Miracle-dz/UniFAR-FTUs huggingface dataset:
Isoperimetry in supercritical bond percolation in dimensions three and higher

We study the isoperimetric subgraphs of the infinite cluster $\textbf{C}_\infty$ for supercritical bond percolation on $\mathbb{Z}^d$ with $d\geq 3$. Specifically, we consider the subgraphs of $\textbf{C}_\infty \cap [-n,n]^d$ which have minimal open edge boundary to volume ratio. We prove a shape theorem for these subgraphs, obtaining that when suitably rescaled, these subgraphs converge almost surely to a translate of a deterministic shape. This deterministic shape is itself an isoperimetric set for a norm we construct. As a corollary, we obtain sharp asymptotics on a natural modification of the Cheeger constant for $\textbf{C}_\infty \cap [-n,n]^d$. This settles a conjecture of Benjamini for the version of the Cheeger constant defined here.
Tori with hyperbolic dynamics in 3-manifolds

Let M be a closed orientable irreducible 3-manifold, and let f be a diffeomorphism over M. We call an embedded 2-torus T an Anosov torus if it is invariant and the induced action of f over \pi_1(T) is hyperbolic. We prove that only few irreducible 3-manifolds admit Anosov tori: (1) the 3-torus, (2) the mapping torus of -id, and (3) the mapping torus of hyperbolic automorphisms of the 2-torus. This has consequences for instance in the context of partially hyperbolic dynamics of 3-manifolds: if there is an invariant center-unstable foliation, then it cannot have compact leaves [19]. This has lead to the first example of a non-dynamically coherent partially hyperbolic diffeomorphism with one-dimensional center bundle [19].
A generalized Schwarz lemma for two domains related to μ-synthesis

Abstract We present a set of necessary and sufficient conditions that provides a Schwarz lemma for the tetrablock E. As an application of this result, we obtain a Schwarz lemma for the symmetrized bidisc G2. In either case, our results generalize all previous results in this direction for E and G2.
Magnon inflation: slow roll with steep potentials

We find multi-scalar effective field theories (EFTs) that can achieve a slow inflationary roll despite having a scalar potential that does not satisfy 𝒢ab ∂a V ∂b V ≪ V2/Mp2 (where 𝒢ab is the target-space metric). They evade the usual slow-roll conditions on V because their kinetic energies are dominated by single-derivative terms rather than the usual two-derivative terms. Single derivatives dominate during slow roll and so do not require a breakdown of the usual derivative expansion that underpins calculational control in much of cosmology. The presence of such terms requires some sort of UV Lorentz-symmetry breaking during inflation (besides the usual cosmological breaking). Chromo-natural inflation provides one particular example of a UV theory that can generate the multi-field single-derivative terms we consider, and we argue that the EFT we find indeed captures the slow-roll conditions for its background evolution. We also show that our EFT can be understood as a multi-field generalization of the single-field Cuscuton models. The multi-field case introduces a new feature, however: the scalar kinetic terms define a target-space 2-form, ℱab, whose antisymmetry gives new ways for slow roll to be achieved.
The unreasonable effectiveness of Nonstandard Analysis

As suggested by the title, the aim of this paper is to uncover the vast computational content of classical Nonstandard Analysis. To this end, we formulate a template $\mathfrak{CI}$ which converts a theorem of 'pure' Nonstandard Analysis, i.e. formulated solely with the nonstandard definitions (of continuity, integration, differentiability, convergence, compactness, et cetera), into the associated effective theorem. The latter constitutes a theorem of computable mathematics no longer involving Nonstandard Analysis. To establish the vast scope of $\mathfrak{CI}$, we apply this template to representative theorems from the Big Five categories from Reverse Mathematics. The latter foundational program provides a classification of the majority of theorems from 'ordinary', that is non-set theoretical, mathematics into the aforementioned five categories. The Reverse Mathematics zoo gathers exceptions to this classification, and is studied in [70,71] using $\mathfrak{CI}$. Hence, the template $\mathfrak{CI}$ is seen to apply to essentially all of ordinary mathematics, thanks to the Big Five classification (and associated zoo) from Reverse Mathematics. Finally, we establish that certain 'highly constructive' theorems, called Herbrandisations, imply the original theorem of Nonstandard Analysis from which they were obtained via $\mathfrak{CI}$.
Metabelian groups with large return probability

We study the return probability of finitely generated metabelian groups. We give a characterization of metabelian groups whose return probability is equivalent to $\exp(-n^\frac1{3} )$ in purely algebraic terms, namely the Krull dimension of the group. Along the way, we give lower bounds on the return probability for metabelian groups with torsion derived subgroup, according to the dimension. We also establish a variation of the famous embedding theorem of Kaloujinine and Krasner for metabelian groups that respects the Krull dimension.
On the chromatic number of almost s-stable Kneser graphs

In 2011, Meunier conjectured that for positive integers $n,k,r,s$ with $ k\geq 2$, $r\geq 2$, and $n\geq \max (\{r,s\})k$, the chromatic number of $s$ -stable $r$-uniform Kneser hypergraphs is equal to $\left\lceil \frac{n-\max (\{r,s\})(k-1)}{r-1}\right\rceil $. It is a strengthened version of the conjecture proposed by Ziegler (2002), and Alon, Drewnowski and \L uczak (2009). The problem about the chromatic number of almost $s$-stable $r$ -uniform Kneser hypergraphs has also been introduced by Meunier (2011). For the $r=2$ case of the Meunier conjecture, Jonsson (2012) provided a purely combinatorial proof to confirm the conjecture for $s\geq 4$ and $n$ sufficiently large, and by Chen (2015) for even $s$ and any $n$. The case $ s=3$ is completely open, even the chromatic number of the usual almost $s$ -stable Kneser graphs. In this paper, we obtain a topological lower bound for the chromatic number of almost $s$-stable $r$-uniform Kneser hypergraphs via a different approach. For the case $r=2$, we conclude that the chromatic number of almost $s$-stable Kneser graphs is equal to $n-s(k-1)$ for all $s\geq 2$. Set $t=n-s(k-1)$. We show that any proper coloring of an almost $s$-stable Kneser graph must contain a completely multicolored complete bipartite subgraph $K_{\left\lceil \frac{t}{2}\right\rceil \left\lfloor \frac{t}{2} \right\rfloor }$. It follows that the local chromatic number of almost $s$ -stable Kneser graphs is at least $\left\lceil \frac{t}{2}\right\rceil +1$. It is a strengthened result of Simonyi and Tardos (2007), and Meunier's (2014) lower bound for almost $s$-stable Kneser graphs.
KAZHDAN-LUSZTIG-POLYNOME UND UNZERLEGBARE BIMODULN ÜBER POLYNOMRINGEN

Wir entwickeln eine Strategie zum Beweis der Positivität der Koeffizienten von Kazhdan-Lusztig-Polynomen für beliebige Coxeter-Gruppen. We develop a strategy to prove the positivity of coefficients of Kazhdan–Lusztig polynomials for arbitrary Coxeter groups.
Chern–Schwartz–MacPherson cycles of matroids

We define Chern–Schwartz–MacPherson (CSM) cycles of an arbitrary matroid. These are balanced weighted fans supported on the skeleta of the corresponding Bergman fan. In the case that the matroid arises from a complex hyperplane arrangement A , we show that these cycles represent the CSM class of the complement of A . We also prove that for any matroid, the degrees of its CSM cycles are given by the coefficients of (a shift of) the reduced characteristic polynomial, and that CSM cycles are valuations under matroid polytope subdivisions.
Applications of ternary rings to $C^*$-algebras

We show that there is a functor from the category of positive admissible ternary rings to the category of $*$-algebras, which induces an isomorphism of partially ordered sets between the families of $C^*$-norms on the ternary ring and its corresponding $*$-algebra. We apply this functor to obtain Morita-Rieffel equivalence results between cross sectional $C^*$-algebras of Fell bundles, and to extend the theory of tensor products of $C^*$-algebras to the larger category of full Hilbert $C^*$-modules. We prove that, like in the case of $C^*$-algebras, there exist maximal and minimal tensor products. As applications we give simple proofs of the invariance of nuclearity and exactness under Morita-Rieffel equivalence of $C^*$-algebras.
German Verb Particle Constructions in CCG

As a theory of grammar, CCG (Steedman, 2000) is said to keep theory closely linked to psychological and computational mechanisms, to model how child or computer can learn any language (Steedman, 2017). In this paper, I test a Combinatory Categorial Grammar (CCG) against German Verb Particle Constructions (VPCs). Following previous work on English VPCs (Constable and Curran, 2009) and a German CCGbank (Hockenmaier, 2006), I analyze three types of German VPC constructions in CCG – main clauses, embedded clauses, and coordination clauses. Problems with modeling these sentences using CCG are discussed, and an alternative to deriving coordination sentences is presented in the Minimalist framework.
Random many-particle systems: applications from biology, and propagation of chaos in abstract models

The paper discusses a family of Markov processes that represent many particle systems, and their limiting behaviour when the number of particles go to infinity. The first part concerns model of biological systems: a model for sympatric speciation, i.e. the process in which a genetically homogeneous population is split in two or more different species sharing the same habitat, and models for swarming animals. The second part of the paper deals with abstract many particle systems, and methods for rigorously deriving mean field models.
First photometric and orbital period investigations of four W UMa-type eclipse binaries

Abstract We presented the first photometric and orbital period investigations for four W Ursae Majoris-type binaries: V473 And, V805 And, LQ Com, and EG CVn. The photometric solutions suggested that V805 And and LQ Com are two total-eclipse contact binaries, while V473 And and EG CVn are partial-eclipse ones. V473 And and LQ Com belong to the A-subtype contact binaries, while V805 And and EG CVn belong to the W subtype. The O’Connell effects found in the light curves of V805 And, LQ Com, and EG CVn can be interpreted as a result of a cool spot on the surface of their less massive and hotter primary components. Based on two different methods, the absolute physical parameters were properly determined. Combining the eclipse timings derived from our observations and survey’s data with those collected from literature, we investigated their orbital period variations. The results show that the orbital periods of V473 And, V805 And, and EG CVn are undergoing a secular decrease/increase superposed a periodic variation, while LQ Com exhibits a possible cyclic period variation with a small amplitude. The secular period changes are caused mainly by the mass transfer between two components, while the cyclic period oscillations may be interpreted as the results of either the light-time effect due to the third body or the cyclic magnetic activity. Finally, we made a statistical investigation for nearly 200 contact binaries with reliable physical parameters. The statistical results suggested that the W-subtype systems are more evolved than the A-subtype ones. Furthermore, the evolutionary direction of A-subtype into W-subtype systems is also discussed. The opposite evolutionary direction seems to be unlikely because it requires an increase of the total mass, the orbital angular momentum, and the temperature differences between two components of a binary system.
Recurrent flow analysis in spatiotemporally chaotic 2-dimensional Kolmogorov flow

Motivated by recent success in the dynamical systems approach to transitional flow, we study the efficiency and effectiveness of extracting simple invariant sets (recurrent flows) directly from chaotic/turbulent flows and the potential of these sets for providing predictions of certain statistics of the flow. Two-dimensional Kolmogorov flow (the 2D Navier-Stokes equations with a sinusoidal body force) is studied both over a square [0, 2π]2 torus and a rectangular torus extended in the forcing direction. In the former case, an order of magnitude more recurrent flows are found than previously [G. J. Chandler and R. R. Kerswell, “Invariant recurrent solutions embedded in a turbulent two-dimensional Kolmogorov flow,” J. Fluid Mech. 722, 554–595 (2013)] and shown to give improved predictions for the dissipation and energy pdfs of the chaos via periodic orbit theory. Analysis of the recurrent flows shows that the energy is largely trapped in the smallest wavenumbers through a combination of the inverse cascade process and a feature of the advective nonlinearity in 2D. Over the extended torus at low forcing amplitudes, some extracted states mimic the statistics of the spatially localised chaos present surprisingly well recalling the findings of Kawahara and Kida [“Periodic motion embedded in plane Couette turbulence: Regeneration cycle and burst,” J. Fluid Mech. 449, 291 (2001)] in low-Reynolds-number plane Couette flow. At higher forcing amplitudes, however, success is limited highlighting the increased dimensionality of the chaos and the need for larger data sets. Algorithmic developments to improve the extraction procedure are discussed.
Shallow mixing layers over hydraulically smooth bottom in a tilted open channel

Abstract Shallow mixing layers (SMLs) behind a splitter plate were studied in a tilted rectangular open-channel flume for a range of flow depths and the initial shear parameter ${\lambda = (U_{2}-U_{1})/(U_{2}+U_{1})}$, where $U_1$ and $U_2$ are streamwise velocities of the slow and fast streams, respectively. The main focus of the study is on (i) key parameters controlling the time-averaged SMLs; and (ii) the emergence and spatial development of Kelvin–Helmholtz coherent structures (KHCSs) and large- and very-large-scale motions (LSMs and VLSMs) and associated turbulence statistics. The time-averaged flow features of the SMLs are mostly controlled by bed-friction length scale $h/c_f$ and shear parameter $\lambda$ as well as by time-averaged spanwise velocities $V$ and momentum fluxes $UV$, where $h$ and $c_f$ are flow depth and bed-friction coefficient, respectively. For all studied cases, the effect of shear layer turbulence on the SML growth is comparatively weak, as the fluxes $UV$ dominate over the spanwise turbulent fluxes. Initially, the emergence of KHCSs and their length scales largely depend on $\lambda$. The KHCSs cannot form if ${\lambda \lessapprox 0.3}$ and the turbulence behind the splitter plate resembles that of free mixing layers. Further downstream, shear layer turbulence becomes dependent on the bed-friction number $S = c_f \delta _v /(4 h \lambda )$, where $\delta _v$ is vorticity thickness. When $S \gtrapprox 0.01$, the KHCSs are longitudinally stretched and the scaled transverse turbulent fluxes decrease with increasing $S$. The presence and streamwise development of LSMs/VLSMs away from the splitter plate depends on the $\lambda$-value, particularly when $\lambda > 0.3$, resembling LSMs/VLSMs in conventional open-channel flows when $\lambda$ is small.
Ages and metallicities of faint red galaxies in the Shapley Supercluster

Abstract We present results on the stellar populations of 232 quiescent galaxies in the Shapley Supercluster, based on spectroscopy from the AAOmega spectrograph at the AAT. The key characteristic of this survey is its coverage of many low-luminosity objects (σ ~ 50 kms−1), with high signal-to-noise (~45 Å−1). Balmer-line age estimates are recovered with ~25% precision even for the faintest sample members. We summarize the observations and absorption line data, and present correlations of derived ages and metallicities with mass and luminosity. We highlight the strong correlation between age and α-element abundance ratio, and the anti-correlation of age and metallicity at fixed mass, which is shown to extend into the low-luminosity regime.
On some geometric properties of slice regular functions of a quaternion variable

Purpose of this paper is to study some geometric properties of functions of a quaternion variable slice regular in the unit ball-like subordination, starlikeness, convexity and spirallikeness. In this framework, we prove some results, among which is the Rogosinski inequality. Moreover, we show some geometric and algebraic interpretations of our results in terms of maps from to itself. As a tool for subordination, we define a suitable notion of composition of slice regular functions which is of independent interest.
Game Demands of a Professional Ice Hockey Team with Special Emphasis on Fatigue Development and Playing Position

Abstract The aim of this study was to describe the game activity profile of a professional ice hockey team with special emphasis on fatigue development and playing position. Data were collected using a wearable 200-Hz accelerometric system and heart rate (HR) throughout eight official games in a professional ice hockey team (6 defensemen and 11 forwards; n = 122 files). On-ice 10- and 30-m sprint performance, repeated sprint ability and HR responses to the submaximal Yo-Yo Intermittent recovery level 1 test were assessed to determine associations with game performance. Although the 3rd period was largely longer than the 1st and 2nd periods (r = 0.56–0.59), no differences were observed between periods in activity pattern, except a moderate decline in the number of decelerations <-2 m·s-2 per min (Dec2/min) in the 2nd period for forwards (r = 0.06–0.60). Mean HR, time spent >85% HRmax (t85HR), as well as the total number of intense accelerations and decelerations were higher for defensemen. However, demands were similar when expressed relative to time on-ice, except that defenders performed more Dec2/min than forwards in all periods, whereas forwards spent more t85HR during the 2nd period (r = 0.46–0.57). Time spent on ice was inversely correlated with the total number of accelerations (Acctot), accelerations >2 m·s-2 per min (Acc2/min), total decelerations per min (Dectot/min), Dec2/min and t85HR (r = -0.63 to -0.18) and positively correlated with mean HR and peak HR (r = 0.20– 0.53). No significant correlations were found between physical fitness and game activity variables scaled by individual time on ice. Absolute acceleration and HR demands of professional ice hockey seem to differ between playing positions, but not in relation to time on ice. Further, no clear signs of fatigue were captured, possibly due to the longer duration of rest intervals in the 3rd period.
Effects of Elevated Body Temperature on Selected Physiological Indices and Thermal Stress in Athletes and Non-Athletes

Abstract The purpose of this study was to determine the effects of active and passive overheating. A group of athletes (A) and non-athletic men (N) underwent an exercise stress test at elevated ambient temperature and sauna bathing until an increase in rectal temperature of 1.2°C was observed. It was shown that group A performed physical exercise for a longer period of time, which elicited significantly higher amounts of work performed in the stress test. Both forms of overheating caused a significant decrease in BM and a significant change in plasma volume, while greater dehydration was observed after active overheating. Changes observed in group A were higher than in group N. MCV levels were initially higher in group A. The levels in both groups decreased after sauna bathing, although in non-athletes the decrease was greater. Both forms of overheating increased Hb, HCT, and SBP, while only the non-athletic group showed a decrease in DBP after the exercise stress test. However, a decrease in DBP was observed in both groups after sauna bathing. The PSI increased after both tests, yet to a higher extent after the stress test than after sauna bathing. The PSI was negatively correlated with VO2max in both groups. The increase in cortisol concentration was higher after sauna bathing. There was a correlation between cortisol levels and the work performed during the stress test in group A. Endurance training resulted in more efficient thermoregulatory mechanisms in athletes.
Almost Finiteness for General Étale Groupoids and Its Applications to Stable Rank of Crossed Products

We extend Matui’s notion of almost finiteness to general étale groupoids and show that the reduced groupoid C$^{\ast }$-algebras of minimal almost finite groupoids have stable rank 1. The proof follows a new strategy, which can be regarded as a local version of the large subalgebra argument. The following three are the main consequences of our result: (1) for any group of (local) subexponential growth and for any its minimal action admitting a totally disconnected free factor, the crossed product has stable rank 1; (2) any countable amenable group admits a minimal action on the Cantor set, all whose minimal extensions form the crossed product of stable rank 1; and (3) for any amenable group, the crossed product of the universal minimal action has stable rank 1.
Infrared-faint radio sources: a cosmological view - AGN number counts, the cosmic X-ray background and SMBH formation

Context. Infrared-faint radio sources (IFRS) are extragalactic emitters clearly detected at radio wavelengths but barely detected or undetected at optical and infrared wavelengths, with 5σ sensitivities as low as 1 μJy. Aims. Spectral energy distribution (hereafter SED) modelling and analyses of their radio properties indicate that IFRS are consistent with a population of (potentially extremely obscured) high-redshift AGN at 3 ≤ z ≤ 6. We demonstrate some astrophysical implications of this population and compare them to predictions from models of galaxy evolution and structure formation. Methods. We compiled a list of IFRS from four deep extragalactic surveys and extrapolated the IFRS number density to a surveyindependent value of (30.8 ± 15.0) deg −2 . We computed the IFRS contribution to the total number of AGN in the Universe to account for the cosmic X-ray background. By estimating the black hole mass contained in IFRS, we present conclusions for the SMBH mass density in the early universe and compare it to relevant simulations of structure formation after the Big Bang. Results. The number density of AGN derived from the IFRS density was found to be ∼310 deg −2 , which is equivalent to a SMBH