Self-referential method and apparatus for creating stimulus representations that are invariant under systematic transformations of sensor states

A method of detecting and processing time-dependent signals from a stimulus source, the method comprising the steps of:

• a) detecting with a detector the signal energy from stimuli from the stimulus source at predetermined time points;
• b) processing the output signals of the detector to produce a sensor state x(t) at each time point tin a collection of predetermined time points, said sensor state x(t) including one or more numbers;
• c) saving in computer memory said output signals of the detector and said sensor states x(t) at each time point of said collection;
• d) determining a reference sensor state x0 in the space of possible sensor states;
• e) determining one or more reference vectors h0a at the reference sensor state x0, the reference vector label a having integer values and each said reference vector having one or more dimensions;
• f) processing at least one of said saved sensor states x(t) and said reference sensor state x0 and said reference vectors h0a to determine one or more preferred vectors ha at each sensor state x in a predetermined collection of sensor states, each said preferred vector having one or more dimensions;
• g) processing at least one of said saved sensor states x(t) and said reference sensor state x0 and said reference vectors h0a to determine paths in the space of possible sensor states, each said path connecting the reference sensor state x0 to a sensor state of interest in a predetermined collection of sensor states;
• h) determining the representation s = ∫ x 0 x ⁢ δ ⁢ ⁢ s
• of each sensor state x in a predetermined collection of sensor states, said integral being along the path connecting x0 to x, δs at each sensor state on said path satisfying δ ⁢ ⁢ x = ∑ a = 1 , … , N ⁢ h a ⁢ δ ⁢ ⁢ s a ,
• δx being a small displacement along the path at said sensor state on said path, ha denoting the preferred vectors near said sensor state on said path, and N being the number of dimensions of the space of possible sensor states;
• i) saving in computer memory said sensor states in said predetermined collection of sensor states and said representations of the sensor states in said predetermined collection of sensor states;
• and
• j) processing at least one of the saved output signals of the detector and the sensor states in said predetermined collection and corresponding representations to determine aspects of the nature of the stimuli producing the sensor states in said predetermined collection.

A method of detecting and processing time-dependent signals from a stimulus source, the method comprising the steps of:

• a) detecting with a detector the signal energy from stimuli from said stimulus source at predetermined time points;
• b) processing the output signals of the detector to produce a sensor state x(t) at each time point tin a collection of predetermined time points, said sensor state x(t) including one or more numbers;
• c) saving in computer memory said output signals of the detector and said sensor states x(t) at each of said predetermined time points;
• d) determining a reference sensor state x0 in the space of possible sensor states;
• e) determining one or more preferred vectors ha at each sensor state x in a predetermined collection of sensor states by processing a predetermined collection of said saved sensor states, the sensor states in said predetermined collection being in a small neighborhood of said sensor state x and said preferred vectors having one or more dimensions;
• f) processing at least one of said reference sensor state x0 and said preferred vectors ha to determine paths in the space of possible sensor states, each said path being between the reference sensor state x0 and a sensor state x in a predetermined collection of sensor states;
• g) determining the representation s = ∫ x 0 x ⁢ δ ⁢ ⁢ s
• of each sensor state x in a predetermined collection of sensor states, said integral being along said path connecting x0 to x, δs at each sensor state on said path satisfying δ ⁢ ⁢ x = ∑ a = 1 , ⁢ … ⁢ , N ⁢ h a ⁢ δ ⁢ ⁢ s a ,
• δx being a small displacement along the path at said sensor state on said path, ha denoting the preferred vectors near said sensor state on said path, and N being the number of dimensions of the space of possible sensor states;
• h) saving in computer memory said sensor states in said predetermined collection of sensor states and said representations of the sensor states in said predetermined collection of sensor states;
• and
• i) processing at least one of the saved output signals of the detector and the sensor states in said predetermined collection and corresponding representations to determine aspects of the nature of the stimuli producing the sensor states in said predetermined collection.

A method of detecting and processing time-dependent signals from a stimulus source, the method comprising the steps of:

• a) detecting with a detector the signal energy from stimuli from the stimulus source at predetermined time points;
• b) processing the output signals of the detector to produce a sensor state x(t) at each time point tin a collection of predetermined time points, said sensor state x(t) including one or more numbers;
• c) saving in computer memory said output signals of the detector and said sensor states x(t) at each of said predetermined time points;
• d) determining a reference sensor state x0 in the space of possible sensor states;
• e) determining one or more reference vectors h0a at the reference sensor state x0, each said reference vector having one or more dimensions;
• f) determining a parallel transport operation at each sensor state x in a predetermined collection of sensor states by processing a predetermined collection of said saved sensor states, the saved sensor states in said predetermined collection being in a small neighborhood of said sensor state x and said parallel transport operation transporting vectors across the space of possible sensor states near x;
• g) processing at least one of said saved sensor states x(t), said reference sensor state x0, said reference vectors h0a and said parallel transport operation to determine one or more preferred vectors ha at each sensor state x in a predetermined collection of sensor states, each said preferred vector having one or more dimensions;
• h) processing at least one of said saved sensor states x(t), the reference sensor state x0, said reference vectors h0a and said parallel transport operation to determine paths across the space of possible sensor states, each said path being between the reference sensor state x0 and a sensor state x in a predetermined collection of sensor states;
• i) determining the representation s = ∫ x 0 x ⁢ δ ⁢ ⁢ s
• of each sensor state x in a predetermined collection of sensor states, said integral being along said path connecting x0 to x, δs at each sensor state on said path satisfying δ ⁢ ⁢ x = ∑ a = 1 , … ⁢ , ⁢ N ⁢ h a ⁢ δ ⁢ ⁢ s a ,
• δx being a small displacement along the path at said sensor state on said path, ha denoting the preferred vectors near said sensor state on said path, and N being the number of dimensions of the space of possible sensor states;
• j) saving in computer memory said sensor states in said predetermined collection of sensor states and said representations of the sensor states in said predetermined collection of sensor states;
• and
• k) processing at least one of the saved output signals of the detector and the sensor states in said predetermined collection and corresponding representations to determine aspects of the nature of the stimuli producing the sensor states in said predetermined collection.

A method of detecting and processing time-dependent signals from a stimulus source, the method comprising the steps of:

• a) detecting with a detector the signal energy from stimuli from the stimulus source at predetermined time points;
• b) processing the output signals of the detector to produce a sensor state x(t) at each time point t in a collection of predetermined time points, said sensor state x(t) including one or more numbers;
• c) saving in computer memory said output signals of the detector and said sensor states x(t) at each of said predetermined time points;
• d) determining a reference sensor state x0 in the space of possible sensor states;
• e) determining one or more reference vectors h0a at the reference sensor state x0, each said reference vector having one or more dimensions;
• f) determining a metric operation at each sensor state x in a collection of predetermined sensor states by processing a predetermined collection of said saved sensor states, the saved sensor states in said predetermined collection being in a small neighborhood of said sensor state x and said metric operation assigning lengths to vectors near x;
• g) determining a parallel transport operation at each sensor state x in a predetermined collection of sensor states, said parallel transport operation transporting vectors across the space of possible sensor states near x;
• h) processing at least one of said saved sensor states x(t), said reference sensor state x0, said reference vectors h0a, said metric operation and said parallel transport operation to determine one or more preferred vectors ha at each sensor state x in a predetermined collection of sensor states, each said preferred vector having one or more dimensions;
• i) processing at least one of said saved sensor states x(t), said reference sensor state x0, said reference vectors h0a, said metric operation and said parallel transport operation to determine paths across the space of possible sensor states, each said path being between the reference sensor state x0 and a sensor state x in a predetermined collection of sensor states;
• j) determining the representation s = ∫ x 0 x ⁢ δ ⁢ ⁢ s
• of each sensor state x in a predetermined collection of sensor states, said integral being along said path connecting x0 to x, δs at each sensor state on said path satisfying δ ⁢ ⁢ x = ∑ a = 1 , … ⁢ , N ⁢ h a ⁢ δ ⁢ ⁢ s a ,
• δx being a small displacement along the path at said sensor state on said path, ha denoting the preferred vectors near said sensor state on said path, and N being the number of dimensions of the space of possible sensor states;
• k) saving in computer memory said sensor states in said predetermined collection of sensor states and said representations of the sensor states in said predetermined collection of sensor states;
• and
• l) processing at least one of the saved output signals of the detector and the sensor states in said predetermined collection and corresponding representations to determine aspects of the nature of the stimuli producing the sensor states in said predetermined collection.

A method of translating stimuli from one stimulus source S into stimuli from another stimulus source {overscore (S)}, the method comprising the steps of:

• a) detecting with a detector the signal energy from stimuli from said source S at predetermined time points;
• b) processing the output signals of the detector to produce a sensor state x(t) at each time point tin a collection of predetermined time points, said sensor state x(t) including one or more numbers;
• c) saving in computer memory said sensor state x(t) at each time point in said collection;
• d) processing said saved sensor states x(t) to produce a representation of each sensor state x of a predetermined collection of sensor states in the space of possible sensor states, each said representation including one or more numbers and said processing having the property that the representation of a sensor state x determined by processing a time series of sensor states x(t) is approximately the same as the representation of the transformed sensor state x′=x′(x) determined by processing the transformed time series of sensor states x′(t)=x′[x(t)], x′(x) being an invertible transformation on the space of possible sensor states;
• e) using a computer to save said sensor states x in said predetermined collection of sensor states and to save said representations of the sensor states in said predetermined collection of sensor states;
• f) detecting with a detector the signal energy from stimuli from said source {overscore (S)} at predetermined time points;
• g) processing the output signals of said detector to produce a sensor state {overscore (x)}(t) at each time point t in a collection of predetermined time points, said sensor state {overscore (x)}(t) including one or more numbers;
• h) saving in computer memory said sensor state {overscore (x)}(t) at each time point in said collection;
• i) processing said saved sensor states {overscore (x)}(t) to produce a representation of each sensor state {overscore (x)} of a predetermined collection of sensor states in the space of sensor states produced by possible stimuli from source {overscore (S)}, each said representation including one or more numbers;
• j) using a computer to save said sensor states {overscore (x)} in said predetermined collection of sensor states and to save said representations of the sensor states in said predetermined collection of sensor states:
• and
• k) determining a time series of stimuli from said stimulus source S that produces a time series of sensor states, and determining a time series of stimuli from said stimulus source {overscore (S)} that produces a time series of sensor states, the sensor state at each time in said time series of sensor states produced by said stimuli from S having the same representation as the sensor state at the same said time in the time series of sensor states produced by said stimuli from {overscore (S)}.

A method of communicating information from a transmitter to a receiver, the method comprising the steps of

• a) determining information to be communicated from the transmitter to the receiver, said information consisting of a collection of number arrays, each said number array including one or more numbers;
• b) saving in computer memory said information;
• c) determining a transmitter state x (t) at each time point t in a predetermined collection of time points, x(t) at each said time point being one or more numbers, the processing of said time series of transmitter states determining a representation of each transmitter state in a predetermined collection of said transmitter states, the representations of the transmitter states in a predetermined collection of said transmitter states being said information, each said representation including one or more numbers and said processing having the property that the representation of a transmitter state x determined by a time series of transmitter states x(t) is approximately the same as the representation of the transformed transmitter state x′=x′(x) determined by the transformed time series of transmitter states x′(t)=x′[x(t)], x′(x) being an invertible transformation on the space of possible transmitter states;
• d) saving in computer memory said transmitter states x(t) at each time point t in said predetermined collection of time points;
• e) using the transmitter to transmit energy, said energy transmission being controlled by said determined time series of transmitter states;
• f) detecting with a detector of the receiver energy transmitted by the transmitter at a set of predetermined time points;
• g) processing the output of the detector of the receiver to produce a time series of receiver states {overscore (x)}(t) at predetermined time points t, {overscore (x)}(t) at each said time point t being one or more numbers;
• h) saving in computer memory said receiver states {overscore (x)}(t) at each of said predetermined time points t;
• i) processing said saved receiver states {overscore (x)}(t) to produce a representation of each saved receiver state in a predetermined collection of said saved receiver states;
• j) saving in computer memory said representations of the saved receiver states in said collection;
• k) processing the saved representations to determine said information;
• and
• l) saving in computer memory said information.