Miracle-dz/UniFAR-FTUs huggingface dataset:
Spectral Distribution of Typical Daylight as a Function of Correlated Color Temperature

Spectral distributions of 622 samples of daylight (skylight, and sunlight plus skylight) have been subjected to characteristic vector analysis, as composite data and in three subgroups (99 distributions measured by Budde; 249, by Condit; and 274, by Henderson and Hodgkiss). The chromaticity coordinates (x,y) computed from these distributions have been compared with direct visual determinations of chromaticity coordinates of daylight by Nayatani and Wyszecki, and by Chamberlin, Lawrence, and Belbin. It was found that the chromaticities indicated by the spectral distributions and by direct visual colorimetry cluster about the curve: y = 2.870x−3.000x2−0.275. This curve of typical daylight chromaticities falls slightly on the green side of the Planckian locus. From the mean and the first two characteristic vectors of the composite data, spectral distribution curves have been reconstituted by choice of scalar multiples of the vectors such that the chromaticity points fall on the curve of typical daylight chromaticities at places corresponding to correlated color temperatures of 4800°, 5500°, 6500°, 7500°, and 10 000°K. The representative character of these reconstituted spectral-distribution curves has been established by comparison with the measured curves from each subgroup yielding the closest approximation to the same chromaticities. The agreement so found suggests that this family of curves is more representative of the various phases of daylight between correlated color temperatures 4800° and 10 000°K than any previously derived distributions.
Self‐consistent mean field electrodynamics of turbulent dynamos

A turbulent dynamo in a conducting fluid is accompanied by the generation of small‐scale magnetic fields, which are much stronger than the mean dynamo‐generated magnetic field. These small‐scale fields modify the α effect in such a way as to stabilize the dynamo process, α=(α0+β0R⋅/B∇×R)/(1+R2), where α0, β0 are the standard kinematic dynamo parameters, and R is proportional to the mean magnetic field B0, R=B0/(4πρV2/Rm)1/2, ρ is the fluid density, V is the characteristic turbulent velocity, and Rm is the magnetic Reynolds number. The derivation of this formula is illustrated using a simple model—the turbulent dynamo for an asymmetrical top.
Digit Preserving Multiplication in Continued Fraction Representations

A permutiple is a number which is an integer multiple of some permutation of its digits. A well-known example is 9801 since it is an integer multiple of its reversal, 1089. In this paper, we consider the permutiple problem in an entirely different setting: continued fractions. We pose the question of when the simple continued fraction representation of a rational number is an integer multiple of a permutation of its partial quotients (or digits, as we shall call them). We develop some general results and apply them to finding new examples. In doing so, we attempt to classify all 2, 3, and 4-digit continued fraction permutiples in terms of basic permutiple types which we discover along the way. We also generate new examples from old by finding conditions which guarantee that digit-string concatenation yields other permutiples.
On cardinality bounds involving the weak Lindelöf degree

Abstract We give a general closing-off argument in Theorem 2.3 from which several corollaries follow, including (1) if X is a locally compact Hausdorff space then |X| ≤ 2wL(X)ψ(X), and (2) if X is a locally compact power homogeneous Hausdorff space then |X| ≤ 2wL(X)t(X). The first extends the well-known cardinality bound 2ψ(X) for a compactum X in a new direction. As |X| ≤ 2wL(X)χ(X) for a normal spaceX[4], this enlarges the class of known Tychonoff spaces for which this bound holds. In 2.12 we give a short, direct proof of (1) that does not use 2.3. Yet 2.3 is broad enough to establish results much more general than (1), such as if X is a regular space with a π-base ℬ such that |B| ≤ 2wL(X)χ(X) for all B ∈ ℬ, then |X| ≤ 2wL(X)χ(X). Separately, it is shown that if X is a regular space with a π-base whose elements have compact closure, then |X| ≤ 2wL(X)ψ(X)t(X). This partially answers a question from [4] and gives a third, separate proof of (1). We also show that if X is a weakly Lindelöf, normal, sequential space with χ(X) ≤ 2ℵ0, then |X| ≤ 2ℵ0. Result (2) above is a new generalization of the cardinality bound 2t(X) for a power homogeneous compactum X (Arhangel'skii, van Mill, and Ridderbos [3], De la Vega in the homogeneous case [10]). To this end we show that if U ⊆ clD ⊆ X, where X is power homogeneous and U is open, then |U| ≤ |D|πχ(X). This is a strengthening of a result of Ridderbos [19].
Simulations of tidally driven eccentric instabilities with application to superhumps

The tidally induced eccentric evolution of a fluid disk having pressure and viscosity is numerically analyzed. The effects of the 3:1 eccentric inner Lindblad resonance on disks in close binaries are studied, as a model for superhumps, using a two-dimensional SPH code. The numerical results for the m = 3 component of the perturbing potential are presented
Zeta-functions of root systems and Poincaré polynomials of Weyl groups

We consider a certain linear combination $S(\mathbf{s},\mathbf{y};I;\Delta)$ of zeta-functions of root systems, where $\Delta$ is a root system of rank $r$ and $I\subset\{1,2,\ldots,r\}$. Showing two different expressions of $S(\mathbf{s},\mathbf{y};I;\Delta)$, we find that a certain signed sum of zeta-functions of root systems is equal to a sum involving Bernoulli functions of root systems. This identity gives a non-trivial functional relation among zeta-functions of root systems, if the signed sum does not identically vanish. This is a genralization of the authors' previous result proved in \cite{KMTLondon}, in the case when $I=\emptyset$. We present several explicit examples of such functional relations. A criterion of the non-vanishing of the signed sum, in terms of Poincar{\'e} polynomials of associated Weyl groups, is given. Moreover we prove a certain converse theorem, which implies that the generating function for the case $I=\emptyset$ essentially knows all information on generating functions for general $I$.
Lipschitz stability in an inverse problem for the wave equation

We are interested in the inverse problem of the determination of the potential $p(x),~x\in\Omega\subset\mathbb{R}^n$ from the measurement of the normal derivative $\partial_\nu u$ on a suitable part $\Gamma_0$ of the boundary of $\Omega$, where $u$ is the solution of the wave equation $\partial_{tt}u(x,t)-\Delta u(x,t)+p(x)u(x,t)=0$ set in $\Omega\times(0,T)$ and given Dirichlet boundary data. More precisely, we will prove local uniqueness and stability for this inverse problem and the main tool will be a global Carleman estimate, result also interesting by itself.
Direct and inverse scattering problem for a stratified nonreciprocal chiral medium

Propagation of a transversely polarized time-harmonic electromagnetic plane wave normally incident on a stratified nonreciprocal chiral (bi-isotropic) slab is considered. The medium is modelled by the constitutive relations in the frequency domain. The structure of the scattering matrix is analysed. The inverse problem of reconstruction of material characteristics of a medium is studied.
Electrostatic potential of interstellar grains

The equilibrium electrostatic potential of interstellar grains, subjected to an ultraviolet radiation field in a dilute ambient plasma, is calculated for a variety of radiation fields and plasma parameters, and for two different grain materials. For an environment typical of an H I region, the results show that the various components of interstellar grains in the multicomponent model may charge to opposite potentials, thus favoring the formation of mixed composite grains due to Coulomb attraction. In H II regions, a three-shell model of the grain charge is presented, which includes a sphere of positively charged grains around the central star bounded by a transition region in which grains of low and of high photoyield are oppositely charged. Here grain growth and the formation of mixed composite grains may take place. In the outer shell all grains are charged negative. Estimated radii of these shells are given for exciting B0 and O5-type stars. (auth)
Spontaneous spin-lattice coupling in the geometrically frustrated triangular lattice antiferromagnet CuFeO2

We use high-resolution synchrotron x-ray and neutron diffraction to study the geometrically frustrated triangular lattice antiferromagnet CuFeO2. On cooling from room temperature, CuFeO2 undergoes two antiferromagnetic phase transitions with incommensurate and commensurate magnetic order at T-N1=14 K and T-N2=11 K, respectively. The occurrence of these two magnetic transitions is accompanied by second- and first-order structural phase transitions from hexagonal to monoclinic symmetry. Application of a 6.9 T magnetic field lowers both transition temperatures by similar to 1 K, and induces an additional incommensurate structural modulation in the temperature region where the field-driven ferroelectricity occurs. These results suggest that a strong magneto-elastic coupling is intimately related to the multiferroic effect.
Dissolved, Labile, and Total Particulate Trace Metal Dynamics on the Northeast Greenland Shelf

We present high‐resolution profiles of dissolved, labile, and total particulate trace metals (TMs) on the Northeast Greenland shelf from GEOTRACES cruise GN05 in August 2016. Combined with radium isotopes, stable oxygen isotopes, and noble gas measurements, elemental distributions suggest that TM dynamics were mainly regulated by the mixing between North Atlantic‐derived Intermediate Water, enriched in labile particulate TMs (LpTMs), and Arctic surface waters, enriched in Siberian shelf‐derived dissolved TMs (dTMs; Co, Cu, Fe, Mn, and Ni) carried by the Transpolar Drift. These two distinct sources were delineated by salinity‐dependent variations of dTM and LpTM concentrations and the proportion of dTMs relative to the total dissolved and labile particulate ratios. Locally produced meltwater from the Nioghalvfjerdsbræ (79NG) glacier cavity, distinguished from other freshwater sources using helium excess, contributed a large pool of dTMs to the shelf inventory. Localized peaks in labile and total particulate Cd, Co, Fe, Mn, Ni, Cu, Al, V, and Ti in the cavity outflow, however, were not directly contributed by submarine melting. Instead, these particulate TMs were mainly supplied by the re‐suspension of cavity sediment particles. Currently, Arctic Ocean outflows are the most important source of dFe, dCu, and dNi on the shelf, while LpTMs and up to 60% of dMn and dCo are mainly supplied by subglacial discharge from the 79NG cavity. Therefore, changes in the cavity‐overturning dynamics of 79NG induced by glacial retreat, and alterations in the transport of Siberian shelf‐derived materials with the Transport Drift may shift the shelf dTM‐LpTM stoichiometry in the future.
Dual-Server Boolean Data Retrieval for Highly-Scalable Secure File Sharing Services

Searchable encryption (SE) is a promising strategy for cloud-based file retrieval services, via structuring correspondences between files and keywords. Public key encryption with keyword search (PEKS) has been generally employed in file-sharing services, as compared to searchable symmetric encryption (SSE). However, PEKS is inherently vulnerable to keyword guessing attacks (KGA) launched by a malicious server. To resist such attacks, classic solutions are dual-server PEKS (DS-PEKS) [TIFS’2015] and server-aided PEKS (SA-PEKS) [TIFS’2016]. However, the query model in these two solutions only support single keyword search pattern, which inevitably limits their wide deployments in practice due to efficiency concern. In this work, we present DSB-SE, a new cloud-based file sharing & retrieval system that supports boolean queries while retaining KGA-resistance. Compared to DS-PEKS and SA-PEKS, the cost of documents searching in DSB-SE is 25, 000 times (resp. 6, 600 times) faster when <inline-formula> <tex-math notation="LaTeX">$\#\text {keyword}=10$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$s\text {-term}=1$ </tex-math></inline-formula>, where <inline-formula> <tex-math notation="LaTeX">$s$ </tex-math></inline-formula>-term is the least frequent keyword in the query pattern. Technically, the performance gain derives from revisiting traditional boolean SSE by: (i) introducing a pairing-free DDH-based transformation key modular that allows a data reader’s query pattern to be treated as a data writer’s; (ii) employing the dual-server methodology to support boolean query with efficient validity checks. In particular, the client-to-cloud communication cost for retrieving index of a single document is bounded to <inline-formula> <tex-math notation="LaTeX">$10^{-2}s$ </tex-math></inline-formula>, and the cost of sending a token ranges from <inline-formula> <tex-math notation="LaTeX">$8\times 10^{-2}s\sim 13\times 10^{-2}s$ </tex-math></inline-formula>. Nevertheless, DSB-SE is <inline-formula> <tex-math notation="LaTeX">$1.5\times 10^{-2}s$ </tex-math></inline-formula> slightly slower than DS-PEKS (but <inline-formula> <tex-math notation="LaTeX">$1.35\times 10^{-2}s$ </tex-math></inline-formula> faster than SA-PEKS) for key generation cost. Overall, the experiments show that the DSB-SE is practical and sufficient for real cloud applications, which is conducted over Enron dataset under a real-world cloud platform.
The magnetic Weyl calculus

In the presence of a variable magnetic field, the Weyl pseudodifferential calculus must be modified. The usual modification, based on “the minimal coupling principle” at the level of the classical symbols, does not lead to gauge invariant formulas if the magnetic field is not constant. We present a gauge covariant quantization, relying on the magnetic canonical commutation relations. The underlying symbolic calculus is a deformation, defined in terms of the magnetic flux through triangles, of the classical Moyal product.
Learning Outcome Modeling in Computer-Based Assessments for Learning: A Sequential Deep Collaborative Filtering Approach

Learning outcome modeling is a technical underpinning for the successful evaluation of learners' learning outcomes through computer-based assessments. In recent years, collaborative filtering approaches have gained popularity as a technique to model learners' item responses. However, how to model the temporal dependencies between item responses using a collaborative filtering approach for learning outcome modeling is still under investigation. Leveraging the advantages of deep learning, this study proposes a novel deep-learning-based collaborative filtering approach for learning outcome modeling. Unlike conventional collaborative filtering approaches, the proposed model, utilizing recurrent neural networks, is capable of sequentially predicting learners' future learning outcomes based on their history learning records. Moreover, the proposed model has the capacity to discover item-skill associations from the scratch without expert input based on attentive modeling. The experimental results demonstrate that the proposed model outperforms a popular deep-learning approach and can be successfully used to discover item-skill associations for both real-world and synthetic datasets.
Improvement in Error Recognition of Real-Time Football Images by an Object-Augmented AI Model for Similar Objects

In this paper, we analyze the recognition error of the general AI recognition model and propose the structure-modified and object-augmented AI recognition model. This model has object detection features that distinguish specific target objects in target areas where players with similar shapes and characteristics overlapped in real-time football images. We implemented the AI recognition model by reinforcing the training dataset and augmenting the object class. In addition, it is shown that the recognition rate increased by modifying the model structure based on the recognition errors analysis of general AI recognition models. Recognition errors were decreased by applying the modules of HSV processing and differentiated classes (overlapped player groups) learning to the general AI recognition model. We experimented in order to compare the recognition error reducing performance with the general AI model and the proposed AI model by the same real-time football images. Through this study, we have confirmed that the proposed model can reduce errors. It showed that the proposed AI model structure to recognize similar objects in real-time and in various environments could be used to analyze football games.
Maximum Matching and the Rank of a Matrix

The rank of a matrix A is related to the cardinality of a maximum matching in a graph G formed from A by considering whether the matrix entries of A are nonzero, but ignoring their magnitudes otherwise. We consider real matrices which can be written as the sum of a skew matrix and a diagonal matrix. The graphs considered are undirected and have loops at the vertices; the usual definition of matching and Edmonds’ maximum matching algorithm are extended to include this class of graphs. The particular matrix–graph relationship considered here is suggested by the Volterra–Lotka equations of mathematical biology.
Structure Formation Cosmic Rays: Identifying Observational Constraints

Shocks that arise from baryonic in-fall and merger events during the structure formation are believed to be a source of cosmic rays. These "structure formation cosmic rays" (SFCRs) would essentially be primordial in composition, namely, mostly made of protons and alpha particles. However, very little is known about this population of cosmic rays. One way to test the level of its presence is to look at the products of hadronic reactions between SFCRs and the ISM. A perfect probe of these reactions would be Li. The rare isotope Li is produced only by cosmic rays, dominantly in αα → 6Li fusion reactions with the ISM helium. Consequently, this nuclide provides a unique diagnostic of the history of cosmic rays. Exactly because of this unique property is Li affected most by the presence of an additional cosmic ray population. In turn, this could have profound consequences for the Big-Bang nucleosynthesis: cosmic rays created during cosmic structure formation would lead to pre-Galactic Li production, which would act as a "contaminant" to the primordial 7Li content of metalpoor halo stars. Given the already existing problem of establishing the concordance between Li observed in halo stars and primordial 7Li as predicted by the WMAP, it is crucial to set limits to the level of this "contamination". However, the history of SFCRs is not very well known. Thus we propose a few model-independent ways of testing the SFCR species and their history, as well as the existing lithium problem: 1) we establish the connection between gamma-ray and Li production, which enables us to place constraints on the SFCR-made lithium by using the observed Extragalactic Gamma-Ray Background (EGRB); 2) we propose a new site for testing the primordial and SFCR-made lithium, namely, low-metalicity High-Velocity Clouds (HVCs), which retain the pre-Galactic composition without any significant depletion. Although using one method alone may not give us strong constraints, using them in concert will shed a new light on the SFCR population and possibly give some answers about the pressing lithium problem.
The Elliott-Halberstam conjecture implies the Vinogradov least quadratic nonresidue conjecture

For each prime $p$, let $n(p)$ denote the least quadratic nonresidue modulo $p$. Vinogradov conjectured that $n(p) = O(p^\eps)$ for every fixed $\eps>0$. This conjecture follows from the generalised Riemann hypothesis, and is known to hold for almost all primes $p$ but remains open in general. In this paper we show that Vinogradov's conjecture also follows from the Elliott-Halberstam conjecture on the distribution of primes in arithmetic progressions, thus providing a potential "non-multiplicative" route to the Vinogradov conjecture. We also give a variant of this argument that obtains bounds on short centred character sums from "Type II" estimates of the type introduced recently by Zhang and improved upon by the Polymath project, or from bounds on the level of distribution on variants of the higher order divisor function. In particular, we can obtain an improvement over the Burgess bound would be obtained if one had Type II estimates with level of distribution above $2/3$ (when the conductor is not cube-free) or $3/4$ (if the conductor is cube-free); morally, one would also obtain such a gain if one had distributional estimates on the third or fourth divisor functions $\tau_3, \tau_4$ at level above $2/3$ or $3/4$ respectively. Some applications to the least primitive root are also given.
Homogenization of a pseudo-parabolic system via a spatial-temporal decoupling: Upscaling and corrector estimates for perforated domains

We determine corrector estimates quantifying the convergence speed of the upscaling of a pseudo-parabolic system containing drift terms incorporating the separation of length scales with relative size $\epsilon\ll1$. To achieve this goal, we exploit a natural spatial-temporal decomposition, which splits the pseudo-parabolic system into an elliptic partial differential equation and an ordinary differential equation coupled together. We obtain upscaled model equations, explicit formulas for effective transport coefficients, as well as corrector estimates delimitating the quality of the upscaling. Finally, for special cases we show convergence speeds for global times, i.e., $t\in\mathbf{R}_+$, by using time intervals expanding to the whole $\mathbf{R}_+$ simultaneously with passing to the homogenization limit $\epsilon\downarrow0$.
Quantum ergodicity for large equilateral quantum graphs

Consider a sequence of finite regular graphs converging, in the sense of Benjamini–Schramm, to the infinite regular tree. We study the induced quantum graphs with equilateral edge lengths, Kirchhoff conditions (possibly with a non‐zero coupling constant α ) and a symmetric potential U on the edges. We show that in the spectral regions where the infinite quantum tree has absolutely continuous spectrum, the eigenfunctions of the converging quantum graphs satisfy a quantum ergodicity theorem. In case α=0 and U=0 , the limit measure is the uniform measure on the edges. In general, it has an explicit C1 density. We finally prove a stronger quantum ergodicity theorem involving integral operators, the purpose of which is to study eigenfunction correlations.
Quantum Gaudin model and classical KP hierarchy

This short note is a review of the intriguing connection between the quantum Gaudin model and the classical KP hierarchy recently established in [1]. We construct the generating function of integrals of motion for the quantum Gaudin model with twisted boundary conditions (the master T-operator) and show that it satisfies the bilinear identity and Hirota equations for the classical KP hierarchy. This implies that zeros of eigenvalues of the master T-operator in the spectral parameter have the same dynamics as the Calogero-Moser system of particles.