Miracle-dz/UniFAR-FTUs huggingface dataset:
The little desert? Some subfactors with index in the interval $5+3+{\sqrt 5}$

Progress on classifying small index subfactors has revealed an almost empty landscape. In this paper we give some evidence that this desert continues up to index . There are two known quantum-group subfactors with index in this interval, and we show that these subfactors are the only way to realize the corresponding principal graphs. One of these subfactors is 1-supertransitive, and we demonstrate that it is the only 1-supertransitive subfactor with index between 5 and . Computer evidence shows that any other subfactor in this interval would need to have rank at least 38. We prove our uniqueness results by showing that there is a unique flat connection on each graph. The result on 1-supertransitive subfactors is proved by an argument using intermediate subfactors, running the "odometer" from the FusionAtlas' Mathematica package and paying careful attention to dimensions. This is the published version of arXiv:1205.2742.
Demonstration of a 320×256 two-color focal plane array using InAs/InGaAs quantum dots in well detectors

We report the demonstration of a two-color infrared focal plane array based on a voltage-tunable quantum dots-in-well (DWELL) design. The active region consists of multiple layers of InAs quantum dots in an In0.15Ga0. 85As quantum well. Spectral response measurements yielded a peak at 5. 5μm for lower biases and at 8–10μm for higher biases. Using calibrated blackbody measurements, the midwavelength and long wavelength specific detectivity (D*) were estimated to be 7.1×1010cmHz1∕2∕W(Vb=1.0V) and 2.6×1010cmHz1∕2∕W(Vb=2.6V) at 78 K, respectively. This material was processed into a 320×256 array and integrated with an Indigo 9705 readout chip and thermal imaging was achieved at 80 K.
Concentration of information content for convex measures

We establish sharp exponential deviation estimates of the information content as well as a sharp bound on the varentropy for the class of convex measures on Euclidean spaces. This generalizes a similar development for log-concave measures in the recent work of Fradelizi, Madiman and Wang (2016). In particular, our results imply that convex measures in high dimensions are concentrated in an annulus between two convex sets (as in the log-concave case) despite their possibly having much heavier tails. Various tools and consequences are developed, including a sharp comparison result for Renyi entropies, inequalities of Kahane-Khinchine type for convex measures that extend those of Koldobsky, Pajor and Yaskin (2008) for log-concave measures, and an extension of Berwald's inequality (1947).
The last zero-crossing of an iterated brownian motion with drift

ABSTRACT In this paper, we consider the iterated Brownian motion where are two independent Brownian motions with drift . Here, we study the last zero crossing before the maximum time span travelled by the inner process of and for this purpose we derive the last zero-crossing distribution of the drifted Brownian motion. We derive also the joint distribution of the last zero crossing before t and of the first passage time through the zero level of a Brownian motion with drift μ after t. All these results permit us to derive explicit formulas for . Also, the iterated zero-crossing is analysed and extended to the case where the level of nesting is arbitrary.
Intracavity quasi-phase-matched self-frequency conversion in a periodically poled Nd:Mg:LiNbO3 crystal

The theory of intracavity quasi-phase-matched self-frequency conversion in an active nonlinear periodically poled structure is developed. The processes of quasi-phase-matched self-frequency doubling, self-halving and mixing using the pump wave in a periodically poled Nd:Mg:LiNbO{sub 3} crystal are studied. The dependences of the efficiency of nonlinear optical conversion in these processes on the reflection coefficient of the output mirror and on linear losses in the medium are investigated. (nonlinear optical phenomena)
Convex Hull of $\left(t, t^2, \cdots, t^N\right)$

This paper analyzes the convex hull of the parametric curve $\left(t, t^2, \cdots, t^N\right)$, where $t$ is in a closed interval. It finds that every point in the convex hull is representable as a convex combination of $\frac{N+1}{2}$ points on the curve. It also finds that the evaluation of the convex combination is a homeomorphism from the convex combinations of $\frac{N+1}{2}$ points on the curve to the convex hull of the curve, as long as the points are listed in increasing order, and as long as two representations that are reachable from each other by removing terms with coefficient zero, combining terms with the same point, the inverses of these operations, or a sequence of these operations in any order, are considered to be equivalent.
Radio-Excess IRAS Galaxies. II. Host Galaxies

This is the second of a series of papers studying a sample of radio-excess IRAS galaxies. These galaxies have radio emission in excess of that expected due to star formation, but largely fall between the traditional categories of radio-loud and radio-quiet active galaxies. R-band images of the hosts of far-infrared (FIR)-luminous radio-excess galaxies are presented and analyzed. The hosts of the FIR-luminous radio-excess galaxies are luminous galaxies, on average 0.8 mag brighter than M. Their optical luminosities and morphologies are similar to comparison samples of radio-loud compact steep-spectrum and gigahertz peaked-spectrum sources and extended radio galaxies. We find a similar fraction of galaxies in our sample (∼70%) with companions or distorted morphologies as in radio-loud comparison samples. This is consistent with radio activity being associated with tidal interaction. The majority (65%) of the FIR-luminous radio-excess galaxies have radio source sizes that are smaller than the optical host by more than an order of magnitude. These compact radio sources may be young precursors to classical radio galaxies or a different population of radio sources, possibly confined by the host interstellar medium. The host galaxy types were determined by analysis of the surface brightness distributions. The elliptical hosts have effective surface brightnesses and radii consistent with known ellipticals but inconsistent with a population of brightest cluster galaxies. Thus, it is unlikely these objects are the precursors of FR I radio galaxies. The disk hosts have smaller sizes and low radio excesses. However, they have a range of radio source sizes, which is not expected if they are radio-"loud" Seyfert galaxies.
On the Description of Shape and Spatial Configuration inside Buildings: Convex Partitions and Their Local Properties

As we move through buildings, we experience not only continuous changes of perspective but also discrete transitions from one space to another. To describe movement as a pattern of such transitions we need methods for partitioning space into relevant elementary units. Here we explore several convex partitions including one based on the thresholds at which edges, corners, and surfaces appear into the field of vision of a moving subject, or disappear outside it. Our purpose is to contribute to the development of quantitative descriptions of building shape and spatial configuration.
The Role of Initial Uncertainties in Predicion

Abstract When the initial values, or the parameters, of prognostic equations are not known with certainty, there must also be errors in the solution. The initial conditions may be represented by an ensemble, each member of which is consistent with all available knowledge. The mean of this ensemble is a reasonable "best" solution to the prognostic equation. Following Gleeson, we have examined the behavior of the error in the forecast, as represented by the rms deviation of the ensemble members from their mean, for a few simple equations. We have further examined the time-dependent behavior of the ensemble mean, as opposed to the solution obtained by applying the prognostic equation to the original mean values. These are, in general, different. It is concluded that optimum procedures for forecasting, i.e., solving prognostic equations, require includingterms in the equations to represent the influence of the initial uncertainties. Since the nature of these uncertainties may also have profound influences on .
Hubble Space Telescope STIS Spectroscopy of the White Dwarfs in the Ultrashort-Period Dwarf Novae VY Aquarii and WX Ceti

We present the results of a multicomponent synthetic spectral analysis of Hubble Space Telescope (HST) STIS spectra of the ultrashort-period dwarf novae VY Aqr and WX Ceti during their deep quiescence following their last superoutburst. The white dwarf in these extremely low accretion rate systems dominates the far-UV light. We find that the accreting white dwarfs in VY Aqr and WX Ceti are remarkably similar. Both systems contain white dwarfs with Teff = 13,000-13,500 K, a rotation velocity below 800-1200 km s-1, and subsolar metallicity. Both white dwarfs are better fitted with a two-temperature white dwarf plus accretion belt model in which part of the white dwarf is cooler and "slowly" rotating and part is hotter, smaller, and spinning at the Keplerian speed. We discuss the implications of the surface temperatures we have derived for the white dwarfs in VY Aqr, WX Ceti, and the nine other WZ Sge-like dwarf novae below the period gap which have been observed with HST. Their surface temperatures cluster closely around 15,000 K and their orbital periods are between 1.3 and 1.5 hr. We show that long-term compressional heating due to time-averaged accretion is the mechanism responsible for the clustering around 15,000 K. The time-averaged accretion rate corresponding to this cluster of observed temperatures is almost precisely what is predicted if gravitational wave emission is driving mass transfer below the period gap.
A trust-region method for derivative-free nonlinear constrained stochastic optimization

In this work we introduce the algorithm (S)NOWPAC (Stochastic Nonlinear Optimization With Path-Augmented Constraints) for stochastic nonlinear constrained derivative-free optimization. The algorithm extends the derivative-free optimizer NOWPAC to be applicable to nonlinear stochastic programming. It is based on a trust region framework, utilizing local fully linear surrogate models combined with Gaussian process surrogates to mitigate the noise in the objective function and constraint evaluations. We show several benchmark results that demonstrate (S)NOWPAC's efficiency and highlight the accuracy of the optimal solutions found.
Compact and Fossil Groups

Abstract We present a short review on poor groups of galaxies focusing on the evolution of compact groups and formation of fossil groups. Fossil groups are systems with one dominant luminous elliptical galaxy surrounded by faint companions, in an extended X-ray halo. We will briefly discuss the possibility of fossil groups being the end-products of the merging of compact groups.
The monomer-dimer problem and moment Lyapunov exponents of homogeneous Gaussian random fields

We consider an "elastic'' version of the statistical mechanical monomer-dimer problem on the $n$-dimensional integer lattice. Our setting includes the classical "rigid'' formulation as a special case and extends it by allowing each dimer to consist of particles at arbitrarily distant sites of the lattice, with the energy of interaction between the particles in a dimer depending on their relative position. We reduce the free energy of the elastic dimer-monomer (EDM) system per lattice site in the thermodynamic limit to the moment Lyapunov exponent (MLE) of a homogeneous Gaussian random field (GRF) whose mean value and covariance function are the Boltzmann factors associated with the monomer energy and dimer potential. In particular, the classical monomer-dimer problem becomes related to the MLE of a moving average GRF. We outline an approach to recursive computation of the partition function for "Manhattan'' EDM systems where the dimer potential is a weighted $l_1$-distance and the auxiliary GRF is a Markov random field of Pickard type which behaves in space like autoregressive processes do in time. For one-dimensional Manhattan EDM systems, we compute the MLE of the resulting Gaussian Markov chain as the largest eigenvalue of a compact transfer operator on a Hilbert space which is related to the annihilation and creation operators of the quantum harmonic oscillator and also recast it as the eigenvalue problem for a pantograph functional-differential equation.
Representations of the inverse hull of a 0-left cancellative semigroup

A semigroup S containing a zero element is said to be 0-left cancellative if st = sr \neq 0 implies that t = r. Given such an S we build an inverse semigroup H(S), called the inverse hull of S. Motivated by the study of certain C*-algebras associated to H(S) (a task that we will address in a subsequent article) we carry out a detailed analysis of the spectrum of the idempotent semilattice E(S) of H(S) with a special interest in identifying the ultra-characters. In order to produce examples of characters on E(S), we introduce the notion of "strings" in a semigroup, attempting to make sense of the "infinite paths" which are fundamental in the study of graph C*-algebras. Our strongest results are obtained under the assumption that S admits "least common multiples", but we also touch upon the notion of "finite alignment", motivated by the corresponding notion from the theory of higher rank graphs, and which has also appeared in recent papers by Spielberg and collaborators.
On post-glacial sea level – II. Numerical formulation and comparative results on spherically symmetric models

SUMMARY Theoretical approaches to computing gravitationally self-consistent sea-level changes in consequence of ice growth and ablation are comprised of two parts. The first is a mapping between variations in global sea level and changes in ocean height (required to define the surface load), and the second is a method for computing global sea-level change arising from an arbitrary surface loading. In Mitrovica & Milne (2003) (Paper I) we described a new, generalized mapping between sea-level change and ocean height that takes exact account of the evolution of shorelines associated with both transgression and regression cycles and time-dependent marine-based ice margins. The theory is valid for any earth model. In this paper we extend our previous work in three ways. First, we derive an efficient, iterative numerical algorithm for solving the generalized sea-level equation. Secondly, we consider a special case of the new sea-level theory involving spherically symmetric earth models. Specifically, we combine our iterative numerical formulation with viscoelastic Love number theory to derive an extended pseudo-spectral algorithm for solving the new sea-level equation. This algorithm represents an extension of earlier methods developed for the fixed-shoreline case to precisely incorporate shoreline migration processes. Finally, using this special case, we quantitatively assess errors incurred in previous efforts to extend the traditional (fixed shoreline) sea-level equation of Farrell & Clark (1976) to treat time-dependent shorelines. We find that the approximations adopted by Johnston (1993) and Milne (1998) to treat transgression and regression at shorelines introduce negligible (∼1 per cent) error into predictions of post-glacial relative sea-level histories. In contrast, the errors associated with the Peltier (1994) sea-level equation are an order of magnitude larger, and comparable to the error incurred using the traditional sea-level theory. Furthermore, our numerical tests verify the high accuracy of the Milne (1998) approximation for treating the influence of grounded, marine-based ice.
Generalised hot-wire technique for high pressure thermal conductivity measurements

The application of the generalised hot-wire technique to high pressure thermal conductivity measurement is discussed. Results for the thermal conductivity of NaCl obtained with a wire sandwiched between two homogeneous discs, one of NaBr and one of NaCl, were recorded in the pressure range 0-4 GPa. The results obtained are compared with those for a homogeneous cell. This comparison indicates that the generalised hot-wire technique appears to be applicable to high pressure thermal conductivity measurement. However, the errors in the generalised technique are larger than those in the standard technique.
Spinors, strings, integrable models, and decomposed Yang-Mills theory

This paper deals with various interrelations between strings and surfaces in three-dimensional ambient space, two-dimensional integrable models, and two-dimensional and four-dimensional decomposed SU(2) Yang-Mills theories. Initially, a spinor version of the Frenet equation is introduced in order to describe the differential geometry of static three-dimensional stringlike structures. Then its relation to the structure of the su(2) Lie algebra valued Maurer-Cartan one-form is presented, while by introducing time evolution of the string a Lax pair is obtained, as an integrability condition. In addition, it is shown how the Lax pair of the integrable nonlinear Schrodinger equation becomes embedded into the Lax pair of the time extended spinor Frenet equation, and it is described how a spinor-based projection operator formalism can be used to construct the conserved quantities, in the case of the nonlinear Schrodinger equation. Then the Lax pair structure of the time extended spinor Frenet equation is related to properties of flat connections in a two-dimensional decomposed SU(2) Yang-Mills theory. In addition, the connection between the decomposed Yang-Mills and the Gauss-Codazzi equation that describes surfaces in three-dimensional ambient space is presented. In that context the relation between isothermic surfaces and integrable models is discussed. Finally, the utility of the Cartan approach to differential geometry is considered. In particular, the similarities between the Cartan formalism and the structure of both two-dimensional and four-dimensional decomposed SU(2) Yang-Mills theories are discussed, while the description of two-dimensional integrable models as embedded structures in the four-dimensional decomposed SU(2) Yang-Mills theory are presented.
Uniqueness issues for evolution equations with density constraints

In this paper, we present some basic uniqueness results for evolution equations under density constraints. First, we develop a rigorous proof of a well-known result (among specialists) in the case where the spontaneous velocity field satisfies a monotonicity assumption: we prove the uniqueness of a solution for first-order systems modeling crowd motion with hard congestion effects, introduced recently by Maury et al. The monotonicity of the velocity field implies that the [Formula: see text]-Wasserstein distance along two solutions is [Formula: see text]-contractive, which in particular implies uniqueness. In the case of diffusive models, we prove the uniqueness of a solution passing through the dual equation, where we use some well-known parabolic estimates to conclude an [Formula: see text]-contraction property. In this case, by the regularization effect of the nondegenerate diffusion, the result follows even if the given velocity field is only [Formula: see text] as in the standard Fokker–Planck equation.
A linear regularization scheme for inverse problems with unbounded linear operators on Banach spaces

This paper extends the linear regularization scheme known as the approximate inverse to unbounded linear operators on Banach spaces. The principle of feature reconstruction is adapted from bounded operators to the unbounded scenario and, in addition, a new situation is examined where the data need to be pre-processed to fit into the mathematical model. In all these cases, invariance and regularization properties are surveyed and established for the example of fractional differentiation. Numerical results confirm the derived characteristics of the presented methods.
Optical modulation processes in thin films based on thermal effects of surface plasmons

Experimental results are presented for light-on-light modulation at low rates using coupling to nonradiative surface plasmons and their associated thermal effects in a thin gold foil. It is first shown that several modulated Gaussian beams simultaneously exciting surface plasmons in the same region of a thin gold film, will result in a coupling that is revealed in the reflected beams. The observed effects result in the reflected beams undergoing changes in both spatial distribution and intensity levels. A brief study is then presented of the coupling between surface plasmons and an electrical current in the excitation region to further support the role of the surface plasmon induced thermal processes in the gold foil.
About presentations of braid groups and their generalizations

In the paper we give a survey of rather new notions and results which generalize classical ones in the theory of braids. Among such notions are various inverse monoids of partial braids. We also observe presentations different from standard Artin presentation for generalizations of braids. Namely, we consider presentations with small number of generators, Sergiescu graph-presentations and Birman-Ko-Lee presentation. The work of V.V. Chaynikov on the word and conjugacy problems for the singular braid monoid in Birman-Ko-Lee generators is described as well.
The Topology of the $m$-Tamari Lattices

Them-Tamari Lattices T (m) n were recently introduced by Bergeron and Préville-Ratelle as posets on m-Dyck paths, and it was later shown by Bousquet-Mélou, Fusy and Préville-Ratelle that these form intervals in the classical Tamari lattice. It follows from a theorem by Björner and Wachs and a basic property of EL-shellable posets, that the m-Tamari lattices are EL-shellable. In this article, we give a new proof of this property, completely in terms of m-Dyck paths. Moreover, we derive properties of the Möbius function of T (m) n , and we characterize the intervals of T (m)
On the Rate of Convergence for Monotone Numerical Schemes for Nonlocal Isaacs Equations

We study monotone numerical schemes for nonlocal Isaacs equations, the dynamic programming equations of stochastic differential games with jump-diffusion state processes. These equations are fully-nonlinear non-convex equations of order less than $2$. In this paper they are also allowed to be degenerate and have non-smooth solutions. The main contribution is a series of new a priori error estimates: The first results for nonlocal Isaacs equations, the first general results for degenerate non-convex equations of order greater than $1$, and the first results in the viscosity solution setting giving the precise dependence on the fractional order of the equation. We also observe a new phenomena, that the rates differ when the nonlocal diffusion coefficient depend on $x$ and $t$, only on $x$, or on neither.
On the Harnack inequality for parabolic minimizers in metric measure spaces

In this note we consider problems related to parabolic partial dif- ferential equations in geodesic metric measure spaces, that are equipped with a doubling measure and a Poincare inequality. We prove a location and scale invariant Harnack inequality for a minimizer of a variational problem related to a doubly non-linear parabolic equation involving the p-Laplacian. Moreover, we prove the sufficiency of the Grigor'yan-Saloff-Coste theorem for general p > 1 in geodesic metric spaces. The approach used is strictly variational, and hence we are able to carry out the argument in the metric setting.