In search of a cyberspace … to launch                         1
biologically-inspired advanced computing strategies:
     ...
2
Biologically-inspired computing (BIC)…?

Simply, known as bio-inspired computing (or just bio-computing),
BIC denotes…
 ...
In search of a cyberspace …                         3
…to launch biologically-inspired advanced computing
strategies….

Wh...
4

 Now what is “digital ecology”?

Digital ecology (DE) is a neoteric terminology mostly
applied to the evolution of soci...
5

Now what is “digital ecology”? … Continued

In short, DE refers to an environment, which is:
        - open in visibly ...
6
“Digital ecology” …a cyberspace to launch
biologically-inspired advanced computing strategies

Digital ecology enables a...
7
Biologically-inspired computing (BIC)…More

     BIC bears the perspectives of cybernetics in the
     computational eff...
Biologically-inspired   computing   (BIC)……potential 8
applications in:

  DNA computation
  nanofabrication
  storage dev...
9
Biologically-inspired computing (BIC)…


   BIC… its scope
      Enabling new themes of computing technologies
   and fr...
10
 Biologically-inspired computing (BIC)…
               … BIC and its cousins: Areas of emphasis


Genetic algorithms (G...
11

BIC and its cousins: Areas of emphasis… continued

    Biodegradability prediction ↔ Accurate sequence
details and gen...
12

BIC and its cousins: Areas of emphasis… continued

Cellular automata ↔ Cellular automaton is a discrete
model of a reg...
13

BIC and its cousins: Areas of emphasis… continued

Emergent systems ↔ The way complex systems and
patterns arise out o...
14
BIC and its cousins: Areas of emphasis… continued


Neural networks ↔ Biological neural networks are made up of
real bi...
15
BIC and its cousins: Areas of emphasis… continued

  Artificial life ↔ Commonly known as Alife or alife, it
depicts a f...
16
BIC and its cousins: Areas of emphasis… continued

 Artificial immune systems (AIS) ↔ Abstracting and
mapping the struc...
17
BIC and its cousins: Areas of emphasis… continued

Rendering (computer graphics) ↔ a process of generating
an image fro...
18
BIC and its cousins: Areas of emphasis… continued

Lindenmeyer systems ↔ Computing self-organization in
the context of ...
19
BIC and its cousins: Areas of emphasis… continued

Communication networks and protocols ↔ Analogy
between viral dynamic...
20
BIC and its cousins: Areas of emphasis… continued


Membrane computers ↔ The membrane computing is
an effort to replica...
21
BIC and its cousins: Areas of emphasis… continued

Excitable media ↔ An excitable medium is a nonlinear
dynamical syste...
22
BIC and its cousins: Areas of emphasis… continued

Sensor networks ↔ Sensor networks are a sensing,
computing and commu...
23
BIC and its cousins: Areas of emphasis… continued


DNA computing ↔ a computing strategy that uses
interdisciplinary as...
24
BIC: CAN IT BE COMPREHENDED IN A UNIFIED
CYBERSPACE?

Biologically-inspired computing will be “wonderful tools,
(and) w...
25
BIC: CAN IT BE COMPREHENDED IN A UNIFIED
CYBERSPACE? …Continued

In modern perspective, in sheltering the BIC within th...
26
BIC: CAN IT BE COMPREHENDED IN A UNIFIED
CYBERSPACE? …Continued

Can the underlying abstract of a unified cyberspace of...
27
BIC: CAN IT BE COMPREHENDED IN A UNIFIED
CYBERSPACE? …Continued

Digital ecosystems have been conceived in “the image o...
28
    BIC: A COMPLEX SYSTEM THAT FOLLOWS
      A DIGITAL ECOSYSTEM ONTOLOGY...


… a possible suite for modeling the comp...
29
    BIC: SPELT IN THE ONTOLOGY OF DIGITAL
          ECOLOGY – AN EXAMPLE…ANN

{Species}     ⇒ {Domain, Task, Profit, Ru...
30
BIC: SPELT IN THE ONTOLOGY OF DIGITAL
 ECOLOGY – AN ANN EXAMPLE…continued



                                          ...
BIC: SPELT IN THE ONTOLOGY OF DIGITAL ECOLOGY                              31
                 – AN ANN EXAMPLE…continued
...
BIC: SPELT IN THE ONTOLOGY OF DIGITAL ECOLOGY                    32
                 – AN ANN EXAMPLE…continued
(B)      S...
BIC: SPELT IN THE ONTOLOGY OF DIGITAL ECOLOGY                       33
                – AN ANN EXAMPLE…continued
Computat...
BIC: SPELT IN THE ONTOLOGY OF DIGITAL ECOLOGY                    34
                – AN ANN EXAMPLE…continued
Subfunction...
35A


REFERENCES

[1]   N. Forbes, Biologically inspired computing, Computing in Science and Engineering,
      November/D...
35B
    In search of a cyberspace … to launch BIC…
                     Conclusions

This study attempts to portray biolog...
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In search of a cyberspace …to launch Biologically-Inspired Advanced Computing Strategies: A Digital Ecology Solution

  1. 1. In search of a cyberspace … to launch 1 biologically-inspired advanced computing strategies: a digital ecology solution Dr. Perambur S. Neelakanta, Ph.D., C. Eng., Fellow IEE Professor Department of Electrical Engineering College of Engineering and Computer Science Florida Atlantic University Boca Raton, Florida 33431, USA neelakan@fau.edu Invited Lecture International Conference on Advanced Computing (ICAC 2009), August 7-8, 2009, Tiruchirappalli, Tamil Nadu, India 1
  2. 2. 2 Biologically-inspired computing (BIC)…? Simply, known as bio-inspired computing (or just bio-computing), BIC denotes… “a field of study that loosely knits together subfields related to the topics of connectionism, social behavior and emergence. It is often closely related to the field of artificial intelligence, as many of its pursuits can be linked to machine learning. It relies heavily on the fields of biology, computer science and mathematics…”. In nut-shell, BIC is the use of computers to model nature, and simultaneously the study of nature to improve the usage of computers. It is, therefore a major subset of natural computation. 2
  3. 3. In search of a cyberspace … 3 …to launch biologically-inspired advanced computing strategies…. Whether the strategies of BIC comes within the purview of information technology (IT)-oriented considerations is still unclear and remains as an open-question. This paper heuristically searches for a cyberspace wherein BIC efforts can be viewed cohesively in the broader sense of IT-paradigms. Hence, attempted here is an exploration to cast comprehensively the universe of BIC in the domain of so-called… “digital ecology” (DE) Now what is “digital ecology”? 3
  4. 4. 4 Now what is “digital ecology”? Digital ecology (DE) is a neoteric terminology mostly applied to the evolution of social and civic ecosystem commensurate with modern IT perspectives Its usage in modern context includes the plethora of (i) entertainment media ecology, (ii) the entirety of computing ambient and (iii) the environment of communication networks. In each of this gamut, the transfer of information (or informatics) negotiates a sizable cardinality of stochastically interacting stochastically interacting subsets that structuralize a complex open-source network and computational environment. 4
  5. 5. 5 Now what is “digital ecology”? … Continued In short, DE refers to an environment, which is: - open in visibly portraying the interactions involved; - loosely-coupled in mediating the open relationships between species; - domain-clustered in creating a field of balanced common interest; - demand-driven in conglomerating the species as interest groups; - self-organizing in autonomous decision-making; and, - agent-based in rendering an ambient of synergism between human and machines where each agent participates proactively in the computational endeavors as well as in the information transfers akin to the species of biological ecosystem. 5
  6. 6. 6 “Digital ecology” …a cyberspace to launch biologically-inspired advanced computing strategies Digital ecology enables a unified presentation of computational tools and algorithmic endeavors modern and advanced computing schemes) in an IT-specific domain. So attempted here in an ambient of BIC efforts towards… … constructing a DE platform to support BIC concepts As an illustrative example, the strategy of artificial neural networks (ANN) mapped in terms of relevant ontological norms of digital ecology is presented. 6
  7. 7. 7 Biologically-inspired computing (BIC)…More BIC bears the perspectives of cybernetics in the computational efforts involving … simulated annealing artificial neural networks genetic algorithms DNA and molecular computing biological ecology etc. Thus, the field of BIC is highly multidisciplinary, attracting a host of disciplines… - …computer science, molecular biology, genetics, engineering, mathematics, physics, chemistry and others. 7
  8. 8. Biologically-inspired computing (BIC)……potential 8 applications in: DNA computation nanofabrication storage devices sensing healthcare basic scientific research – for example … …providing biologists with an IT-oriented paradigm to look at how cells “compute” or process the information …helping computer scientists and engineers to construct algorithms based on natural systems, such as evolutionary and genetic algorithms 8
  9. 9. 9 Biologically-inspired computing (BIC)… BIC… its scope Enabling new themes of computing technologies and fresh areas of computer science using biology or biological processes as metaphor/inspiration Expanding information science concepts and tools to explore biology from a different theoretical perspective. BIC as such, however, does not include in its scope the framework of, (i) the general use of computers; (ii) the strategies of computational analyses, and/or (iii) data management in biology - for example, bioinformatics or computational biology. 9
  10. 10. 10 Biologically-inspired computing (BIC)… … BIC and its cousins: Areas of emphasis Genetic algorithms (GAs) ↔ Follows natural evolution with the rules of selection, recombination, reproduction, mutation and more recently transposition. Such simple rules of evolution in complex organisms are observed and adopted in GAs constituting BIC approach. Artificial Intelligence (AI) ↔ Traditional AI is the intelligence of machines towards the design of intelligent agents. The way in which BIC differs from traditional AI is in how it takes a more evolutionary approach to learning, as opposed to what could be described as 'creationist' methods used in traditional AI. In this perspective AI inclines towards BIC. 10
  11. 11. 11 BIC and its cousins: Areas of emphasis… continued Biodegradability prediction ↔ Accurate sequence details and genetic information vis-à-vis biodegradation are essential for assessing molecular basis of enzyme specificity, their catalytic mechanism, the evolutionary origin of related metabolism and proliferation of such activities in the environment. (Although some basic formalization toward useful tools as a predictor of chemical/biodegradability is feasible, the absence of information at the sequence level of proteins etc. are imminently required for systematic studies of biodegradation. This is facilitated via biocomputing). 11
  12. 12. 12 BIC and its cousins: Areas of emphasis… continued Cellular automata ↔ Cellular automaton is a discrete model of a regular grid of cells, each in one of a finite number of states. Relevant evolutionary computation programs with cellular arrays in decentralized platforms (where the information processing occurs in the form of global and local pattern dynamics) lead to emergent computation (expressed in terms of GAs) and adopted to evolve patterns in cellular automata in the perspectives of BIC. 12
  13. 13. 13 BIC and its cousins: Areas of emphasis… continued Emergent systems ↔ The way complex systems and patterns arise out of a multiplicity of relatively simple interactions as in biological systems is specified by “emergence”. It has been the holy grail of BIC. Emergence is something like a macro phenomenon that appears as a by-product of a (generally but not always large) collection of micro phenomena. 13
  14. 14. 14 BIC and its cousins: Areas of emphasis… continued Neural networks ↔ Biological neural networks are made up of real biological neurons that are connected or functionally related in the peripheral nervous system or the central nervous system. Artificial neural networks (ANNs) are composed of simulated neuron units made “in the image of real neurons”. By interconnecting “artificial neurons” – a programming strategy is set up that constructs a massively parallel connectivity, mimicing the biological neurons. ANN with its interconnected structure of artificial neuron uses a paradigm of mathematical or computational model for information processing based on a connectionist approach to computation adaptively to changes in external or internal information via biological-inspiration. 14
  15. 15. 15 BIC and its cousins: Areas of emphasis… continued Artificial life ↔ Commonly known as Alife or alife, it depicts a field of study and an associated art form which examine systems related to life, its processes, and its evolution through simulations using computer models, robotics, and biochemistry. There are three major versions of alife, based on their approaches: soft- from software; hard- from hardware; and wet- from biochemistry. Artificial life imitates traditional biology in recreating biological phenomena. Essentially, the term "artificial life" is often used to specifically refer to soft alife. 15
  16. 16. 16 BIC and its cousins: Areas of emphasis… continued Artificial immune systems (AIS) ↔ Abstracting and mapping the structure and function of an immune system to a computational set of frameworks so as to investigate the application of such systems towards solving computational problems with the aid of mathematics, engineering, and information technology. AIS is a sub-field of computational intelligence, BIC, and natural computation, with a focus on machine learning. It can be said to belong the broader field of AI. Further, AIS are adaptive systems, inspired by theoretical immunology and observed immune functions, principles and models, which are applied to problem solving. 16
  17. 17. 17 BIC and its cousins: Areas of emphasis… continued Rendering (computer graphics) ↔ a process of generating an image from a model (description of 3D objects in a strictly defined language or data structure) using computer programs. It contains features of geometry, viewpoint, texture, lighting, and shading information in digital image or a raster graphics image format. The term rendering in computing context is an analogy of an "artist's rendering" of a scene. (In biological context, rendering simply refers to patterning and rendering of animal skins, bird feathers, mollusk shells and bacterial colonies) 17
  18. 18. 18 BIC and its cousins: Areas of emphasis… continued Lindenmeyer systems ↔ Computing self-organization in the context of environmentally sensitive growth and/or development modeling behavior and visualization of cells of plants/plant structures: - Mathematical, spatial models that treat plant geometry as a continuum or as discrete components in space. - Developmental models that describe form as a result of growth in terms of growth influencing variables - Simulations produce numerical output, which can be complemented by rendered images and animations for the purpose of easy comprehension 18
  19. 19. 19 BIC and its cousins: Areas of emphasis… continued Communication networks and protocols ↔ Analogy between viral dynamics in humans and in computers is useful in assessing infectious disease epidemiology on human social networks versus communication in wireless networks Epidemiology as a metaphor may hold insights into communication networks. New paradigms of mathematics and methodologies sought towards linking epidemiology and the spread of disease are generalized biological-inspirations seen toward modeling modern communication systems. 19
  20. 20. 20 BIC and its cousins: Areas of emphasis… continued Membrane computers ↔ The membrane computing is an effort to replicate organic structures of the brain and the intra-membrane molecular processes in the living cells onto silicone. This is to create indeterminate outcome machines that are capable of learning through external stimuli. Such membrane computers will be a interesting technology when it is finally developed, say in creating artificial brains and teaching machines… a dream sought in BIC. 20
  21. 21. 21 BIC and its cousins: Areas of emphasis… continued Excitable media ↔ An excitable medium is a nonlinear dynamical system that has the capacity to propagate a wave of some description, experiencing an elapsed time (refractory time). A forest is an example of an excitable medium: That is, when a wildfire burns through the forest, no fire can return to a burnt spot until the vegetation has gone through its refractory period and re-grown. BIC implications are related to… Pathological activities in the heart and brain can also be modeled as excitable media. In cellular automata the state of a particular cell in the next time step depends on the state of the cells around it--its neighbors-at the current time. 21
  22. 22. 22 BIC and its cousins: Areas of emphasis… continued Sensor networks ↔ Sensor networks are a sensing, computing and communication infrastructure that allows to instrument, observe, and respond to phenomena in the natural environment, and in the physical as well as cyber infrastructure. Akin to biological systems that present remarkable adaptation, reliability, and robustness in various environments, even under hostility (in a distributed and self-organized way), they provide useful resources for designing the dynamical and adaptive routing schemes of wireless mobile sensor networks. 22
  23. 23. 23 BIC and its cousins: Areas of emphasis… continued DNA computing ↔ a computing strategy that uses interdisciplinary aspects of DNA, biochemistry and molecular biology, instead of the traditional silicon-based computer technologies. It is a molecular computing stategy similar to parallel computing and employs many different molecules of DNA to try many different information processing at once. Mostly, DNA computers are faster and smaller than any other computer built so far. However, unlike quantum computing, in DNA machines to solve extremely large EXPSPACE problems, the amount of DNA required is too large to be practical. 23
  24. 24. 24 BIC: CAN IT BE COMPREHENDED IN A UNIFIED CYBERSPACE? Biologically-inspired computing will be “wonderful tools, (and) will eventually lead the way to a “molecular revolution,” which ultimately will have a very dramatic effect on the world”. As such biocomputing, in general has the potential to be a very powerful tool. BIC shouldering the marvels of computation per se is not the traditional “computing with silicon-chips”, but in essence, it. It relies on information-science (technology?) and borrows the metaphors from biological sciences. The query that lingers is whether the various avenues of BIC can be comprehended in a unified cyberspace. If so, how? 24
  25. 25. 25 BIC: CAN IT BE COMPREHENDED IN A UNIFIED CYBERSPACE? …Continued In modern perspective, in sheltering the BIC within the scope of IT-oriented considerations is still unclear and remains as an open-question. Suppose BIC-related computational tools and algorithmic endeavors are to be viewed in an IT-specific cyberspace. It is then necessary to seek a platform that permits a cohesive activity of a complex system where biological evolutionary principles are invoked in terms of interacting species having self-organizing features. Further overlaid thereon are feasible aspects of informatics and paradigms of computation. 25
  26. 26. 26 BIC: CAN IT BE COMPREHENDED IN A UNIFIED CYBERSPACE? …Continued Can the underlying abstract of a unified cyberspace of BIC be specified in the so-called digital ecology (DE) platform towards a compatible solution? DE is “the medley of digital code and environmentalism” that prescribes information ecosystems constituted by information flows being processed through various mediating species across biological ecology. In this perspective, considering the intersecting aspects of a complex system and ecological prescriptions, models of BIC can be projected in the realm of digital ecosystem ontology. 26
  27. 27. 27 BIC: CAN IT BE COMPREHENDED IN A UNIFIED CYBERSPACE? …Continued Digital ecosystems have been conceived in “the image of” complex biological ecology expressed in terms of "digital environment" ontology and is populated by "digital species" that mediate massive information exchange. Compared with natural ecosystems where species may follow adaptation to local conditions, in digital ecosystem, new digital species continuously emerge and they help cleanse the ecosystem (for example supplanting older scheme of computation with an advanced one). Digital ecosystems thus capture the essence of classical, complex ecological environment in nature, where organisms cohesively constitute a dynamic, self-organizing and interrelated complex ecosystem conserving and utilizing the environment of its resources. 27
  28. 28. 28 BIC: A COMPLEX SYSTEM THAT FOLLOWS A DIGITAL ECOSYSTEM ONTOLOGY... … a possible suite for modeling the complex system profile of BIC is to apply DE considerations identified in terms of certain DE ontology nomenclature: {Species} ⇔ {Domain, Task, Profit, Rule, Role, Supplier, Requester, Available Service, Requested Service} {Environment} ⇔ {Technology, Service, (Species), Open-environment, Loosely-coupled environment, Demand-driven environment, Domain-clustered environment} 28
  29. 29. 29 BIC: SPELT IN THE ONTOLOGY OF DIGITAL ECOLOGY – AN EXAMPLE…ANN {Species} ⇒ {Domain, Task, Profit, Rule, Role, Supplier, Requester, Available Service, Requested Service} {Environment} ⇒ {Open, loosely-coupled, demand- driven; domain-clustered} ⇑ ⇓ {Interacting neurons, layered ANN architecture, massively parallel computation, output/goal-realization, nonlinear processing of collective information, supervised learning; output validation via teacher value, input ambient, user (programmer), convergence of the output against learned pattern, testing an input set against learned pattern} 29
  30. 30. 30 BIC: SPELT IN THE ONTOLOGY OF DIGITAL ECOLOGY – AN ANN EXAMPLE…continued Teacher Input Hidden Input layer layers Weights Weights Ouput Ti zi layer + Σ – Inputs Oi yi = f(xi) Σ Oi = KΣzi A neuronal Weight vector εi = (Oi, Ti) unit adjustments Error 30
  31. 31. BIC: SPELT IN THE ONTOLOGY OF DIGITAL ECOLOGY 31 – AN ANN EXAMPLE…continued (A) Subfunction PeudoCode I on: DEFINE_(ANN-DE)_SPECIES & ENVIRONMENT–ONTOLOGY: Initialize ⇒ FOR Complex ANN system: Neurons/neuronal units CALL: DEFINE_ENVIRONMENT: ANN DEFINE_SPECIES: Neuronal units ⇒ comesFrom -domain ANN architecture DEFINE_DOMAIN: ⇒ common field for all species DEFINE_TASK carriesOut goal-oriented tasks Goal: converged ANN output DEFINE_PROFIT relatesTo task - computational advantage isDrivenBy species: neurons DEFINE_RULE:-follows nonlinear norms regulating species collectively DEFINE_ROLE- role of interaction with other Species (neurons) defineBy weight-modification, inter-play of input data at the hidden layer(s) CALL: DEFINE_SUPPLIER CALL: DEFINE_REQUESTER 31
  32. 32. BIC: SPELT IN THE ONTOLOGY OF DIGITAL ECOLOGY 32 – AN ANN EXAMPLE…continued (B) Subfunction Code II on: ENVIRONMENT ontology - Initialize: Inputs: Training and prediction sets: DEFINE_DIGITAL_ECOSYSTEM: ANN DEFINE_ENVIRONMENT ⇒ architecture items of SPECIES DEFINE_TECHNOLOGY of the Environment isSupportedBy INPUTS and Teacher values Connectivity isProvidedBy SPECIES GOTO: SPECIES DEFINE_SERVICES Error feedback –backpropagation etc. Weighting is rendered on SPECIES/Interconnected DEFINE_ENVIRONMENT set:{open, demand-driven, agent-based, self- organizing, domain-clustered, loosely-coupled}-ANN architecture 32
  33. 33. BIC: SPELT IN THE ONTOLOGY OF DIGITAL ECOLOGY 33 – AN ANN EXAMPLE…continued Computation of: ANN Output Inputs to: { Species and Environment}: ←DOMAIN data set {details on neurons, layers, logistic function, momentum function, learning coefficient} ← ENVIRONMENT data set {Training data set to visible neurons, teacher values} ← TASK data set {Defining error, type of feedback etc.} ← RULE data set {Stop criterion on iterations, tuning the weighting coefficients} ← ROLE data set {Adjusting the nonlinearity, momentum and learning towards convergence} ← REQUESTER data set {Input data to visible neurons, teacher set}} ← SUPPLIER data set {ANN user} Compute I: Related subfunctions towards output Oi(t) ← REQUESTER observation at the output node Compute II: IF computed error is too high, ← THEN do iteration ← OR ELSE, GOTO Compute I END 33
  34. 34. BIC: SPELT IN THE ONTOLOGY OF DIGITAL ECOLOGY 34 – AN ANN EXAMPLE…continued Subfunction Codes on: SUPPLIER and REQUESTER Subfunction Code IIA Subfunction Code IIB on: on: REQUESTER SUPPLIER suite of suite of SPECIES ontology SPECIES ontology DEFINE_ROLE Convergence toward DEFINE_ROLE objective function DEFINE_SUPPLIER DEFINE_REQUESTER -ANN user ⇒ ANN output DEFINE_REQUESTED_ DEFINE_AVAILABLE_ SERVICE SERVICE ⇒ Convergence - ANN capability towards the goal sought 34
  35. 35. 35A REFERENCES [1] N. Forbes, Biologically inspired computing, Computing in Science and Engineering, November/December 2000, vol. 2(6), 84-87 [2] H. Boley and E. Chang, “Digital ecosystem: Principles and semantics,” in 2007 Inaugural IEEE International Conference in Digital Ecosystems and Technologies (IEEE DEST 2007), 2007, 1-4244-047003/07. [3] H. Dong, F. K. Hussain, and E. Chong, “Ontology-based digital ecosystem conceptual representation,” in Proceedings of the Third International Conference on Automatic and Autonomous Systems (ICAS’07), 2007, 0-7695-2859-5/07 [4] P. S. Neelakanta and R. C. Tourinho, Modeling an It-centric complex system via digital ecology concepts, Presented in Third IEEE International Conference on Digital Ecosystems and Technologies (IEEE-DEST 2009), Istanbul, Turkey, 31 May 2009 – 3 June 2009) [5] G. W. Flake: The Computational Beauty of Nature, MIT Press. Boston, MA: 2000 [6] P.S. Neelakanta and D. De Groff, Neural Network Modeling: Statistical Mechanics and Cybernetic Perspectives, CRC Press, Boca Raton, FL, 1994. [7] P.S. Neelakanta, “Dynamics of neural learning in the information theoretic plane,” Chapter 5, Information-Theoretic Aspects of Neural Networks (Editor: P.S. Neelakanta), CRC Press, Boca Raton, FL, 1999. [8] L. M. Adleman, Computing with DNA, Scientific American, August 1998, 54-61 35
  36. 36. 35B In search of a cyberspace … to launch BIC… Conclusions This study attempts to portray biologically-motivated computing considerations… … in the framework of a complex digital ecosystem. … the ANN is chosen as an example and characterized in the domain of interest. … Relevant details on ANN describe the relational aspects of Species and Environment vis-à-vis the BIC in terms of the ontological details of [3]. 36 THANK YOU!!!
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