GenBank database). Representative populations of C. (M.) morbillosus were sampled in four countries, namely Italy, Malta, Spain, and Tunisia. The present findings support the validity of four C. (M.) morbillosus subspecies, specifically C. (M.) m. alternans, C. (M.) m. bruttianus, C. (M.) m. constantinus, and C. (M.) m. macilentus, and redefine these subspecies’ distributions. Notably, within the C. (M.) m. constantinus clade, two (i.e., Sardinia/Tuscany and Lampedusa) out of the three subgroups appear as homogeneous geographical groupings.
EXTREME ACTIVE MOLECULAR JETS IN L1448C

The protostellar jet driven by L1448C was observed in the SiO J = 8–7 and CO J = 3–2 lines, and 350 GHz dust continuum at ∼1″ resolution with the Submillimeter Array. A narrow jet from the northern source L1448C(N) was observed in the SiO and the high-velocity CO. The jet consists of a chain of emission knots with an inter-knot spacing of ∼2″ (500 AU) and a semi-periodic velocity variation. These knots are likely to be the internal bow shocks in the jet beam that were formed due to the periodic variation of the ejection velocity with a period of ∼15–20 yr. The innermost pairs of knots, which are significant in the SiO map but barely seen in the CO, are located at ∼1″ (250 AU) from the central source, L1448C(N). Since the dynamical timescale for the innermost pair is only ∼10 yr, SiO may have been formed in the protostellar wind through the gas-phase reaction, or formed on the dust grain and directly released into the gas phase by means of shocks. It is found that the jet is extremely active with a mechanical luminosity of ∼7 L☉, which is comparable to the bolometric luminosity of the central source (7.5 L☉). The mass accretion rate onto the protostar derived from the mass-loss rate is ∼10−5 M☉ yr−1. Such a high mass accretion rate suggests that the mass and the age of the central star are 0.03–0.09 M☉ and (4–12)×103 yr, respectively, implying that the central star is in the very early stage of protostellar evolution. The low-velocity CO emission delineates two V-shaped shells with a common apex at L1448C(N). The kinematics of these shells are reproduced by the model of a wide-opening angle wind. The co-existence of the highly collimated jets and the wide-opening angle shells can be explained by the “unified X-wind model” in which highly collimated jet components correspond to the on-axis density enhancement of the wide-opening angle wind. The CO J = 3–2 map also revealed the second outflow driven by the southern source L1448C(S) located at ∼8. ″3 (2000 AU) from L1448C(N). Although L1448C(S) is brighter than L1448C(N) in the mid-IR bands, the momentum flux of the outflow from L1448C(S) is 2 or 3 orders of magnitude smaller than that of the L1448C(N) outflow. It is likely that the evolution of L1448C(S) has been strongly affected by the powerful outflow from L1448C(N).
Cumulants, spreadability and the Campbell–Baker–Hausdorff series

We define spreadability systems as a generalization of exchangeability systems in order to unify various notions of independence and cumulants known in noncommutative probability. In particular, our theory covers monotone independence and monotone cumulants which do not satisfy exchangeability. To this end we study generalized zeta and M\"obius functions in the context of the incidence algebra of the semilattice of ordered set partitions and prove an appropriate variant of Faa di Bruno's theorem. With the aid of this machinery we show that our cumulants cover most of the previously known cumulants. Due to noncommutativity of independence the behaviour of these cumulants with respect to independent random variables is more complicated than in the exchangeable case and the appearance of Goldberg coefficients exhibits the role of the Campbell-Baker-Hausdorff series in this context. In a final section we exhibit an interpretation of the Campbell-Baker-Hausdorff series as a sum of cumulants in a particular spreadability system, thus providing a new derivation of the Goldberg coefficients.
Finite Subgroups of Group Rings: A survey

In the 1940's Graham Higman initiated the study of finite subgroups of the unit group of an integral group ring. Since then many fascinating aspects of this structure have been discovered. Major questions such as the Isomorphism Problem and the Zassenhaus Conjectures have been settled, leading to many new challenging problems. In this survey we review classical and recent results, sketch methods and list questions relevant for the state of the art.
Cubic alternating harmonic number sums

A recent paper of A. Sofo proves some results about sums of products of quadratic alternating harmonic numbers and reciprocal binomial coefficients. In this paper, we extend his result to cubic alternating harmonic number sums and develop new closed form representations of sums of cubic alternating harmonic numbers and reciprocal binomial coefficients. Some inter- esting (known or new) illustrative special cases as well as immediate consequences of the main results are also considered.
Optical angular momentum in dispersive media

The angular momentum density and flux of light in a dispersive, rotationally symmetric medium are derived from Noether's theorem. Optical angular momentum in a dispersive medium has no simple relation to optical linear momentum, even if the medium is homogeneous. A circularly polarized monochromatic beam in a homogeneous, dispersive medium carries a spin angular momentum of ±ℏ per energy ℏω, as in vacuum. This result demonstrates the nontrivial interplay of dispersive contributions to optical angular momentum and energy.
Warped product submanifolds in metallic Riemannian manifolds

In this paper, we study the existence of proper warped product submanifolds in metallic (or Golden) Riemannian manifolds and we discuss about semi-invariant, semi-slant and, respectively, hemi-slant warped product submanifolds in metallic and Golden Riemannian manifolds. Also, we provide some examples of warped product submanifolds in Euclidean spaces.
Casimir forces from a loop integral formulation

We reformulate the Casimir force between bodies in non-trivial background media. The force may be written in terms of loop variables, the loop being a curve around the scattering sites. A natural path ordering of exponentials takes place when a particular representation of the scattering centres is given. The basic object to be evaluated is a reduced (or abbreviated) classical pseudo-action that can be operator valued, and can be obtained from a classical path integral description.
The average size of the kernel of a matrix and orbits of linear groups

Let O be a compact discrete valuation ring of characteristic 0. Given a module M of matrices over O , we study the generating function encoding the average sizes of the kernels of the elements of M over finite quotients of O . We prove rationality and establish fundamental properties of these generating functions and determine them explicitly for various natural families of modules M . Using p ‐adic Lie theory, we then show that special cases of these generating functions enumerate orbits and conjugacy classes of suitable linear pro‐ p groups.
Spectroscopy of very low mass stars and brown dwarfs in the Lambda Orionis star forming region I. Enlarging the census down to the planetary mass domain in Collinder 69

Context. Whilst there is a generally accepted evolutionary scheme for the formation of low‐mass stars, the analogous processes when moving down in mass to the brown dwarfs regime are not yet well understood. Aims. In this first paper we try to build the most complete and unbiased spectroscopically confirmed census of the population of Collinder 69, the central cluster of the Lambda Orionis star forming region, as a first step in addressing the question of how brown dwarfs and planetary mass objects form. Methods. We have studied age dependent features in optical and near-infrared spectra of candidate members to the cluster (such as alkali lines and accretion associated indicators). In addition, we have complemented that study with the analysis of other youth indicators like X-ray emission or mid-infrared excess. Results. We have confirmed the membership to Collinder 69 of 90 photometric candidate members. As a byproduct we have determined a temperature scale for young M, very low‐mass stars and brown dwarfs. We have assembled one of the most complete Initial Mass Functions from 0.016 to 20 M . And, finally, we have studied the implications of the spatial distribution of the confirmed members on the proposed mechanisms of brown dwarfs formation.
Noisy soccer balls

Giovanni Amelino-Camelia, Laurent Freidel, Jerzy Kowalski-Glikman, Lee Smolin Dipartimento di Fisica, Università “La Sapienza” and Sez. Roma1 INFN, P.le A. Moro 2, 00185 Roma, Italy Institute for Theoretical Physics, University of Wroclaw, Pl. Maxa Borna 9, 50-204 Wroclaw, Poland Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario N2J 2Y5, Canada (Dated: May 7, 2014)
Desingularization of binomial varieties in arbitrary characteristic. Part II. Combinatorial desingularization algorithm

In this paper we construct a combinatorial algorithm of resolution of singularities for binomial ideals, over a field of arbitrary characteristic. This algorithm is applied to any binomial ideal. This means ideals generated by binomial equations without any restriction, including monomials and $p$-th powers, where $p$ is the characteristic of the base field. In particular, this algorithm works for toric ideals. However, toric geometry tools are not needed, the algorithm is constructed following the same point of view as Villamayor algorithm of resolution of singularities in characteristic zero.
Cylinder absolute games on solenoids

Let $A$ be any affine surjective endomorphism of a solenoid $\Sigma_{\mathcal{P}}$ over the circle $S^1$ which is not an infinite-order translation of $\Sigma_{\mathcal{P}}$. We prove the existence of a cylinder absolute winning (CAW) subset $F \subset \Sigma_{\mathcal{P}}$ with the property that for any $x \in F$, the orbit closure $\overline{\{ A^{\ell} x \mid \ell \in \mathbb{N} \}}$ does not contain any periodic orbits. The class of infinite solenoids considered in this paper provides, to our knowledge, some of the first examples of non-Federer spaces where absolute games can be played and won. Dimension maximality and incompressibility of CAW sets is also discussed for a number of possibilities in addition to their winning nature for the games known from before.
Almost-prime $k$-tuples

Let $k\ge 2$ and $\Pi(n)=\prod_{i=1}^k(a_in+b_i)$ for some integers $a_i, b_i$ ($1\le i\le k$). Suppose that $\Pi(n)$ has no fixed prime divisors. Weighted sieves have shown for infinitely many integers $n$ that $\Omega(\Pi(n))\le r_k$ holds for some integer $r_k$ which is asymptotic to $k\log{k}$. We use a new kind of weighted sieve to improve the possible values of $r_k$ when $k\ge 4$.
Some virtually abelian subgroups of the group of analytic symplectic diffeomorphisms of $S^2$

We show that if $M$ is a compact oriented surface of genus 0 and $G$ is a subgroup of $\Symp^\omega_\mu(M)$ which has an infinite normal solvable subgroup, then $G$ is virtually abelian. In particular the centralizer of an infinite order $f \in \Symp^\omega_\mu(M)$ is virtually abelian. Another immediate corollary is that if $G$ is a solvable subgroup of $\Symp^\omega_\mu(M)$ then $G$ is virtually abelian. We also prove a special case of the Tits Alternative for subgroups of $\Symp^\omega_\mu(S^2). $
The Bishop–Phelps–Bollobás properties in complex Hilbert spaces

In this paper, we consider the Bishop–Phelps–Bollobás point property for various classes of operators on complex Hilbert spaces, which is a stronger property than the Bishop–Phelps–Bollobás property. We also deal with analogous problem by replacing the norm of an operator with its numerical radius.
On the Initial Boundary-Value Problem in the Kinetic Theory of Hard Particles II: Non-uniqueness

In the first of two papers, we study the initial boundary-value problem that underlies the theory of the Boltzmann equation for general non-spherical hard particles. In this work, for two congruent ellipses and for a large class of associated boundary conditions, we identify initial conditions for which there do not exist local-in-time weak solutions of Newton's equations of motion. To our knowledge, this is the first time the necessity of rolling in the energy-conserving dynamics of strictly-convex rigid bodies has been demonstrated. This study was, in part, motivated by a recent observation of Palffy-Muhoray, Virga, Wilkinson and Zheng on the interpenetration of strictly-convex rigid bodies.
Approximating Relu Networks by Single-Spike Computation

Developing energy-saving neural network models is a topic of rapidly increasing interest in the artificial intelligence community. Spiking neural networks (SNNs) are biologically inspired models that strive to leverage the energy efficiency stemming from a long process of evolution under limited resources. In this paper we propose a SNN model where each neuron integrates piecewise linear postsynaptic potentials caused by input spikes and a positive bias, and spikes maximally once. Transformation of such a network into the ANN domain yields an approximation of a standard ReLU network, leading to a facilitated training based on backpropagation and an adaptation of the batch normalization. With backpropagation-trained weights, SNN inference offers a sparse-signal and low-latency classification, which can be readily adapted for a stream of input patterns, lending itself to an efficient hardware implementation. The supervised classification of MNIST and Fashion-MNIST datasets, using this approach, provides accuracy close to that of an ANN and surpassing other single-spike SNNs.
Causality and hyperbolicity of Lovelock theories

In Lovelock theories, gravity can travel faster or slower than light. The causal structure is determined by the characteristic hypersurfaces. We generalize a recent result of Izumi to prove that any Killing horizon is a characteristic hypersurface for all gravitational degrees of freedom of a Lovelock theory. Hence gravitational signals cannot escape from the region inside such a horizon. We investigate the hyperbolicity of Lovelock theories by determining the characteristic hypersurfaces for various backgrounds. First we consider Ricci flat type N spacetimes. We show that characteristic hypersurfaces are generically all non-null and that Lovelock theories are hyperbolic in any such spacetime. Next we consider static, maximally symmetric black hole solutions of Lovelock theories. Again, characteristic surfaces are generically non-null. For some small black holes, hyperbolicity is violated near the horizon. This implies that the stability of such black holes is not a well-posed problem.
Stochastic geometry of critical curves, Schramm–Loewner evolutions and conformal field theory

Conformally invariant curves that appear at critical points in two-dimensional statistical mechanics systems and their fractal geometry have received a lot of attention in recent years. On the one hand, Schramm (2000 Israel J. Math. 118 221 (Preprint math.PR/9904022)) has invented a new rigorous as well as practical calculational approach to critical curves, based on a beautiful unification of conformal maps and stochastic processes, and by now known as Schramm–Loewner evolution (SLE). On the other hand, Duplantier (2000 Phys. Rev. Lett. 84 1363; Fractal Geometry and Applications: A Jubilee of Benot Mandelbrot: Part 2 (Proc. Symp. Pure Math. vol 72) (Providence, RI: American Mathematical Society) p 365 (Preprint math-ph/0303034)) has applied boundary quantum gravity methods to calculate exact multifractal exponents associated with critical curves. In the first part of this paper, I provide a pedagogical introduction to SLE. I present mathematical facts from the theory of conformal maps and stochastic processes related to SLE. Then I review basic properties of SLE and provide practical derivation of various interesting quantities related to critical curves, including fractal dimensions and crossing probabilities. The second part of the paper is devoted to a way of describing critical curves using boundary conformal field theory (CFT) in the so-called Coulomb gas formalism. This description provides an alternative (to quantum gravity) way of obtaining the multifractal spectrum of critical curves using only traditional methods of CFT based on free bosonic fields.