Lyapunov Exponent and the Solid-Fluid Phase Transition

We study changes in the chaotic properties of a many-body system undergoing a solid-fluid phase transition. To do this, we compute the temperature dependence of the largest Lyapunov exponents $\lambda_{max}$ for both two- and three-dimensional periodic systems of $N$-particles for various densities. The particles interact through a soft-core potential. The two-dimensional system exhibits an apparent second-order phase transition as indicated by a $\lambda$-shaped peak in the specific heat. The first derivative of $\lambda_{max}$ with respect to the temperature shows a peak at the same temperature. The three-dimensional system shows jumps, in both system energy and $\lambda_{max}$, at the same temperature, suggesting a first-order phase transition. Relaxation phenomena in the phase-transition region are analyzed by using the local time averages.Comment: 16 pages, REVTeX, 10 eps figures, epsfig.st

Seventeenth-century musical fantasy : origins of freedom and irrationality

The essence of seventeenth-century musical fantasy lies in the contemporary notion of freedom. Contemporary fantasy genres and verbal descriptions of fantasy highlight freedom from given tonal, harmonic, and temporal frameworks. This freedom assumes the composer's ingenuity (freedom to command the rules of counterpoint) and spontaneity (freedom to breach the rules and conventional expectations), both important sources to understand the distinctiveness of seventeenth-century musical fantasy. Given that a manifestation of freedom could be perceived as either fantastic or 'irrational', I survey the cultural and intellectual background concerning an assumed norm and the contemporary notion of 'rationality' through differing views on reason and the senses. In order to clarify the environment in which musical fantasy was sensed and defined, I turn to the analogy between music and its sister arts: imitation (philosophical mimesis and rhetorical imitatio as key concepts of artistic representation) and empirical thought (the growing interest in the role of the senses and imagination in aesthetic experience) are taken as bases for contemporary artists' understanding of nature and art. To discern the freedom that seventeenth-century musicians exercised in their representation of nature, I trace the varied properties and fantastic aspects of expressive resources in dramatic and improvisatory genres by exploring three metaphorical subjects: lament, melancholy, and humour. In all, this study focuses on how fantasy was musically represented and perceived in the era, and elucidates the distinctive and universal aspects of fantasy in the seventeenth-century context through an interdisciplinary approach that combines the historical, the philosophical, and the musical

Robust imputation method for missing values in microarray data

<p>Abstract</p> <p>Background</p> <p>When analyzing microarray gene expression data, missing values are often encountered. Most multivariate statistical methods proposed for microarray data analysis cannot be applied when the data have missing values. Numerous imputation algorithms have been proposed to estimate the missing values. In this study, we develop a robust least squares estimation with principal components (RLSP) method by extending the local least square imputation (LLSimpute) method. The basic idea of our method is to employ quantile regression to estimate the missing values, using the estimated principal components of a selected set of similar genes.</p> <p>Results</p> <p>Using the normalized root mean squares error, the performance of the proposed method was evaluated and compared with other previously proposed imputation methods. The proposed RLSP method clearly outperformed the weighted <it>k</it>-nearest neighbors imputation (kNNimpute) method and LLSimpute method, and showed competitive results with Bayesian principal component analysis (BPCA) method.</p> <p>Conclusion</p> <p>Adapting the principal components of the selected genes and employing the quantile regression model improved the robustness and accuracy of missing value imputation. Thus, the proposed RLSP method is, according to our empirical studies, more robust and accurate than the widely used kNNimpute and LLSimpute methods.</p

A Portrait of Emotion: Empowering Self-Expression through AI-Generated Art

We investigated the potential and limitations of generative artificial intelligence (AI) in reflecting the authors' cognitive processes through creative expression. The focus is on the AI-generated artwork's ability to understand human intent (alignment) and visually represent emotions based on criteria such as creativity, aesthetic, novelty, amusement, and depth. Results show a preference for images based on the descriptions of the authors' emotions over the main events. We also found that images that overrepresent specific elements or stereotypes negatively impact AI alignment. Our findings suggest that AI could facilitate creativity and the self-expression of emotions. Our research framework with generative AIs can help design AI-based interventions in related fields (e.g., mental health education, therapy, and counseling).Comment: Accepted CogSci 202

Bernoulli Identities and Combinatoric Convolution Sums with Odd Divisor Functions

We study the combinatoric convolution sums involving odd divisor functions, their relations to Bernoulli numbers, and some interesting applications