Family of 2-simplex cognitive tools and their application for decision-making and its justifications

Urgency of application and development of cognitive graphic tools for usage in intelligent systems of data analysis, decision making and its justifications is given. Cognitive graphic tool "2-simplex prism" and examples of its usage are presented. Specificity of program realization of cognitive graphics tools invariant to problem areas is described. Most significant results are given and discussed. Future investigations are connected with usage of new approach to rendering, cross-platform realization, cognitive features improving and expanding of n-simplex family.Comment: 14 pages, 6 figures, conferenc

Visualizing Creative Destruction

We introduce a series of methods for visualizing the dynamics of firmsize as indicative of the way the creation of new economic entitiesdestroy the existing order in the manner first sketched bySchumpeter (1938). We examine firm size distributions for every yearfrom 1955 to 1994 for the top 100 firms listed in the Fortune 500. Weshow that although rank-size distributions from this data areremarkably stable, this masks a much more detailed microdynamicswhere firms are changing their size and rank in the prevailing orderquite rapidly. These provide the signatures of creation anddestruction and to visualize their form, we introduce the idea of halflives, rank clocks and distance statistics which reveal a cornucopia ofdynamic behaviors. We first examine changes in firm size measuredby revenue earnings and then we contrast this with profits perearnings data which reveals another picture of these processes ofcreation and destruction. We introduce a series of methods for visualizing the dynamics of firmsize as indicative of the way the creation of new economic entitiesdestroy the existing order in the manner first sketched bySchumpeter (1938). We examine firm size distributions for every yearfrom 1955 to 1994 for the top 100 firms listed in the Fortune 500. Weshow that although rank-size distributions from this data areremarkably stable, this masks a much more detailed microdynamicswhere firms are changing their size and rank in the prevailing orderquite rapidly. These provide the signatures of creation anddestruction and to visualize their form, we introduce the idea of halflives, rank clocks and distance statistics which reveal a cornucopia ofdynamic behaviors. We first examine changes in firm size measuredby revenue earnings and then we contrast this with profits perearnings data which reveals another picture of these processes ofcreation and destruction

Visualizing dimensionality reduction of systems biology data

One of the challenges in analyzing high-dimensional expression data is the detection of important biological signals. A common approach is to apply a dimension reduction method, such as principal component analysis. Typically, after application of such a method the data is projected and visualized in the new coordinate system, using scatter plots or profile plots. These methods provide good results if the data have certain properties which become visible in the new coordinate system and which were hard to detect in the original coordinate system. Often however, the application of only one method does not suffice to capture all important signals. Therefore several methods addressing different aspects of the data need to be applied. We have developed a framework for linear and non-linear dimension reduction methods within our visual analytics pipeline SpRay. This includes measures that assist the interpretation of the factorization result. Different visualizations of these measures can be combined with functional annotations that support the interpretation of the results. We show an application to high-resolution time series microarray data in the antibiotic-producing organism Streptomyces coelicolor as well as to microarray data measuring expression of cells with normal karyotype and cells with trisomies of human chromosomes 13 and 21

Visualizing the Quantum Interaction Picture in Phase Space

We illustrate the correspondence between the quantum Interaction Picture-evolution of the state of a quantum system in Hilbert space and a combination of local and global transformations of its Wigner function in phase space. To this aim, we consider the time-evolution of a quantized harmonic oscillator driven by both a linear and a quadratic (in terms of bosonic creation and annihilation operators) potentials and employ the Magnus series to derive the exact form of the time-evolution operator. In this case, the Interaction Picture corresponds to a local transformation of phase space-reference frame into the one that is co-moving with the Wigner function.Comment: Submitted to New Journal of Physic