Miracle-dz/UniFAR-FTUs huggingface dataset:
Inductive Definition in Type Theory

Type theories can provide a foundational account of constructive mathematics, and for the computer scientist, they can also serve the dual roles of specification and programming languages. In the search for natural and expressive extensions to the N sc UP sc RL type theory, we are led to consider forms of inductive and co-inductive definition. We realize these notions through the addition of two new type constructors, denoted $\mu$ and $\nu$. This represents a step towards a more expressive theory, without adopting a completely impredicative notion of type. With these constructors we can define all the common inductive data types, from natural numbers to infinite trees. Through the propositions-as-types principle, these type constructors yield inductively defined propositions. The induction principle associated with the $\mu$ types lets us define well-founded recursive functions, and dual principle for the $\nu$ types lets us inductively define their "infinite" elements. We present another induction principle for the $\mu$ types which takes advantage of the information hiding properties of the $\{\sb-\vert\sb-\}$ type, and can be used to define an unbounded search operator, or more generally, to compute not with elements of the $\mu$ type, but under the assumption of its inhabitation. After presenting the proof rules for these new type constructors we give a semantic account, from which intuitionistic consistency is a consequence. First, we consider the question of inductive types in the simpler setting of the second-order lambda calculus, where we prove a strong normalization property. We also consider typing terms in the presence of type constraints, and present a condition on the constraints (of polynomial complexity in the size of the constraints) for determining if the terms will be strongly normalizable or there will be a diverging typed term. Second, we develop a semantic account of the basic type theory, then relativize it to account for the impredicativity inherent in the definition of the new type constructors. We also show how this model can justify other impredicative type constructors, such as an impredicative type abstraction operation.
0.1–10‐keV x‐ray‐induced electron emissions from solids—Models and secondary electron measurements

Analytical models are presented describing the x‐ray‐excited emission of ’’no‐loss’’ photoelectrons and Auger electrons and the energy distribution of emitted secondary electrons. The secondary electron energy distribution is given in terms of the electron kinetic energy EK, work function W, photon energy Eo, and mass photoionization coefficient μ (Eo), as proportional to Eoμ (Eo) EK(EK+W)−4. Techniques of electron spectral measurements utilizing uniform field preacceleration and limited acceptance angle spectrometers are discussed. Secondary electron energy distributions are measured at about 10−8 Torr from thick evaporated films of gold and aluminum at photon energies 277, 1487, and 8050 eV. The shapes of these distributions do not depend significantly upon photon energy. The full width at half‐maximum (FWHM) of these distributions are 3.9, 6.7, and 4.4 eV for Au and ion‐cleaned Au and Al photocathodes, respectively. The data agree well with the model predictions.
The estimation of the parameters of the stable laws

SUMMARY Estimation of the parameters of the stable laws is considered for samples of size at least 50. The modulus of the difference between the empirical and theoretical characteristic functions is weighted and integrated over the real line; this function of the sample values and the parameters is then minimized with respect to the parameters via a gradient search routine nested within a sequential search. Extensive simulation experiments validate the effectiveness of the estimation procedure over the entire parameter space. Application of the procedure to stock market price behaviour is made.
Recent Developments in Nonparametric Density Estimation

Advances in computation and the fast and cheap computational facilities now available to statisticians have had a significant impact upon statistical research, and especially the development of nonparametric data analysis procedures. In particular, theoretical and applied research on nonparametric density estimation has had a noticeable influence on related topics, such as nonparametric regression, nonparametric discrimination, and nonparametric pattern recognition. This article reviews recent developments in nonparametric density estimation and includes topics that have been omitted from review articles and books on the subject. The early density estimation methods, such as the histogram, kernel estimators, and orthogonal series estimators are still very popular, and recent research on them is described. Different types of restricted maximum likelihood density estimators, including order-restricted estimators, maximum penalized likelihood estimators, and sieve estimators, are discussed, where restrictions are imposed upon the class of densities or on the form of the likelihood function. Nonparametric density estimators that are data-adaptive and lead to locally smoothed estimators are also discussed; these include variable partition histograms, estimators based on statistically equivalent blocks, nearest-neighbor estimators, variable kernel estimators, and adaptive kernel estimators. For the multivariate case, extensions of methods of univariate density estimation are usually straightforward but can be computationally expensive. A method of multivariate density estimation that did not spring from a univariate generalization is described, namely, projection pursuit density estimation, in which both dimensionality reduction and density estimation can be pursued at the same time. Finally, some areas of related research are mentioned, such as nonparametric estimation of functionals of a density, robust parametric estimation, semiparametric models, and density estimation for censored and incomplete data, directional and spherical data, and density estimation for dependent sequences of observations.
An Experimental Evaluation of Four Elementary School Math Curricula

Abstract This article examines the effectiveness of four elementary school math curricula: (a) Investigations in Number, Data, and Space; (b) Math Expressions; (c) Saxon Math; and (d) Scott Foresman–Addison Wesley Mathematics (SFAW). These curricula are distinct from one another and represent many of the diverse approaches used to teach elementary school math in the United States. The results are based on 39 schools that were randomly assigned to use the various curricula at the first-grade level. The results show that average spring first-grade math achievement of Math Expressions and Saxon students was 0.30 SD higher than Investigations students and 0.24 SD higher than SFAW students. These effect sizes mean that an average-performing student's percentile rank in math would be 9 to 12 points higher if the school used Math Expressions or Saxon, instead of Investigations or SFAW. We also conducted correlational analyses that examine whether curriculum-group differences in math instructional time and content coverage account for the differences in curriculum effects and found that a portion of the relative effects is due to differences in content coverage.
The microwave absorbing and resonance phenomena of Y‐type hexagonal ferrite microwave absorbers

The microwave absorbing characteristics and resonance of Y‐type hexagonal ferrite–rubber composites were investigated. The complex permeability and permittivity of Ni2−xZnxY ferrite bodies were measured using a network analyzer in the frequency range of 200 MHz–14 GHz. Two types of resonance, the domain wall and the spin rotational resonance, were observed. With a ferrite particle with a diameter of about 1 μm, only spin rotational resonance was observed. The first matching frequency, found in the ferrite–rubber composites, which was higher than that of spin rotational resonance, increased with spin rotational resonance frequency. It was also found that domain wall resonance had no effects on the microwave absorbing characteristics. Based on these findings, it could be concluded that the microwave absorbing characteristics were caused by only one type of resonance, the spin rotational resonance.
Signal-to-noise ratio–based quality assessment method for ICESat/GLAS waveform data

Abstract. Data quality determines the accuracy of results associated with remote sensing data processing and applications. However, few effective studies have been carried out on quality assessment methods for the full-waveform light detecting and ranging data. Using the geoscience laser altimeter system (GLAS) waveform data as an example, a signal-to-noise ratio (SNR)-based waveform quality assessment method is proposed to analyze the relationship between the SNR and its controlling factors, i.e., laser type, laser using time, topographic relief, and land cover type, and study the impacts of these factors on the quality of the GLAS waveform data. Results show that the SNR-based data quality assessment method can quantitatively and effectively assess the GLAS waveform data quality. The SNR linearly attenuates with the laser using time, and the attenuation rate varies with laser type. The topographic relief is inversely correlated with the SNR of the GLAS data. As the land cover structure (especially the vertical structure) becomes more complex, the SNR of the GLAS data decreases. It was found that land cover types in descending order of the SNR values are desert, farmland, water body, grassland, city, and forest.
LXXVI. Conditions for the occurrence of electrical discharges in astrophysical systems

Summary Discharges are shown to be a possible source of high energy particles, if the current density is very large. The growth of the current density is discussed using the fact that the magnetic lines of force are approximately frozen into the ionized gas. It is shown that discharges are unlikely to occur anywhere except at neutral points of the magnetic field. Neutral points are found to be unstable in such a way that a small perturbation will start a discharge in a time of the order of the characteristic time of the system. Such discharges may account for aurorae, and may also occur in solar flares and the interstellar gas.
PHOTOMETRIC PROPERTIES FOR SELECTED ALGOL-TYPE BINARIES. VI. THE NEWLY DISCOVERED oEA STAR FR ORIONIS

New photometry of the neglected eclipsing binary FR Orionis was obtained in 2012 November and December. Using the updated Wilson–Devinney program, the photometric elements were deduced from two-color light curves. The results indicate that this system is a semi-detached binary, with a mass ratio of 0.325(± 0.002) and a fill-out factor of the primary of fp = 73.5(± 0.2)%. The oscillating light curves imply that FR Ori may be an oscillating EA (oEA)-type star with a rapidly pulsating, mass-accreting primary component. After we removed the theoretical light curves from the observations, Fourier analysis revealed that the more massive component possibly shows a δ Scuti type pulsation with four detected frequencies. The dominant frequency is f1 = 38.6c day−1 (i.e., Ppuls = 37.3 minutes), and the pulsation constant is Q = 0.014 days. Based on all available eclipsing times, the orbital period is undergoing a secular period increase with a rate of dP/dt = +8.85(±0.66) × 10−8 day yr−1, which may be interpreted by mass transfer from the secondary to the primary. We expect that the more massive component will fill its Roche lobe due to mass transfer of the secondary. Therefore, the oEA star FR Ori may evolve into a contact configuration.
Toda vowels in non-initial syllables

It has been observed (Emeneau (1957), 63–4) that Toda and Kota show loss of many vowels in the non-initial syllables of reconstructed proto-Dravidian (PDr.) or proto-South Dravidian (PSDr.) forms. An attempt was made to state a rule as follows: ‘every non-initial syllable of PSDr. (or perhaps PDr.) that has a short vowel loses its vocalic peak in Toda; vowels of all qualities are lost except that *i > y'. Exceptions were noted, and an attempt was made, with some misgivings, to save the rule by several manoeuvres. One of these was to insist that the rule applied only to pre-Toda short vowels and to note that some at least of the short vowels that appear in non-initial syllables in Toda words ‘originally’ were long vowels, i.e. some Toda short vowels in non-initial syllables were derived from pre-Toda by a rule that stated that PSDr. (or PDr.) long vowels in non-initial syllables became short vowels in Toda and remained as such. This latter rule can be demonstrated to hold for a greater number of examples than the few that were mentioned in the 1957 paper. It should be noted at once that the rule applies only to Toda, and that when cognates are to be found, Kota retains the length of these vowels.
Numerical Analysis of Bubble Growth and Departure from a Microcavity

A numerical approach is presented for analysis of bubble growth and departure from a microcavity during nucleate boiling. The level-set formulation for tracking the phase interfaces is modified to include the effect of phase change on the liquid–vapor interface and to treat the no-slip and contact angle conditions on the immersed (or irregularly shaped) solid surface of the microcavity. Also, the formulation is coupled with a simple and efficient model for predicting the evaporative heat flux from the liquid microlayer on an immersed solid surface. The effects of cavity size and geometry on the bubble growth and departure in nucleate boiling are investigated.
A Circularly Polarized Array Composed of Linear Polarized Microstrip Patches Fed by Metamaterial Transmission Line

A novel single-feed circularly polarized antenna array is constructed by a 2 × 2 array of four square linear polarized microstrip patches with orthogonal orientation and phase shift of 90° in between. The sequential rotation and suitable phasing of linear polarized microstrip patches improve the radiation pattern symmetry and input impedance matching of the array antenna. A metamaterial transmission line is designed and applied to feeding the antenna array. The metamaterial transmission line works at its zeroth order resonant mode and there is no phase shift between its four output ports. A circularly polarized antenna array at 5.8 GHz is built and demonstrated, which is fed by the metamaterial transmission line. The antenna array is compact and the whole dimension is about 1. 1λ g 2. The antenna gain reaches 9 dBi, and shows a good axial ratio. Experimental results and simulation agree well.
Dynamics of the pianoforte string and narrow hammers

A new method of solution to the equation of a perfectly flexible string, when struck at any point by hard or soft narrow hammers, is developed. The hard hammer is modeled as a point mass, and the soft hammer is modeled as a point mass backed by a linear or nonlinear spring and a dashpot, representing the compliance and dissipation of the felt. For each hammer the equation describing the string–hammer contact force during the periods of contact, and of recontacts, is derived explicitly. The Green’s function for a fixed‐fixed string is represented by an infinite series of Heaviside functions. The analysis is exact in the spatial domain thereby eliminating modal truncation error and capturing all discontinuities in the contact force. The method predicts the contact force and system response under impacts given any hammer to string mass ratio that experiences any number of multiple contacts during the hammer strike.
Correlated Variations in the Solar Neutrino Flux and the Solar Wind and the Relation to the Solar Neutrino Problem

Solar wind parameters from the Massachusetts Institute of Technology (MIT) plasma experiment on the IMP 8 spacecraft overlap ∼19 years of published neutrino flux observations from the Homestake experiment. A strong correlation is found between neutrino flux and solar wind properties, in particular, the solar wind mass flux. The correlation is significantly better than any anticorrelation with sunspot number and is comparable to those previously found with photospheric magnetic flux and shifts in p-mode frequencies. If current notions of solar structure are correct, these observations require new fundamental physics of neutrinos. For a proper choice of neutrino parameters, the level of variations is consistent with resonant conversion of electron neutrinos to a nondetected flavor eigenstate mediated by the magnetic field in the sun's convective zone. The solar wind mass flux may act as a proxy for this field, producing the solar wind-neutrino flux connection.
Field equations in the neighbourhood of a particle in a conformal theory of gravitation. II

The field equations in the neighbourhood of a particle for a spherically symmetric metric in the conformal theory of gravitation put forward by Hoyle & Narlikar are examined. As the theory is conformally invariant, one can use different but physically equivalent conformal frames to study the equations. Previously these equations were studied in a conformal frame which, though suitable far away from the isolated particle, turns out not to be suitable in the neighbourhood of the particle. In the present paper a solution in a conformal frame is obtained that is suitable for considering regions near the particle. The solution thus obtained differs from the previous one in several respects. For example, it has no coordinate singularity for any non-zero value of the radial variable, unlike the previous solution or the Schwarzschild solution. It is also shown with the use of this solution that in this theory distant matter has an effect on local geometry.
Local conditions for the stochastic comparison of particle systems

We study the stochastic comparison of interacting particle systems where the state space of each particle is a finite set endowed with a partial order, and several particles may change their value at a time. For these processes we give local conditions, on the rates of change, that assure their comparability. We also analyze the case where one of the processes does not have any changes that involve several particles, and obtain necessary and sufficient conditions for their comparability. The proofs are based on the explicit construction of an order-preserving Markovian coupling. We show the applicability of our results by studying the stochastic comparison of infinite-station Jackson networks and batch-arrival, batch-service, and assemble-transfer queueing networks.
ON THE DISTANCES AND RADIAL VELOCITIES OF EXTRA-GALACTIC NEBULAE, AND THE EXPLANATION OF THE LATTER BY THE RELATIVITY THEORY OF INERTIA.

1. The large radial velocities of extragalactic nebulae measured by the observers at Mount Wilson during the last year have enhanced the importance of the problem of the determination of the distances of these objects. Evidently both the apparent diameter and the integrated apparent magnitude must be correlated with the distance. In trying to derive a mathematical expression for this correlation it is necessary to start with a certain number of known distances as a basis. For a few of the largest and nearest nebulae the distances have been determined directly by Hubble, Lundmark, Shapley and others from cepheids or novae in them. For others the brightest stars have been used as a criterion of the distance. This criterion, however, is less reliable than the other two, because, as Shapley has pointed out, we cannot be sure that what is assumed to be a star may not in reality be a cluster of stars. Some of the distances determined by this method have, however, been used, as the number of distances depending on cepheids or novae alone would be too small as a basis for the discussion. Other methods have also been employed, based on rotation, or the distance of condensations in spiral arms, or other hypothetical considerations; the distances so determined have not been used in my discussion. 2. The first step in the discussion was an investigation of the correlation between the apparent diameters and integrated magnitudes. The discussion is being published in full in B. A. N. 185, to which publication the reader must be referred for details. If we assume: 1st, that both the true diameters and the true total magnitudes are distributed according to a Gaussian (or other symmetrical) frequency function round constant average values (constant meaning independent of the distance from us), and 2nd, that the measured (or estimated) values of the apparent diameters and magnitudes are referred to a consistent scale throughout, then we should have, for all objects of one class
Feedback instability of the ionospheric resonant cavity

The exponential increase of the Alfven speed in the topside ionosphere leads to the formation of a resonant cavity (Lysak, 1988) which has been termed the ionospheric Alfven resonator by Trakhtengertz and Feldstein (1984). These authors primarily considered the situation where the ionospheric Pedersen conductivity is low, while Lysak (1988) considered the opposite limit of the infinite ionospheric conductivity. These results have been extended to arbitrary ionospheric conductivity by performing a numerical solution of the cavity dispersion relation, which involves Bessel functions of complex argument and order. These results indicate that the damping of excitations of this resonant cavity is strongest when the ionospheric Pedersen and Alfven conductivities are comparable and that growth is possible for incoming wave boundary conditions. The existence of this cavity leads to a modification of the Alfven wave reflection coefficient at the ionosphere. While this reflection coefficient is independent of frequency at low frequencies, it exhibits structure due to the resonant cavity modes at frequencies around 0.1-1 Hz. These cavity modes can also be excited by feedback instabilities (Sato, 1978; Lysak, 1986), leading to growth rates which are enhanced over the case without the cavity. These waves have maximum growth at short wavelengths, particularly whenmore » the background Pedersen conductivity is large. The perturbations associated with these instabilities can lead to structuring of auroral currents during substorms, and may help explain the westward traveling surge. « less
Performance Analysis of Machine Learning and Deep Learning Models for Classification of Alzheimer’s Disease from Brain MRI

Alzheimer's disease (AD) is an irreversible and degenerative brain condition that gradually damages memory and thinking abilities. Despite being incurable, AD causes significant pain and financial hardship to patients and their families. However, medications are most effective when administered early in the course of the disease and early diagnosis is crucial in the treatment of AD to restrict its progression. There are several approaches proposed for computer-assisted AD diagnosis that involve structural and functional imaging modalities, such as sMRI, fMRI, DTI, and PET. Machine learning and deep learning techniques have facilitated the development of novel models for diagnostic accuracy in AD. This research compares the performance of several machine learning and deep convolutional architectures to detect AD from MCI. It is essential to find the effective baseline model for classifying AD, hence all the pre-trained models are evaluated with benchmark dataset. Experimental observations indicate that the DenseNet-169 performed best out of different state-of-the-art architectures, with an average accuracy of 82.2%.
Quantum gates using the orbital angular momentum of photons

A quantum field theory approach is presented to show that paraxial photons of any frequency in the full electromagnetic spectrum may posses arbitrary values of the orbital angular momentum along their propagation direction. Our framework also enables to propose multi-dimensional geometric quantum gates exploiting the orbital angular momentum of photons. The action of these gates is shown to be describable in a remarkably compact form by resorting to the Wigner representation.