Minimal bounds and members of effectively closed sets

We show that there exists a non-empty $\Pi^0_1$ class, with no recursive element, in which no member is a minimal cover for any Turing degree.Comment: 15 pages, 4 figures, 1 acknowledgemen

On the Cardinality of Many-Worlds in Discrete Spacetime Structures

We make an analysis over a variation of causal sets where the light cone of an event is represented by finitely branching trees with respect to any given arbitrary dynamics. We argue through basic topological properties of Cantor space that under certain assumptions about the spacetime structure and causation, given any event $x$, if all worldlines extending the event $x$ are `eventually deterministic', then within the many-worlds interpretation the number of alternate universes with respect to $x$ is exactly $\aleph_0$. We also observe that if there are countably many alternate universes with respect to $x$, then at least one of these universes must be necessarily `decidable' in the sense that there is an algorithm which determines whether or not any given event belongs to the given worldline. We finally point out the fact that there can be only countably many universes with an ultimate end

Degrees of members of ∏01 classes

Abstract unable to be displayed accurately. Please see eThesis for full detail

Fibonacci graphs

Apart from its applications in Chemistry, Biology, Physics, Social Sciences, Anthropology, etc., there are close relations between graph theory and other areas of Mathematics. Fibonacci numbers are of utmost interest due to their relation with the golden ratio and also due to many applications in different areas from Biology, Architecture, Anatomy to Finance. In this paper, we define Fibonacci graphs as graphs having degree sequence consisting of n consecutive Fibonacci numbers and use the invariant omega to obtain some more information on these graphs. We give the necessary and sufficient conditions for the realizability of a set D of n successive Fibonacci numbers for every n and also list all possible realizations called Fibonacci graphs for 1 <= n <= 4

Modelling Marshall Design Test Results of Polypropylene Modified Asphalt by Genetic Programming Techniques

Determining Marshall design test results is time consuming. If the researchers can obtain stability and flow values by mechanical testing, rest of the calculations will just be mathematical manipulations. Marshall stability and flow tests were carried out on specimens fabricated with dierent type of polypropylene fibers. It has been shown that addition of polypropylene fibers improved Marshall stabilities and Marshall quotient values in a considerable manner. Input variables in the developed genetic programming model use the physical properties of standard Marshall specimens such as polypropylene type, polypropylene percentage, bitumen percentage, specimen height, calculated unit weight, voids in mineral aggregate, voids filled with asphalt and air voids. Performance of the genetic programming model is quite satisfactory. Besides, to obtain main eects plot, a wide range of parametric studies have been performed.The presented closed form solution will also help further researchers willing to perform similar studies, without carrying out destructive tests

Indoor Localization by using Particle Filtering Approach with Wireless Sensor Nodes

Jennic type wireless sensor nodes are utilized together with a novel particle filtering technique for indoor localization. Target objects are localized with an accuracy of around 0.25 meters. The proposed technique introduces a new particle generation and distribution technique to improve current estimation of object positions. Particles are randomly distributed around the object in the sensing area within a circular strip of 2 STD of object distance measurements. Particle locations are related to object locations by using Gaussian weight distribution methods. Object distances from the transmitters are determined by using received RSSI values and ITU-R indoor propagation model. Measured object distances are used together with the particle distances from the transmitters to predict the object locations