Pointwise universal trigonometric series

A series $S_a=\sum\limits_{n=-\infty}^\infty a_nz^n$ is called a {\it pointwise universal trigonometric series} if for any $f\in C(\T)$, there exists a strictly increasing sequence $\{n_k\}_{k\in\N}$ of positive integers such that $\sum\limits_{j=-n_k}^{n_k} a_jz^j$ converges to $f(z)$ pointwise on $\T$. We find growth conditions on coefficients allowing and forbidding the existence of a pointwise universal trigonometric series. For instance, if $|a_n|=O(\e^{\,|n|\ln^{-1-\epsilon}\!|n|})$ as $|n|\to\infty$ for some $\epsilon>0$, then the series $S_a$ can not be pointwise universal. On the other hand, there exists a pointwise universal trigonometric series $S_a$ with $|a_n|=O(\e^{\,|n|\ln^{-1}\!|n|})$ as $|n|\to\infty$.

'The Arbitrarium' and 'The Universal Key' (short stories)

Short stories

Detecting Anomalies in Graphs with Numeric Labels

This paper presents Yagada, an algorithm to search labelled graphs for anomalies using both structural data and numeric attributes. Yagada is explained using several security-related examples and validated with experiments on a physical Access Control database. Quantitative analysis shows that in the upper range of anomaly thresholds, Yagada detects twice as many anomalies as the best-performing numeric discretization algorithm. Qualitative evaluation shows that the detected anomalies are meaningful, representing a com- bination of structural irregularities and numerical outliers.

Computational Verification of Two Universal Relations for Simple Ionic Liquids. Kinetic Properties of a Model 2:1 Molten Salt

Two semianalytical relations [Nature, 1996, 381, 137 and Phys. Rev. Lett. 2001, 87, 245901] predicting dynamical coefficients of simple liquids on the basis of structural properties have been tested by extensive molecular dynamics simulations for an idealized 2:1 model molten salt. In agreement with previous simulation studies, our results support the validity of the relation expressing the self-diffusion coefficient as a Function of the radial distribution functions for all thermodynamic conditions such that the system is in the ionic (ie., fully dissociated) liquid state. Deviations are apparent for high-density samples in the amorphous state and in the low-density, low-temperature range, when ions condense into AB(2) molecules. A similar relation predicting the ionic conductivity is only partially validated by our data. The simulation results, covering 210 distinct thermodynamic states, represent an extended database to tune and validate semianalytical theories of dynamical properties and provide a baseline for the interpretation of properties of more complex systems such as the room-temperature ionic liquids.

A comparative analysis of multidimensional features of objects resembling sets of graphs

In the present paper, we introduce a notion of a style representing abstract, complex objects having characteristics that can be represented as structured objects. Furthermore, we provide some mathematical properties of such styles. As a main result, we present a novel approach to perform a meaningful comparative analysis of such styles by defining and using graph-theoretic measures. We compare two styles by comparing the underlying feature sets representing sets of graph structurally. To determine the structural similarity between the underlying graphs, we use graph similarity measures that are computationally efficient. More precisely, in order to compare styles, we map each feature set to a so-called median graph and compare the resulting median graphs. As an application, we perform an experimental study to compare special styles representing sets of undirected graphs and present numerical results thereof. (C) 2007 Elsevier Inc. All rights reserved.

Topological mappings between graphs, trees and generalized trees

We present novel topological mappings between graphs, trees and generalized trees that means between structured objects with different properties. The two major contributions of this paper are, first, to clarify the relation between graphs, trees and generalized trees, a graph class recently introduced. Second, these transformations provide a unique opportunity to transform structured objects into a representation that might be beneficial for a processing, e.g., by machine learning techniques for graph classification. (c) 2006 Elsevier Inc. All rights reserved.

Comparing large graphs efficiently by margins of feature vectors

Measuring the structural similarity of graphs is a challenging and outstanding problem. Most of the classical approaches of the so-called exact graph matching methods are based on graph or subgraph isomorphic relations of the underlying graphs. In contrast to these methods in this paper we introduce a novel approach to measure the structural similarity of directed and undirected graphs that is mainly based on margins of feature vectors representing graphs. We introduce novel graph similarity and dissimilarity measures, provide some properties and analyze their algorithmic complexity. We find that the computational complexity of our measures is polynomial in the graph size and, hence, significantly better than classical methods from, e.g. exact graph matching which are NP-complete. Numerically, we provide some examples of our measure and compare the results with the well-known graph edit distance. (c) 2006 Elsevier Inc. All rights reserved.

Europe’s Information Society project and Digital Inclusion: universal service obligations or social solidarity?

The importance of digital inclusion to Europe is obvious: as we move towards an ever more internet-communicating society the lack of access to basic digital infrastructures for a significant segment of the population is both problematic for those individuals without access and also problematic for those providing services which should be efficient and fully utilised. The EU’s ‘Information Society’ project has been the central plank of the European attempt to build a European digital marketplace, a concept which necessitates digital inclusion of the population at large. It is a project which prefers universal service obligations to achieve inclusion. If that is to be the preferred solution I suggest that we must consider exclusion from the banking system, given that the Information Society is at root an economic community.

However, universal service obligations are not the only method whereby digital inclusion can be encouraged and I posit we may need to reconsider the role of the state as supplier of services through the concept of ‘social solidarity’.

Stereotypes of Age Differences in Personality Traits: Universal and Accurate?

Age trajectories for personality traits are known to be similar across cultures. To address whether stereotypes of age groups reflect these age-related changes in personality, we asked participants in 26 countries (N = 3,323) to rate typical adolescents, adults, and old persons in their own country. Raters across nations tended to share similar beliefs about different age groups; adolescents were seen as impulsive, rebellious, undisciplined, preferring excitement and novelty, whereas old people were consistently considered lower on impulsivity, activity, antagonism, and Openness. These consensual age group stereotypes correlated strongly with published age differences on the five major dimensions of personality and most of 30 specific traits, using as criteria of accuracy both self-reports and observer ratings, different survey methodologies, and data from up to 50 nations. However, personal stereotypes were considerably less accurate, and consensual stereotypes tended to exaggerate differences across age groups.

A universal measure of chaotropicity and kosmotropicity

Diverse parameters, including chaotropicity, can limit the function of cellular systems and thereby determine the extent of Earth's biosphere. Whereas parameters such as temperature, hydrophobicity, pressure, pH, Hofmeister effects, and water activity can be quantified via standard scales of measurement, the chao-/kosmotropic activities of environmentally ubiquitous substances have no widely accepted, universal scale. We developed an assay to determine and quantify chao-/kosmotropicity for 97 chemically diverse substances that can be universally applied to all solutes. This scale is numerically continuous for the solutes assayed (from +361kJkg^-1mol^-1 for chaotropes to -659kJkg^-1mol^-1 for kosmotropes) but there are key points that delineate (i) chaotropic from kosmotropic substances (i.e. chaotropes =+4; kosmotropes =-4kJkg^-1mol^-1); and (ii) chaotropic solutes that are readily water-soluble (log P<1.9) from hydrophobic substances that exert their chaotropic activity, by proxy, from within the hydrophobic domains of macromolecular systems (log P>1.9). Examples of chao-/kosmotropicity values are, for chaotropes: phenol +143, CaCl₂ +92.2, MgCl₂ +54.0, butanol +37.4, guanidine hydrochloride +31.9, urea +16.6, glycerol [>6.5M] +6.34, ethanol +5.93, fructose +4.56; for kosmotropes: proline -5.76, sucrose -6.92, dimethylsulphoxide (DMSO) -9.72, mannitol -6.69, trehalose -10.6, NaCl -11.0, glycine -14.2, ammonium sulfate -66.9, polyethylene glycol- (PEG-)1000 -126; and for relatively neutral solutes: methanol, +3.12, ethylene glycol +1.66, glucose +1.19, glycerol [<5M] +1.06, maltose -1.43 (kJkg^-1mol^-1). The data obtained correlate with solute interactions with, and structure-function changes in, enzymes and membranes. We discuss the implications for diverse fields including microbial ecology, biotechnology and astrobiology.