3,474 research outputs found
A Topological Separation Condition for Fractal Attractors
We consider finite systems of contractive homeomorphisms of a complete metric
space, which are non-redundant on every level. In general this separation
condition is weaker than the strong open set condition and is not equivalent to
the weak separation property. We prove that this separation condition is
equivalent to the strong Markov property (see definition below). We also show
that the set of -tuples of contractive homeomorphisms, which are
non-redundant on every level, is a set in the topology of pointwise
convergence of every component mapping with an additional requirement that the
supremum of contraction coefficients of mappings be strictly less than one. We
give several sufficient conditions for this separation property. For every
fixed -tuple of invertible contraction matrices from a certain
class, we obtain density results for -tuples of fixed points which define
-tuples of mappings non-redundant on every level.Comment: 19 page
An Interdisciplinary Understanding of the Economic and Political Policies behind Network Neutrality in the United States
The focus of this paper is to explore the associative benefits to why network neutrality in the U.S. benefits the fundamental principles of freedom of speech and expression. While at the same time gaining a deeper understanding of why politics may incentivize or undermine data collection by billion-dollar conglomerate companies such as Tiktok and other internet service provider companies. In doing so, this paper will review internet privacy regulations on a federal level and examine the history of the FCC’s regulatory practices on ISPs over the last three decades. Lately, this paper will discuss the economics behind network neutrality and how they influence the everyday American consumer
Crinkly curves, Markov partitions and dimension
We consider the relationship between fractals and
dynamical systems. In particular we look at how the
construction of fractals in (D1) can be interpreted-in a
dynamical setting and additionally used as a simple method
of describing the construction of invariant sets of
dynamical systems. There is often a confusion between
Hausdorff dimension and capacity -which is much easier to
compute- and we show that simple examples of fractals,
arising in dynamical systems, exist for which the two
quantities differ.
In Chapter One we outline the mathematical background
required in the rest of the thesis.
Chapter Two reviews the work of F. M. Dekking on generating
'recurrent sets', which are types of fractals. We show how
to interpret this construction dynamically. This approach
enables us to calculate Hausdorff dimension and describe
Hausdorff measure for certain recurrent sets. We also
prove a conjecture of Dekking about conditions under which
the best general estimate of dimension actually equals
dimension.
In Section One of Chapter Three recurrent sets are used
to construct special Markou partitions for expanding
endomorphisms of T2 and hyperbolic automorphisms of T3.
These partitions have transition matrices closely related
to the covering maps. It is also shown that Markov
partitions can be constructed for the same map whose
boundaries have different capacities. Section Two looks
at the problem of coding between two Markov partitions
for the same expanding endomorphism of T2. It is shown
that there is a relationship between mean coding time and
the capacities of the boundaries. Section Three uses
recurrent sets to construct fractal subsets of tori
which have non-dense orbits under the above mappings.
Finally, Chapter Four calculates capacity and Hausdorff
dimension for a class of fractals (which are also recurrent
sets) whose scaling maps are-not similitudes. Examples
are given for which capacity and Hausdorff dimension give
different answers
Computational and Experimental Investigation into the Determinants of Protein Structure, Folding, and Stability in the β-Grasp Superfamily
Elucidating the mechanisms of protein folding and unfolding is one of the greatest scientific challenges in basic science. The overarching goal is to predict three-dimensional structures from their amino acid sequences. Understanding the determinants of protein folding and stability can be facilitated through the study of evolutionarily related but diverse proteins. Insights can also be gained through the study of proteins from extremophiles that may more closely resemble the primordial proteins. In this doctoral research, three aims were accomplished to characterize the structure, folding and unfolding behavior within the β-grasp superfamily. We propose that the determinants of structure, stability, and folding are conserved as sequence and interaction patterns in the β-grasp fold. To elucidate key residues, bioinformatics studies were conducted and identified nine structurally conserved amino acids in the core of the B1 domain of protein G (GB1). A network analysis of all long-range interactions in the structure of GB1 revealed the relative significance of each conserved amino acid. Within the β-grasp superfamily, two proteins, GB1 and the small archaeal modifier protein 1 (SAMP1), were investigated to elucidate the key determinants of structural stability at the level of individual interactions. They were subjected to high temperature molecular dynamics simulations and the detailed behavior of each long-range interaction was characterized. The results revealed that in GB1 the most stable region was the C-terminal hairpin and in SAMP1 it was the opposite, the N-terminal hairpin. The folding behavior of SAMP1 was investigated due to its nature as a divergent superfamily member and extremophile. The results revealed that SAMP1 at high ionic strength folds more rapidly than in low ionic strength. These findings clearly indicate that adaption at high salt produces rapid and less-frustrated folding. The results of these research aims provide insight into determinants of the β-grasp fold and the folding and unfolding behavior of two key members. Perhaps the most surprising finding is the presence of a significant number of non-native long-range interactions during unfolding which has largely gone unnoticed in the scientific community and appears to be pivotal
Configurations of control: An exploratory analysis
© 2015 Elsevier Ltd. There is growing interest in how management controls operate together as a package of interrelated mechanisms. Although theoretical debate dates back to the seminal paper of Otley (1980), there remains little empirical analysis of how control mechanisms combine. To increase knowledge in this area this study explores how multiple accounting and other control mechanisms commonly combine and the associations these combinations have with firm context. From a cross-sectional sample of 400 firms, this study presents an empirically derived taxonomy of five control configurations used by top managers, labelled as simple, results, action, devolved, and hybrid. Many of these patterns closely resemble control configurations common to the literature, while others represent distinctively contemporary arrangements, such as flexible variants of traditional bureaucracy (action), and instances where multiple and seemingly conflicting control types intermesh (hybrid). In analyzing these configurations this study provides accounting and control researchers with empirical observations to refine and extend existing control frameworks and theory
Matrix Big Brunch
Following the holographic description of linear dilaton null Cosmologies with
a Big Bang in terms of Matrix String Theory put forward by Craps, Sethi and
Verlinde, we propose an extended background describing a Universe including
both Big Bang and Big Crunch singularities. This belongs to a class of exact
string backgrounds and is perturbative in the string coupling far away from the
singularities, both of which can be resolved using Matrix String Theory. We
provide a simple theory capable of describing the complete evolution of this
closed Universe.Comment: 15 pages, no figures. References adde
Modeling the emergence of universality in color naming patterns
The empirical evidence that human color categorization exhibits some
universal patterns beyond superficial discrepancies across different cultures
is a major breakthrough in cognitive science. As observed in the World Color
Survey (WCS), indeed, any two groups of individuals develop quite different
categorization patterns, but some universal properties can be identified by a
statistical analysis over a large number of populations. Here, we reproduce the
WCS in a numerical model in which different populations develop independently
their own categorization systems by playing elementary language games. We find
that a simple perceptual constraint shared by all humans, namely the human Just
Noticeable Difference (JND), is sufficient to trigger the emergence of
universal patterns that unconstrained cultural interaction fails to produce. We
test the results of our experiment against real data by performing the same
statistical analysis proposed to quantify the universal tendencies shown in the
WCS [Kay P and Regier T. (2003) Proc. Natl. Acad. Sci. USA 100: 9085-9089], and
obtain an excellent quantitative agreement. This work confirms that synthetic
modeling has nowadays reached the maturity to contribute significantly to the
ongoing debate in cognitive science.Comment: Supplementery Information available here
http://www.pnas.org/content/107/6/2403/suppl/DCSupplementa
Management control effectiveness and strategy: An empirical analysis of packages and systems
© 2016 Elsevier Ltd. This study examines management control (MC) combinations that are effective in different strategic contexts through two related approaches - MC as a package and MC as a system. First, this study identifies how a set of MC practices combine (i.e. MC packages) to achieve effective control outcomes for firms operating in defender and prospector strategic contexts by applying fuzzy set qualitative comparative analysis (fsQCA). Using data from a survey of top managers the analysis reveals that there are multiple ways by which firms can effectively combine MC practices in a given strategic context. Furthermore, the analysis shows that not all MC practices found to be relevant in isolation are relevant when examined simultaneously as a package. Second, based on a comparison of effective MC packages this study examines interdependencies between MC practices (i.e. MC systems). Results show that in defender firms a diagnostic control use of accounting and mechanistic structural controls act as complements, while mechanistic structural controls and measure diversity act as substitutes. In prospector firms an interactive control use of accounting and organic structural controls are found to have complementary effects. These results indicate that the effectiveness of accounting control and structural control choices are determined not only by their fit with strategic context but also by how they fit with each other. This study also demonstrates how an understanding of MC packages can provide guidance for theory development and empirical analysis of MC systems
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