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