Inconstancy of finite and infinite sequences

In order to study large variations or fluctuations of finite or infinite sequences (time series), we bring to light an 1868 paper of Crofton and the (Cauchy-)Crofton theorem. After surveying occurrences of this result in the literature, we introduce the inconstancy of a sequence and we show why it seems more pertinent than other criteria for measuring its variational complexity. We also compute the inconstancy of classical binary sequences including some automatic sequences and Sturmian sequences.Comment: Accepted by Theoretical Computer Scienc

Exploitation of Memetics for Melodic Sequences Generation

Music, or in narrower sense, melodic contours of the aesthetically arranged pitches and the respective durations attracts our cognition since the beginning and now shaping the way we think in the complex life of culture. From evolutionary school of thoughts we could learn our perspective of seeing the musical diversity of folk songs in Indonesian archipelago by hypothesizing the aligning memes throughout the data sets. By regarding the memeplexes constructed from the the Zipf-Mandelbrot Law in melodic sequences and some mathematical characteristics of songs e.g.: gyration and spiraling effect, we construct evolutionary steps i.e.: genetic algorithm as tools for generating melodic sequences as an alternating computational methods to model the cognitive processes creating songs. While we build a melodic-contour generator, we present the enrichment on seeing the roles of limitless landscape of creativity and innovation guided by particular inspirations in the creation of work of art in general

Texture analysis of aggressive and nonaggressive lung tumor CE CT images

This paper presents the potential for fractal analysis of time sequence contrast-enhanced (CE) computed tomography (CT) images to differentiate between aggressive and nonaggressive malignant lung tumors (i.e., high and low metabolic tumors). The aim is to enhance CT tumor staging prediction accuracy through identifying malignant aggressiveness of lung tumors. As branching of blood vessels can be considered a fractal process, the research examines vascularized tumor regions that exhibit strong fractal characteristics. The analysis is performed after injecting 15 patients with a contrast agent and transforming at least 11 time sequence CE CT images from each patient to the fractal dimension and determining corresponding lacunarity. The fractal texture features were averaged over the tumor region and quantitative classification showed up to 83.3% accuracy in distinction between advanced (aggressive) and early-stage (nonaggressive) malignant tumors. Also, it showed strong correlation with corresponding lung tumor stage and standardized tumor uptake value of fluoro deoxyglucose as determined by positron emission tomography. These results indicate that fractal analysis of time sequence CE CT images of malignant lung tumors could provide additional information about likely tumor aggression that could potentially impact on clinical management decisions in choosing the appropriate treatment procedure

A Quantitative Model for Human Olfactory Receptors

A wide variety of chemicals having distinct odors are smelled by humans. Odor perception initiates in the nose, where it is detected by a large family of olfactory receptors (ORs). Based on divergence of evolutionary model, a sequence of human ORs database has been proposed by D. Lancet et al (2000, 2006). It is quite impossible to infer whether a given sequence of nucleotides is a human OR or not, without any biological experimental validation. In our perspective, a proper quantitative understanding of these ORs is required to justify or nullify whether a given sequence is a human OR or not. In this paper, all human OR sequences have been quantified, and a set of clusters have been made using the quantitative results based on two different metrics. Using this proposed quantitative model, one can easily make probable justification or deterministic nullification whether a given sequence of nucleotides is a probable human OR homologue or not, without seeking any biological experiment. Of course a further biological experiment is essential to validate the probable human OR homologue

Fluids mobilization in Arabia Terra, Mars: depth of pressurized reservoir from mounds self-similar clustering

Arabia Terra is a region of Mars where signs of past-water occurrence are recorded in several landforms. Broad and local scale geomorphological, compositional and hydrological analyses point towards pervasive fluid circulation through time. In this work we focus on mound fields located in the interior of three casters larger than 40 km (Firsoff, Kotido and unnamed crater 20 km to the east) and showing strong morphological and textural resemblance to terrestrial mud volcanoes and spring-related features. We infer that these landforms likely testify the presence of a pressurized fluid reservoir at depth and past fluid upwelling. We have performed morphometric analyses to characterize the mound morphologies and consequently retrieve an accurate automated mapping of the mounds within the craters for spatial distribution and fractal clustering analysis. The outcome of the fractal clustering yields information about the possible extent of the percolating fracture network at depth below the craters. We have been able to constrain the depth of the pressurized fluid reservoir between ~2.5 and 3.2 km of depth and hence, we propose that mounds and mounds alignments are most likely associated to the presence of fissure ridges and fluid outflow. Their process of formation is genetically linked to the formation of large intra-crater bulges previously interpreted as large scale spring deposits. The overburden removal caused by the impact crater formation is the inferred triggering mechanism for fluid pressurization and upwelling, that through time led to the formation of the intra-crater bulges and, after compaction and sealing, to the widespread mound fields in their surroundings