michael's space

• getting connected - not static, but temporally evolving
• "small-world" effect - biology, humans, society organized in clusters or communities
  • it is a "small-world" in terms of who knows who ("6 degrees of Separation...")
• networks for transport include: internet, veins in body or leaves, highways
•  

• how do biological networks, such as fungi manage to continually re-route food supplies without a centralized resource manager?
• to what extent biological systems use or avoid potentially congested hubs?
• how does underlying nutrient supply network in cancer tumours or in AVM (brain becomes starved)?
• transmission of viruses through populations - ie. bird flu?

• in networks with modest resources:
  • adding a small amount of connectivity between members increased success rate
• in higher resource populations:
  • low levels of interconnectivity increased mean success rate

" .. it might be good to get connected - as long as you don't get too connected"

• complex patterns in traffic systems, due to:
  • interactions of cars (or the actions and decisions of drivers)

• Traffic dilemma 1. whether or not to take a particular road
  • all roads - comfort limit, L
  • # cars, greater than L = the road is uncomfortable
    • won't know until it's too late!
• Traffic dilemma 2. choose between 2 routes
  • 2 routes 1 + 0; both nominally identical
    • Wins if/when we take the road less travelled
• Traffic dilemma 3. to go through the center, or around the outside
  • through center - risk congestion; outside - risk longer route/time
• Costs - travel through center of hub and spoke network:
  • time taken to get through center
    • center congestion determined by car volume on roads, and
      • combination and number of roads

• for fungi, how to transport food from one side of an organism to another
  • fungi feature a balance between centralized and decentralized suppy routes (like the forest floor)
• shortest route between any two points may not be quickest, if for instance, there is a lengthy delay at any hub

• adding more spoke roads will provide more short routes through the center, thereby shortening travel time, so
  • build as many spoke roads to the center as possible, BUT
• the more cars that pass through the center - the more congested it will be, thus
  • will take longer to get from side to side, so
  • build as few spoke roads through the center, as possible
    • So the message is that moderation is the key

• London currently charges  flat fee to travel in city center, regardless of congestion condition when you are there
• WHY?
  • shouldn't this depend on how many others are travelling at the same time as you?
  • Jarrett and Ashton suggest:
    • by varying the congestion cost according to how many people are also driving through the center
    • the traffic can be optimized to coincide more closely with the actual number of access roads through the center
      • the more drivers passing through the center will push the congestion charge up at that moment
        • with strategically placed displays noting traffic volume and cost, then drivers can make an informed decision regarding alternative routes

• needs to efficiently distribute nutrients around its network to survive
  • ex. finds food on its perimeter
    • needs to transport this food (such as carbon (C), nitrogen (N), phosphorus (P) across the structure to all other parts of the organism in order to feed itself

from www.botany.hawaii.edu/.../BOT135/Lect03_b.htm

Fig. 7. Illustration of the process of absorption, the mechanism by which fungi consume their food.

• if no transport congestion, the most efficient path is through the center
• but congestion is possible at center, since tubes do not have infinite capacity
• organism must decide how many pathways to build through the center, in order to ensure that nutrients get passed across the structure in the correct time-frame
  • which pathways are correct? The ones that share the same amount of time for transport  

      

• How to get message to someone in another layer? Which route involves the fewest people?
  • If designing a corporate ladder, which design will lead to the quickest exchange of information?

• by embedding one network in another, the hub + spoke of one network becomes a new "Super-Hub" - or renormalized hub - for a larger, multiple-ring network
  • redefines cost of travel through center
  • can be combined with other rings, repeating over and over

• rings within rings - feature several different zones
  • if 2 zones, one charges £8, the other £2
  • or even better, adjusted in real time
• cost of using central hub variable
  • dependent on # of agents using hub and capacity of hub
  • if comfort level is exceeded, then a congestion charge is imposed on all subsequent traffic
    • each agent must decide whether to pay, or go around the center
  • The resulting patterns are rich, due to interplay between the creation of, and the transition between particular stable traffic states, which arise as the conditions on the network change

• existence of congestion in the network is a dynamic process, and is
  • as much dependent on the agents' decisions as it is on the network structure itself

• time-distance
• potential costs of tolls
• time-congestion through center (or other hub)
  • No congestion = WINNER

    

• the different area scales were used to track travel between one central location and five different locations in the Tees Valley.
• important elements included:
  • ability to take alternative routes, due to
    • distance
    • congestion
    • personal taste (for example, a quiet route, or beautiful scenery) - if speed/efficiency is not most important
    • speed limit
      • Here are the road speeds in the UK:

  i 

     

Onto each network, nodal points were identified where and an ellipse and a street met.

• each point was given a value that could alternatively be used for pitch, time or gesture 
• further each street was given a value to be used for pitch
  • for active sections (regions of high flow), 24 values were used (assuming equal temperament, using equally-spaced 1/4 tones)
  • for musically homophonic sections, 36 values were used (assuming equal temperament, using equally-spaced 1/6 tones) 

      

examples of nodal values assigned at the intersection of road and ellipse

     

 

here are a few examples of nodal values converted to rhythmic notation

        

• each instrument traced seperate paths
• not every journey was designed to maximize efficiency; in some instances, it could have been a lazy Sunday journey with family/friends and the neighbor's pooch.
• ratios between nodal points at each ellipse was considered
• rate of speed was considered, that effected local gesture and form
• congestion = the density of instruments and/or pitch at any single node
• distance = time (more or less - not strictly)
• costs, such as tolls were applied to extreme instrumental or vocal technique
  • such as singing past the comfortable pulmonic reserve, and deeper into the physiological reserve capacity
  • the idea was to find a capale metaphor for "giving something you can't give back"
  • the toll could be applied when L is too high, ie. when all 5 instruments were in a similar region

• transitional states - as congestion begins and alternative routes begin to be accessed
  • if variable congestion charge is levied, both time and real cost of toll is factored in

• taken from ellipses
  • based on groupings
    • numerator - based on proximity
    • denominator - based on relative distance amongst those grouped together

• the pitch information gathered from the journeys did not provide enough raw data for the sections of high complexity, so these pitches were used to define structurally significant points
  • additional pitch information was gathered from an intermediate region of deterministic chaos, using the logistic equation, and in particular region 3.83 

• at the heart of most real-world examples of complexity, is the situation in which a collection of objects are competing for some kind of limited resource

• what is remarkable about emergent phenomena, is that they can arise in the absence of any central conroller or coordinator
  • it turns out that a suitably chosen collection of such objects can work better as a group if they are not being coordinated by a single controller, but are indeed competing for some limited resource.
  • the precise nature of the crowd-like phenomena which emerge will depend on how the individual objects interact and how interconnected they are

• the system contains a collection of many interacting objects or agents
  • interactions due to:
    • agents are physically close to each other
    • are members of the same group
    • share common information
• objects' behavior is effected by memory or feedback
  • something in the past effects the present
  • objects' can adapt their strategies according to history
  • agent/object can adapt its behaviour by itself

• system is typically open (closed system - not in contact with outside)
  • system can be influenced by its environment
    • market effected by company earnings, or traffic effected by road closure

• system appears "alive"
  • evolves in a highly non-trivial and complicated way
• system exhibits emergent phenomena which are generally surprising and may be extreme
  • emergent phenomena typically arise in the absence of any sort of "invisible hand" or central controller
  • biases in the arrangements of objects can arise as a result of external conditions

 

• system a complicated mix of ordered and disordered behaviour
  • all complex systems seem to be able to move between order and disorder of their own accord
    • Increasing complexity as number of possible arrangements increase
      • 2 files = 2 arrangements; 3 files = 6 arrangements; 4 files = 24 arrangements; 5 files = 120 arrangement; 10 files = more than 3 1/2 million
    • entropy - tendency to progress towards disorder
      • feedback necessary to correct disorder

• contain collections of objects whose complicated overall interactions feature memory and feedback
• can move between order and disorder
• its complexity cannot be generted through simple iteration, such as applying a mathematical procedure over and over

the 'Universal Pattern of Life' lies somewhere in the middle-ground between completely ordered and disordered patterns.

Limited Resources and Competition

Binary decision problem - Go to the bar?

• comfort level of people in bar = L (L = 60)
• how many people decide to go to bar = N (N = 100)
  • if you stay at home + bar is crowded, then you WIN
  • if you stay at home + bar is not crowded, then you LOSE
    • a gamble - competition for limited resources
      • everyday, a series of binary (at least) decisions.

             

• integration of memory/feedback
  • p = 1, history always repeats; p = 0, history never repeats; p = 0.5, somewhere in between
  • in large groups, people tend towards the extremes - either history repeats or not
  • 

• completely systematic - fixed response to past outcomes
  • external constraints is high 
  • 

" ... Arnold Schoenberg (1977, p. 20) makes a number of interesting observations concerning the nature of musical forms in general, and their importance for the reception of the music:

• Form means that the piece is organized, and organization means that the music “consists of elements functioning like those of a living organism.”
• Like the elements of an organism, the constituent parts of music must be differentiated according to their importance and function, but the differentiation must never endanger the underlying unity of the composition.
• Form in this sense ensures intelligibility, logic and coherence; it is what makes the music comprehensible.
• Concern about form is a means of surmounting limited powers of human understanding; as a person is unable to keep in mind very long time stretches, the musical discourse must be subdivided into manageable segments.
  • However, these shorter segments must again be joined by relation to the others in such a way that one segment presupposes the other and vice versa.
  • This is what one could call formal functions, in a sense similar to that we have with harmonic functions.

• Variety can endanger comprehensibility and logic, and this can be avoided by subjecting the musical elements to appropriate constraints.
  • Delimitation, subdivision and simple repetition are useful in counteracting the tendency toward disproportionate variety.
  • In fact, Schoenberg states that musical comprehension is impossible without repetition. But repetition can easily cause monotony and boredom on the part of the listener.
  • This must be counteracted by variation of the repeated elements.
• In a true work of music that obeys the classical laws of internal unity, even musical contrasts should be related.

 

• phrases and sections, as well as through simultaneous layers.
  • harmonic fields, thematic recurrence, tensions and relaxations, or contrasting textures
• Musical forms as emergent forms is fundamentally different from approaching musical forms as normative conventions
  • rationality to the listener’s ear
  • willing to bracket her preconceptions of form during the first hearings of a piece of music
  • only afterwards apply his already acquired assumptions of form with sensitivity and honesty in order to avoid forcing the music into a wrong or inadequate mould
  • conception of musical form that would regard good form more in terms of its emergent wholeness and rationality
    • rather than as compliance to formal conventions and codes

Aural Sonology has developed consistent approaches to three aspects of musical form:

• form-building functions (dynamic forms)
• form-building processes (forms based on recurrence and contrast)
• form-building transformations (forms contrasting ‘loose and firm gestalts’)

3.2.1. Typology of Form-Building Elements

• perception of musical form arises from the perceived interrelationships between certain constituent elements
• elements constitutive of form will be called form-building elements (or simple form elements)
  • often found in the melodic/rhythmic lines in the foreground layer(s)
  • background elements can be left out - however, there are cases in which musical textures as such obtain form-building significance
  • form-elements will have to apply both to lines (i.e. melodic/rhythmic elements) and to textures

The typology of form-building elements is based on their complexity (see Figure 1):

Figure 1

• Very simple elements. Examples: repetitive figures with a couple of pitches and even rhythmical values such as very simple accompaniment figures (lines); monophony or basic homophony (texture).
• Relatively simple elements. Examples: articulated yet simple figures such as scales/passages or refined accompaniment figures (lines); heterophony, or homophony with slight polyphonic elements (texture).
• Medium complex elements. Examples: a classical, simple theme (lines); a two- or three-part simple polyphony (texture).
• Relatively complex elements. Examples: complex themes with great diversity of pitch and rhythm (lines); complex polyphony (texture).
• Very complex elements. Examples: extremely asymmetric lines using a large number of values in an unpredictable manner (lines); accumulations in electroacoustic and avant-garde music (texture).

The scale of complexity may to some extent be considered relative to the composition or to the style of the composition that is being analyzed.

A form-element, e.g. a theme, will often be presented in its integral form, then broken down by being partitioned into smaller units. The symmetrically opposite shapes of the sign for partitioned elements may be used to suggest the opening or closing features of the context or of the (often preceding) integral element from which they have been partitioned.

The simple arrangement of degrees from simple to complex is not sufficient to describe the total range of elements embodied in the aural experience of musical form

• such as articulation or distinction (i.e. of being characteristic)
  • well-articulated form-element - in possession of details that are distinctly perceivable as such
    • high articulation - additionally feature middle range complexities - most classical themes are well articulated
      • passagework, soloist figurations etc. may have medium complexity without being highly articulated
      • theme-like passages have “structural” complexity, passagework “ornamental” complexity
      • structural complexity is by definition highly articulated, while ornamental complexity is not.

distinctive element - a character that tends to set it apart

• also means that certain form-elements are unique to the particular piece in question, setting it apart from other pieces within the same style
  • for example - a piece of bebop jazz that presents the theme to begin with; this will be a distinctive element
    • The improvisations that follow will be characterized by passages and figurations, often rather complex, but they will mostly be more typical of the genre of bebop jazz, or of the player, than of the piece as such

3.2.2. Context Organization of Form-Elements

• Form-building segments will be defined through the combination of form-elements (as presented in the typology above) into an organized context.
• A form-segment is a coherent succession of form-elements, where the evaluation of similarity and contrast between adjoining elements will serve as the main criterion for determining what belongs to the form-segment and what does not
  • when there is similarity between juxtaposed form-elements, a coherent form-segment is easily created.
  • Contrasts tend to fragment coherent segments or set them off from each other
    • however, fragmented form elements, too, can be held together in unifying gestalt (a phrase) due to other musical dimensions, such as harmony, or constant background layers.
  • Although the form-segments generally tend to be a succession, there are also situations in which elements are superposed in simultaneity.

Formal types identified:

A. form-elements w/ grouping indicating similarity                                                      B. greater degree of contrast

C. fragment - if further abbreviated or set off by pauses                                             D. shorter segments combine to form larger segments

                                        

Figure 6 Janacek, String Quartet, Kreutzer Sonata, mmt3          Figure 7 Beethoven op. 2:1, mmt I

E. superposition, different simulataneous layers                                                             F. upper limit of complexity - perceptual fusion

Figure 8 J. S. Bach, Ihr aber seid nicht fleischlich