Miracle-dz/UniFAR-FTUs huggingface dataset:
Discrete amenable group actions on von Neumann algebras and invariant nuclear C*-subalgebras

Let $G$ be a countable discrete amenable group, ${\cal M}$ a McDuff factor von Neumann algebra, and $A$ a separable nuclear weakly dense C$^*$-subalgebra of ${\cal M}$. We show that if two centrally free actions of $G$ on ${\cal M}$ differ up to approximately inner automorphisms then they are outer conjugate by an approximately inner automorphism, in the operator norm topology, which makes $A$ invariant. In addition, when $A$ is unital, simple, and with a unique tracial state and $\alpha$ is an automorphism of $A$ we also show that the aperiodicity of $\alpha$ on the von Neumann algebra is equivalent to the weak Rohlin property.
Theory of active particle penetration through a planar elastic membrane

With the rapid advent of biomedical and biotechnological innovations, a deep understanding of the nature of interaction between nanomaterials and cell membranes, tissues, and organs, has become increasingly important. Active penetration of nanoparticles through cell membranes is a fascinating phenomenon that may have important implications in various biomedical and clinical applications. Using a fully analytical theory supplemented by particle-based computer simulations, the penetration process of an active particle through a planar two-dimensional elastic membrane is studied. The membrane is modeled as a self-assembled sheet of particles, uniformly arranged on a square lattice. A coarse-grained model is introduced to describe the mutual interactions between the membrane particles. The active penetrating particle is assumed to interact sterically with the membrane particles. State diagrams are presented to fully characterize the system behavior as functions of the relevant control parameters governing the transition between different dynamical states. Three distinct scenarios are identified. These compromise trapping of the active particle, penetration through the membrane with subsequent self-healing, in addition to penetration with permanent disruption of the membrane. The latter scenario may be accompanied by a partial fragmentation of the membrane into bunches of isolated or clustered particles and creation of a hole of a size exceeding the interaction range of the membrane components. It is further demonstrated that the capability of penetration is strongly influenced by the size of the approaching particle relative to that of the membrane particles. Accordingly, active particles with larger size are more likely to remain trapped at the membrane for the same propulsion speed. Such behavior is in line with experimental observations. Our analytical theory is based on a combination of a perturbative expansion technique and a discrete-to-continuum formulation. It well describes the system behavior in the small-deformation regime. Particularly, the theory allows to determine the membrane displacement of the particles in the trapping state. Our approach might be helpful for the prediction of the transition threshold between the trapping and penetration in real-space experiments involving motile swimming bacteria or artificial active particles.
Appearance of light clusters in post-bounce evolution of core-collapse supernovae

We explore the abundance of light clusters in core-collapse supernovae at post-bounce stage in a quantum statistical approach. Adopting the profile of a supernova core from detailed numerical simulations, we study the distribution of light bound clusters up to \ensuremath{\alpha} particles ($2\ensuremath{\leqslant}A\ensuremath{\leqslant}4$) as well as heavy nuclei ($Ag4$) in dense matter at finite temperature. Within the frame of a cluster-mean-field approach, the abundances of light clusters are evaluated accounting for self-energy, Pauli blocking, and effects of continuum correlations. We find that deuterons and tritons, in addition to $^{3}\mathrm{He}$ and $^{4}\mathrm{He}$, appear abundantly in a wide region from the surface of the proto-neutron star to the position of the shock wave. The appearance of light clusters may modify the neutrino emission in the cooling region and the neutrino absorption in the heating region and, thereby, influence the supernova mechanism.
Coarse graining flow of spin foam intertwiners

Simplicity constraints play a crucial role in the construction of spin foam models, yet their effective behavior on larger scales is scarcely explored. In this article we introduce intertwiner and spin net models for the quantum group $\mathrm{SU}(2{)}_{k}\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(2{)}_{k}$, which implement the simplicity constraints analogous to four-dimensional Euclidean spin foam models, namely the Barrett-Crane (BC) and the Engle-Pereira-Rovelli-Livine/Freidel-Krasnov (EPRL/FK) model. These models are numerically coarse grained via tensor network renormalization, allowing us to trace the flow of simplicity constraints to larger scales. In order to perform these simulations we have substantially adapted tensor network algorithms, which we discuss in detail as they can be of use in other contexts. The BC and the EPRL/FK model behave very differently under coarse graining: While the unique BC intertwiner model is a fixed point and therefore constitutes a two-dimensional topological phase, BC spin net models flow away from the initial simplicity constraints and converge to several different topological phases. Most of these phases correspond to decoupling spin foam vertices; however we find also a new phase in which this is not the case, and in which a nontrivial version of the simplicity constraints holds. The coarse graining flow of the BC spin net models indicates furthermore that the transitions between these phases are not of second order. The EPRL/FK model by contrast reveals a far more intricate and complex dynamics. We observe an immediate flow away from the original simplicity constraints; however, with the truncation employed here, the models generically do not converge to a fixed point. The results show that the imposition of simplicity constraints can indeed lead to interesting and also very complex dynamics. Thus we need to further develop coarse graining tools to efficiently study the large scale behavior of spin foam models, in particular for the EPRL/FK model.
Efficient Randomized Algorithms for the Fixed-Precision Low-Rank Matrix Approximation

Randomized algorithms for low-rank matrix approximation are investigated, with the emphasis on the fixed-precision problem and computational efficiency for handling large matrices. The algorithms are based on the so-called QB factorization, where Q is an orthonormal matrix. Firstly, a mechanism for calculating the approximation error in Frobenius norm is proposed, which enables efficient adaptive rank determination for large and/or sparse matrix. It can be combined with any QB-form factorization algorithm in which B's rows are incrementally generated. Based on the blocked randQB algorithm by P.-G. Martinsson and S. Voronin, this results in an algorithm called randQB EI. Then, we further revise the algorithm to obtain a pass-efficient algorithm, randQB FP, which is mathematically equivalent to the existing randQB algorithms and also suitable for the fixed-precision problem. Especially, randQB FP can serve as a single-pass algorithm for calculating leading singular values, under certain condition. With large and/or sparse test matrices, we have empirically validated the merits of the proposed techniques, which exhibit remarkable speedup and memory saving over the blocked randQB algorithm. We have also demonstrated that the single-pass algorithm derived by randQB FP is much more accurate than an existing single-pass algorithm. And with data from a scenic image and an information retrieval application, we have shown the advantages of the proposed algorithms over the adaptive range finder algorithm for solving the fixed-precision problem.
Constraints on the gas masses of low-z damped Lyman α systems

We report a deep search for redshifted Hi 21cm emission from three damped and sub-damped Lyman-α absorbers (DLAs) at z≈ 0.1 with the Green Bank Telescope (GBT). No evidence for a redshifted Hi 21cm emission signal was obtained in the GBT spectra of two absorbers, with the data on the third rendered unusable by terrestrial i nterference. The non-detections of Hi 21cm emission yield strong constraints on the Hi masses of the associated galaxies, MHI< 2.3× 10 9 × (�V/100) 1/2 M⊙ for the sub-DLA at z = 0.0830 towards J1553+3548, and MHI< 2.7× 10 9 × (�V/100) 1/2 M⊙ for the DLA at z = 0.0963 towards J1619+3342, where �V is the Hi 21cm line width, in km s −1 . This continues the trend of low Hi masses found in all low-z DLAs and sub-DLAs that have been searched for redshifted Hi 21cm emission. Low-redshift absorbers with relatively low Hi column densities,. f ew× 10 20 cm −2 , thus do
On the Gorensteinness of broken circuit complexes and Orlik--Terao ideals

It is proved that the broken circuit complex of an ordered matroid is Gorenstein if and only if it is a complete intersection. Several characterizations for a matroid that admits such an order are then given, with particular interest in the $h$-vector of broken circuit complexes of the matroid. As an application, we prove that the Orlik--Terao algebra of a hyperplane arrangement is Gorenstein if and only if it is a complete intersection. Interestingly, our result shows that the complete intersection property (and hence the Gorensteinness as well) of the Orlik--Terao algebra can be determined from the last two nonzero entries of its $h$-vector.
Positive solutions for super-sublinear indefinite problems: high multiplicity results via coincidence degree

We study the periodic boundary value problem associated with the second order nonlinear equation \begin{equation*} u'' + ( \lambda a^{+}(t) - \mu a^{-}(t) ) g(u) = 0, \end{equation*} where $g(u)$ has superlinear growth at zero and sublinear growth at infinity. For $\lambda, \mu$ positive and large, we prove the existence of $3^{m}-1$ positive $T$-periodic solutions when the weight function $a(t)$ has $m$ positive humps separated by $m$ negative ones (in a $T$-periodicity interval). As a byproduct of our approach we also provide abundance of positive subharmonic solutions and symbolic dynamics. The proof is based on coincidence degree theory for locally compact operators on open unbounded sets and also applies to Neumann and Dirichlet boundary conditions. Finally, we deal with radially symmetric positive solutions for the Neumann and the Dirichlet problems associated with elliptic PDEs.
EVOLUTION OF SUPER STAR CLUSTER WINDS WITH STRONG COOLING

We study the evolution of super star cluster winds driven by stellar winds and supernova explosions. Time-dependent rates at which mass and energy are deposited into the cluster volume, as well as the time-dependent chemical composition of the re-inserted gas, are obtained from the population synthesis code Starburst99. These results are used as input for a semi-analytic code which determines the hydrodynamic properties of the cluster wind as a function of cluster age. Two types of winds are detected in the calculations. For the quasi-adiabatic solution, all of the inserted gas leaves the cluster in the form of a stationary wind. For the bimodal solution, some of the inserted gas becomes thermally unstable and forms dense warm clumps which accumulate inside the cluster. We calculate the evolution of the wind velocity and energy flux and integrate the amount of accumulated mass for clusters of different mass, radius, and initial metallicity. We also consider conditions with low heating efficiency of the re-inserted gas or mass loading of the hot thermalized plasma with the gas left over from star formation. We find that the bimodal regime and the related mass accumulation occur if at least one of the two conditions above is fulfilled.
Construction of exact control for a one-dimensional heat equation with delay

We prove an exact controllability result for a one-dimensional heat equation with delay in both lower and highest order terms and nonhomogeneous Dirichlet boundary conditions. Moreover, we give an explicit representation of the control function steering the system into a given final state. Under certain decay properties for corresponding Fourier coefficients which can be interpreted as a sufficiently high Sobolev regularity of the data, both control function and the solution are proved to be regular in the classical sense both with respect to time and space variables.
Some cosmological solutions in Einstein-Chern-Simons gravity

In this paper we find new solutions for the so called Einstein-Chern-Simons Friedmann-Robertson-Walker field equations studied in refs. (Phys. Rev. D 84 (2011) 063506, Eur. Phys. J. C 74 (2014) 3087). We consider three cases:(i) in the first case we find some solutions of the five-dimensional ChS-FRW field equations when the $h^a$ field is a perfect fluid that obeys a barotropic equation of state; (ii) in the second case we study the solutions, for the cases $\gamma =1/2,\ 3/4$, when the $h^a$ field is a five dimensional politropic fluid that obeys the equation $P^{(h)}=\omega ^{(h)}\rho ^{(h)\gamma }$; (iii) in the third case we find the scale factor and the state parameter $\omega (t)$ when the $h^a$ field is a variable modified Chaplygin gas. We consider also a space-time metric which contains as a subspace to the usual four-dimensional FRW and then we study the same three cases considered in the five-dimensional, namely when (i) the $h^a$ field is a perfect fluid, (ii) the $h^a$ field is a five dimensional politropic fluid and (iii) the $h^a$ field is a variable modified Chaplygin gas.
Star formation and molecular hydrogen in dwarf galaxies: a non-equilibrium view

We study the connection of star formation to atomic (H I) and molecular hydrogen (H2) in isolated, low-metallicity dwarf galaxies with high-resolution (mgas = 4 M, Nngb = 100) smoothed particle hydrodynamics simulations. The model includes self-gravity, nonequilibrium cooling, shielding from a uniform and constant interstellar radiation field, the chemistry of H2 formation, H2-independent star formation, supernova feedback and metal enrichment. We find that the H2 mass fraction is sensitive to the adopted dust-to-gas ratio and the strength of the interstellar radiation field, while the star formation rate is not. Star formation is regulated by stellar feedback, keeping the gas out of thermal equilibrium for densities n < 1 cm−3. Because of the long chemical time-scales, the H2 mass remains out of chemical equilibrium throughout the simulation. Star formation is well correlated with cold (T ≤ 100 K) gas, but this dense and cold gas – the reservoir for star formation – is dominated by H I, not H2. In addition, a significant fraction of H2 resides in a diffuse, warm phase, which is not star-forming. The interstellar medium is dominated by warm gas (100 K < T ≤ 3 × 104 K) both in mass and in volume. The scaleheight of the gaseous disc increases with radius while the cold gas is always confined to a thin layer in the mid-plane. The cold gas fraction is regulated by feedback at small radii and by the assumed radiation field at large radii. The decreasing cold gas fractions result in a rapid increase in depletion time (up to 100 Gyr) for total gas surface densities H I+H2 10 M pc−2, in agreement with observations of dwarf galaxies in the Kennicutt–Schmidt plane.
HOW CAN NEWLY BORN RAPIDLY ROTATING NEUTRON STARS BECOME MAGNETARS?

In a newly born (high-temperature and Keplerian rotating) neutron star, r-mode instability can lead to stellar differential rotation, which winds the seed poloidal magnetic field (∼1011 G) to generate an ultra-high (∼1017 G) toroidal field component. Subsequently, by succumbing to the Tayler instability, the toroidal field could be partially transformed into a new poloidal field. Through such dynamo processes, the newly born neutron star with sufficiently rapid rotation could become a magnetar on a timescale of ∼102 − 3 s, with a surface dipolar magnetic field of ∼1015 G. Accompanying the field amplification, the star could spin down to a period of ∼5 ms through gravitational wave radiation due to the r-mode instability and, in particular, the non-axisymmetric stellar deformation caused by the toroidal field. This scenario provides a possible explanation for why the remnant neutron stars formed in gamma-ray bursts and superluminous supernovae could be millisecond magnetars.
An investigation of the line of sight towards QSO PKS 0237−233

We present a detailed analysis of absorption systems along the line of sight towards QSO PKS 0237-233 using a high resolution spectrum of signal-to-noise ratio (SNR) ~ 60-80 obtained with the Ultraviolet and Visual Echelle Spectrograph mounted on the Very Large Telescope. This line of sight is known to show a remarkable overdensity of CIV systems that has been interpreted as revealing the presence of a supercluster of galaxies. A detailed analysis of each of these absorption systems is presented. In particular, for the z_abs = 1.6359 (with two components of logN(HI) = 18.45, 19.05) and z_abs = 1.6720 (logN(H I) = 19.78) sub-Damped Ly-alpha systems (sub-DLAs), we measure accurate abundances (resp. [O/H] = -1.63(0.07) and [Zn/H] = - 0.57(0.05) relative to solar). While the depletion of refractory elements onto dust grains in both sub-DLAs is not noteworthy, photoionization models show that ionization effects are important in a part of the absorbing gas of the sub-DLA at z_abs = 1.6359 (HI is 95 percent ionized) and in part of the gas of the sub-DLA at z_abs = 1.6359. The CIV clustering properties along the line of sight is studied in order to investigate the nature of the observed overdensity. We conclude that despite the unusually high number of CIV systems detected along the line of sight, there is no compelling evidence for the presence of a single unusual overdensity and that the situation is consistent with chance coincidence.
Long-range hydrodynamic effect due to a single vesicle in linear flow

Vesicles are involved in a vast variety of transport processes in living organisms. Additionally, they serve as a model for the dynamics of cell suspensions. Predicting the rheological properties of their suspensions is still an open question, as even the interaction of pairs is yet to be fully understood. Here we analyse the effect of a single vesicle, undergoing tank-treading motion, on its surrounding shear flow by studying the induced disturbance field , the difference between the velocity field in its presence and absence. The comparison between experiments and numerical simulations reveals an impressive agreement. Tracking ridges in the disturbance field magnitude landscape, we identify the principal directions along which the velocity difference field is analysed in the vesicle vicinity. The disturbance magnitude is found to be significant up to about 4 vesicle radii and can be described by a power law decay with the distance d from the vesicle . This is consistent with previous experimental results on the separation distance between two interacting vesicles under similar conditions, for which their dynamics is altered. This is an indication of vesicles long-range effect via the disturbance field and calls for the proper incorporation of long-range hydrodynamic interactions when attempting to derive rheological properties of vesicle suspensions.
Linear programming formulations of deterministic infinite horizon optimal control problems in discrete time

This paper is devoted to a study of infinite horizon optimal control problems with time discounting and time averaging criteria in discrete time. We establish that these problems are related to certain infinite-dimensional linear programming (IDLP) problems. We also establish asymptotic relationships between the optimal values of problems with time discounting and long-run average criteria.
Seasonal accumulation of photoassimilated carbon relates to growth rate and use for new aboveground organs of young apple trees in following spring

Abstract Deciduous trees accumulate carbon (C) in woody parts during the growth season which is subsequently used for the initial development and growth of newly formed organs in the following season; however, it is unclear which period during the growth season contributes to C accumulation. Three-year-old potted Malus domestica (apple) trees were grown in controlled growth chambers during the growth season and exposed to 13CO2 in an exposure chamber at seven different periods of the growth season, including vegetative and reproductive growth periods. Approximately half of the trees were harvested in late autumn, and the remaining trees were grown in a field in the following year. The 13C accumulation in the different organs in late autumn, and its concentration in the new aboveground growth during the following growth season, was determined. The concentration of the photoassimilated 13C in woody parts (shoots, trunk, rootstock and coarse roots) in the late autumn was higher in the trees labeled during the period of vigorous vegetative growth than in those labeled during other periods of growth. Furthermore, 13C concentration in the leaves, annual shoots, flower buds and flowers in the following early spring was also high in the trees labeled during this period. The concentration of 13C in the flower buds and flowers was positively correlated with that in the woody parts in the late autumn and old shoots in the following spring. Hence, the seasonal accumulation of photoassimilated C in woody parts in late autumn is related to growth rates during the growth season and its use for the initial development of newly formed organs in the following spring. These results suggest that under non-stressed conditions, C accumulated during the period of vigorous vegetative growth largely contributes to the C reserves that are used for the development of new organs in the following year.
Variance-based stochastic extragradient methods with line search for stochastic variational inequalities

A dynamic sampled stochastic approximated (DS-SA) extragradient method for stochastic variational inequalities (SVI) is proposed that is \emph{robust} with respect to an unknown Lipschitz constant $L$. To the best of our knowledge, it is the first provably convergent \emph{robust} SA \emph{method with variance reduction}, either for SVIs or stochastic optimization, assuming just an unbiased stochastic oracle in a large sample regime. This widens the applicability and improves, up to constants, the desired efficient acceleration of previous variance reduction methods, all of which still assume knowledge of $L$ (and, hence, are not robust against its estimate). Precisely, compared to the iteration and oracle complexities of $\mathcal{O}(\epsilon^{-2})$ of previous robust methods with a small stepsize policy, our robust method obtains the faster iteration complexity of $\mathcal{O}(\epsilon^{-1})$ with oracle complexity of $(\ln L)\mathcal{O}(d\epsilon^{-2})$ (up to logs). This matches, up to constants, the sample complexity of the sample average approximation estimator which does not assume additional problem information (such as $L$). Differently from previous robust methods for ill-conditioned problems, we allow an unbounded feasible set and an oracle with multiplicative noise (MN) whose variance is not necessarily uniformly bounded. These properties are seen in our complexity estimates which depend only on $L$ and local second or forth moments at solutions. The robustness and variance reduction properties of our DS-SA line search scheme come at the expense of nonmartingale-like dependencies (NMD) due to the needed inner statistical estimation of a lower bound for $L$. In order to handle a NMD and a MN, our proofs rely on a novel localization argument based on empirical process theory. We also propose another robust method for SVIs over the wider class of Holder continuous operators.