International Journal of Pure and Applied Mathematics Volume 118 No. 24 2018 ISSN: 1314-3395 (on-line version) url: http://www.acadpubl.eu/hub/ Special Issue http://www.acadpubl.eu/hub/ Category Theory Infused Probabilistic Policy Learning Based Mission - Aware Middleware Services for Collaborative Communication Ankush Rai 1,R. Jagadeesh Kannan 2 School of Computing Science & Engineering, VIT Chennai, India [email protected], [email protected] 2 May 23, 2018 Abstract During catastrophic incident caused by natural disas- ter, a rescue team composed of combining the workforce of players such as Fire-fighters, Robots and Autonomous Aerial vehicles needs effective cooperation mechanism from team members to save the affected people in order to avoid a major loss. To tackle this challenge of adaptive control and communication b/w team members, the paper proposes Mission-Aware Middleware architecture which is capable of dispensing a dynamic infrastructure for uninterrupted com- munication between the players. The middleware monitors the mission context for any deviation and reconfiguration action is executed if there is an abnormality. Semantic modelling facilitates the middleware to comprehend the dif- ferent mission contexts and Semantic Web Rule Language instructions are used to understand the degree/severity of context. Providing generic resolutions for automatic self- reconfiguration is motivated via rule-based reconfiguration 1 International Journal of Pure and Applied Mathematics Special Issue policies utilizing ontology. Finally, the research work illus- trates different mission contexts and middleware solutions followed by the implementation. Key Words:Semantic model, Reconfiguration, Adap- tive Communication, Ontology, Event-based communica- tion. 1 Introduction Natural disasters bring out a situation in which victims need to be located and saved. To protect endangered people, rescue mission is launched instantly at the intervention area where players such as Autonomous Aerial Vehicle (AAV), Robots and Firefighters work together to speed up the recovery process. In this mission, the play- ers actively communicate, collaborate and coordinate the mission tasks with the help of smart devices. These coordinated activi- ties for the rescue of victims from natural disasters are termed as Crisis Management System (CMS) [1]. In [2], the authors have pro- posed a framework to support multimedia services and each service is offered with various QoS dynamically. A posteriori, the met- rics for resource utilization is calculated and according to that, the system reconfigures by itself. Normally, for an information sys- tem, the reasons for adaptation could be corrective, evolutional or perspective [3]. The work in [4] has developed a middleware that provide constant performance by mediating the resource to the needed applications. The authors in [5] have introduced a context- aware middleware for dynamic environment that uses ontology to describe the semantics of various conceptions. Their model incorpo- rates context-triggered action for real-time ubiquitous application. In [6] it was proposed that the adaptive middleware can ensures context processing functions that can be added dynamically. Here context processing patterns are used to customize attributes and schemes using Domain Specific Language. An architecture com- posed of multi-level context mechanism has been proposed in [7] and it is used for context-specific dissemination protocol. [8] de- scribed a mobile middleware which uses the concept of reflection to improve the construction of adaptive applications. In [9], the au- thors have introduced a holistic approach in which the issue is how the context management should be integrated with an adaptive 2 International Journal of Pure and Applied Mathematics Special Issue middleware. In [10], a middleware supports ubiquitous context- aware services that ease integration while autonomy is addressed at situation modelling components. This research concentrates on event based communication for context retrieval and processing. A new event in the environment forces the middleware to adapt it- self with the new context changes. This reaction by the middleware generally comes under structure and behaviour changes. Structural adaptation refers to reconfigure the functionality of the communi- cation services whereas behavioural adaptation refers to the quality of the communication according to battery level of smart devices. 2 Category Theory Based Rule Gen- eration Here, Ontology is used to represent the architecture models for context reconfigurations. Concepts and relations are derived from the general Collaborative Ontology (GCO); which are instantiated and rules are processed over these ontological instances such as GCO:CommunicationFlow, thus creating the corresponding event based communication that comprises channel administrator, event regulators and event producers. The resultant group of ontologi- cally connected instances outline into a collaboration level graph. Latter, it is converted in form of GraphML language by the uti- lization of XSLT transformation. For refining purposes, the graph grammar construct a valid configuration that contains terminal nodes only (i.e. nodes belonging to the Event Based Communi- cation:EBC ). The research work discusses the following context: Context 1: Firstly, consider a situation from Fig 1 in which an in- vestigator, AAV intends to drop water in a fired area where another investigator, fireman2 is in rescue process. The initial situation at mission and communication levels is represented by ontology in Fig- ure 3(a) as well as by EBC in Figure 3(b). In this particular case, AAV has to be notified to stop dropping water until the fireman2 finishes his task. Another investigator (fireman1), aware of the lo- cation of fireman2, establishes a data flow to its coordinator and the coordinator reports to the supervisor subsequently. As the su- pervisor communicates with AAVs coordinator, a warning message is sent to AAV to stop the action. 3 International Journal of Pure and Applied Mathematics Special Issue Fig. 3. (a) EBC deployment: Initial ontology and (b) EBC deployment: Graph representation But there is no connection between the AAV and fireman2 and AAV has to obtain the supervisors decision through its coordina- tor that will eventually take time. The other solution could be to establish a connection between the AAV and fireman1 through use of a new cooperation flow obtained by running the SWRL rule in decision model. This is represented by reconfiguration rule in Table 1. The configuration and decision rule is modelled based on category theory as a universal modelling language. Here, we have certain observable aspect of the subject which is then formal- ize with observable relationship between them. The configuration rule and decision rule in table 2 is dependent on Boolean value of the variables and the functors connecting them. The whole process of derivating the rule from the given set of player conditions can be derived based on following category modelling. Let p be the set of feature points of a given dataset p1, p2, pn where the model features are embedded based on its{ locality··· where} a func- tion is defined to gauge the closing distance between a category set S= p1(u, v, z), p2(u, v, z) pi(u, v, z)pj(u, v, z) and a set of other points{ in (u,v,z) coordinate··· system. Thus, the} energy function or global distance of a category set is a weighted area where each el- ements of this category sets is weighted in correspondence with its distance to its closest point in the data set Σ F¯(s) = ( dp(x)ds)1/p, 1 p 4 (1) x s ≤ ≤ Z ∈ where d(x) is the distance from x IR3 to its closest point ∈ 4 International Journal of Pure and Applied Mathematics Special Issue in S. We can utilize a detailing the development of a variational formulation of an evolution equation (like that of table 1 and table 2) to construct this minimal forces in a category set to withstand the deformation forces in the model of the given dataset such as twisting and stretching of feature points by plunging on the vital- ity of a decent initial enclosing approximation of the category set. Therefore, at every iteration the evolution equation runs a gradient descent of the energy function in order to get it minimized. At each step, every point x of the category set S(t) at time t evolves towards the interior of the category set, along the normal direction to S(t) at point x, with a displacement from convergent condition that is relative to : d(x)K ∆d(x). n (2) T − −→ where, −→n is the inner normal at x and K is a notation denoting the mean curvature of the category set at x. The tension of the category set is represented byte first term (d(x)K)/T which is non- linear, such that the evolution process requires a certain number of steps before reaching its equilibrium. A consistent condition of this development of evolution equation is a boolean connector in setting of a finite state model which has K = 0 over the place aside at the input data points where d = 0. The better the initial approxima- tion of the category set in successive iteration, lesser the non linear tedious effect of the evolution model is encountered and its defor- mation or restoration property is carried to the consequent itera- tion. The scalibility and degree of freedom of the boolean topology can be modeled with settings of transitional parameters by model- ing its deformation produced by experimentally extracted feature sets. At the equilibrium, it achieves a stable Boolean topology of which belongs to the cued feature data set in form of semantic database ruled by functors defined previously. This is compara- ble to making every point of the category set to evolve along the normal direction to S(t) with a displacement vector from conver- gent model is set in correspondence to the first term∆d(x).n¯ Each point of the subsequent category set likewise fulfills the relentless steady state equation :∆d(x).−→n =o .