Visualizing High Dimensional Dynamical Processes

Manifold learning techniques for dynamical systems and time series have shown their utility for a broad spectrum of applications in recent years. While these methods are effective at learning a low-dimensional representation, they are often insufficient for visualizing the global and local structure of the data. In this paper, we present DIG (Dynamical Information Geometry), a visualization method for multivariate time series data that extracts an information geometry from a diffusion framework. Specifically, we implement a novel group of distances in the context of diffusion operators, which may be useful to reveal structure in the data that may not be accessible by the commonly used diffusion distances. Finally, we present a case study applying our visualization tool to EEG data to visualize sleep stages.Comment: 7 pages, 3 figure

Visualizing quantum mechanics in phase space

We examine the visualization of quantum mechanics in phase space by means of the Wigner function and the Wigner function flow as a complementary approach to illustrating quantum mechanics in configuration space by wave functions. The Wigner function formalism resembles the mathematical language of classical mechanics of non-interacting particles. Thus, it allows a more direct comparison between classical and quantum dynamical features

CompEngine: a self-organizing, living library of time-series data

Modern biomedical applications often involve time-series data, from high-throughput phenotyping of model organisms, through to individual disease diagnosis and treatment using biomedical data streams. Data and tools for time-series analysis are developed and applied across the sciences and in industry, but meaningful cross-disciplinary interactions are limited by the challenge of identifying fruitful connections. Here we introduce the web platform, CompEngine, a self-organizing, living library of time-series data that lowers the barrier to forming meaningful interdisciplinary connections between time series. Using a canonical feature-based representation, CompEngine places all time series in a common space, regardless of their origin, allowing users to upload their data and immediately explore interdisciplinary connections to other data with similar properties, and be alerted when similar data is uploaded in the future. In contrast to conventional databases, which are organized by assigned metadata, CompEngine incentivizes data sharing by automatically connecting experimental and theoretical scientists across disciplines based on the empirical structure of their data. CompEngine's growing library of interdisciplinary time-series data also facilitates comprehensively characterization of algorithm performance across diverse types of data, and can be used to empirically motivate the development of new time-series analysis algorithms

Driven coupled Morse oscillators --- visualizing the phase space and characterizing the transport

Recent experimental and theoretical studies indicate that intramolecular energy redistribution (IVR) is nonstatistical on intermediate timescales even in fairly large molecules. Therefore, it is interesting to revisit the the old topic of IVR versus quantum control and one expects that a classical-quantum perspective is appropriate to gain valuable insights into the issue. However, understanding classical phase space transport in driven systems is a prerequisite for such a correspondence based approach and is a challenging task for systems with more then two degrees of freedom. In this work we undertake a detailed study of the classical dynamics of a minimal model system - two kinetically coupled coupled Morse oscillators in the presence of a monochromatic laser field. Using the technique of wavelet transforms a representation of the high dimensional phase space, the resonance network or Arnold web, is constructed and analysed. The key structures in phase space which regulate the dissociation dynamics are identified. Furthermore, we show that the web is nonuniform with the classical dynamics exhibiting extensive stickiness, resulting in anomalous transport. Our work also shows that pairwise irrational barriers might be crucial even in higher dimensional systems.Comment: 10 pages, 5 figures. Contribution to William H. Miller festschrif

Belavkin-Kolokoltsov watch-dog effects in interactively controlled stochastic computer-graphic dynamic systems

Stochastic properties of the long time behavior of a continuously observed (and interactively controlled) quantum--field top are investigated mathematically. Applications to interactively controlled stochastic computerographical dynamic systems are discussed.Comment: A mathematical study. 11pp, amstex [revised: 8.X.94]., (e mail: [email protected]

Belavkin-Kolkoltsov watch-dog effects in interactively controlled stochastic computer-graphic dynamic systems. A mathematical study

Stochastic properties of the long-time behaviour of a continuously observed (and interactively controlled) quantum-field top are investigated mathematically. Applications to interactively controlled stochastic computer-graphic dynamic systems are discussed.Comment: an essentially completed version of chao-dyn/940601

PDFSense: Mapping the sensitivity of hadronic experiments to nucleon structure

Recent high precision experimental data from a variety of hadronic processes opens new opportunities for determination of the collinear parton distribution functions (PDFs) of the proton. In fact, the wealth of information from experiments such as the Large Hadron Collider (LHC) and others, makes it difficult to quickly assess the impact on the PDFs, short of performing computationally expensive global fits. As an alternative, we explore new methods for quantifying the potential impact of experimental data on the extraction of proton PDFs. Our approach relies crucially on the correlation between theory-data residuals and the PDFs themselves, as well as on a newly defined quantity --- the sensitivity --- which represents an extension of the correlation and reflects both PDF-driven and experimental uncertainties. This approach is realized in a new, publicly available analysis package PDFSense, which operates with these statistical measures to identify particularly sensitive experiments, weigh their relative or potential impact on PDFs, and visualize their detailed distributions in a space of the parton momentum fraction x and factorization scale \mu. This tool offers a new means of understanding the influence of individual measurements in existing fits, as well as a predictive device for directing future fits toward the highest impact data and assumptions.Comment: 6 pages, 3 figures. arXiv admin note: substantial text overlap with arXiv:1803.0277

Time-resolved x-ray microscopy for materials science

X-ray microscopy has been an indispensable tool to image nanoscale properties for materials research. One of its recent advances is to extend microscopic studies to the time domain for visualizing the dynamics of nanoscale phenomena. Large-scale x-ray facilities have been the powerhouse of time-resolved x-ray microscopy. Their upgrades including a significant reduction of the x-ray emittance at storage rings and fully coherent ultrashort x-ray pulses at free electron lasers, will lead to new developments in instrumentation and open new scientific opportunities for x-ray imaging of nanoscale dynamics with the simultaneous attainment of unprecedentedly high spatial and temporal resolutions. This review presents recent progress in and the outlook for time-resolved x-ray microscopy in the context of ultrafast nanoscale imaging and its applications to condensed matter physics and materials science

Open Quantum Systems and Quantum Algorithms

The model of open quantum systems is adopted to describe the non-local dynamical behaviour of qubits processed by entangling gates. The analysis gets to the conclusion that a distinction between evaluation steps and task-oriented computing steps is justified only within classical computation. In fact, the use of entangling gates permits to reduce two steps (evaluation and calculation) to a single computational one, and this determines an effective computational speed-up. The application of the open quantum systems model suggests that the reduction to one-computational step is strongly related to the existence of Universal Dynamical Maps describing the evolution of component systems of two-qubits gates. As the description in terms of Universal Dynamical Map is possible only in the presence of a separable initial state, it turns out that the internal reduced dynamics with respect to entangling gates is neither unitary nor Markovian. The fact imposes a holistic vision on the structure of the algorithm, where the entangling gates shall remain indivisible unities, or black boxes, in order to preserve computational speed as well as reversibility. This fact suggests to adopt a perspective on computation which is completely non-classical: the whole algorithm turns out not to be the sequence of its temporal parts

Belavkin-Kolokoltsov Watch-Dog Effects in Interactively Controlled Stochastic Computer-Graphic Dynamical Systems. A Summary of Mathematical Researches

This paper contains a summary of mathematical researches of stochastic properties of the long time behavior of a continuously observed (and interactively controlled) quantum--field top. Applications to interactively controlled stochastic computer-graphic dynamical systems are also discussed.Comment: 15 pages amstex [printing errors corrected]. This is the enlarged version of chao-dyn/9406013 supplied by Comments from hep-th/9401047 and hep-th/940106