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speech gestures are constrictions of tongue tip and tongue body

• tongue tip and palatal
• speaker differences in lip closure synergies
• achieves a low value of the release

Introduction to Dynamical Systerms

• provide potntial solution of one of the problems
• phonolgy units are discrete
• physical measurment is continous

Dynamical system = motion of objects

• used for models with nature phonmonane

what is a dymamical system

• equation that quantitatively describes the change in something over time or space or both
• 2 parts
  • state of the system = quantity whose change is being described
  • law for how the state changes, depending on the current state, whic predicts the state at the next instant in time = shows the current state predcits
  • useful for modeling something like a unit
  • the dynamical system is constoant, but the law does not useually change, asosoicated with a particiaukar gesture
  • the equation defines it does not change, the state varibale changes
  • the dynamical law changes with time varies or time invaries

Goal or Point Attractor

• the fucntion is different, and the end state is the same
• goal = attracotr = equallium state = all end up in the same state

Rate of Goal Attainment

• stiffness of the system = stress the string and let it go, it will come back faster
• change in x = -k times x

= the change of x depends only on x

• frist order system and this is linear
• present the value of x against the change of x, we get x as a expendensially decreasing value
• goal is approached at rate determined by k, slow for k near 0, fast for k near 1

First-order system as model of phonological units

• defining phonological units as dynmaicial system
  • laws for fixed values
  • x = phonetic states
  • phonological constonats and time-varying phonetic quantities are in same equation
  • phonetics and phonology does not require any interface
  • equation which includes the phonological primatives and state variables, you can not have one without the other
• a segment is a phonolgical segment, as we see the geasture composed a segment does not really mean they are constrainted at the same time
• tone gestures = syllables and how they are organized, during the interval

• context dependence in real speech
• motion of tongue tip during /d/
  • all trajectories arrived at distance 0

Multiple Dynamical Systems

• Possibilities
  • Sequence of two goal values
  • Overlap in time of two systems

Gesture activation time

• when they are no longer active and govern the behavior of a system only within some fixed epoch of time
• modeling the height of the tongue
  • 0 - 5

Overlap of two systems in time

• most challenging overlap in time
  • two dynamical systems which control the temperature outside and inside the house
    • thermostat
    • chill from outside
• Blending of Overlapping Gestures
  • overlap in time in velar stop and vowels
    • both for the tongue body
    • the vowels and velar stops can’t both achieve their tasks, there is no detendency
    • other cases of overlap, such as overlapping sequences of t and k
    • during the overlapping interval, the articulator syneury achieve the goal without overlapping
    • blending the velar stop and the back vowel
    • In English the stop is still the stop, the blending does not affect the degree but the constriction
    • Blending is a property of these gestures in English
    • phobological property of some language

TaDA: Task Dynamic model of phonetic structure