In biological systems, individual phenotypes are typically adopted by multiple genotypes. Examples include protein structure phenotypes, where each structure can be adopted by a myriad individual amino acid sequence genotypes. These genotypes form vast connected ‘neutral networks’ in genotype space. The size of such neutral networks endows biological systems not only with robustness to genetic change, but also with the ability to evolve a vast number of novel phenotypes that occur near any one neutral network. Whether technological systems can be designed to have similar properties is poorly understood.
Here we ask this question for a class of programmable electronic circuits that compute digital logic functions. We demonstrate that circuits that compute the same logic function are connected in large neutral networks that span circuit space. Their robustness or fault-tolerance varies very widely. The vicinity of each neutral network contains circuits with a broad range of novel functions. Two circuits computing different functions can usually be converted into one another via few changes in their architecture. These observations show that properties important for the evolvability of biological systems exist in a commercially important class of electronic circuitry. They also point to generic ways to generate fault-tolerant, adaptable and evolvable electronic circuitry, likely to find use in synthetic biology as well.
The document provides an overview of the history and development of the novel genre. It begins by outlining some key parameters of novels, including their use of prose fiction and extended length to achieve verisimilitude. Notable early novels are then discussed from various regions, such as Murasaki Shikibu's Tale of Genji in 11th century Japan. The rise of the English novel in the 17th-18th centuries is covered, along with influential authors like Daniel Defoe, Samuel Richardson, Henry Fielding, and the Brontë sisters. The document concludes by describing various novel types/styles that emerged over time, such as Gothic, historical, realist/naturalist, and social novels.
This document defines and describes various literary genres. It discusses fiction genres like historical fiction, science fiction, fantasy, and realistic fiction. It also covers non-fiction genres such as persuasive writing, informational writing, autobiography, and biography. Additionally, it summarizes folklore genres including fairy tales, fables, myths, legends, and tall tales. Finally, it provides overviews of the drama genres of comedy and tragedy and defines characteristics of poetry.
The Russian Formalists were a group of writers in the early 20th century who focused on analyzing the form and technique of literature rather than its historical or philosophical context. Major figures included Victor Shklovsky, Mikhail Bakhtin, and Roman Jakobson. Jakobson analyzed the different functions of language and how they are used in different genres of poetry. New Criticism originated in the 1920s and advocated an aesthetic, text-focused approach to criticism pioneered by I.A. Richards and John Crowe Ransom. While both were formalist schools, the Russian Formalists took a more theoretical approach while New Critics emphasized the practical close reading of individual texts.
The document summarizes the history and development of the novel genre. It discusses how novels originated in the 18th century with the emergence of the middle class and focus on human characters. It then describes the rise of historical novels in the 19th century led by writers like Walter Scott. The document also outlines the major developments in the English novel from the 18th-20th centuries, including the influence of romanticism, Victorian novelists focusing on middle and working class stories, and 20th century novels reflecting world events like wars and political issues.
Miguel de Cervantes was a Spanish author born in 1547. He served as a soldier and was wounded at the Battle of Lepanto, which left his hand disabled. He struggled financially for much of his life. His masterwork, Don Quixote, was published in 1605 and became an instant bestseller, though it did not improve Cervantes' financial situation. In his later years, he published several other successful works while still living in poverty until his death in 1616.
Joseph andrews characeter ... joseph andrewsFRK NIAZI
The document provides a character list for the novel "Joseph Andrews" by Henry Fielding. It includes over 40 characters, primarily those encountered by Joseph Andrews and Mr. Adams on their journey from London to the countryside. The main characters are Joseph Andrews, a virtuous footman; Mr. Abraham Adams, a curate who supports Joseph; and Fanny Goodwill, the beautiful milkmaid beloved of Joseph. Other characters include Joseph's employer Lady Booby, who lusts after him, and various other servants, innkeepers, and minor characters they meet along the way.
The document provides an overview of the history and development of the novel genre. It begins by outlining some key parameters of novels, including their use of prose fiction and extended length to achieve verisimilitude. Notable early novels are then discussed from various regions, such as Murasaki Shikibu's Tale of Genji in 11th century Japan. The rise of the English novel in the 17th-18th centuries is covered, along with influential authors like Daniel Defoe, Samuel Richardson, Henry Fielding, and the Brontë sisters. The document concludes by describing various novel types/styles that emerged over time, such as Gothic, historical, realist/naturalist, and social novels.
This document defines and describes various literary genres. It discusses fiction genres like historical fiction, science fiction, fantasy, and realistic fiction. It also covers non-fiction genres such as persuasive writing, informational writing, autobiography, and biography. Additionally, it summarizes folklore genres including fairy tales, fables, myths, legends, and tall tales. Finally, it provides overviews of the drama genres of comedy and tragedy and defines characteristics of poetry.
The Russian Formalists were a group of writers in the early 20th century who focused on analyzing the form and technique of literature rather than its historical or philosophical context. Major figures included Victor Shklovsky, Mikhail Bakhtin, and Roman Jakobson. Jakobson analyzed the different functions of language and how they are used in different genres of poetry. New Criticism originated in the 1920s and advocated an aesthetic, text-focused approach to criticism pioneered by I.A. Richards and John Crowe Ransom. While both were formalist schools, the Russian Formalists took a more theoretical approach while New Critics emphasized the practical close reading of individual texts.
The document summarizes the history and development of the novel genre. It discusses how novels originated in the 18th century with the emergence of the middle class and focus on human characters. It then describes the rise of historical novels in the 19th century led by writers like Walter Scott. The document also outlines the major developments in the English novel from the 18th-20th centuries, including the influence of romanticism, Victorian novelists focusing on middle and working class stories, and 20th century novels reflecting world events like wars and political issues.
Miguel de Cervantes was a Spanish author born in 1547. He served as a soldier and was wounded at the Battle of Lepanto, which left his hand disabled. He struggled financially for much of his life. His masterwork, Don Quixote, was published in 1605 and became an instant bestseller, though it did not improve Cervantes' financial situation. In his later years, he published several other successful works while still living in poverty until his death in 1616.
Joseph andrews characeter ... joseph andrewsFRK NIAZI
The document provides a character list for the novel "Joseph Andrews" by Henry Fielding. It includes over 40 characters, primarily those encountered by Joseph Andrews and Mr. Adams on their journey from London to the countryside. The main characters are Joseph Andrews, a virtuous footman; Mr. Abraham Adams, a curate who supports Joseph; and Fanny Goodwill, the beautiful milkmaid beloved of Joseph. Other characters include Joseph's employer Lady Booby, who lusts after him, and various other servants, innkeepers, and minor characters they meet along the way.
The document provides background information on Henry Fielding's novel "Joseph Andrews". Published in 1742, it was one of the first novels written in English and tells the story of the adventures of the title character Joseph Andrews and his friend Parson Adams. The novel brought together two different literary aesthetics that were popular during the 18th century Augustan period: the mock heroic style of authors like Alexander Pope and Jonathan Swift, and the domestic prose fiction of writers such as Daniel Defoe and Samuel Richardson. The story embodied the principles of reason and empiricism that defined the Augustan Age. While some critics praised Fielding's realistic depictions of human nature, others disliked his satirical parody of Samuel Richardson's novel Pamela
- Sir Francis Bacon was an English philosopher, statesman, scientist, jurist, orator, and author. He served as both Attorney General and Lord Chancellor of England.
- He was born in 1561 in London to an upper-class family. He attended Trinity College before studying law. Throughout his career he authored many influential works on science, philosophy, and politics.
- Bacon is considered one of the founding fathers of the scientific method. He proposed a new, evidence-based approach to science and the advancement of knowledge called The Great Instauration. His works helped establish an empirical approach to science based on inductive reasoning and experimentation.
Of marrige and single life (euro. lit.)Ysa Garcera
This document contains a summary of Francis Bacon's life and works:
[1] Francis Bacon was born in 1561 in London to an aristocratic family. He studied law at Trinity College, Cambridge at age 12. [2] Bacon established the scientific method still used today and held various government positions but lost favor after being convicted of corruption. [3] He authored influential essays and believed himself a mouthpiece for society. The document also provides quick facts about Bacon and lists some of his literary works, including "Of Marriage and Single Life."
Henry Fielding was an 18th century English novelist born in 1707 who wrote notable works such as Joseph Andrews, Amelia, and Tom Jones. Tom Jones was a picaresque novel published in 1749 containing 18 books that centered around the contrast between the good nature of the protagonist Tom Jones and the corruption of the world.
The document discusses the role and importance of the reader in Henry Fielding's novels Joseph Andrews and Tom Jones. It explains that Fielding viewed the reader as an active participant in constructing the meaning of the novel, rather than a passive receiver. He used techniques like contrast, ambiguity, and direct addresses to the reader to encourage participation and independent thinking. The document also analyzes how Fielding provided guidance to readers through author-reader dialogue, while still allowing complexity and open-ended interpretations.
Mikhail Bakhtin was a Russian philosopher and scholar who worked on literary theory, ethics, and philosophy of language. He believed that language is learned through social interaction and that all language use has a point of view and context, making it inherently ideological. Bakhtin also argued that every utterance is a product of interaction between speakers and is influenced by the social situation. He developed concepts of how languages have centripetal forces that aim to standardize language but also centrifugal forces from diverse social uses that challenge standardization and make language heteroglossic.
This document defines the novel and its key elements. It states that a novel is an extended fictional narrative in prose that tells a story through elements like plot, characters, point of view, setting, and theme. It discusses different types of plots, characters, points of view, settings, and how theme unifies all the elements to make a comment on human life. Theme is the central idea or statement about life that emerges from how the elements work together.
The document summarizes the development of the novel genre and women's roles in novels over time. It notes that as the middle classes prospered in the 18th century, women gained more freedom to read and write novels. Early novels by women mostly depicted domestic lives but some showed rebellious women. Novels also portrayed changing gender roles and expectations. The genre spread globally through colonialism and translations, with early Indian novels influenced by translations and adapting Western styles to local contexts.
Francis Bacon was born in 1561 in London, England to parents Nicholas and Anne Bacon. He attended Trinity College at the University of Cambridge and the University of Poitiers. Bacon is renowned for developing the scientific method and empiricism, influencing the scientific revolution. He never made experimental discoveries himself but his ideas encouraged experimentation and use of evidence to establish facts. Bacon died in 16026 after contracting pneumonia while experimenting with preserving meat with snow.
The document discusses the history and development of the novel form. It notes that novels first took root in 17th century England and France, but flourished in the 18th century. Initially only read by the gentlemanly classes, the lower-middle class became avid readers of novels as well. As readership grew, authors gained more financial independence. The novel form allowed for new styles of writing and helped popularize regional languages. Novels also helped shape national identities under colonial rule and gave voice to women writers and themes of domestic life.
This document defines and provides examples of different literary genres, including fiction and non-fiction. It discusses sub-genres such as biographies, autobiographies, historical fiction, realistic fiction, science fiction, mystery, fantasy, fairy tales, fables, myths, and modern fantasy. Examples are provided for each genre and sub-genre to illustrate the types of stories that fall into each category. Readers are prompted to consider which genres describe their favorite stories.
There are several ways to divide books into genres or categories including by format, content, and literary genre. The document discusses the major genres of fiction, nonfiction, drama, folktale, and poetry. It also lists some common subgenres within each category such as realistic fiction, mystery, science fiction, biography, and informational texts.
Timeline and Characteristics of British LiteratureJavier Aguirre
This document provides an overview of the major periods and characteristics of British literature from Old English/Anglo-Saxon period through the modern period. It discusses the key historical contexts, genres, styles, effects and samples of influential authors for each period. The periods covered include Old English, Middle English, Renaissance, Neoclassical, Romantic, Victorian and Modern.
The document defines and discusses the novel as a genre of fictional prose narrative that emerged in the 18th century. It notes some of the earliest and most influential novels, such as Don Quixote and Tom Jones. The document also examines different types of novels defined by their themes, styles, and subjects, such as epistolary novels, Gothic novels, satirical novels, and romance novels. Finally, it discusses various literary devices and techniques commonly used in novels, such as flashbacks, plot twists, and self-fulfilling prophecies.
This document provides an overview of writing genres and subgenres. It discusses the 5 main genres of poetry, nonfiction, fiction, folklore, and drama. For each genre, it lists related subgenres and provides brief descriptions and examples. The document aims to teach students the categories and subgenres that different types of writing fall into.
This introduction to fiction genres helps young readers to understand the characteristics of historical fiction, realistic fiction, fantasy, science fiction, mystery and folktales. Through pictures, examples, and review, students will learn how to identify and use genres.
The document provides an overview of the major periods in English literature from Old English to the Modern period. It summarizes the key historical events, literary movements, and important authors that defined each period, such as Beowulf in Old English, Chaucer in Middle English, Shakespeare in the Elizabethan period, and T.S. Eliot in the Modern period. Major genres and works that emerged are also mentioned for each literary time period outlined.
Genre analysis is a process used to analyze types of documents produced in particular discourse communities. It examines similarities and differences in genres' purposes, structures, and language features. Key aspects of genre analysis include identifying the communicative purposes and intended audiences of genres, analyzing their macro-level organizational patterns and sections, and studying language features like verb tense and voice. Genre analysis provides insight into how language is used within important discourse communities and can inform applied linguistics in educational settings.
The document provides an overview of English literature from Old English to the 20th century. It begins with Old English literature including Anglo-Saxon poetry such as Beowulf, characterized by alliteration and metaphors. Next it discusses Medieval literature including Geoffrey Chaucer and his masterpiece Canterbury Tales. It then covers the Renaissance period highlighting plays by Christopher Marlowe and William Shakespeare. Finally, it briefly mentions 17th century English literature including the influential King James Bible.
- The document proposes analytical models to estimate electromagnetic field (EMF) emissions from Wi-Fi and powerline communication (PLC) links in a home network.
- It develops a model for Wi-Fi EMF emissions based on assumptions about the transmission system, propagation environment, and a path loss model. This is used to define a "radiant exposure" (RE) routing metric that estimates the expected radiated energy within a radiation-sensitive area from transmitting along a path.
- The RE metric incorporates the effects of distance between the radiating sources and sensitive area, as well as the asymmetry of radiated energy regarding the direction of each link. It is designed to fit within shortest path routing algorithms to find minimum
The document discusses limitations of existing file formats for representing neural morphology and proposes recommendations for a new universal format. Existing formats like SWC and MATLAB Trees have limitations in accurately representing geometric variations and connectivity. Mesh formats allow more accuracy but reduce computational tractability. The document recommends that a new XML-based format should allow both mesh and frustum representations, facilitate load balancing, and not preclude representing dynamic structural changes over time. The goal is an optimized tradeoff between computational feasibility and biophysical accuracy.
The document provides background information on Henry Fielding's novel "Joseph Andrews". Published in 1742, it was one of the first novels written in English and tells the story of the adventures of the title character Joseph Andrews and his friend Parson Adams. The novel brought together two different literary aesthetics that were popular during the 18th century Augustan period: the mock heroic style of authors like Alexander Pope and Jonathan Swift, and the domestic prose fiction of writers such as Daniel Defoe and Samuel Richardson. The story embodied the principles of reason and empiricism that defined the Augustan Age. While some critics praised Fielding's realistic depictions of human nature, others disliked his satirical parody of Samuel Richardson's novel Pamela
- Sir Francis Bacon was an English philosopher, statesman, scientist, jurist, orator, and author. He served as both Attorney General and Lord Chancellor of England.
- He was born in 1561 in London to an upper-class family. He attended Trinity College before studying law. Throughout his career he authored many influential works on science, philosophy, and politics.
- Bacon is considered one of the founding fathers of the scientific method. He proposed a new, evidence-based approach to science and the advancement of knowledge called The Great Instauration. His works helped establish an empirical approach to science based on inductive reasoning and experimentation.
Of marrige and single life (euro. lit.)Ysa Garcera
This document contains a summary of Francis Bacon's life and works:
[1] Francis Bacon was born in 1561 in London to an aristocratic family. He studied law at Trinity College, Cambridge at age 12. [2] Bacon established the scientific method still used today and held various government positions but lost favor after being convicted of corruption. [3] He authored influential essays and believed himself a mouthpiece for society. The document also provides quick facts about Bacon and lists some of his literary works, including "Of Marriage and Single Life."
Henry Fielding was an 18th century English novelist born in 1707 who wrote notable works such as Joseph Andrews, Amelia, and Tom Jones. Tom Jones was a picaresque novel published in 1749 containing 18 books that centered around the contrast between the good nature of the protagonist Tom Jones and the corruption of the world.
The document discusses the role and importance of the reader in Henry Fielding's novels Joseph Andrews and Tom Jones. It explains that Fielding viewed the reader as an active participant in constructing the meaning of the novel, rather than a passive receiver. He used techniques like contrast, ambiguity, and direct addresses to the reader to encourage participation and independent thinking. The document also analyzes how Fielding provided guidance to readers through author-reader dialogue, while still allowing complexity and open-ended interpretations.
Mikhail Bakhtin was a Russian philosopher and scholar who worked on literary theory, ethics, and philosophy of language. He believed that language is learned through social interaction and that all language use has a point of view and context, making it inherently ideological. Bakhtin also argued that every utterance is a product of interaction between speakers and is influenced by the social situation. He developed concepts of how languages have centripetal forces that aim to standardize language but also centrifugal forces from diverse social uses that challenge standardization and make language heteroglossic.
This document defines the novel and its key elements. It states that a novel is an extended fictional narrative in prose that tells a story through elements like plot, characters, point of view, setting, and theme. It discusses different types of plots, characters, points of view, settings, and how theme unifies all the elements to make a comment on human life. Theme is the central idea or statement about life that emerges from how the elements work together.
The document summarizes the development of the novel genre and women's roles in novels over time. It notes that as the middle classes prospered in the 18th century, women gained more freedom to read and write novels. Early novels by women mostly depicted domestic lives but some showed rebellious women. Novels also portrayed changing gender roles and expectations. The genre spread globally through colonialism and translations, with early Indian novels influenced by translations and adapting Western styles to local contexts.
Francis Bacon was born in 1561 in London, England to parents Nicholas and Anne Bacon. He attended Trinity College at the University of Cambridge and the University of Poitiers. Bacon is renowned for developing the scientific method and empiricism, influencing the scientific revolution. He never made experimental discoveries himself but his ideas encouraged experimentation and use of evidence to establish facts. Bacon died in 16026 after contracting pneumonia while experimenting with preserving meat with snow.
The document discusses the history and development of the novel form. It notes that novels first took root in 17th century England and France, but flourished in the 18th century. Initially only read by the gentlemanly classes, the lower-middle class became avid readers of novels as well. As readership grew, authors gained more financial independence. The novel form allowed for new styles of writing and helped popularize regional languages. Novels also helped shape national identities under colonial rule and gave voice to women writers and themes of domestic life.
This document defines and provides examples of different literary genres, including fiction and non-fiction. It discusses sub-genres such as biographies, autobiographies, historical fiction, realistic fiction, science fiction, mystery, fantasy, fairy tales, fables, myths, and modern fantasy. Examples are provided for each genre and sub-genre to illustrate the types of stories that fall into each category. Readers are prompted to consider which genres describe their favorite stories.
There are several ways to divide books into genres or categories including by format, content, and literary genre. The document discusses the major genres of fiction, nonfiction, drama, folktale, and poetry. It also lists some common subgenres within each category such as realistic fiction, mystery, science fiction, biography, and informational texts.
Timeline and Characteristics of British LiteratureJavier Aguirre
This document provides an overview of the major periods and characteristics of British literature from Old English/Anglo-Saxon period through the modern period. It discusses the key historical contexts, genres, styles, effects and samples of influential authors for each period. The periods covered include Old English, Middle English, Renaissance, Neoclassical, Romantic, Victorian and Modern.
The document defines and discusses the novel as a genre of fictional prose narrative that emerged in the 18th century. It notes some of the earliest and most influential novels, such as Don Quixote and Tom Jones. The document also examines different types of novels defined by their themes, styles, and subjects, such as epistolary novels, Gothic novels, satirical novels, and romance novels. Finally, it discusses various literary devices and techniques commonly used in novels, such as flashbacks, plot twists, and self-fulfilling prophecies.
This document provides an overview of writing genres and subgenres. It discusses the 5 main genres of poetry, nonfiction, fiction, folklore, and drama. For each genre, it lists related subgenres and provides brief descriptions and examples. The document aims to teach students the categories and subgenres that different types of writing fall into.
This introduction to fiction genres helps young readers to understand the characteristics of historical fiction, realistic fiction, fantasy, science fiction, mystery and folktales. Through pictures, examples, and review, students will learn how to identify and use genres.
The document provides an overview of the major periods in English literature from Old English to the Modern period. It summarizes the key historical events, literary movements, and important authors that defined each period, such as Beowulf in Old English, Chaucer in Middle English, Shakespeare in the Elizabethan period, and T.S. Eliot in the Modern period. Major genres and works that emerged are also mentioned for each literary time period outlined.
Genre analysis is a process used to analyze types of documents produced in particular discourse communities. It examines similarities and differences in genres' purposes, structures, and language features. Key aspects of genre analysis include identifying the communicative purposes and intended audiences of genres, analyzing their macro-level organizational patterns and sections, and studying language features like verb tense and voice. Genre analysis provides insight into how language is used within important discourse communities and can inform applied linguistics in educational settings.
The document provides an overview of English literature from Old English to the 20th century. It begins with Old English literature including Anglo-Saxon poetry such as Beowulf, characterized by alliteration and metaphors. Next it discusses Medieval literature including Geoffrey Chaucer and his masterpiece Canterbury Tales. It then covers the Renaissance period highlighting plays by Christopher Marlowe and William Shakespeare. Finally, it briefly mentions 17th century English literature including the influential King James Bible.
- The document proposes analytical models to estimate electromagnetic field (EMF) emissions from Wi-Fi and powerline communication (PLC) links in a home network.
- It develops a model for Wi-Fi EMF emissions based on assumptions about the transmission system, propagation environment, and a path loss model. This is used to define a "radiant exposure" (RE) routing metric that estimates the expected radiated energy within a radiation-sensitive area from transmitting along a path.
- The RE metric incorporates the effects of distance between the radiating sources and sensitive area, as well as the asymmetry of radiated energy regarding the direction of each link. It is designed to fit within shortest path routing algorithms to find minimum
The document discusses limitations of existing file formats for representing neural morphology and proposes recommendations for a new universal format. Existing formats like SWC and MATLAB Trees have limitations in accurately representing geometric variations and connectivity. Mesh formats allow more accuracy but reduce computational tractability. The document recommends that a new XML-based format should allow both mesh and frustum representations, facilitate load balancing, and not preclude representing dynamic structural changes over time. The goal is an optimized tradeoff between computational feasibility and biophysical accuracy.
Analysis and Simulation of Scientic NetworksFelix Puetsch
This document is Felix Putsch's 2003 diploma thesis submitted to the Institute of Theoretical Physics at the University of Cologne under the supervision of Prof. D. Stauffer. The thesis analyzes and simulates scientific collaboration networks using network models such as regular lattices, Erdos-Renyi random networks, Watts-Strogatz small-world networks, and Barabasi-Albert scale-free networks. It builds an empirical collaboration network from bibliographic data and compares its properties to these theoretical network models. The thesis also uses spin models on the empirical network to study phenomena like leadership effects and phase transitions.
The document provides an acknowledgment and abstract for a thesis on modeling the AODV routing protocol for mobile ad-hoc networks using colored Petri nets. The author thanks their supervisor and others for their guidance and support during the project. The abstract indicates that AODV will be modeled using colored Petri nets to evaluate performance measures like workload and packet transmission efficiency, and the results will be compared to simulations run in the NS2 network simulator.
MIMO-OFDM communication systems_ channel estimation and wireless.pdfSamerSamerM
This dissertation addresses two problems in MIMO-OFDM communication systems: channel estimation and wireless location. For channel estimation, a pilot-tone based least squares algorithm is proposed. A unitary pilot matrix is designed to estimate the MIMO channel with minimum mean squared error and reduced complexity. For wireless location, a least squares approach is formulated to estimate location from time difference of arrival and angle of arrival measurements. The method is applied to WiMax networks and simulations demonstrate its accuracy.
The document is a thesis submitted by Harry W. Liu to the University of Toronto for the degree of Master of Applied Science. It investigates the effect of base station antenna configurations on soft handoff and coverage performance in wireless CDMA systems through analytical modeling and simulations. The investigation shows that antenna patterns, downtilting, azimuth configuration, and cell layout can substantially affect the handoff and coverage distributions but their percentage variations are not significant. The model provides a basic framework for optimizing the forward link of CDMA networks.
This document summarizes an interdisciplinary master's project that evaluates machine learning algorithms for tracking neuronal signals recorded by electronic depth control probes. The project aims to identify recording channels and track neural activity over time by classifying features extracted from neuronal signal measurements. Different supervised learning algorithms are tested and evaluated to determine the most appropriate method. Preliminary results show it is possible to track neural activity between recording sessions, and shifts in probe position between sessions may be detectable from the classification results.
This document summarizes a master's thesis that studied techniques for managing interference in heterogeneous networks (HetNets). The thesis customized the LTE-Sim simulator to implement and evaluate existing techniques like cell range extension (CRE) and almost blank subframes (ABS), as well as a new proposed uplink interference management technique. Simulations were performed to compare the techniques' impact on key performance metrics like throughput and fairness. The results demonstrated that the proposed technique improved uplink performance for picocell users compared to CRE and ABS approaches.
This master's thesis explores designing, analyzing, and experimentally evaluating a distributed community detection algorithm. Specifically:
- A distributed version of the Louvain community detection method is developed using the Apache Spark framework. Its convergence and quality of detected communities are studied theoretically and experimentally.
- Experiments show the distributed algorithm can effectively parallelize community detection.
- Graph sampling techniques are explored for accelerating parameter selection in a resolution-limit-free community detection method. Random node selection and forest fire sampling are compared.
- Recommendations are made for choice of sampling algorithm and parameter values based on the comparison.
Any form of education in an engineering or science discipline is incomplete without a means of testing and appreciating theories learned in class. The ability to carry out experimentation demonstrating theories through laboratory work is an integral part of an engineering, science and technology education. In laboratories, students can learn how to process real data, understand and appreciate discrepancies between their observations and the predictions according to theories. Not only do students appreciate those discrepancies, they learn how to make compromises to minimize the imperfections of their observations. This is a valuable skill for an engineer to have as engineers are problem solvers.
This dissertation proposes and analyzes methods for adaptive transceiver design and performance enhancement in OFDM systems. It first develops a new model for the time-varying indoor wireless channel based on Doppler spectrum measurements. It then presents adaptive synchronization techniques for OFDM receivers, including windowing and Kalman filtering approaches, to mitigate timing estimation errors under different channel conditions. An enhanced DFT-based MMSE channel estimator using Kalman smoothing is also proposed to minimize spectral leakage effects from virtual carriers. Finally, a method is introduced to improve throughput by adaptively optimizing constellation sizes and power distributions across sub-carriers during transmissions. Simulation results show the proposed estimation methods and throughput optimization can significantly improve synchronization accuracy and system performance.
This thesis examines self-organization and polychronization in liquid state machines (LSMs). LSMs are a type of recurrent neural network inspired by the brain. The thesis introduces machine learning concepts and neural network models. It discusses how self-organized recurrent neural networks can develop input separation and perform tasks through spike-timing dependent plasticity and other mechanisms. Polychronization, where groups of neurons fire together in precise patterns, is also examined. The thesis hypothesizes that an LSM incorporating both self-organization and polychronization could have improved information processing abilities compared to models without these features.
Extended LTE Coverage for Indoor Machine Type Communication.pdfYAAKOVSOLOMON1
This document discusses extending LTE coverage for indoor machine type communication. It proposes using repetition to increase coverage without requiring hardware upgrades. Simulations show that with a 20 dB coverage increase through repetition, coverage can be almost complete for inter-site distances up to 2500 m, where standard LTE has gaps. Higher resource usage is required but the number of supported users is limited more by coverage at longer distances than resources. Uplink performance is also evaluated through link and system level simulations.
Nonlinear image processing using artificial neuralHưng Đặng
The document discusses the use of artificial neural networks (ANNs) for nonlinear image processing tasks. It first provides background on image processing problems, ANNs, and why ANNs may be suitable for nonlinear image processing. It then reviews literature on applying ANNs to image processing. The rest of the document focuses on using supervised ANNs for classification/feature extraction tasks like object recognition, and regression ANNs for image restoration/filtering tasks. It aims to determine when ANNs can effectively solve problems and how prior knowledge can improve ANN design/interpretability.
This document provides a summary of three key points:
1) The document is Sara Modarres Razavi's licentiate thesis on tracking area planning in cellular networks, which deals with planning and optimizing the configuration of tracking areas in LTE networks.
2) Tracking area design must be revised over time to adapt to changes in user equipment location and mobility patterns. The thesis presents an algorithm based on repeated local search to solve the problem of re-optimizing the initial tracking area planning.
3) By extending the research, the thesis considers the trade-off between signaling overhead performance and reconfiguration cost, modeling it as a bi-objective optimization problem. Both an integer programming model and a genetic algorithm
This thesis examines the performance of Space Shift Keying (SSK) modulation in Multiple Input Multiple Output (MIMO) wireless systems in the presence of co-channel interference. The author derives exact analytical expressions for the Average Bit Error Rate (ABER) of SSK modulation with co-channel interference and supports the analysis with MATLAB simulations. Performance is analyzed for systems with single and multiple receiving antennas over both correlated and uncorrelated Rayleigh fading channels, with and without co-channel interference.
This thesis examines distributed search algorithms for swarm robotics. It implements and compares four algorithms: Particle Swarm Optimization (PSO), Cellular Decomposition, Modified Bacterial Foraging Optimization (MBFO), and Dynamic MBFO. Simulations were conducted in an environment representing possible real-world applications. PSO showed the fastest search times but lacked thorough coverage. Cellular Decomposition and MBFO provided better coverage but were slower. Dynamic MBFO adapted to target locations, achieving a balance of speed and coverage.
- The document is a master's thesis that proposes a self-optimized algorithm for downlink interference management in local area LTE-A deployments using femtocells.
- The algorithm uses Flexible Spectrum Usage (FSU) to allow neighboring cells to share and flexibly use spectrum, and power control to limit interference while ensuring good performance.
- Simulation results show that the proposed FSU mechanism, with and without power control, provides higher throughput and lower outage compared to traditional frequency reuse schemes in indoor office and home scenarios.
This document summarizes a thesis by Ibrahim Samir Raad titled "Applying diversity to OFDM". The thesis proposes three applications of diversity to improve the performance of OFDM systems in terms of bit error rate. First, it proposes a new spreading matrix called the Rotation Spreading matrix to introduce frequency diversity. Second, it employs time diversity using delaying the block symbols of Block Spread OFDM. Third, it presents Parallel Concatenated Spreading Matrices OFDM to employ coding gain and improve the performance of Block Spread OFDM. As a result of the work in this thesis, 15 international peer reviewed publications were achieved.
This document is a dissertation that investigates techniques to enhance the performance of cognitive radios using orthogonal frequency division multiplexing (OFDM). It proposes a novel non-contiguous OFDM (NC-OFDM) technique that achieves high data rates by using a large number of non-contiguous subcarriers while avoiding interference to existing transmissions. It also presents five novel algorithms for reducing the peak-to-average power ratio (PAPR) of OFDM signals, which is important for cognitive radios with limited power amplifiers. Additionally, it proposes an efficient FFT pruning algorithm to reduce the complexity of FFT evaluation when many subcarriers are deactivated, as is common in NC-OFDM systems operating in a dynamic spectrum access environment
Similar to Robustness and evolution of novel functions in programmable hardware (20)
EWOCS-I: The catalog of X-ray sources in Westerlund 1 from the Extended Weste...Sérgio Sacani
Context. With a mass exceeding several 104 M⊙ and a rich and dense population of massive stars, supermassive young star clusters
represent the most massive star-forming environment that is dominated by the feedback from massive stars and gravitational interactions
among stars.
Aims. In this paper we present the Extended Westerlund 1 and 2 Open Clusters Survey (EWOCS) project, which aims to investigate
the influence of the starburst environment on the formation of stars and planets, and on the evolution of both low and high mass stars.
The primary targets of this project are Westerlund 1 and 2, the closest supermassive star clusters to the Sun.
Methods. The project is based primarily on recent observations conducted with the Chandra and JWST observatories. Specifically,
the Chandra survey of Westerlund 1 consists of 36 new ACIS-I observations, nearly co-pointed, for a total exposure time of 1 Msec.
Additionally, we included 8 archival Chandra/ACIS-S observations. This paper presents the resulting catalog of X-ray sources within
and around Westerlund 1. Sources were detected by combining various existing methods, and photon extraction and source validation
were carried out using the ACIS-Extract software.
Results. The EWOCS X-ray catalog comprises 5963 validated sources out of the 9420 initially provided to ACIS-Extract, reaching a
photon flux threshold of approximately 2 × 10−8 photons cm−2
s
−1
. The X-ray sources exhibit a highly concentrated spatial distribution,
with 1075 sources located within the central 1 arcmin. We have successfully detected X-ray emissions from 126 out of the 166 known
massive stars of the cluster, and we have collected over 71 000 photons from the magnetar CXO J164710.20-455217.
Authoring a personal GPT for your research and practice: How we created the Q...Leonel Morgado
Thematic analysis in qualitative research is a time-consuming and systematic task, typically done using teams. Team members must ground their activities on common understandings of the major concepts underlying the thematic analysis, and define criteria for its development. However, conceptual misunderstandings, equivocations, and lack of adherence to criteria are challenges to the quality and speed of this process. Given the distributed and uncertain nature of this process, we wondered if the tasks in thematic analysis could be supported by readily available artificial intelligence chatbots. Our early efforts point to potential benefits: not just saving time in the coding process but better adherence to criteria and grounding, by increasing triangulation between humans and artificial intelligence. This tutorial will provide a description and demonstration of the process we followed, as two academic researchers, to develop a custom ChatGPT to assist with qualitative coding in the thematic data analysis process of immersive learning accounts in a survey of the academic literature: QUAL-E Immersive Learning Thematic Analysis Helper. In the hands-on time, participants will try out QUAL-E and develop their ideas for their own qualitative coding ChatGPT. Participants that have the paid ChatGPT Plus subscription can create a draft of their assistants. The organizers will provide course materials and slide deck that participants will be able to utilize to continue development of their custom GPT. The paid subscription to ChatGPT Plus is not required to participate in this workshop, just for trying out personal GPTs during it.
Current Ms word generated power point presentation covers major details about the micronuclei test. It's significance and assays to conduct it. It is used to detect the micronuclei formation inside the cells of nearly every multicellular organism. It's formation takes place during chromosomal sepration at metaphase.
Travis Hills' Endeavors in Minnesota: Fostering Environmental and Economic Pr...Travis Hills MN
Travis Hills of Minnesota developed a method to convert waste into high-value dry fertilizer, significantly enriching soil quality. By providing farmers with a valuable resource derived from waste, Travis Hills helps enhance farm profitability while promoting environmental stewardship. Travis Hills' sustainable practices lead to cost savings and increased revenue for farmers by improving resource efficiency and reducing waste.
The debris of the ‘last major merger’ is dynamically youngSérgio Sacani
The Milky Way’s (MW) inner stellar halo contains an [Fe/H]-rich component with highly eccentric orbits, often referred to as the
‘last major merger.’ Hypotheses for the origin of this component include Gaia-Sausage/Enceladus (GSE), where the progenitor
collided with the MW proto-disc 8–11 Gyr ago, and the Virgo Radial Merger (VRM), where the progenitor collided with the
MW disc within the last 3 Gyr. These two scenarios make different predictions about observable structure in local phase space,
because the morphology of debris depends on how long it has had to phase mix. The recently identified phase-space folds in Gaia
DR3 have positive caustic velocities, making them fundamentally different than the phase-mixed chevrons found in simulations
at late times. Roughly 20 per cent of the stars in the prograde local stellar halo are associated with the observed caustics. Based
on a simple phase-mixing model, the observed number of caustics are consistent with a merger that occurred 1–2 Gyr ago.
We also compare the observed phase-space distribution to FIRE-2 Latte simulations of GSE-like mergers, using a quantitative
measurement of phase mixing (2D causticality). The observed local phase-space distribution best matches the simulated data
1–2 Gyr after collision, and certainly not later than 3 Gyr. This is further evidence that the progenitor of the ‘last major merger’
did not collide with the MW proto-disc at early times, as is thought for the GSE, but instead collided with the MW disc within
the last few Gyr, consistent with the body of work surrounding the VRM.
Unlocking the mysteries of reproduction: Exploring fecundity and gonadosomati...AbdullaAlAsif1
The pygmy halfbeak Dermogenys colletei, is known for its viviparous nature, this presents an intriguing case of relatively low fecundity, raising questions about potential compensatory reproductive strategies employed by this species. Our study delves into the examination of fecundity and the Gonadosomatic Index (GSI) in the Pygmy Halfbeak, D. colletei (Meisner, 2001), an intriguing viviparous fish indigenous to Sarawak, Borneo. We hypothesize that the Pygmy halfbeak, D. colletei, may exhibit unique reproductive adaptations to offset its low fecundity, thus enhancing its survival and fitness. To address this, we conducted a comprehensive study utilizing 28 mature female specimens of D. colletei, carefully measuring fecundity and GSI to shed light on the reproductive adaptations of this species. Our findings reveal that D. colletei indeed exhibits low fecundity, with a mean of 16.76 ± 2.01, and a mean GSI of 12.83 ± 1.27, providing crucial insights into the reproductive mechanisms at play in this species. These results underscore the existence of unique reproductive strategies in D. colletei, enabling its adaptation and persistence in Borneo's diverse aquatic ecosystems, and call for further ecological research to elucidate these mechanisms. This study lends to a better understanding of viviparous fish in Borneo and contributes to the broader field of aquatic ecology, enhancing our knowledge of species adaptations to unique ecological challenges.
Remote Sensing and Computational, Evolutionary, Supercomputing, and Intellige...University of Maribor
Slides from talk:
Aleš Zamuda: Remote Sensing and Computational, Evolutionary, Supercomputing, and Intelligent Systems.
11th International Conference on Electrical, Electronics and Computer Engineering (IcETRAN), Niš, 3-6 June 2024
Inter-Society Networking Panel GRSS/MTT-S/CIS Panel Session: Promoting Connection and Cooperation
https://www.etran.rs/2024/en/home-english/
8.Isolation of pure cultures and preservation of cultures.pdf
Robustness and evolution of novel functions in programmable hardware
1. . . . . . . . . . .
Introduction
. . . . . . . . .
Genotype Space and Neutral Networks
. . . . . . . . . .
Robustness and Evolvability
. . . . . .
Summary
.
.
. ..
.
.
Robustness and evolution of novel functions
in programmable hardware
Karthik Raman
Andreas Wagner Lab
Institute of Evolutionary Biology and Environmental Studies
University of Zürich
April 1, 2011
1 / 40
2. . . . . . . . . . .
Introduction
. . . . . . . . .
Genotype Space and Neutral Networks
. . . . . . . . . .
Robustness and Evolvability
. . . . . .
Summary
Outline
.
. .1 Introduction
Robustness and Evolvability
Neutral Networks
.
. .2 Genotype Space and Neutral Networks
Genotype space
Phenotype space
Neutral networks
.
. .3 Robustness and Evolvability
Robustness of circuits
Evolving new functions
.
. .4 Summary
2 / 40
3. . . . . . . . . . .
Introduction
. . . . . . . . .
Genotype Space and Neutral Networks
. . . . . . . . . .
Robustness and Evolvability
. . . . . .
Summary
Biological systems vs. Man-made systems
.
Biological systems
..
.
. ..
.
.
Shaped through the forces of mutation and natural selection
Survive onslaught of disruptive agents — hostile
environments/random mutations: robust
Show a remarkable ability to adapt and evolve novel properties
through such random mutations: evolvable
.
Man-made systems
..
.
. ..
.
.
Product of rational design, rather than biological evolution
Generally not as robust: often fragile — modification/removal of
components results in catastrophic failure
Their ability to acquire novel and useful features through random
change is limited
3 / 40
4. . . . . . . . . . .
Introduction
. . . . . . . . .
Genotype Space and Neutral Networks
. . . . . . . . . .
Robustness and Evolvability
. . . . . .
Summary
Biological systems vs. Man-made systems
.
Biological systems
..
.
. ..
.
.
Shaped through the forces of mutation and natural selection
Survive onslaught of disruptive agents — hostile
environments/random mutations: robust
Show a remarkable ability to adapt and evolve novel properties
through such random mutations: evolvable
.
Man-made systems
..
.
. ..
.
.
Product of rational design, rather than biological evolution
Generally not as robust: often fragile — modification/removal of
components results in catastrophic failure
Their ability to acquire novel and useful features through random
change is limited
3 / 40
5. . . . . . . . . . .
Introduction
. . . . . . . . .
Genotype Space and Neutral Networks
. . . . . . . . . .
Robustness and Evolvability
. . . . . .
Summary
Biological systems vs. Man-made systems
.
Biological systems
..
.
. ..
.
.
Shaped through the forces of mutation and natural selection
Survive onslaught of disruptive agents — hostile
environments/random mutations: robust
Show a remarkable ability to adapt and evolve novel properties
through such random mutations: evolvable
.
Man-made systems
..
.
. ..
.
.
Product of rational design, rather than biological evolution
Generally not as robust: often fragile — modification/removal of
components results in catastrophic failure
Their ability to acquire novel and useful features through random
change is limited
3 / 40
6. . . . . . . . . . .
Introduction
. . . . . . . . .
Genotype Space and Neutral Networks
. . . . . . . . . .
Robustness and Evolvability
. . . . . .
Summary
Robustness
Fundamental feature of most biological systems — ability to continue
normal function in the face of perturbations
Man-made systems — generally not very robust to failure
Design of fault-tolerant systems is receiving increased attention
4 / 40
7. . . . . . . . . . .
Introduction
. . . . . . . . .
Genotype Space and Neutral Networks
. . . . . . . . . .
Robustness and Evolvability
. . . . . .
Summary
Evolvability
“The ability to produce phenotypic diversity, novel solutions to the problems
faced by organisms and evolutionary innovations”
Common feature of biological systems — novel functions, which help an
organism survive and reproduce, are acquired through genetic change.
The need for adaptation in artificial systems is being recognised — ability
to learn and adapt to new situations, e. g. autonomous robots
5 / 40
8. . . . . . . . . . .
Introduction
. . . . . . . . .
Genotype Space and Neutral Networks
. . . . . . . . . .
Robustness and Evolvability
. . . . . .
Summary
Evolvable Hardware
Principles of evolution have been applied in computer science for
solving many complex optimisation problems — evolutionary
computationa
implements aspects such as random variation, reproduction,
selection, . . .
Artificial evolution can automatically generate designs of digital
circuits, as well as circuits that are robust to noise and faultsb
Evolvable hardware = evolutionary algorithms applied to electronic
circuits and devices
a
Foster JA (2001) Nat Rev Genet 2:428–436
b
Hartmann M & Haddow P (2004) IEE Proceedings - Computers and Digital Techniques 151:287–294
6 / 40
9. . . . . . . . . . .
Introduction
. . . . . . . . .
Genotype Space and Neutral Networks
. . . . . . . . . .
Robustness and Evolvability
. . . . . .
Summary
Key Questions
How ‘robust’ is a typical circuit to changes in the
wiring/configuration?
Do neutral networks exist in this circuit space?
Can circuits with significantly different configuration compute the
same Boolean function?
Does the organisation of neutral networks facilitate the adoption of
novel phenotypes (logic function computations) through small
numbers of gate changes?
7 / 40
10. . . . . . . . . . .
Introduction
. . . . . . . . .
Genotype Space and Neutral Networks
. . . . . . . . . .
Robustness and Evolvability
. . . . . .
Summary
Neutral Networks
Genotype space
Nodes: Genotypes
Edges: mutation/simple genetic
change
Phenotypes mapped to genotypes
Largest neutral network
Smaller neutral network
Smaller and more fragmented neutral
set
Disconnected multiple neutral sets
8 / 40
11. . . . . . . . . . .
Introduction
. . . . . . . . .
Genotype Space and Neutral Networks
. . . . . . . . . .
Robustness and Evolvability
. . . . . .
Summary
Neutral Networks
Genotype space
Nodes: Genotypes
Edges: mutation/simple genetic
change
Phenotypes mapped to genotypes
Largest neutral network
Smaller neutral network
Smaller and more fragmented neutral
set
Disconnected multiple neutral sets
Neutral networks — Genotypes sharing the same phenotype
8 / 40
12. . . . . . . . . . .
Introduction
. . . . . . . . .
Genotype Space and Neutral Networks
. . . . . . . . . .
Robustness and Evolvability
. . . . . .
Summary
Neutral Networks
Genotype space
Nodes: Genotypes
Edges: mutation/simple genetic
change
Phenotypes mapped to genotypes
Largest neutral network
Smaller neutral network
Smaller and more fragmented neutral
set
Disconnected multiple neutral sets
Neutral networks — Genotypes sharing the same phenotype
8 / 40
13. . . . . . . . . . .
Introduction
. . . . . . . . .
Genotype Space and Neutral Networks
. . . . . . . . . .
Robustness and Evolvability
. . . . . .
Summary
Neutral Networks
Genotype space
Nodes: Genotypes
Edges: mutation/simple genetic
change
Phenotypes mapped to genotypes
Largest neutral network
Smaller neutral network
Smaller and more fragmented neutral
set
Disconnected multiple neutral sets
Neutral networks — Genotypes sharing the same phenotype
8 / 40
14. . . . . . . . . . .
Introduction
. . . . . . . . .
Genotype Space and Neutral Networks
. . . . . . . . . .
Robustness and Evolvability
. . . . . .
Summary
Neutral Networks
Genotype space
Nodes: Genotypes
Edges: mutation/simple genetic
change
Phenotypes mapped to genotypes
Largest neutral network
Smaller neutral network
Smaller and more fragmented neutral
set
Disconnected multiple neutral sets
Neutral networks — Genotypes sharing the same phenotype
8 / 40
15. . . . . . . . . . .
Introduction
. . . . . . . . .
Genotype Space and Neutral Networks
. . . . . . . . . .
Robustness and Evolvability
. . . . . .
Summary
Neutral Networks
Genotype space
Nodes: Genotypes
Edges: mutation/simple genetic
change
Phenotypes mapped to genotypes
Largest neutral network
Smaller neutral network
Smaller and more fragmented neutral
set
Disconnected multiple neutral sets
Neutral networks — Genotypes sharing the same phenotype
8 / 40
16. . . . . . . . . . .
Introduction
. . . . . . . . .
Genotype Space and Neutral Networks
. . . . . . . . . .
Robustness and Evolvability
. . . . . .
Summary
Neutral Networks
Genotype space
Nodes: Genotypes
Edges: mutation/simple genetic
change
Phenotypes mapped to genotypes
Largest neutral network
Smaller neutral network
Smaller and more fragmented neutral
set
Disconnected multiple neutral sets
Neutral networks — Genotypes sharing the same phenotype
The genotype space is covered with multiple neutral sets/networks
Neutral networks have implications for robustness/evolvability
8 / 40
17. . . . . . . . . . .
Introduction
. . . . . . . . .
Genotype Space and Neutral Networks
. . . . . . . . . .
Robustness and Evolvability
. . . . . .
Summary
Genotype vs. Phenotype
Genotype evolves through mutation and is inherited; selection acts
on phenotype
Genotype–phenotype mapping — required to distinguish neutral
networks
Mapping may not be straightforward always
System Genotype Phenotype
RNA/Proteins Sequence Structure
Regulatory networks Regulatory interactions Gene expression patterns
Circadian oscillators Regulatory interactions Oscillations
Digital circuits Circuit components/wiring Boolean function computed
Protein–protein interactions Network topology ?
Signal transduction Network topology ?
9 / 40
18. . . . . . . . . . .
Introduction
. . . . . . . . .
Genotype Space and Neutral Networks
. . . . . . . . . .
Robustness and Evolvability
. . . . . .
Summary
Neutral networks vs. Robustness/Evolvability
Neutral networks can be traversed in small evolutionary steps,
through simple changes/mutations
Larger neutral network ⇒ higher robustness, scope for evolutionary
innovation …
10 / 40
19. . . . . . . . . . .
Introduction
. . . . . . . . .
Genotype Space and Neutral Networks
. . . . . . . . . .
Robustness and Evolvability
. . . . . .
Summary
Neutral Networks vs. Robustness
Time
High robustness
Low robustness
Low robustness: more deleterious mutations
High robustness: likely to encounter more novel phenotypes 11 / 40
20. . . . . . . . . . .
Introduction
. . . . . . . . .
Genotype Space and Neutral Networks
. . . . . . . . . .
Robustness and Evolvability
. . . . . .
Summary
Neutral Networks vs. Robustness
Time
High robustness
Low robustness
Low robustness: more deleterious mutations
High robustness: likely to encounter more novel phenotypes 11 / 40
21. . . . . . . . . . .
Introduction
. . . . . . . . .
Genotype Space and Neutral Networks
. . . . . . . . . .
Robustness and Evolvability
. . . . . .
Summary
Neutral Networks vs. Robustness
Time
High robustness
Low robustness
—Wagner A (2008a) Nat Rev Genet 9:965–974
Low robustness: more deleterious mutations
High robustness: likely to encounter more novel phenotypes 11 / 40
22. . . . . . . . . . .
Introduction
. . . . . . . . .
Genotype Space and Neutral Networks
. . . . . . . . . .
Robustness and Evolvability
. . . . . .
Summary
Robustness vs. Evolvability
Robustness and evolvability — both correlate with neutral network
size/connectivity
Robust phenotypes tend to have higher evolvability
Low Robustness
Low Innovation
High Robustness
Low Innovation
High Robustness
High Innovation
—Ciliberti S et al. (2007) Proc Natl Acad Sci U S A 104:13591–13596
Populations evolving on larger neutral networks have greater access
to variation*
12 / 40
23. . . . . . . . . . .
Introduction
. . . . . . . . .
Genotype Space and Neutral Networks
. . . . . . . . . .
Robustness and Evolvability
. . . . . .
Summary
Outline
.
. .1 Introduction
Robustness and Evolvability
Neutral Networks
.
. .2 Genotype Space and Neutral Networks
Genotype space
Phenotype space
Neutral networks
.
. .3 Robustness and Evolvability
Robustness of circuits
Evolving new functions
.
. .4 Summary
13 / 40
24. . . . . . . . . . .
Introduction
. . . . . . . . .
Genotype Space and Neutral Networks
. . . . . . . . . .
Robustness and Evolvability
. . . . . .
Summary
Field Programmable Gate Arrays (FPGAs)
I
N
P
U
T
S
1
2
3
4
6
7
O
U
T
P
U
T
S
5 8
9
10 13
12
11
OR
A
B
Y
AND
A
B
Y
NAND
A
B
Y
NOR
A
B
Y
XOR
A
B
Y
Y=A+B
Y=A×B
Y=AÅB
___
Y=(A×B)
____
Y=(A+B)
n × m array of logic gates
Configuration can be dynamically reprogrammed: ‘field
programmable’
Maps a Boolean input of nI variables to an output of no variables:
f : {0, 1}nI
→ {0, 1}no
14 / 40
25. . . . . . . . . . .
Introduction
. . . . . . . . .
Genotype Space and Neutral Networks
. . . . . . . . . .
Robustness and Evolvability
. . . . . .
Summary
Generic FPGA
inputs
outputs
nI inputs, mapped to no outputs
All nI inputs must be used in column 1
n × m array of logic gates, Lij, each with two inputs
Inter-connections are feed-forward: a gate in column i can take an
input from any of the previous levels
no outputs can come from any of the mn gate outputs
15 / 40
26. . . . . . . . . . .
Introduction
. . . . . . . . .
Genotype Space and Neutral Networks
. . . . . . . . . .
Robustness and Evolvability
. . . . . .
Summary
Representation of FPGAs
I
N
P
U
T
S
1
2
3
4
6
7
O
U
T
P
U
T
S
5 8
9
10 13
12
11
4 2 3
L11
1 1 5
L12
3 2 2
L13
2 2 5
L21
1 7 2
L22
5 2 3
L23
10 5 3
L31
3 3 1
L32
6 6 4
L33
11 12 10 13
Outputs
Size of representation = 3mn + no = diameter of circuit space
[Similar to Cartesian Genetic Programming — Miller & Thomson (2000)]
16 / 40
27. . . . . . . . . . .
Introduction
. . . . . . . . .
Genotype Space and Neutral Networks
. . . . . . . . . .
Robustness and Evolvability
. . . . . .
Summary
Genotype space: Circuits with various configurations
I
N
P
U
T
S
1
2
4
53
6
O
U
T
P
U
T
S
I
N
P
U
T
S
1
2
4
53
6
O
U
T
P
U
T
S
I
N
P
U
T
S
1
2
4
53
6
O
U
T
P
U
T
S
I
N
P
U
T
S
1
2
4
53
6
O
U
T
P
U
T
S
I
N
P
U
T
S
1
2
4
53
6
O
U
T
P
U
T
S
C1 C2
C3C4C5
C6
I
N
P
U
T
S
1
2
4
53
6
O
U
T
P
U
T
S
Every node in genotype space is a circuit (of a particular size)
Neighbours vary by a small elementary change in: (a) Internal wiring
(C2), (b) Logic function of one of the gates (C3), (c) Input mapping
(C5), or (d) Output mapping (C6)
d(C4, C1) = 1 ⇒ not neighbours
17 / 40
28. . . . . . . . . . .
Introduction
. . . . . . . . .
Genotype Space and Neutral Networks
. . . . . . . . . .
Robustness and Evolvability
. . . . . .
Summary
Phenotype Space: Boolean functions
Every circuit maps a Boolean input of nI bits to an output of no bits:
f : {0, 1}nI
→ {0, 1}no
For example,
i j k l ⇒ j k l i
Circular [Left] Shift
i j k l ⇒ 0 i j k
[Unsigned] Right Shift
I1 I2 I3 I4 O1 O2 O3 O4
0 0 0 0 0 0 0 0
0 0 0 1 0 0 1 0
0 0 1 0 0 1 0 0
0 0 1 1 0 1 1 0
0 1 0 0 1 0 0 0
0 1 0 1 1 0 1 0
0 1 1 0 1 1 0 0
0 1 1 1 1 1 1 0
1 0 0 0 0 0 0 1
1 0 0 1 0 0 1 1
1 0 1 0 0 1 0 1
1 0 1 1 0 1 1 1
1 1 0 0 1 0 0 1
1 1 0 1 1 0 1 1
1 1 1 0 1 1 0 1
1 1 1 1 1 1 1 1
Circular left shift
truth table
Total Boolean functions = 2entries in truth table
= 264
= 1.84 × 1019
18 / 40
29. . . . . . . . . . .
Introduction
. . . . . . . . .
Genotype Space and Neutral Networks
. . . . . . . . . .
Robustness and Evolvability
. . . . . .
Summary
Sampling circuit space
Sample size = 2 × 107
Circuit space sampled uniformly
FPGA size Genotype
space size
Functions observed
in sample
3 × 3 1.08 ×1024
1.59 ×107
4 × 4 8.43 ×1045
1.74 ×107
5 × 5 2.90 ×1076
1.80 ×107
6 × 6 6.05 ×10116
1.83 ×107
Total Boolean functions = 264
= 1.84 × 1019
Small fraction of total Boolean functions observed: ≈ 10−12
Most observed functions are computed only by one circuit in the
sample
Few functions are computed by large number of circuits
19 / 40
30. . . . . . . . . . .
Introduction
. . . . . . . . .
Genotype Space and Neutral Networks
. . . . . . . . . .
Robustness and Evolvability
. . . . . .
Summary
Majority of functions are rare
10
0
10
5
10
−8
10
−7
10
−6
10
−5
10
−4
Rank of logic function (decreasing size of circuit sets)
Frequencyoflogicfunction
Some functions appear over a 1000
times
Long tail: Huge number of functions
appear only once
Functions such as right shift/circular
shift do not appear in the sample of
2 × 107
20 / 40
31. . . . . . . . . . .
Introduction
. . . . . . . . .
Genotype Space and Neutral Networks
. . . . . . . . . .
Robustness and Evolvability
. . . . . .
Summary
Neutral networks in circuit space
Circuits computing the same function can be reached through
function-preserving random walks in circuit space
⇒ Circuit space is spanned by large neutral networks
0 0.2 0.4 0.6 0.8 1
10
0
10
1
10
2
10
3
Maximal circuit distance (D)
Numberoffunctions
4x4 Circuits
10
−7
10
−6
10
−5
10
−4
0.3
0.5
0.7
1
Frequency of the logic functionMaximalcircuitdistance(D)
4x4 Circuits
Spearman’s r = 0.56; p < 10−300
; n = 1000
A function-preserving random walk in circuit space can take us very
far away from the initial circuit
⇒ Neutral networks have very large diameter
21 / 40
32. . . . . . . . . . .
Introduction
. . . . . . . . .
Genotype Space and Neutral Networks
. . . . . . . . . .
Robustness and Evolvability
. . . . . .
Summary
Diverse circuits can compute the same function
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4 2 3 1 1 5 3 2 2 2 2 5 1 7 2 5 2 3 10 5 3 3 3 1 6 6 4 11 12 10 13
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2 3 1 4 4 1 1 1 3 5 3 4 7 6 1 7 3 1 1 1 2 1 5 2 5 2 2 13 10 9 11
Both circuits compute
circular shift
Differ in every logic
gate, wiring, input &
output mapping
Thus, the diameters of
neutral networks can be
quite large
22 / 40
33. . . . . . . . . . .
Introduction
. . . . . . . . .
Genotype Space and Neutral Networks
. . . . . . . . . .
Robustness and Evolvability
. . . . . .
Summary
Outline
.
. .1 Introduction
Robustness and Evolvability
Neutral Networks
.
. .2 Genotype Space and Neutral Networks
Genotype space
Phenotype space
Neutral networks
.
. .3 Robustness and Evolvability
Robustness of circuits
Evolving new functions
.
. .4 Summary
23 / 40
34. . . . . . . . . . .
Introduction
. . . . . . . . .
Genotype Space and Neutral Networks
. . . . . . . . . .
Robustness and Evolvability
. . . . . .
Summary
Robustness to change in configuration
10
−7
10
−6
10
−5
10
−4
0
0.2
0.4
0.6
0.8
1
Frequency of the logic function
Robustnesstoconfigurationchange
4x4 Circuits
Spearman’s r = 0.32; p < 10
−300
0 0.2 0.4 0.6 0.8 1
0
50
100
Circular shift (3x3)
0 0.2 0.4 0.6 0.8 1
0
20
40
Numberofcircuits
Circular shift (4x4)
0 0.2 0.4 0.6 0.8 1
0
20
40
Fraction of neutral neighbors
Circular shift (6x6)
Robustness = fraction of neutral neighbours
Robustness distribution is quite broad
Larger circuits are more robust (regardless of function)
24 / 40
35. . . . . . . . . . .
Introduction
. . . . . . . . .
Genotype Space and Neutral Networks
. . . . . . . . . .
Robustness and Evolvability
. . . . . .
Summary
Robustness to gate failure
10
−7
10
−6
10
−5
10
−4
0
0.2
0.4
0.6
0.8
1
Frequency of the logic function
Robustnesstogatefailure
4x4 Circuits
0 0.2 0.4 0.6 0.8 1
0
50
Circular shift (3x3)
0 0.2 0.4 0.6 0.8 1
0
20
40
Numberofcircuits
Circular shift (4x4)
0 0.2 0.4 0.6 0.8 1
0
20
40
Failure robustness
Circular shift (6x6)
Gate failures are common in digital circuits
Types of failures considered: zero output (and inverted output)
Failure robustness = fraction of single gate failures that do not affect
the computed function
Failure robustness distribution is also quite broad
Larger circuits are more robust to gate failure
25 / 40
36. . . . . . . . . . .
Introduction
. . . . . . . . .
Genotype Space and Neutral Networks
. . . . . . . . . .
Robustness and Evolvability
. . . . . .
Summary
Evolving new functions
On large neutral networks, genotypes can change substantially
without changing phenotype
Phenotypes in different neighbourhoods of a neutral network can be
quite different
In biological systems, this feature facilitates the exploration of new
phenotypesab
For circuits, this will have implications for the ease with which
evolvable hardware can acquire new functions
a
Ciliberti S et al. (2007) Proc Natl Acad Sci U S A 104:13591–13596
b
Wagner A (2008b) Proc Biol Sci 275:91–100
26 / 40
37. . . . . . . . . . .
Introduction
. . . . . . . . .
Genotype Space and Neutral Networks
. . . . . . . . . .
Robustness and Evolvability
. . . . . .
Summary
Neighbourhood of evolving circuits
0 500 1000 1500 2000
0
500
1000
1500
2000
2500
3000
Random walk steps
Cumulativenovelfunctions
encounteredinneighborhood
0 1000 2000
0
1000
2000
3000
f = 5.00 ⋅ 10
−8
Cumulativenovelfunctions
encounteredinneighborhood
0 1000 2000
0
1000
2000
3000
f = 5.00 ⋅ 10
−8
0 1000 2000
0
1000
2000
3000
f = 3.00 ⋅ 10
−7
0 1000 2000
0
1000
2000
3000
f = 4.65 ⋅ 10
−6
0 1000 2000
0
1000
2000
3000
f = 6.35 ⋅ 10−6
Random walk steps
Cumulativenovelfunctions
encounteredinneighborhood
0 1000 2000
0
1000
2000
3000
f = 9.40 ⋅ 10−6
Random walk steps
0 1000 2000
0
1000
2000
3000
f = 1.24 ⋅ 10−5
Random walk steps
0 1000 2000
0
1000
2000
3000
f = 5.09 ⋅ 10−5
Random walk steps
As we explore the neutral network (through a function-preserving
random walk), a large number of new phenotypes are encountered
The number of new phenotypes keeps increasing, as we prolong the
random walk
This property holds for a large number of functions
Indicates the high accessibility of innovation in the neighbourhood
27 / 40
38. . . . . . . . . . .
Introduction
. . . . . . . . .
Genotype Space and Neutral Networks
. . . . . . . . . .
Robustness and Evolvability
. . . . . .
Summary
Neighbourhood of evolving circuits
What is the fraction of new phenotypes encountered in the
neighbourhood of any circuit?
With reference to a starting circuit C0,
u(C0, Ci) = 1 −
|N0 ∩ Ni|
|N0 ∪ Ni|
28 / 40
39. . . . . . . . . . .
Introduction
. . . . . . . . .
Genotype Space and Neutral Networks
. . . . . . . . . .
Robustness and Evolvability
. . . . . .
Summary
Neighbourhood of evolving circuits
What is the fraction of new phenotypes encountered in the
neighbourhood of any circuit?
With reference to a starting circuit C0,
u(C0, Ci) = 1 −
|N0 ∩ Ni|
|N0 ∪ Ni|
G1
G2
shared
unique
u(G1, G2) = = 5
8
= 0.625
28 / 40
40. . . . . . . . . . .
Introduction
. . . . . . . . .
Genotype Space and Neutral Networks
. . . . . . . . . .
Robustness and Evolvability
. . . . . .
Summary
Neighbourhood of evolving circuits
0 50 100 150 200
0
0.2
0.4
0.6
0.8
1
Random walk steps
Fractionofnewfunctions
inneighborhood
0 1000 2000
0
0.5
1
f = 5.00 ⋅ 10
−8
Fractionofnewfunctions
inneighborhood
0 1000 2000
0
0.5
1
f = 5.00 ⋅ 10
−8
0 1000 2000
0
0.5
1
f = 3.00 ⋅ 10
−7
0 1000 2000
0
0.5
1
f = 4.65 ⋅ 10
−6
0 1000 2000
0
0.5
1
f = 6.35 ⋅ 10−6
Random walk steps
Fractionofnewfunctions
inneighborhood
0 1000 2000
0
0.5
1
f = 9.40 ⋅ 10−6
Random walk steps
0 1000 2000
0
0.5
1
f = 1.24 ⋅ 10−5
Random walk steps
0 1000 2000
0
0.5
1
f = 5.09 ⋅ 10−5
Random walk steps
Beyond the distance of ≈ one network diameter, over 80% of the
functions found in the neighbourhood are new
At increasing distances from a circuit, a very large number of new
phenotypes are accessible; this property holds for a large number of
functions
29 / 40
41. . . . . . . . . . .
Introduction
. . . . . . . . .
Genotype Space and Neutral Networks
. . . . . . . . . .
Robustness and Evolvability
. . . . . .
Summary
Fraction of new phenotypes at the end of a random walk
10
−7
10
−6
10
−5
10
−4
0
0.2
0.4
0.6
0.8
1
Frequency of the logic function
Fractionofnewfunctionsin
neighborhoodatendofrandomwalk
4x4 Circuits
0 0.2 0.4 0.6 0.8 1
0
10
20
30
40
50
60
Fraction of new functions in neighborhood
at the end of random walk
Numberofcircuits
Circular shift (4x4)
A lot of innovation is accessible in the neighbourhood, once we walk
sufficiently far awaya
from a starting circuit . . .
a
2,000 steps, in this case
30 / 40
42. . . . . . . . . . .
Introduction
. . . . . . . . .
Genotype Space and Neutral Networks
. . . . . . . . . .
Robustness and Evolvability
. . . . . .
Summary
Proximity of neutral networks
How far must one travel in circuit space from one neutral set, to find
another neutral set?
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43. . . . . . . . . . .
Introduction
. . . . . . . . .
Genotype Space and Neutral Networks
. . . . . . . . . .
Robustness and Evolvability
. . . . . .
Summary
Proximity of neutral networks
How far must one travel in circuit space from one neutral set, to find
another neutral set?
0 0.2 0.4 0.6 0.8 1
0
50
100
150
200
Minimum distance between circuits
computing right shift and circular shift
(as fraction of circuit space diameter)
Pairsofcircuits
0 0.2 0.4 0.6 0.8 1
0
200
400
600
800
Minimum distance between neutral networks
(as fraction of circuit space diameter)
Pairsofneutralnetworksd(CS, RS) ≤ 3!
It is possible to discover new functions through a relatively small
number of elementary changes
31 / 40
44. . . . . . . . . . .
Introduction
. . . . . . . . .
Genotype Space and Neutral Networks
. . . . . . . . . .
Robustness and Evolvability
. . . . . .
Summary
Similarity with Biological Systems
The system of circuits studied show intriguing similarities with biological
systems:
Existence of large highly connected neutral networks
Large number of diverse genotypes adopt the same phenotype
Robustness to change in configurations
Large number of novel phenotypes accessible in the neighbourhood
of evolving genotypes
Proximity of different neutral networks
Importance of “junk” non-functional components …
32 / 40
45. . . . . . . . . . .
Introduction
. . . . . . . . .
Genotype Space and Neutral Networks
. . . . . . . . . .
Robustness and Evolvability
. . . . . .
Summary
Role of ‘non-functional components’
Many circuits have non-functional gates, system parts that are not involved in the
computation a given circuit carries out
In biological systems, many amino acids in a proteinab
, many regulatory interactions
in a gene regulation circuitc
, and many metabolic reactions in a metabolic reaction
networkd
may appear as ‘non-functional’ or ‘dispensable’
Tempting to call such system parts ‘junk’ parts — however, such parts play a crucial
role for evolvability, and it is precisely their ability to vary freely in some
environments that allows biological systems to evolve novel phenotypes
For example, in laboratory evolution experiments, proteins with new function evolve
often through changes that do not affect the protein’s principal functionb
Circuits of a minimal size may have the merit of computing a function in an elegant
and simple way — at the same time, they would be utterly unevolvable
Evolvability comes at the price of high complexity
a
Bloom JD et al. (2005) Proc Natl Acad Sci U S A 102:606–611
b
Aharoni A et al. (2005) Nat Genet 37:73–76
c
Ciliberti S et al. (2007) Proc Natl Acad Sci U S A 104:13591–13596
d
Matias Rodrigues JF & Wagner A (2009) PLoS Comput Biol 5:e1000613
33 / 40
46. . . . . . . . . . .
Introduction
. . . . . . . . .
Genotype Space and Neutral Networks
. . . . . . . . . .
Robustness and Evolvability
. . . . . .
Summary
Outline
.
. .1 Introduction
Robustness and Evolvability
Neutral Networks
.
. .2 Genotype Space and Neutral Networks
Genotype space
Phenotype space
Neutral networks
.
. .3 Robustness and Evolvability
Robustness of circuits
Evolving new functions
.
. .4 Summary
34 / 40
47. . . . . . . . . . .
Introduction
. . . . . . . . .
Genotype Space and Neutral Networks
. . . . . . . . . .
Robustness and Evolvability
. . . . . .
Summary
Limitations
Many other factors decide the suitability of a particular circuit, e. g.
power consumption, robustness to temperature variations, and
trade-offs between functional flexibility and performance
Fine differences exist between two silicon chips – circuits evolved on
one silicon chip are not guaranteed to work on anothera
!
Differences exist, between software simulation and hardware
evolution
Some properties of our (or any other) study system may depend on
the choice of representation for a circuit’s architecture
Possible major computational issues with very large circuit sizes
Due to the astronomical numbers of circuits and functions, one
needs to resort to sampling to understand circuit space — not
limiting if one is interested in generic properties of this space
a
Thompson A (1995) In: F Morán, A Moreno, JJ Merelo, & P Chacon (eds.), Advances in Artificial Life:
Proc. 3rd Eur. Conf. on Artificial Life (ECAL95), volume 929 of LNAI, pages 640–656. Springer-Verlag
35 / 40
48. . . . . . . . . . .
Introduction
. . . . . . . . .
Genotype Space and Neutral Networks
. . . . . . . . . .
Robustness and Evolvability
. . . . . .
Summary
Summary
A random sampling of circuit space reveals that majority of the
functions are computed by very few circuits
Circuits computing the same function form large connected neutral
networks with large diameters
Diverse circuits can compute the same function
Larger circuits tend to be more robust; the distribution of robustness
is broad
for a given function and size, the most robust configuration may be
useful in applications
A number of new functions are accessible in the neighbourhood of
evolving circuits
evolvable circuits may find application in the design of adaptive
devices
Neutral networks are also located close together in space
access to new functions through few changes
‘minimal reconfiguration’ may be particularly useful/efficient
36 / 40
49. . . . . . . . . . .
Introduction
. . . . . . . . .
Genotype Space and Neutral Networks
. . . . . . . . . .
Robustness and Evolvability
. . . . . .
Summary
Summary
A random sampling of circuit space reveals that majority of the
functions are computed by very few circuits
Circuits computing the same function form large connected neutral
networks with large diameters
Diverse circuits can compute the same function
Larger circuits tend to be more robust; the distribution of robustness
is broad
for a given function and size, the most robust configuration may be
useful in applications
A number of new functions are accessible in the neighbourhood of
evolving circuits
evolvable circuits may find application in the design of adaptive
devices
Neutral networks are also located close together in space
access to new functions through few changes
‘minimal reconfiguration’ may be particularly useful/efficient
36 / 40
50. . . . . . . . . . .
Introduction
. . . . . . . . .
Genotype Space and Neutral Networks
. . . . . . . . . .
Robustness and Evolvability
. . . . . .
Summary
Summary
A random sampling of circuit space reveals that majority of the
functions are computed by very few circuits
Circuits computing the same function form large connected neutral
networks with large diameters
Diverse circuits can compute the same function
Larger circuits tend to be more robust; the distribution of robustness
is broad
for a given function and size, the most robust configuration may be
useful in applications
A number of new functions are accessible in the neighbourhood of
evolving circuits
evolvable circuits may find application in the design of adaptive
devices
Neutral networks are also located close together in space
access to new functions through few changes
‘minimal reconfiguration’ may be particularly useful/efficient
36 / 40
51. . . . . . . . . . .
Introduction
. . . . . . . . .
Genotype Space and Neutral Networks
. . . . . . . . . .
Robustness and Evolvability
. . . . . .
Summary
Summary
A random sampling of circuit space reveals that majority of the
functions are computed by very few circuits
Circuits computing the same function form large connected neutral
networks with large diameters
Diverse circuits can compute the same function
Larger circuits tend to be more robust; the distribution of robustness
is broad
for a given function and size, the most robust configuration may be
useful in applications
A number of new functions are accessible in the neighbourhood of
evolving circuits
evolvable circuits may find application in the design of adaptive
devices
Neutral networks are also located close together in space
access to new functions through few changes
‘minimal reconfiguration’ may be particularly useful/efficient
36 / 40
52. . . . . . . . . . .
Introduction
. . . . . . . . .
Genotype Space and Neutral Networks
. . . . . . . . . .
Robustness and Evolvability
. . . . . .
Summary
Summary
A random sampling of circuit space reveals that majority of the
functions are computed by very few circuits
Circuits computing the same function form large connected neutral
networks with large diameters
Diverse circuits can compute the same function
Larger circuits tend to be more robust; the distribution of robustness
is broad
for a given function and size, the most robust configuration may be
useful in applications
A number of new functions are accessible in the neighbourhood of
evolving circuits
evolvable circuits may find application in the design of adaptive
devices
Neutral networks are also located close together in space
access to new functions through few changes
‘minimal reconfiguration’ may be particularly useful/efficient
36 / 40
53. . . . . . . . . . .
Introduction
. . . . . . . . .
Genotype Space and Neutral Networks
. . . . . . . . . .
Robustness and Evolvability
. . . . . .
Summary
Outlook: Exploiting robustness and evolvability
.
In technological systems
..
.
. ..
.
.
For any desired Boolean function, it may be beneficial to use the
most robust circuit (one that is resistant to a number of gate failures
as well as configuration changes) of a particular size
Circuits that have access to a greater amount of innovation (diverse
Boolean functions), may be useful in designing systems with adaptive
behaviour
.
In biology …
..
.
. ..
.
.
Such circuits can also be viewed as generalised models of signalling
networks/gene regulatory networks
Such circuits also find applications in synthetic biology, for the
design of synthetic circuitsa
a
Marchisio MA & Stelling J (2011) PLoS Comput Biol 7:e1001083+
37 / 40
54. . . . . . . . . . .
Introduction
. . . . . . . . .
Genotype Space and Neutral Networks
. . . . . . . . . .
Robustness and Evolvability
. . . . . .
Summary
Not all circuits computing the same function are equal …
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Circuit A
Robustness = 0.0556
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Circuit B
Robustness = 0.5725
…is complexity the price for evolvability?
38 / 40