Branch-counting in the Everett interpretation of quantum mechanics

A defence is offered of a version of the branch-counting rule in the Everett interpretation (otherwise known as many worlds interpretation) of quantum mechanics that both depends on the state and is continuous in the norm topology on Hilbert space. The well-known branch-counting rule, for realistic models of measurements, in which branches are defined by decoherence theory, fails this test. The new rule hinges on the use of decoherence theory in defining branching structure, and specifically decoherent histories theory. On this basis ratios of branch numbers are defined, free of any convention. They agree with the Born rule and deliver a notion of objective probability similar to naive frequentism, save that the frequencies of outcomes are not confined to a single world at different times, but spread over worlds at a single time. Nor is it ad hoc : it is recognizably akin to the combinatorial approach to thermodynamic probability, as introduced by Boltzmann in 1879. It is identical to the procedure followed by Planck, Bose, Einstein and Dirac in defining the equilibrium distribution of the Bose–Einstein gas. It also connects in a simple way with the decision-theory approach to quantum probability.

Ferromagnetic Dirac Half-Metallicity in Transition Metal Embedded Honeycomb Borophene

Exploring two-dimensional (2D) ferromagnetic materials with intrinsic Dirac half-metallicity is crucial for the development of next-generation spintronic devices. Based on first-principles calculations, here we propose a simple valence electron-counting rule...

Counting to Infinity: Does learning the syntax of the count list predict knowledge that numbers are infinite?

By around the age of 5½, many children in the US judge that numbers never end, and that it is always possible to add +1 to a set. These same children also generally perform well when asked to label the quantity of a set after 1 object is added (e.g., judging that a set labeled “five” should now be “six”). These findings suggest that children have implicit knowledge of the “successor function”: every natural number, n, has a successor, n+1. Here, we explored how children discover this recursive function, and whether it might be related to discovering productive morphological rules that govern language-specific counting routines (e.g., the rules in English that represent base 10 structure). We tested 4- and 5-year-old children’s knowledge of counting with three tasks, which we then related to (1) children’s belief that 1 can always be added to any number (the successor function), and (2) their belief that numbers never end (infinity). Children who exhibited knowledge of a productive counting rule were significantly more likely to believe that numbers are infinite (i.e., there is no largest number), though such counting knowledge wasn’t directly linked to knowledge of the successor function, per se. Also, our findings suggest that children as young as four years of age are able to implement rules defined over their verbal count list to generate number words beyond their spontaneous counting range, an insight which may support reasoning over their acquired verbal count sequence to infer that numbers never end.

Measuring Students’ Understanding in Probability Concept between Two Different Cohort using Rasch Measurement

The students’ level of proficiency in any particular course is individually distinctive. Therefore, it is necessary for the educators to be able to address their student’s level of ability in understanding of the course they enrolled. Particularly, educators should be able to design a set of questions which suits the level of their students’ ability. For this reason, this study is concentrated on identifying the level of student’s ability in understanding probability concepts that has been included in the statistics course (STA150: Probability and Statistics 1). This course was enrolled by two groups of students (Group A and Group B) from the Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA Perak branch. Group A enrolled the course in December 2015 until March 2016 whilst Group B enrolled in June until November 2016 sessions. Since the aims of this study are to investigate the difference in students’ conceptual knowledge and understanding of probability concepts, as well as to examine which concepts were found most difficult by the students, hence the Rasch measurement approach was used to explore those aims. An instrument consists of 20 items in a test based on the “Counting Rule” topic was formed by an experienced lecturer to measure the level of student’s ability between the two groups. Based on the findings, it was found that there is a high reliability index of 0.93 (Group A) and 0.88 (Group B) which suggests the suitability of the instrument developed in this study to be replicated to the other samples, even though, the person student’s responses to the items for both groups appeared differently in terms of their difficulties in understanding the probability concepts which represents the student’s ability on this particular topic.

Aspect-Aware Target Detection and Localization by Wireless Sensor Networks

This paper considers the active detection of a stealth target with aspect dependent reflection (e.g., submarine, aircraft, etc.) using wireless sensor networks (WSNs). When the target is detected, its localization is also of interest. Due to stringent bandwidth and energy constraints, sensor observations are quantized into few-bit data individually and then transmitted to a fusion center (FC), where a generalized likelihood ratio test (GLRT) detector is employed to achieve target detection and maximum likelihood estimation of the target location simultaneously. In this context, we first develop a GLRT detector using one-bit quantized data which is shown to outperform the typical counting rule and the detection scheme based on the scan statistic. We further propose a GLRT detector based on adaptive multi-bit quantization, where the sensor observations are more precisely quantized, and the quantized data can be efficiently transmitted to the FC. The Cramer-Rao lower bound (CRLB) of the estimate of target location is also derived for the GLRT detector. The simulation results show that the proposed GLRT detector with adaptive 2-bit quantization achieves much better performance than the GLRT based on one-bit quantization, at the cost of only a minor increase in communication overhead.