2,228 research outputs found
The Heun equation and the Calogero-Moser-Sutherland system V: generalized Darboux transformations
We obtain isomonodromic transformations for Heun's equation by generalizing
Darboux transformation, and we find pairs and triplets of Heun's equation which
have the same monodromy structure. By composing generalized Darboux
transformations, we establish a new construction of the commuting operator
which ensures finite-gap property. As an application, we prove conjectures in
part III.Comment: 24 page
Detecting Drowsy Learners at the Wheel of e-Learning Platforms with Multimodal Learning Analytics
Learners are expected to stay wakeful and focused while interacting with e-learning platforms. Although wakefulness of learners strongly relates to educational outcomes, detecting drowsy learning behaviors only from log data is not an easy task. In this study, we describe the results of our research to model learnersā wakefulness based on multimodal data generated from heart rate, seat pressure, and face recognition. We collected multimodal data from learners in a blended course of informatics and conducted two types of analysis on them. First, we clustered features based on learnersā wakefulness labels as generated by human raters and ran a statistical analysis. This analysis helped us generate insights from multimodal data that can be used to inform learner and teacher feedback in multimodal learning analytics. Second, we trained machine learning models with multiclass-Support Vector Machine (SVM), Random Forest (RF) and CatBoost Classifier (CatBoost) algorithms to recognize learnersā wakefulness states automatically. We achieved an average macro-F1 score of 0.82 in automated user-dependent models with CatBoost. We also showed that compared to unimodal data from each sensor, the multimodal sensor data can improve the accuracy of models predicting the wakefulness states of learners while they are interacting with e-learning platforms
Longitudinal magnetic excitation in KCuCl3 studied by Raman scattering under hydrostatic pressures
We measure Raman scattering in an interacting spin-dimer system KCuCl3 under
hydrostatic pressures up to 5 GPa mediated by He gas. In the pressure-induced
quantum phase, we observe a one-magnon Raman peak, which originates from the
longitudinal magnetic excitationand is observable through the second-order
exchange interaction Raman process. We report the pressure dependence of the
frequency, halfwidth and Raman intensity of this mode.Comment: 4 pages, 3 figures, inpress in JPCS as a proceeding of LT2
Comparative study of macroscopic quantum tunneling in Bi_2Sr_2CaCu_2O_y intrinsic Josephson junctions with different device structures
We investigated macroscopic quantum tunneling (MQT) of
BiSrCaCuO intrinsic Josephson junctions (IJJs) with two device
structures. One is a nanometer-thick small mesa structure with only two or
three IJJs and the other is a stack of a few hundreds of IJJs on a narrow
bridge structure. Experimental results of switching current distribution for
the first switching events from zero-voltage state showed a good agreement with
the conventional theory for a single Josephson junction, indicating that a
crossover temperature from thermal activation to MQT regime for the former
device structure was as high as that for the latter device structure. Together
with the observation of multiphoton transitions between quantized energy levels
in MQT regime, these results strongly suggest that the observed MQT behavior is
intrinsic to a single IJJ in high- cuprates, independent of device
structures. The switching current distribution for the second switching events
from the first resistive state, which were carefully distinguished from the
first switchings, was also compared between two device structures. In spite of
the difference in the heat transfer environment, the second switching events
for both devices were found to show a similar temperature-independent behavior
up to a much higher temperature than the crossover temperature for the first
switching. We argue that it cannot be explained in terms of the self-heating
owing to dissipative currents after the first switching. As possible
candidates, the MQT process for the second switching and the effective increase
of electronic temperature due to quasiparticle injection are discussed.Comment: 10pages, 7figures, submitted to Phys. Rev.
Lattice vibrations and structural instability in Cesium near the cubic to tetragonal transition
Under pressure cesium undergoes a transition from a high-pressure fcc phase
(Cs-II) to a collapsed fcc phase (Cs-III) near 4.2GPa. At 4.4GPa there follows
a transition to the tetragonal Cs-IV phase. In order to investigate the lattice
vibrations in the fcc phase and seek a possible dynamical instability of the
lattice, the phonon spectra of fcc-Cs at volumes near the III-IV transition are
calculated using Savrasov's density functional linear-response LMTO method.
Compared with quasiharmonic model calculations including non-central
interatomic forces up to second neighbours, at the volume (
is the experimental volume of bcc-Cs with =6.048{\AA}), the
linear-response calculations show soft intermediate wavelength
phonons. Similar softening is also observed for
short wavelength and phonons and intermediate
wavelength phonons. The Born-von K\'{a}rm\'{a}n analysis of
dispersion curves indicates that the interplanar force constants exhibit
oscillating behaviours against plane spacing and the large softening of
intermediate wavelength phonons results from a
negative (110)-interplanar force-constant . The frequencies of the
phonons with around 1/3 become imaginary
and the fcc structure becomes dynamically unstable for volumes below .
It is suggested that superstructures corresponding to the
soft mode should be present as a precursor of tetragonal Cs-IV structure.Comment: 12 pages, 5 figure
Markov basis and Groebner basis of Segre-Veronese configuration for testing independence in group-wise selections
We consider testing independence in group-wise selections with some
restrictions on combinations of choices. We present models for frequency data
of selections for which it is easy to perform conditional tests by Markov chain
Monte Carlo (MCMC) methods. When the restrictions on the combinations can be
described in terms of a Segre-Veronese configuration, an explicit form of a
Gr\"obner basis consisting of moves of degree two is readily available for
performing a Markov chain. We illustrate our setting with the National Center
Test for university entrance examinations in Japan. We also apply our method to
testing independence hypotheses involving genotypes at more than one locus or
haplotypes of alleles on the same chromosome.Comment: 25 pages, 5 figure
Rodrigues Formula for the Nonsymmetric Multivariable Hermite Polynomial
Applying a method developed by Takamura and Takano for the nonsymmetric Jack
polynomial, we present the Rodrigues formula for the nonsymmetric multivariable
Hermite polynomial.Comment: 5 pages, LaTe
Rodrigues Formula for the Nonsymmetric Multivariable Laguerre Polynomial
Extending a method developed by Takamura and Takano, we present the Rodrigues
formula for the nonsymmetric multivariable Laguerre polynomials which form the
orthogonal basis for the -type Calogero model with distinguishable
particles. Our construction makes it possible for the first time to
algebraically generate all the nonsymmetric multivariable Laguerre polynomials
with different parities for each variable.Comment: 6 pages, LaTe
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