scholarly journals A Multidimensional Scaling Analysis of Musical Sounds Based on Pseudo Phase Plane

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Miguel F. M. Lima ◽  
J. A. Tenreiro Machado ◽  
António C. Costa
Keyword(s):  
Mutual Information ◽  
Multidimensional Scaling ◽  
Phase Plane ◽  
Musical Composition ◽  
Dynamical Analysis ◽  
Scaling Analysis ◽  
Average Mutual Information ◽  
Pseudo Phase Plane ◽  
Musical Sounds ◽  
Musical Styles

This paper studies musical opus from the point of view of three mathematical tools: entropy, pseudo phase plane (PPP), and multidimensional scaling (MDS). The experiments analyze ten sets of different musical styles. First, for each musical composition, the PPP is produced using the time series lags captured by the average mutual information. Second, to unravel hidden relationships between the musical styles the MDS technique is used. The MDS is calculated based on two alternative metrics obtained from the PPP, namely, the average mutual information and the fractal dimension. The results reveal significant differences in the musical styles, demonstrating the feasibility of the proposed strategy and motivating further developments towards a dynamical analysis of musical sounds.

scholarly journals Analysis of Forest Fires by means of Pseudo Phase Plane and Multidimensional Scaling Methods

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
J. A. Tenreiro Machado ◽  
António M. Lopes
Keyword(s):  
Time Series ◽  
Multidimensional Scaling ◽  
Forest Fires ◽  
Phase Plane ◽  
Dimensional Space ◽  
Second Phase ◽  
Burnt Area ◽  
Long Range Correlations ◽  
Scaling Methods ◽  
Pseudo Phase Plane

Forest fires dynamics is often characterized by the absence of a characteristic length-scale, long range correlations in space and time, and long memory, which are features also associated with fractional order systems. In this paper a public domain forest fires catalogue, containing information of events for Portugal, covering the period from 1980 up to 2012, is tackled. The events are modelled as time series of Dirac impulses with amplitude proportional to the burnt area. The time series are viewed as the system output and are interpreted as a manifestation of the system dynamics. In the first phase we use the pseudo phase plane (PPP) technique to describe forest fires dynamics. In the second phase we use multidimensional scaling (MDS) visualization tools. The PPP allows the representation of forest fires dynamics in two-dimensional space, by taking time series representative of the phenomena. The MDS approach generates maps where objects that are perceived to be similar to each other are placed on the map forming clusters. The results are analysed in order to extract relationships among the data and to better understand forest fires behaviour.

Capacity Analysis for Correlated Multi-Hop MIMO Channels under Colored Noise

2015 ◽  
Vol 1 ◽  
pp. 41
Author(s):  
Nguyen N. Tran ◽  
Ha X. Nguyen
Keyword(s):  
Computational Complexity ◽  
Mutual Information ◽  
Closed Form Solution ◽  
Optimal Solution ◽  
Form Solution ◽  
Maximization Problem ◽  
Capacity Analysis ◽  
Mimo Channels ◽  
Average Mutual Information ◽  
Channel Output

A capacity analysis for generally correlated wireless multi-hop multi-input multi-output (MIMO) channels is presented in this paper. The channel at each hop is spatially correlated, the source symbols are mutually correlated, and the additive Gaussian noises are colored. First, by invoking Karush-Kuhn-Tucker condition for the optimality of convex programming, we derive the optimal source symbol covariance for the maximum mutual information between the channel input and the channel output when having the full knowledge of channel at the transmitter. Secondly, we formulate the average mutual information maximization problem when having only the channel statistics at the transmitter. Since this problem is almost impossible to be solved analytically, the numerical interior-point-method is employed to obtain the optimal solution. Furthermore, to reduce the computational complexity, an asymptotic closed-form solution is derived by maximizing an upper bound of the objective function. Simulation results show that the average mutual information obtained by the asymptotic design is very closed to that obtained by the optimal design, while saving a huge computational complexity.

The Reasons People Give for Taking Overdoses

1976 ◽  
Vol 128 (6) ◽  
pp. 538-548 ◽  
Author(s):  
J. H. J. Bancroft ◽  
A. M. Skrimshire ◽  
S. Simkin
Keyword(s):  
Multidimensional Scaling ◽  
Representative Sample ◽  
Social Acceptability ◽  
Scaling Analysis ◽  
Multidimensional Scaling Analysis ◽  
Suicidal Intent ◽  
After Care ◽  
State Of Mind ◽  
Seeking Help ◽  
Do So

SummaryThis study investigates the reasons people give for taking overdoses of drugs. A representative sample of 128 subjects were interviewed immediately after their recovery from an overdose. During the interview they were given alternative reasons for taking overdoses and asked to choose any that applied to them. Spontaneous comments about suicidal intent were also recorded. Of the subjects, 44 per cent indicated that they had wanted to die. On the basis of their choices 33 per cent were ‘seeking help’, 42 per cent ‘escaping from the situation’, 52 per cent ‘obtaining relief from a terrible state of mind’ and 19 per cent ‘trying to influence someone’. The association between these various reasons and other expected effects or feelings associated with the act were examined by means of multidimensional scaling analysis. In addition, the characteristics of those expressing suicidal intent and other reasons were studied, together with such consequences as toxic effects and psychiatric after-care. The possibility is discussed that a large proportion of those indicating suicidal intent do so either to gain social acceptability for their act or to influence helping agencies.

Sign in / Sign up

Export Citation Format

Share Document