Computing the fundamental group of a higher-rank graph

We compute a presentation of the fundamental group of a higher-rank graph using a coloured graph description of higher-rank graphs developed by the third author. We compute the fundamental groups of several examples from the literature. Our results fit naturally into the suite of known geometrical results about higher-rank graphs when we show that the abelianization of the fundamental group is the homology group. We end with a calculation which gives a non-standard presentation of the fundamental group of the Klein bottle to the one normally found in the literature.

Query Expansion for Slovak to Bulgarian Language Machine Translation using Parallel Search

The paper presents results of the application of a statistical approach for Slovak to Bulgarian language machine translation. It uses Information Retrieval inspired search techniques and employs sever alalgorithmic steps of parallel statistical search with query expansion in Slovak-Bulgarian EUROPARL 7 Corpus using the Sketch Engine software and its scoring. The search includes the generation of concordances,collocations, word sketch differences, word sketches, and thesauri of the studied keyword (query) by using a statistical scoring, which is regarded as intermediate (inter-lingual) semantic standard presentation by means of which the studied keyword (from the source language) is mapped together with its possible translation equivalents (onto the target language. The results present the study of adjectival collocabillity in both Slovak and Bulgarian language from the corpus of political speech texts outlining the standard semantic relations based on the evaluation of statistical scoring. Finally, the advantages and shortcomings of the approach are discussed.

The braid group and its presentation

In this paper, we recall the geometric definition of the braid group by Emil Artin and we give a complete, elementary geometric/topological proof of the standard presentation of the braid group on [Formula: see text] strings.

Generalized small cancellation conditions, non-positive curvature and diagrammatic reducibility

We present a metric condition $\TTMetric$ which describes the geometry of classical small cancellation groups and applies also to other known classes of groups such as two-dimensional Artin groups. We prove that presentations satisfying condition $\TTMetric$ are diagrammatically reducible in the sense of Sieradski and Gersten. In particular, we deduce that the standard presentation of an Artin group is aspherical if and only if it is diagrammatically reducible. We show that, under some extra hypotheses, $\TTMetric$ -groups have quadratic Dehn functions and solvable conjugacy problem. In the spirit of Greendlinger's lemma, we prove that if a presentation P = 〈X| R〉 of group G satisfies conditions $\TTMetric -C'(\frac {1}{2})$ , the length of any nontrivial word in the free group generated by X representing the trivial element in G is at least that of the shortest relator. We also introduce a strict metric condition $\TTMetricStrict$ , which implies hyperbolicity.

The role of mashup music in creating Web 2.0’s democratic promise

This article employs Stuart Hall’s concept of ‘articulation’ to show how, in the mid-2000s, a loose coalition of tech activists and commentators worked to position mashup music as ‘the sound of the Internet’. Key aesthetic characteristics of mashups were utilized to present Web 2.0 as a specific kind of democratic, participatory media environment – one that had the power to dethrone old social institutions, and to render various kinds of borders and boundaries redundant. This short-lived articulation between mashup and the Internet has had significant benefits for contemporary platforms that have made their fortune on user participation; it has been less beneficial for the longevity of mashup as a genre. Thus, this article inverts the standard presentation of mashup music and network technologies. Generally presented as a musical culture that needed the Internet, mashup can be more fruitfully understood as a music culture that the Internet needed. This reformulation provides cause to question our contemporary relationship to ‘digital optimism’ more generally.

Weak KAM Theory and Forcing Equivalence

This chapter describes weak Kolmogorov-Arnold-Moser (KAM) theory and forcing relation. One change from the standard presentation is that one needs to modify the definition of Tonelli Hamiltonians to allow different periods in the t component. The chapter points out an alternative definition of the alpha function, namely, one can replace the class of minimal measures with the class of closed measures. It then considers a dual setting which corresponds to forward dynamic. It also looks at elementary solutions, static classes, and Peierls barrier. In many parts of the proof, the chapter studies the hyperbolic property of a minimizing orbit, for which the concept of Green bundles is very useful.

Ehrlichiosis-Induced Atrial Flutter: An Unusual Cause of Atrial Flutter

Tick-borne illness has been increasingly on the rise, since the first human case was reported in the late 1980s. Ehrlichia chaffeensis is one of the most common reported causes of tick-borne illness, particularly in the southern states of the United States. The clinical picture presents as a paradigm to the clinician, often missing the diagnosis without an appropriate history being taken and sometimes mistreated for other conditions. With the number of cases on the rise, new manifestations and clinical presentations due to E chaffeensis continue to be reported. Our case report is one such case in a 46-year-old male from Arkansas, with known exposure to multiple tick bites who presented with classical symptoms and laboratory values of tick-borne illness leading to atrial flutter. This unusual manifestation of atrial flutter due to tick-borne illness is rare and poorly understood. Further studies on tick-borne illness due to E chaffeensis may be needed to understand the systemic causes of the bacteria. In addition, in our case report, we bring to attention the standard presentation (symptoms, signs, and laboratory values) of tick-borne illness due to E chaffeensis along with the current standard for diagnosis and treatment.

Minimal Frames and Transparent Frames for Risk, Time, and Uncertainty

Behavior differs between transparent and nontransparent presentations of decisions, but “transparent presentation” has not been precisely defined. We formally define “transparent frames” for risk and time, establish their uniqueness, provide algorithms for constructing them, and compare them with “standard” presentation formats. A logic emerges for predicting systematic shifts in choice under risk and over time, and how violations of rational choice theory will depend on frames. An experiment verifies most of those predictions in choice under risk. We extend results to choice under uncertainty and also predict frame dependence of ambiguity aversion, a result supported by recent experimental evidence. This paper was accepted by Elke Weber, judgment and decision making.

Perception, Consciousness, and Continuity

This chapter looks at a vexed issue in Leibnizian interpretation––the question of Leibniz’s theory of consciousness. The phenomena of consciousness are apparently discontinuous, and, Leibniz argues, the failure to resolve these apparent discontinuities may lead one astray. I will show that the principle of continuity provides reasons to doubt that some of the main interpretations of Leibniz’s theory of consciousness are correct, and I will propose an interpretation that adheres more closely to this principle. Against those who argue that Leibniz’s theory of consciousness is a higher-order theory, this chapter argues that the standard presentation of such an interpretation violates the principle of continuity. An alternative threshold theory is presented and defended.