Self-assembly of the discrete Sierpinski carpet and related fractals

It is well known that the discrete Sierpinski triangle can be defined as the nonzero residues modulo 2 of Pascal's triangle, and that from this definition one can easily construct a tileset with which the discrete Sierpinski triangle self-assembles in Winfree's tile assembly model. In this paper we introduce an infinite class of discrete self-similar fractals that are defined by the residues modulo a prime p of the entries in a two-dimensional matrix obtained from a simple recursive equation. We prove that every fractal in this class self-assembles using a uniformly constructed tileset. As a special case we show that the discrete Sierpinski carpet self-assembles using a set of 30 tiles

Entropy increase in switching systems

The relation between the complexity of a time-switched dynamics and the complexity of its control sequence depends critically on the concept of a non-autonomous pullback attractor. For instance, the switched dynamics associated with scalar dissipative affine maps has a pullback attractor consisting of singleton component sets. This entails that the complexity of the control sequence and switched dynamics, as quantified by the topological entropy, coincide. In this paper we extend the previous framework to pullback attractors with nontrivial components sets in order to gain further insights in that relation. This calls, in particular, for distinguishing two distinct contributions to the complexity of the switched dynamics. One proceeds from trajectory segments connecting different component sets of the attractor; the other contribution proceeds from trajectory segments within the component sets. We call them “macroscopic” and “microscopic” complexity, respectively, because only the first one can be measured by our analytical tools. As a result of this picture, we obtain sufficient conditions for a switching system to be more complex than its unswitched subsystems, i.e., a complexity analogue of Parrondo’s paradox

Recurrence Quantification Analysis and Principal Components in the Detection of Short Complex Signals

Recurrence plots were introduced to help aid the detection of signals in complicated data series. This effort was furthered by the quantification of recurrence plot elements. We now demonstrate the utility of combining recurrence quantification analysis with principal components analysis to allow for a probabilistic evaluation for the presence of deterministic signals in relatively short data lengths.Comment: 10 pages, 3 figures; Elsevier preprint, elsart style; programs used for analysis available for download at http://homepages.luc.edu/~cwebbe

Metallic phase of disordered graphene superlattices with long-range correlations

Using the transfer matrix method, we study the conductance of the chiral particles through a monolayer graphene superlattice with long-range correlated disorder distributed on the potential of the barriers. Even though the transmission of the particles through graphene superlattice with white noise potentials is suppressed, the transmission is revived in a wide range of angles when the potential heights are long-range correlated with a power spectrum $S(k)\sim1/k^{\beta}$. As a result, the conductance increases with increasing the correlation exponent values gives rise a metallic phase. We obtain a phase transition diagram in which a critical correlation exponent depends strongly on disorder strength and slightly on the energy of the incident particles. The phase transition, on the other hand, appears in all ranges of the energy from propagating to evanescent mode regimes.Comment: 8 pages, 11 figure

Liver segments: an anatomical rationale for explaining inconsistencies with Couinaud's eight-segment concept

Background and purpose: An increasing number of surgical and radiological observations call Couinaud's concept of eight liver segments into question and such inconsistencies are commonly explained with anatomical variations. This paper was intended to demonstrate that, beyond variability, another anatomical principle may allow to understand supposedly differing concepts on liver segmentation. Materials and methods: The study was performed on 25 portal vein casts scanned by helical CT. The branches of the right and left portal vein and their corresponding territories were determined both anatomically and mathematically (MEVIS LiverAnalyzer, MEVISLab). Results: The number of branches coming-off the right and left portal vein was never 8, but many more (mean number 20, range 9-44). Different combinations of these branches and their respective territories, carried out in this study, yielded larger entities and supposedly contradictory subdivisions (including Couinaud's eight segments), without calling upon anatomical variability. Conclusions: We suggest the human liver to be considered as corresponding to 1 portal venous territory at the level of the portal vein, to 2 territories at the level of the right and left branch of the portal vein, and to 20 at the level of the rami of the right and left branch. This "1-2-20-concept” is a rationale for reconciling apparent discrepancies with the eight-segment concept. On a pragmatic level, in cases in which imaging or surgical observations do not fit with Couinaud's scheme, we propose clinicians not to autonomically conclude to the presence of an anatomical variation, but to become aware of the presence of an average of 20 (and not 8) second-order portal venous territories within the human live

Bedeutung molekularer Alterationen kritischer Regionen auf Chromosom 12p für die Differenzierung testikulärer Keimzelltumoren

Es handelt sich um eine experimentelle Doktorarbeit unter der Leitung von Professor Dr. med. Axel Heidenreich, ehemals leitender Oberarzt der Urologie am Universitätsklinikum Marburg, jetzt Bereichsleiter Uroonkologie am Universitätsklinikum zu Köln. Die Arbeit beruht vor allem auf molekularbiologischen Methoden. Es gehörte zu meinen Aufgaben, diese Methoden im urologischen Labor zu etablieren. Das Thema verbindet Elemente aus der Molekularbiologie, Urologie und Onkologie. Hodenkrebs ist der häufigste solide maligne Tumor bei Männern zwischen 15 und 35 Jahren. In der Tat, 95 Prozent aller Hodentumore sind Keimzelltumoren. Die zentrale Fragestellung war zu untersuchen, ob eine aktive spezifische Expression der Gene SOX5, K-ras und JAW1, die auf dem Isochromosom 12p lokalisiert sind, an der Pathogenese und Progression testikulärer Keimzelltumoren beteiligt sind. Erstmalig wurde in dieser Arbeit mit semiquantitativer PCR das tumorspezifische Expressionsmuster von JAW 1, SOX5 und K-ras in testikulären Keimzelltumoren und angrenzendem histologisch normalem Gewebe, das durch Mikrodissektion voneinander separiert wurde, analysiert. In meiner Arbeit konnte ich beweisen, dass SOX5 und K-ras nicht als verantwortliche Gene an der Pathogenese der Keimzelltumoren beteiligt sind. Die Untersuchungen von JAW1 deuten auf eine untergeordnete Rolle in der Entstehung testikulärer Keimzelltumoren hin

Ergodicity properties of pp -adic (2,1)(2,1)-rational dynamical systems with unique fixed point

We consider a family of $(2,1)$-rational functions given on the set of $p$-adic field $Q_p$. Each such function has a unique fixed point. We study ergodicity properties of the dynamical systems generated by $(2,1)$-rational functions. For each such function we describe all possible invariant spheres. We characterize ergodicity of each $p$-adic dynamical system with respect to Haar measure reduced on each invariant sphere. In particular, we found an invariant spheres on which the dynamical system is ergodic and on all other invariant spheres the dynamical systems are not ergodic

On the fractal structure of the rescaled evolution set of Carlitz sequences of polynomials

AbstractSelf-similarity properties of the coefficient patterns of the so-called m-Carlitz sequences of polynomials are considered. These properties are coded in an associated fractal set – the rescaled evolution set. We extend previous results on linear cellular automata with states in a finite field. Applications are given for the sequence of Legendre polynomials and sequences associated with the zero Bessel function

Meta-dynamical adaptive systems and their applications to a fractal algorithm and a biological model

In this article, one defines two models of adaptive systems: the meta-dynamical adaptive system using the notion of Kalman dynamical systems and the adaptive differential equations using the notion of variable dimension spaces. This concept of variable dimension spaces relates the notion of spaces to the notion of dimensions. First, a computational model of the Douady's Rabbit fractal is obtained by using the meta-dynamical adaptive system concept. Then, we focus on a defense-attack biological model described by our two formalisms

Wavelet transforms in a critical interface model for Barkhausen noise

We discuss the application of wavelet transforms to a critical interface model, which is known to provide a good description of Barkhausen noise in soft ferromagnets. The two-dimensional version of the model (one-dimensional interface) is considered, mainly in the adiabatic limit of very slow driving. On length scales shorter than a crossover length (which grows with the strength of surface tension), the effective interface roughness exponent $\zeta$ is $\simeq 1.20$, close to the expected value for the universality class of the quenched Edwards-Wilkinson model. We find that the waiting times between avalanches are fully uncorrelated, as the wavelet transform of their autocorrelations scales as white noise. Similarly, detrended size-size correlations give a white-noise wavelet transform. Consideration of finite driving rates, still deep within the intermittent regime, shows the wavelet transform of correlations scaling as $1/f^{1.5}$ for intermediate frequencies. This behavior is ascribed to intra-avalanche correlations.Comment: RevTeX, 10 pages, 9 .eps figures; Physical Review E, to be publishe