An Analysis of the 4th Movement of György Ligeti’s Musica Ricercata based on Information Theory and Number Partitioning

In this paper we present a mathematically oriented analysis of the 4th Movement of György Ligeti’s Musica Ricercata (MR). The pitch analysis is based on Theory of Information and rhythm is analyzed through the Theory of Partitions of integer numbers. After a brief historical review of Musica Ricercata and its structure we make an analysis of the pitch distribution along the whole MR4 score, as well the Left and Right hand separately, through Theory of Information. We calculate two Information measures, namely, the Shannon’s Entropy and the Kullback-Leibler Divergence for the three cases. In the second part, about rhythm, we introduce a simple notation for coding rhythm patterns in terms of partitions of an integer number. We show that, with few exceptions, Ligeti used the partitions of number 6 to get rhythm variations on the Right hand against the ostinato on the Left one. In addition, we show the usefulness of the so called Hasse Diagram as a pre-compositional device to generate rhythm patterns.

Behaviour and Reasoning Description Language (BRDL)

In this paper we present a basic language for describing human behaviour and reasoning and present the cognitive architecture underlying the semantics of the language. The language is illustrated through a number of examples showing its ability to model human reasoning, problem solving, deliberate behaviour and automatic behaviour. We expect that the simple notation and its intuitive semantics may address the needs of practitioners from non matematical backgrounds, in particular psychologists, linguists and other social scientists. The language usage is twofold, aiming at the formal modelling and analysis of interactive systems and the comparison and validation of alternative models of memory and cognition.

Building Empathy in Young Children Using Augmented Reality

Empathy is the feeling that a person can step out virtually from his/her own world and enter the internal world of another person. In simple notation, empathy means the ability to ‘feel with’ other people, to sense what they are experiencing. Empathy is different than sympathy. It is a hard-wired capacity many of the people today is lacking. A psychological study has found that many people are suffering from Empathy Deficit Disorder (EDD). EDD gets severe by the increasingly polarized social and political culture especially in the under developed countries. Lack of empathy and social wellness can be very damaging to the families, organizations and countries. This research investigates how compassion can be trained as a coping strategy to build social wellness using augmented reality on our young generations. Smart and empathic citizens are the key to the success of Industrial Revolution (IR) 4.0.

The function analysis diagram: Intended benefits and coexistence with other functional models

Understanding product functions is a key aspect of the work undertaken by engineers involved in complex system design. The support offered to these engineers by existing modeling tools such as the function tree and the function structure is limited because they are not intuitive and do not scale well to deal with real-world engineering problems. A research collaboration between two universities and a major power system company in the aerospace domain has allowed the authors to further develop a method for function analysis known as function analysis diagram that was already in use by line engineers. The capability to generate and edit these diagrams was implemented in the Decision Rationale editor, a software tool for capturing design rationale. This article presents the intended benefits of the method and justifies them using an engineering case study. The results of the research have shown that the function analysis diagram method has a simple notation, permits the modeling of product functions together with structure, allows the generation of rich and accurate descriptions of product functionality, is useful to work with variant and adaptive design tasks, and can coexist with other functional modeling methods.

The Function Analysis Diagram

Understanding product functions is a key aspect of the work undertaken by engineers involved in complex system design. The support offered to these engineers by existing modeling tools such as the Function Tree and the Function Structure is limited as they are not intuitive and do not scale well to deal with real world engineering problems. A research collaboration between two universities and a major power system company in the aerospace domain has allowed the authors to further develop a method for function analysis known as Function Analysis Diagram (FAD) which was already in use by line engineers. The capability to generate and edit these diagrams was implemented in the Decision Rationale editor (DRed) a software tool for capturing design rationale. This article presents the main beneficial characteristics of the method and justifies them using two engineering case studies. The results of the research have shown that the FAD method has a simple notation, permits the modeling of product functions together with structure, allows the production of rich and accurate descriptions of product functionality and is suitable to represent complex problems.

A simple notation scheme to describe time-averaged ostracod assemblages (Crustacea, Ostracoda) by their taxonomic composition

A simple notation scheme is presented for the description of Quaternary freshwater ostracod assemblages by means of their taxonomic composition. The notation scheme also allows diagrammatic description of the fauna and assists in palaeoecological interpretation of sequential samples.

Productive Parallel Programming: The PCN Approach

We describe the PCN programming system, focusing on those features designed to improve the productivity of scientists and engineers using parallel supercomputers. These features include a simple notation for the concise specification of concurrent algorithms, the ability to incorporate existing Fortran and C code into parallel applications, facilities for reusing parallel program components, a portable toolkit that allows applications to be developed on a workstation or small parallel computer and run unchanged on supercomputers, and integrated debugging and performance analysis tools. We survey representative scientific applications and identify problem classes for which PCN has proved particularly useful.

Semicontinuity and Multipliers of C*-Algebras

In [5] C. Akemann and G. Pedersen defined four concepts of semicontinuity for elements of A**, the enveloping W*-algebra of a C*-algebra A. For three of these the associated classes of lower semicontinuous elements are , and (notation explained in Section 2), and we will call these the classes of strongly lsc, middle lsc, and weakly lsc elements, respectively. There are three corresponding concepts of continuity: The strongly continuous elements are the elements of A itself, the middle continuous elements are the multipliers of A, and the weakly continuous elements are the quasi-multipliers of A. It is natural to ask the following questions, each of which is three-fold. (Q1) Is every lsc element the limit of a monotone increasing net of continuous elements? (Q2) Is every positive lsc element the limit of an increasing net of positive continuous elements? (Q3) If h ≧ k, where h is lsc and k is usc, does there exist a continuous x such that h ≧ x ≧ k?