SlideShare a Scribd company logo
Natural Computing :  The Virtual Laboratory and  Two Real-World Applications Leandro Nunes de Castro [email_address] ;  [email_address]   Mackenzie University NatComp – From Nature to Business
Agenda Natural Computing Introduction and Motivation Computing Inspired by Nature Synthesis of Nature by Means of Computing Novel Computing Devices The Virtual Laboratory on Natural Computing Main Features and Where to Find Two Real World Applications A Grain Classifier Container Scheduling
Natural Computing Motivation and An Overview
Imagine a world where computers can create new universes, and within these universes there are natural forms that reproduce, grow and adapt. Imagine natural patterns, mountains, ant colonies, immune systems and brains, all learning and evolving, and becoming increasingly more adapted to the environment. Imagine if our computers could contain new forms of life. Think how this would affect our lives. Maybe we could automatically create house and music design, new forms of protecting computers against invaders, new forms of solving complex problems, new organisms and new forms of computing.  Now stop imagining. Welcome to Computing in the New Millennium.  Welcome to the  Natural Computing  age! Adapted from Digital Biology, by P. Bentley.
Current Computer Technology Turing  Machines (TM) Computational device idealized by A. Turing in 1936 If a problem can be computed, then it can be computed by a Turing Machine J. von Neumman architecture
Main Features of Current Computers General-purpose machines Manipulate precisely precise information* Address-based memory Serial processing* Are not capable of generalizing Are not fault tolerant (robust) Are not adaptable* …
Questions Natural Computing help to Answer How to solve intractable problems? How to realistically synthesize natural phenomena? What computing devices will come next? N. of atoms per bit 2020: 1 atom per bit
Natural Computing: An Overview Nature x Computing Natural computing is the terminology used to encompass three paradigms: Computing inspired by nature The simulation and emulation of natural phenomena in computers Computing with natural materials
Natural Computing: An Overview
Computing Inspired by Nature  Nature has evolved through ages in order to solve complex real-world problems Examples abound: nest building, nest cleaning, main senses (hearing, seeing, touching, smelling, tasting), etc. Computer algorithms based or inspired by nature have been developed for some time: Either to model nature, Or to solve complex real-world problems
Computing Inspired by Nature Neurocomputing Evolutionary Computing Swarm Intelligence Immunocomputing etc.
Synthesis of Nature by Means of Computing Biosciences: reductionist approach to understanding life Artificial Life & Fractal Geometry: bottom-up approach to synthesize life patterns and behaviors Focus on the computational synthesis of natural patterns and behaviors, not problem solving Widely used in computer graphics and movie making What is life? “ The property or quality that distinguishes living organisms from dead organisms and inanimate matter, manifested in functions such as metabolism, growth, reproduction, and response to stimuli or adaptation to the environment originating from within the organism. ” (Dictionary.com)
Synthesis of Nature by Means of Computing Artificial Life and Fractal Geometry
Novel Computing Devices If current computing technology will reach its limit in the near future, what would be the alternative material with which to compute? New computing methods based on other natural material than silicon: Molecules Membranes Quantum systems
Novel Computing Devices Quantum bit: | x   =  c 1|0   +  c 2|1 
Fundamentals of Natural Computing Some ideas that form the basis of natural computing: Capacity of dealing with complex problems The use of sets of candidate solutions Capacity of dealing imprecisely with imprecise information Robustness Distributivity Self-repair etc.
The Virtual Laboratory on Natural Computing LVCoN
Virtual Laboratories A virtual laboratory is a tool for distance learning and/or experimentation that allows people to share knowledge, data, voice, video, tools, and many other resources. It provides a suitable environment to extend, improve, integrate, refine, and assist the learning and/or experimentation process of many subjects, thus contributing to an increase of the effectiveness of scientific research and widening the use of scarce or costly equipments.
The Virtual Laboratory on Natural Computing Didactic contents   Biological motivation, theoretical contents, pictures, references and pseudocodes. Simulations Java applets simulators available with a brief tutorial. Exercises with responses  Sets of exercises with their respective answers to allow the students/instructors to evaluate themselves.  http://lsin.unisantos.br/lvcon .
The Virtual Laboratory on Natural Computing
A Grain Classification Machine NatComp – From Nature to Business
Automatic Grain Classification Actors involved: Producers; Local and global consumers; Cooperatives; Banks; Stock Market. Motivation: Automatic certification of quality ; Avoid classification conflicts; No equivalent machine available***; Standardization.
Examples of Grain Defects
The Grain Classifier Project Public Investor, several commercial partners The Development Cycle: Conceptual  Design Hardware  Prototyping Computer Vision Pattern Recognition
Computer Vision Image Capture: Double face capture Feature Extraction: Color, Texture and Shape attributes Based on the RGB histograms Total of 70 attributes extracted per grain
Feature Selection and Classification Feature Selection: Filter and Wrapper Classification: Naïve Bayes KNN Support Vector Machines Multi-Layer Perceptrons aiNet+RBF SRABNET: Supervised RABNET
Experimental Results Estimating the Weight ICS-RBF = aiNet+RBF S tr : average deviation from the desired value (training) E tr :average estimation error for training (training)
Experimental Results Classification Performance E tr % E te % E CV % Std MLP 8,80 1,814 SVM 10,60 3,31 k-NN 15,10 3,00
Discussion The immune system approach demonstrated to be competitive Experiment with binary classification followed by defect classification Experiment hierarchical classification Possibility of automating the classification of grains Benchmark classification performance for humans: 95%
Operation Planning in a Container Terminal  (CONTER) NatComp – From Nature to Business
The Importance of Container Terminals Most World commerce is performed using containers The operation of a CONTER is a very complicated and challenging task, involving space and equipment constraints, short time spans for ship docking, pre-specified ship plans, customs procedures, etc.
A Typical Problem: Scheduling RTGs When a Ship Plan is received in the terminal, the operators have to search and load the selected containers into the ship. The RTGs (Rubber Tyred Gantry Crane) are typical container handling equipments and move in three directions: x, y, and z. The less movements the RTGs make, the faster and cheaper becomes the ship loading.
RTGs Movements: Productive (a) (b) (c) (c) (d) (e)
RTGs Movements: Improductive (Set-Up) (a) (b) (c) (d)
Cost to Remove Containers where  n x ,  n y  and  n z  is the number of movements in direction X, Y and Z, respectively;  V x ,  V y  and  V z  is the RTG velocity in direction X, Y and Z,  respectively;  t T  is the time spent to lock  or unlock the spreader and  n T  is the  number of spreader locking/unlocking.
The copt-aiNet Algorithm
A Demo on the RTG Scheduling Problem
RTG Scheduling Discussion Copt-aiNet was originally used for gene ordering Possibility of using other heuristics A few minutes are available to suggest the removal schedule This type of problem was rarely perceived as a ‘problem’ in container terminals Promotes over 40% reduction in set-up movements and time
Applied AIS: Discussion Vast number of applications available Great potential for further applications and developments Some issues that still deserve investigation: Formal aspects Comparison (theoretical and empirical) with other approaches Loads of testing: validation Real benefits How far to stretch the metaphor? Scalability Robustness to high dimensions
How Far Can We Go? THANK YOU FOR THE ATTENTION! QUESTIONS?

More Related Content

PDF
Deep learning
PPT
2005: Natural Computing - Concepts and Applications
PDF
2012: Natural Computing - The Grand Challenges and Two Case Studies
PPTX
2012: The Grand Challenges in Natural Computing Research
PPTX
Facial expression recognition projc 2 (3) (1)
PDF
Deep Learning: a birds eye view
PPTX
Deep learning
PDF
Neural networks and deep learning
Deep learning
2005: Natural Computing - Concepts and Applications
2012: Natural Computing - The Grand Challenges and Two Case Studies
2012: The Grand Challenges in Natural Computing Research
Facial expression recognition projc 2 (3) (1)
Deep Learning: a birds eye view
Deep learning
Neural networks and deep learning

Viewers also liked (20)

PDF
2016: A Tríade da Persona Virtual - O Que as Mídias Sociais Podem Revelar sob...
PPTX
Natural Computing for Vehicular Networks
PPT
2004: Engineering Applications of Artificial Immune Systems
PPTX
2011: TUILUX_FC
PPT
2002: Comparing Immune and Neural Networks
PPTX
2011: Na Nova Geração do Ecommerce os Produtos Encontrarão os Clientes
PPT
2008: Applied AIS - A Roadmap of AIS Research in Brazil and Sample Applications
PPT
2004: Computação Natural (Cybertecnica)
PPTX
2011: Usando Ferramentas de Recomendação Inteligente para Aumento da Taxa de ...
PPTX
2011: Empreendedorismo Digital - Como Dados Viram Negócios
PPT
2010: Computação Natural e Aplicações
PPTX
2012: O Processo de Checkout em E-commerce
PPTX
2012: LCoN Aplicações em Big Data
PDF
2016: Applying AI Innovation in Business
PDF
2016: Notas sobre Liderança
PPTX
2011: Mineração de Dados - Conceitos Básicos e Aplicações
PPT
2006: Artificial Immune Systems - The Past, The Present, And The Future?
DOC
2010: Agrupamento Evolutivo de Dados
PDF
2012: Computação Natural - Slides do Curso
PDF
2012: Tutorial sobre Sistemas de Recomendação para E-commerce
2016: A Tríade da Persona Virtual - O Que as Mídias Sociais Podem Revelar sob...
Natural Computing for Vehicular Networks
2004: Engineering Applications of Artificial Immune Systems
2011: TUILUX_FC
2002: Comparing Immune and Neural Networks
2011: Na Nova Geração do Ecommerce os Produtos Encontrarão os Clientes
2008: Applied AIS - A Roadmap of AIS Research in Brazil and Sample Applications
2004: Computação Natural (Cybertecnica)
2011: Usando Ferramentas de Recomendação Inteligente para Aumento da Taxa de ...
2011: Empreendedorismo Digital - Como Dados Viram Negócios
2010: Computação Natural e Aplicações
2012: O Processo de Checkout em E-commerce
2012: LCoN Aplicações em Big Data
2016: Applying AI Innovation in Business
2016: Notas sobre Liderança
2011: Mineração de Dados - Conceitos Básicos e Aplicações
2006: Artificial Immune Systems - The Past, The Present, And The Future?
2010: Agrupamento Evolutivo de Dados
2012: Computação Natural - Slides do Curso
2012: Tutorial sobre Sistemas de Recomendação para E-commerce
Ad

Similar to 2008: Natural Computing: The Virtual Laboratory and Two Real-World Applications (20)

PPT
2011.9 Ternary Computing for a Human-Cyber-Physical Universe.ppt
PPTX
Unit_1.ppt.pptx
PDF
Morphogenetic Engineering: Reconciling Architecture and Self-Organization Thr...
PDF
Advanced Soft Computing BINUS July 2025.pdf
PDF
ON SOFT COMPUTING TECHNIQUES IN VARIOUS AREAS
PPTX
A Review on the Application of Natural Computing in Environmental Informatics
PDF
Looking into the Crystal Ball: From Transistors to the Smart Earth
PDF
Reconfigurable data intensive service for low latency cyber-physical systems ...
PPT
Evolving Future Information Systems: Challenges, Perspectives and Applications
PPTX
PhD Admission Pitching
PDF
Survey: Biological Inspired Computing in the Network Security
PDF
An approach for self creating software code in bionets with artificial embryo...
PPTX
The Future is Here
PPT
Cyberinfrastructure and Applications Overview: Howard University June22
PPT
Computing Outside The Box June 2009
PDF
Networks for An Infinite Service Future
PDF
Intelligent Engineering Informatics David Jc Mackay
PPT
Agents In An Exponential World Foster
PDF
2011.9 Ternary Computing for a Human-Cyber-Physical Universe.ppt
Unit_1.ppt.pptx
Morphogenetic Engineering: Reconciling Architecture and Self-Organization Thr...
Advanced Soft Computing BINUS July 2025.pdf
ON SOFT COMPUTING TECHNIQUES IN VARIOUS AREAS
A Review on the Application of Natural Computing in Environmental Informatics
Looking into the Crystal Ball: From Transistors to the Smart Earth
Reconfigurable data intensive service for low latency cyber-physical systems ...
Evolving Future Information Systems: Challenges, Perspectives and Applications
PhD Admission Pitching
Survey: Biological Inspired Computing in the Network Security
An approach for self creating software code in bionets with artificial embryo...
The Future is Here
Cyberinfrastructure and Applications Overview: Howard University June22
Computing Outside The Box June 2009
Networks for An Infinite Service Future
Intelligent Engineering Informatics David Jc Mackay
Agents In An Exponential World Foster
Ad

More from Leandro de Castro (19)

PDF
2021: An Illustrated Journey into Natural Computing
PDF
2019: Folder do LCoN
PDF
2019: LCoN - Centro de Excelência em Inteligência Artificial
PDF
2018: What did I learn about Innovation and Entrepreneurship in Israel
PDF
2018 Academic Innovation Opportunities in Brazil
PDF
2017: Tópicos em Educação Financeira
PDF
2017: The Many Faces of Artificial Intelligence: From AI to Big Data - A Hist...
PDF
2016: Fundamentos Matemáticos para Inteligência Artificial
PPTX
2016: Introdução à Mineração de Dados: Conceitos Básicos, Algoritmos e Aplica...
PDF
2015: Análise de Mercado e Plano de Marketing
PDF
2016 (Updated): Introdução à Mineração de Dados
PDF
2016: Metodologia da Pesquisa em Computação
PDF
2015: Fundamentos Teóricos da Computação
PDF
2010: Plano de Negócios e Incubação de Empresas de Base Tecnológica
PDF
2014: Introdução às Redes Neurais Artificiais
PDF
2013: Empreendedorismo: Slides do Curso
PPT
1998: Técnicas de Otimização Não-Linear Irrestrita para o Treinamento de Rede...
PPT
2000: Artificial Immune Systems - Theory and Applications
PPT
2001: An Introduction to Artificial Immune Systems
2021: An Illustrated Journey into Natural Computing
2019: Folder do LCoN
2019: LCoN - Centro de Excelência em Inteligência Artificial
2018: What did I learn about Innovation and Entrepreneurship in Israel
2018 Academic Innovation Opportunities in Brazil
2017: Tópicos em Educação Financeira
2017: The Many Faces of Artificial Intelligence: From AI to Big Data - A Hist...
2016: Fundamentos Matemáticos para Inteligência Artificial
2016: Introdução à Mineração de Dados: Conceitos Básicos, Algoritmos e Aplica...
2015: Análise de Mercado e Plano de Marketing
2016 (Updated): Introdução à Mineração de Dados
2016: Metodologia da Pesquisa em Computação
2015: Fundamentos Teóricos da Computação
2010: Plano de Negócios e Incubação de Empresas de Base Tecnológica
2014: Introdução às Redes Neurais Artificiais
2013: Empreendedorismo: Slides do Curso
1998: Técnicas de Otimização Não-Linear Irrestrita para o Treinamento de Rede...
2000: Artificial Immune Systems - Theory and Applications
2001: An Introduction to Artificial Immune Systems

Recently uploaded (20)

PPTX
Tartificialntelligence_presentation.pptx
PDF
gpt5_lecture_notes_comprehensive_20250812015547.pdf
PDF
Profit Center Accounting in SAP S/4HANA, S4F28 Col11
PDF
Univ-Connecticut-ChatGPT-Presentaion.pdf
PDF
1 - Historical Antecedents, Social Consideration.pdf
PDF
Assigned Numbers - 2025 - Bluetooth® Document
PDF
Building Integrated photovoltaic BIPV_UPV.pdf
PDF
Hybrid model detection and classification of lung cancer
PDF
A comparative analysis of optical character recognition models for extracting...
PDF
Microsoft Solutions Partner Drive Digital Transformation with D365.pdf
PPTX
1. Introduction to Computer Programming.pptx
PDF
From MVP to Full-Scale Product A Startup’s Software Journey.pdf
PPTX
Group 1 Presentation -Planning and Decision Making .pptx
PDF
A novel scalable deep ensemble learning framework for big data classification...
PDF
ENT215_Completing-a-large-scale-migration-and-modernization-with-AWS.pdf
PPTX
TechTalks-8-2019-Service-Management-ITIL-Refresh-ITIL-4-Framework-Supports-Ou...
PDF
August Patch Tuesday
PDF
Unlocking AI with Model Context Protocol (MCP)
PPTX
Chapter 5: Probability Theory and Statistics
PDF
Hindi spoken digit analysis for native and non-native speakers
Tartificialntelligence_presentation.pptx
gpt5_lecture_notes_comprehensive_20250812015547.pdf
Profit Center Accounting in SAP S/4HANA, S4F28 Col11
Univ-Connecticut-ChatGPT-Presentaion.pdf
1 - Historical Antecedents, Social Consideration.pdf
Assigned Numbers - 2025 - Bluetooth® Document
Building Integrated photovoltaic BIPV_UPV.pdf
Hybrid model detection and classification of lung cancer
A comparative analysis of optical character recognition models for extracting...
Microsoft Solutions Partner Drive Digital Transformation with D365.pdf
1. Introduction to Computer Programming.pptx
From MVP to Full-Scale Product A Startup’s Software Journey.pdf
Group 1 Presentation -Planning and Decision Making .pptx
A novel scalable deep ensemble learning framework for big data classification...
ENT215_Completing-a-large-scale-migration-and-modernization-with-AWS.pdf
TechTalks-8-2019-Service-Management-ITIL-Refresh-ITIL-4-Framework-Supports-Ou...
August Patch Tuesday
Unlocking AI with Model Context Protocol (MCP)
Chapter 5: Probability Theory and Statistics
Hindi spoken digit analysis for native and non-native speakers

2008: Natural Computing: The Virtual Laboratory and Two Real-World Applications

  • 1. Natural Computing : The Virtual Laboratory and Two Real-World Applications Leandro Nunes de Castro [email_address] ; [email_address] Mackenzie University NatComp – From Nature to Business
  • 2. Agenda Natural Computing Introduction and Motivation Computing Inspired by Nature Synthesis of Nature by Means of Computing Novel Computing Devices The Virtual Laboratory on Natural Computing Main Features and Where to Find Two Real World Applications A Grain Classifier Container Scheduling
  • 4. Imagine a world where computers can create new universes, and within these universes there are natural forms that reproduce, grow and adapt. Imagine natural patterns, mountains, ant colonies, immune systems and brains, all learning and evolving, and becoming increasingly more adapted to the environment. Imagine if our computers could contain new forms of life. Think how this would affect our lives. Maybe we could automatically create house and music design, new forms of protecting computers against invaders, new forms of solving complex problems, new organisms and new forms of computing. Now stop imagining. Welcome to Computing in the New Millennium. Welcome to the Natural Computing age! Adapted from Digital Biology, by P. Bentley.
  • 5. Current Computer Technology Turing Machines (TM) Computational device idealized by A. Turing in 1936 If a problem can be computed, then it can be computed by a Turing Machine J. von Neumman architecture
  • 6. Main Features of Current Computers General-purpose machines Manipulate precisely precise information* Address-based memory Serial processing* Are not capable of generalizing Are not fault tolerant (robust) Are not adaptable* …
  • 7. Questions Natural Computing help to Answer How to solve intractable problems? How to realistically synthesize natural phenomena? What computing devices will come next? N. of atoms per bit 2020: 1 atom per bit
  • 8. Natural Computing: An Overview Nature x Computing Natural computing is the terminology used to encompass three paradigms: Computing inspired by nature The simulation and emulation of natural phenomena in computers Computing with natural materials
  • 10. Computing Inspired by Nature Nature has evolved through ages in order to solve complex real-world problems Examples abound: nest building, nest cleaning, main senses (hearing, seeing, touching, smelling, tasting), etc. Computer algorithms based or inspired by nature have been developed for some time: Either to model nature, Or to solve complex real-world problems
  • 11. Computing Inspired by Nature Neurocomputing Evolutionary Computing Swarm Intelligence Immunocomputing etc.
  • 12. Synthesis of Nature by Means of Computing Biosciences: reductionist approach to understanding life Artificial Life & Fractal Geometry: bottom-up approach to synthesize life patterns and behaviors Focus on the computational synthesis of natural patterns and behaviors, not problem solving Widely used in computer graphics and movie making What is life? “ The property or quality that distinguishes living organisms from dead organisms and inanimate matter, manifested in functions such as metabolism, growth, reproduction, and response to stimuli or adaptation to the environment originating from within the organism. ” (Dictionary.com)
  • 13. Synthesis of Nature by Means of Computing Artificial Life and Fractal Geometry
  • 14. Novel Computing Devices If current computing technology will reach its limit in the near future, what would be the alternative material with which to compute? New computing methods based on other natural material than silicon: Molecules Membranes Quantum systems
  • 15. Novel Computing Devices Quantum bit: | x   =  c 1|0   +  c 2|1 
  • 16. Fundamentals of Natural Computing Some ideas that form the basis of natural computing: Capacity of dealing with complex problems The use of sets of candidate solutions Capacity of dealing imprecisely with imprecise information Robustness Distributivity Self-repair etc.
  • 17. The Virtual Laboratory on Natural Computing LVCoN
  • 18. Virtual Laboratories A virtual laboratory is a tool for distance learning and/or experimentation that allows people to share knowledge, data, voice, video, tools, and many other resources. It provides a suitable environment to extend, improve, integrate, refine, and assist the learning and/or experimentation process of many subjects, thus contributing to an increase of the effectiveness of scientific research and widening the use of scarce or costly equipments.
  • 19. The Virtual Laboratory on Natural Computing Didactic contents Biological motivation, theoretical contents, pictures, references and pseudocodes. Simulations Java applets simulators available with a brief tutorial. Exercises with responses Sets of exercises with their respective answers to allow the students/instructors to evaluate themselves. http://lsin.unisantos.br/lvcon .
  • 20. The Virtual Laboratory on Natural Computing
  • 21. A Grain Classification Machine NatComp – From Nature to Business
  • 22. Automatic Grain Classification Actors involved: Producers; Local and global consumers; Cooperatives; Banks; Stock Market. Motivation: Automatic certification of quality ; Avoid classification conflicts; No equivalent machine available***; Standardization.
  • 23. Examples of Grain Defects
  • 24. The Grain Classifier Project Public Investor, several commercial partners The Development Cycle: Conceptual Design Hardware Prototyping Computer Vision Pattern Recognition
  • 25. Computer Vision Image Capture: Double face capture Feature Extraction: Color, Texture and Shape attributes Based on the RGB histograms Total of 70 attributes extracted per grain
  • 26. Feature Selection and Classification Feature Selection: Filter and Wrapper Classification: Naïve Bayes KNN Support Vector Machines Multi-Layer Perceptrons aiNet+RBF SRABNET: Supervised RABNET
  • 27. Experimental Results Estimating the Weight ICS-RBF = aiNet+RBF S tr : average deviation from the desired value (training) E tr :average estimation error for training (training)
  • 28. Experimental Results Classification Performance E tr % E te % E CV % Std MLP 8,80 1,814 SVM 10,60 3,31 k-NN 15,10 3,00
  • 29. Discussion The immune system approach demonstrated to be competitive Experiment with binary classification followed by defect classification Experiment hierarchical classification Possibility of automating the classification of grains Benchmark classification performance for humans: 95%
  • 30. Operation Planning in a Container Terminal (CONTER) NatComp – From Nature to Business
  • 31. The Importance of Container Terminals Most World commerce is performed using containers The operation of a CONTER is a very complicated and challenging task, involving space and equipment constraints, short time spans for ship docking, pre-specified ship plans, customs procedures, etc.
  • 32. A Typical Problem: Scheduling RTGs When a Ship Plan is received in the terminal, the operators have to search and load the selected containers into the ship. The RTGs (Rubber Tyred Gantry Crane) are typical container handling equipments and move in three directions: x, y, and z. The less movements the RTGs make, the faster and cheaper becomes the ship loading.
  • 33. RTGs Movements: Productive (a) (b) (c) (c) (d) (e)
  • 34. RTGs Movements: Improductive (Set-Up) (a) (b) (c) (d)
  • 35. Cost to Remove Containers where n x , n y and n z is the number of movements in direction X, Y and Z, respectively; V x , V y and V z is the RTG velocity in direction X, Y and Z, respectively; t T is the time spent to lock or unlock the spreader and n T is the number of spreader locking/unlocking.
  • 37. A Demo on the RTG Scheduling Problem
  • 38. RTG Scheduling Discussion Copt-aiNet was originally used for gene ordering Possibility of using other heuristics A few minutes are available to suggest the removal schedule This type of problem was rarely perceived as a ‘problem’ in container terminals Promotes over 40% reduction in set-up movements and time
  • 39. Applied AIS: Discussion Vast number of applications available Great potential for further applications and developments Some issues that still deserve investigation: Formal aspects Comparison (theoretical and empirical) with other approaches Loads of testing: validation Real benefits How far to stretch the metaphor? Scalability Robustness to high dimensions
  • 40. How Far Can We Go? THANK YOU FOR THE ATTENTION! QUESTIONS?