The application of The NCC-RCS circuit to data storage and data retrieval and massive parallel processing

Introduction:

*Please note, figures are available in download version only.

1. The NCC-RCS may be used as a data storage, data recording, and data retrieval system, and as a parallel processor that operates more like the human brain than a microprocessor-based computer. Two sample applications will be used to demonstrate the use of an RCS-circuit. The first is an example of memory storage and data retrieval associated with navigating through a street map. The second is application of the RCS as a parallel processor used to solve a problem easily solved by the human brain, but solved with greater difficulty by microprocessor based computers.

There are numerous system applications that result from the utilization of multiple RCS’s within a single device, as robotic control devices, as recording devices, and relational computational devices. Multiple applications of the NCC-RCS have been presented by MCon Inc on its web site www.mcon.org. The NCC-RCS has been applied to visual perception, sensorimotor control of the Somatic Motor System, the Design of a volitional, obstacle avoiding multi-tasking robot, and the design of a control system for a robotic arm (Rosen et al 2003a,b,c).

2 The application of the Relational Correlation Sequencer as a memory storage device, stored data retrieval system, and as a Problem Solving computer Processor: Figure 1 is a block diagram of a RCS for a memory storage devise and a memory data retrieval system. In all cases, a trained correlation sequencer always stores within a trained nodal map, the q-field data and associated desirability ratings and/or global step costs at each node of the nodal map. Data processing and data retrieval is achieved with the sequence stepper that generates sequential pq data, for any given initial conditions.

The q-field represents recorded data such as the data recorded on a photograph, world map, or city street map, or the data recorded in an encyclopedia. The p-field represents control signals that allow one to navigate through the q data field.

2.1 The Nodal Map Module is a Data Storage Device: The data entry of the q-field data associated with the p-field, is achieved by forming a trained nodal map module, with the correct values of p,q-values assigned to each node. The processing is performed by the sequence stepper Module by operating on the p, q-values in a predetermined manner.

2.2 The RCS may be used as a data retrieval module: The sequence stepper is programmed to generate a sequence of pq that are determined by the conditional constraints generated by the TT (Task Initiating Trigger) module. For example the initial conditions generated by the TT may be the initial and final nodal position on the nodal map. Then, for every input, q (qo at t=0) associated with the initial node assigned to qo and po, and a desired final destination assigned to pq-final (q-final at t=0). The sequencer Module will form a sequence of suggested pq,

Series #1 pq(t=0), pq(t=1), pq(t=2),..................pq(t=n-1), pqfinal(t=n)]

Such that all the recorded data along the path between q (qo at t=0) and qfinal (t=0) is “recalled or utilized" by the sequence stepper.

2.3 The RCS may be used as a Data Processing Module: In the case of a data processing module, the RCS may be designed to follow the path of a raster scan that covers the nodal region, and processes the q field data structures at every point along the raster scan trajectory

2.4 An example of a data storage and data retrieval RCS: The intelligent map.

A correlation sequencer may be used to store all the data present in geographic map such as the Thomas Street Guide and Directory (Thomas Guide, 1999). Data retrieval may be obtained in the form of navigational paths (Using shortest distance or time criteria) between any starting and destination point. The configuration of the correlation nodal map is selected to be a 2 dimensional surface array located on an orthogonal xy coordinate system, with the nodes located on the intersection points of the xy grid. The map data, or q-field data is represented by a 2 dimensional surface map, such as a street map taken from the Thomas Guide.

2.4.1 Data entry, training or programming the nodal map: (How the map is filled)
1. A set of orthogonal lines, forming a xy grid are drawn on the 2 dimensional surface map (such as a street map taken from the Thomas Guide). This array of grid lines represent a 2 dimensional Euclidean that mirrors the 2 dimensional nodal space located inside the correlation sequencer. The intersection points of the xy grid must bear a one to one correspondence with the nodal points on the correlation nodal map

NOTE: By reference to the grid points on the street map, q-values and p-values are to be assigned in tabular form (as shown below) to each node of the correlation nodal map.

2. The q-data assigned to each node is a desirability-landmine-obstacle factor. For example, a crude mapping may be generated by assigning one of 3 possible q desirability levels to each grid point on the surface map. (The q-level is assigned to the corresponding node in the correlation nodal map)
q-Level 1: Unobstructed passage point. Good transition point.
q-Level 2: Unobstructed, but undesirable passage point. (Such as a parking lot or empty field) The sequencer will not transition to this point if a level 1 point is available; And the preferred transition starting from a level 2 point is to a level 1 point.

q-Level 3: Land mine, or impenetrable obstacle. This point is to be avoided. Any transition to this point triggers an emergency re-training (or re-programming) process.

Note 1. In this case all q (desirability) level assignments are low priority level desirability assignments, so that the pq sequence generated at time t=0 follows a uninterrupted path, that goes around the q-level 2 and q level 3 desirability nodal positions.

Note 2. The resolution of grid points must be such that there are at least 2 or 3 grid points along the width of any street or passage. For example, freeways may be 10 grid points wide, whereas surface streets may be only 3 grid points wide.)

3. The p-vector field consists of transition signals to adjacent nodes. There are 8 possible p vectors assigned to each node. (Up-north, diagonal-northwest, side-west, down-south, diagonal-southwest, side-east, and diagonal-northeast). Note that all 8 may be assigned to each node and we use the q -field data to reject transitions from a given node towards a land mine. However, we can also simplify the operation and training of the sequencer, by assigning to every nodal point, only that p vectors that does NOT lead to a land mine.

An example of pq Table for a map node located at q(initial) equal to (4,3)

4. We generate an index of names assigned to q-nodal positions that correspond to initial starting locations and destination locations that the map user is likely to use. For example a data entry named “LA International Airport”, or “5600 Century Blvd.", would have a set of nodal q-positions assigned to the name. In the case of street guide directory, such as the Thomas Guide, each street listed in the Street Index (Located at the end of the book) would have the nodal coordinates Npq assigned to the name.

5. Two nodal Npq values, entered into the TIT, would be used as the activation data entry, that activates the correlation sequencer to generate a sequence of suggested pq,

Series #1 [pq (t=0), pq(t=1), pq(t=2),................pq(t=n-1), pq-final(t=n)]

Such that the sequence of pq is represented by a navigational path that tells the user how to navigate through the map, between an initial position and the destination position. Where the node Npq (t=0) represents the starting point q (qo at t=0) associated with the node assigned to qo and po; And Npq (t=0) represents the destination location q (q-final at t=0) associated with the node assigned to pq-final (t=0).

2.4.2 Data Storage Capacity. The amount of data stored in each correlation nodal map is equal to the totality of p-values and q-values assigned to each node, summed over all the nodes that make up the correlation nodal map.

For example, a nodal map for one page of a Thomas Guide, requires approximately 20 grid lines per millimeter. A page that is 20x20 centimeters, would therefore require a 200x200 grid lines and a totality of 40,000 nodes. If there are 3 q-values, and 8 p-values assigned to each node, then 2 bits of q data and 3 bits of p-data, would be required for each node. (A total of 5 bits per node). Therefore each nodal map would store 200,000 bits of data. (Approximately 0.2 megabit)

Data retrieval is always obtained in the form of a navigational path that shows the user how to navigate from a starting point, to a destination point, as determined by the Task Selector Task Initiating Trigger (TIT)

3 An Example of a Problem-Solving, Data-Processing RCS Module.

The RCS Module is a relational parallel processor, NOT a computational devise. Therefore it is best suited for solving problems that demonstrate a strong relationship between adjacent data structures. The data structures or relationships are entered into the nodal map module as q-values. The p-values, also entered into the nodal map module, determine a path along which the q-values are to be analyzed. The sequence Stepper Module follows the path determined by the p-values, and analyzes the all the q-values encountered along its path.

3.1 An Example of a RCS solution to the Problem of the “Traveling Salesman”

A regional salesman is required to travel to a large number of towns (over 1000) located within his assigned region. The constraints are that he must visit each town only once, that he must return to his starting point, and that he must find the shortest possible path for the total round trip. The accuracy of the solution depends on the q-value data structures entered into the nodal map, and the p-value raster scan programmed into the sequence stepper module.

3,1,1 The Nodal Map: The configuration of the nodal map is a 2 dimensional grided surface map, with the location of each town entered at its coordinate location. The desirability rating, or global step cost of each town depends on the selected raster scan, and the location of adjacent towns along the raster scan. Figure 2* is an example of a raster scan that may be used to solve the problem for all possible distributions of towns on the nodal map. The scan path must be carefully selected to avoid errors that may occur at the boundaries of the scan. The raster scan was selected with the knowledge that the shortest total round trip distance would be a circular path scan that covers the total region of the nodal map. The raster scan shown in figure 2* moves in a direction along the path of 3 circles, back and forth in a direction perpendicular to the circles, and covers the region of total map. The raster moves in the A direction, turns 90 degrees to the B direction. At the end of the B path the raster checks the B* segment and the C segment, and determines the path along the encountered towns. (Note that the scan is programmed to avoid the possibility of selecting a C path multiple times, rather than a set of successive B, B* paths). A desirability factor may be assigned to each town at the discretion of the designer. Every town that is clearly situated along the raster scan should be assigned a high desirability factor. The desirability factor is useful if there are many cases of towns located along the boundary of the scan. The designer may resolve possible ambiguities either with the assignment of desirability factors or by modifying the scan path to assure that all ambiguities are resolved.

3.1.2 The Sequence Stepper: the Sequence Stepper controls the scan path of the RCS. As the scan progresses every successively encountered town location is entered into the scanner processor. The succession of towns is the ordered travel path of the traveling salesman. As shown in figure 2* , the total distance traveled by the salesman is the sum of the individual distances between adjacent towns.

3.1.3 The Accuracy of the Solution. Analogy to the Human Brain: The accuracy of the solution depends on the distributions of towns along the circular path, the raster scan characteristics or the desirability factors that may be assigned to each town. The RCS processor may be designed to be 100% accurate for a small number of towns, or a large number of towns that are clearly distributed along a circular path. A comparison of the RCS processor with a microprocessor based computer processor may be made by selecting a large random distribution of towns, and comparing the accuracy of the two. However, that is not the comparison of interest in this presentation. The comparison of interest is between the manner that the RCS solves this problem, and the human brain solves this problem. Both are massive parallel processors. Both are relational processors, not calculational processors. Both examine a total pattern and attempt to discover a relational circular path that encompasses the distribution. And finally both suffer from the same set of possible errors

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