1,955 research outputs found
Refined composite invariants of torus knots via DAHA
We define composite DAHA-superpolynomials of torus knots, depending on pairs
of Young diagrams and generalizing the composite HOMFLY-PT polynomials in the
theory of the skein of the annulus. We provide various examples. Our
superpolynomials extend the DAHA-Jones (refined) polynomials and satisfy all
standard symmetries of the DAHA-superpolynomials of torus knots. The latter are
conjecturally related to the HOMFLY-PT homology; such a connection is a
challenge in the theory of the annulus. At the end, we construct two
DAHA-hyperpolynomials extending the DAHA-Jones polynomials of type E and
closely related to the exceptional Deligne-Gross series of root systems; this
theme is of experimental nature.Comment: v2: 3 references were added and minor editin
Experience : Song
https://digitalcommons.library.umaine.edu/mmb-vp/5775/thumbnail.jp
Non-LTE Spectra of Accretion Disks Around Intermediate-Mass Black Holes
We have calculated the structures and the emergent spectra of stationary,
geometrically thin accretion disks around 100 and 1000 M_sun black holes in
both the Schwarzschild and extreme Kerr metrics. Equations of radiative
transfer, hydrostatic equilibrium, energy balance, ionization equilibrium, and
statistical equilibrium are solved simultaneously and consistently. The six
most astrophysically abundant elements (H, He, C, N, O, and Fe) are included,
as well as energy transfer by Comptonization. The observed spectrum as a
function of viewing angle is computed incorporating all general relativistic
effects. We find that, in contrast with the predictions of the commonly-used
multi-color disk (MCD) model, opacity associated with photoionization of heavy
elements can significantly alter the spectrum near its peak. These ionization
edges can create spectral breaks visible in the spectra of slowly-spinning
black holes viewed from almost all angles and in the spectra of
rapidly-spinning black holes seen approximately pole-on. For fixed mass and
accretion rate relative to Eddington, both the black hole spin and the viewing
angle can significantly shift the observed peak energy of the spectrum,
particularly for rapid spin viewed obliquely or edge-on. We present a detailed
test of the approximations made in various forms of the MCD model. Linear
limb-darkening is confirmed to be a reasonable approximation for the integrated
flux, but not for many specific frequencies of interest.Comment: 30 pages, 11 eps figures, accepted for publication in Ap
Understanding the disorder of the DNA base cytosine on the Au(111) surface
Using ultrahigh vacuum scanning tunneling microscopy (STM) and ab initio density functional theory, we have investigated in detail structures formed by cytosine on the Au(111) surface in clean ultrahigh vacuum conditions. In spite of the fact that the ground state of this DNA base on the surface is shown to be an ordered arrangement of cytosine one-dimensional branches (filaments), this structure has never been observed in our STM experiments. Instead, disordered structures are observed, which can be explained by only a few elementary structural motifs: filaments, five- and sixfold rings, which randomly interconnect with each other forming bent chains, T junctions, and nanocages. The latter may have trapped smaller structures inside. The formation of such an unusual assembly is explained by simple kinetic arguments as a liquid-glass transition. © 2008 American Institute of Physics
Transformative Machine Learning
The key to success in machine learning (ML) is the use of effective data
representations. Traditionally, data representations were hand-crafted.
Recently it has been demonstrated that, given sufficient data, deep neural
networks can learn effective implicit representations from simple input
representations. However, for most scientific problems, the use of deep
learning is not appropriate as the amount of available data is limited, and/or
the output models must be explainable. Nevertheless, many scientific problems
do have significant amounts of data available on related tasks, which makes
them amenable to multi-task learning, i.e. learning many related problems
simultaneously. Here we propose a novel and general representation learning
approach for multi-task learning that works successfully with small amounts of
data. The fundamental new idea is to transform an input intrinsic data
representation (i.e., handcrafted features), to an extrinsic representation
based on what a pre-trained set of models predict about the examples. This
transformation has the dual advantages of producing significantly more accurate
predictions, and providing explainable models. To demonstrate the utility of
this transformative learning approach, we have applied it to three real-world
scientific problems: drug-design (quantitative structure activity relationship
learning), predicting human gene expression (across different tissue types and
drug treatments), and meta-learning for machine learning (predicting which
machine learning methods work best for a given problem). In all three problems,
transformative machine learning significantly outperforms the best intrinsic
representation
Evaluating the noise resilience of variational quantum algorithms
We simulate the effects of different types of noise in state preparation
circuits of variational quantum algorithms. We first use a variational quantum
eigensolver to find the ground state of a Hamiltonian in presence of noise, and
adopt two quality measures in addition to the energy, namely fidelity and
concurrence. We then extend the task to the one of constructing, with a layered
quantum circuit ansatz, a set of general random target states. We determine the
optimal circuit depth for different types and levels of noise, and observe that
the variational algorithms mitigate the effects of noise by adapting the
optimised parameters. We find that the inclusion of redundant parameterised
gates makes the quantum circuits more resilient to noise. For such
overparameterised circuits different sets of parameters can result in the same
final state in the noiseless case, which we denote as parameter degeneracy.
Numerically, we show that this degeneracy can be lifted in the presence of
noise, with some states being significantly more resilient to noise than
others. We also show that the average deviation from the target state is linear
in the noise level, as long as this is small compared to a circuit-dependent
threshold. In this region the deviation is well described by a stochastic
model. Above the threshold, the optimisation can converge to states with
largely different physical properties from the true target state, so that for
practical applications it is critical to ensure that noise levels are below
this threshold.Comment: 22 pages, 13 figure
Dimensionality and Factorial Invariance of Religiosity Among Christians and the Religiously Unaffiliated: A Cross-Cultural Analysis Based on the International Social Survey Programme
We present a study of the dimensionality and factorial invariance of religiosity for 26 countries with a Christian heritage, based on the 1998 and 2008 rounds of the International Social Survey Programme (ISSP) Religion survey, using both exploratory and multi-group confirmatory factor analyses. The results of the exploratory factor analysis showed that three factors, common to Christian and religiously unaffiliated respondents, could be extracted from our initially selected items and suggested the testing of four different three-factor models using multi-group confirmatory factor analysis. For the model with the best fit and measurement invariance properties, we labeled the three resulting factors as “Beliefs in afterlife and miracles”, “Belief and importance of God” and “Religious involvement.” The first factor is measured by four items related to the Supernatural Beliefs Scale (SBS-6); the second by three items related to belief in God and God’s perceived roles as a supernatural agent; and the third one by three items with the same structure found in previous cross-cultural analyses of religiosity using the European Values Survey (ESS) and also by belief in God. Unexpectedly, we found that one item, belief in God, cross-loaded on to the second and third factors. We discussed possible interpretations for this finding, together with the potential limitations of the ISSP Religion questionnaire for revealing the structure of religiosity. Our tests of measurement invariance across gender, age, educational degree and religious (un)affiliation led to acceptance of the hypotheses of metric- and scalar-invariance for these groupings (units of analysis). However, in the measurement invariance tests across the countries, the criteria for metric invariance were met for twenty-three countries only, and partial scalar invariance was accepted for fourteen countries only. The present work shows that the exploration of large multinational and cross-cultural datasets for studying the dimensionality and invariance of social constructs (in our case, religiosity) yields useful results for cross-cultural comparisons, but is also limited by the structure of these datasets and the way specific items are coded
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