II. MANIFOLD SYSTEMS AND DISTRIBUTED INTELLIGENCE

The physical world consists of elements arranged in an n- dimensional (manifold) space. At each spatial point within the space there may exist a dimensional element with a defined set of properties. When the space is seen from the view point of a particular dimensional element, it comprises of other dimensional elements that are interdependent in some way. For example, the temperature of a dimensional element at time t1 may determine the temperatures of its neighbors at time t1+delta.
        A manifold system is a set of interdependent dimensional elements located in manifold space, which interact with each other to perform work of some kind.
        A manifold space consisting of a single point with associated algebraic behavioral model computationally represents a sequential computer. Other simple configurations of manifold systems can be used to represent various forms of parallel computing systems such as SIMD and MIMD. A manifold system can therefore be seen as the most powerful computational behavioral system that can be used to model both simple and complex systems with equal ease.
        A complex intelligent system can be considered as a manifold system comprising of a multitude of planes of dimensional elements, data and relationship elements. A manifold system (Fig. 1) is an autonomous computing system or agent that exists in an operating environment and variably progresses from one manifold frame to another to perform some work, which may involve saving and restoring the state of the system or be mechanical in nature. A manifold frame is a set of manifold planes at a particular instance of manifold time. Each manifold plane consists of a set of manifold elements. A manifold element is a dimensioned entity that supports certain interfaces and can perform some computation, or can learn from its inputs and outputs, or specify a relationship between other manifold elements, or can be a data element, or a composite of these or a plane of manifold elements. Each dimension of a manifold element can have different attributes and possibly exhibit different behavior. Each compute element of a manifold system can be a SISD, SIMD, MISD, MIMD computer. Also, an element of a manifold system can be part of multiple systems. For example, a database component can be part of multiple manifold systems at the same time.

Fig.1 Manifold System

         Each manifold element in a manifold plane is of a specific type. A compute element performs one or more computations possibly in more than one dimension. A cognitive element learns about the mapping between its input and output. A transducer element converts signals from one form to another. A transitive element specifies relationships between other elements of a manifold system. The relationship is specified as a mapping between the signals of the manifold elements. A series of transitive elements allow hierarchical access to data leading to the concept of a telescopic state. A transitive allows a spatial signal to be accessed as a random-access memory object. A temporal signal can be accessed as a stream with a window of size N being loaded or stored on each access. The source (destination) from (to) which the data is streamed into (out of) the manifold system could be a local file system, a network file system, a database, a web location etc. In a transitive, mapping functions can be specified for each signal to transform the input or output data.
        A manifold system operates in a heterogeneous operating environment. The operating environment provides a set of interfaces that allows a manifold system to form and work. A manifold system starts with an initial frame that includes an initial set of manifold planes and an initial manifold configuration model. The configuration model specifies flags which control allocation of resources from the operating environment, scheduling parameters, placement of manifold elements, ratio of hardware and software resources to be used etc. The operation of a manifold system is initiated and continued by means of manifold operations. A forming operation adds or removes manifold elements from the system. A transforming operation adds or removes transitive elements. A projection operation projects one manifold plane to another. A wakeup operation causes the system and its components to resume their operation. A sleep operation causes the system and its components to go to a waiting state. In addition to these, element level operations include (but are not limited to) computing, learning and transducing. Once initiated, a manifold system variably progresses from one manifold frame to another (Fig. 2). The term 'variably progresses' means that each component of a manifold system progresses at its own rate leading to a hierarchical time path within the system.
        A synthetic manifold is a manifold system that is automatically synthesized from an architectural model of the system.

Figure2: Manifold System Progression