A study of cortical network models with realistic connectivity

Structure is fundamental in shaping the types of computations that neuronal circuits can perform. Explaining the laws that determine the connectivity properties of brain networks and their implications in neuronal dynamics is therefore an important step in the understanding of how brains operate. The local circuits of cortex, which are considered to carry out the basic and essential computations for brain functioning, exhibit a highly stereotyped and organized architecture, which is, in very general terms, conserved across different species, brain areas and individuals. An appropriate way to mathematically represent this family of networks is by means of models defined by a set of connectivity laws that include a certain degree of randomness. These laws reflect the common structural scaffold, whereas the randomness should be interpreted as the variability across the different networks in the ensemble. There is growing experimental evidence that the local circuits of cerebral cortex are far from the simplest random model, according to which connections appear independently with a fixed probability. This evidence is based on a set of observed features that have been collectively called the "nonrandomness" of the cortical circuitry. In this thesis we have explored to what extent several alternative architectures (clustered networks, networks with distance-dependent connectivity and networks that exhibit a given in/out-degree distribution) could be compatible with the reported nonrandom features. We showed that all these structural models can explain the experimental observations, which implies that these nonrandom properties do not provide much information about the underlying organization. This is mainly due to the fact that real data are collected from sparse neuronal samples due to experimental limitations. We sought a local measure that can nevertheless help to distinguish between different alternatives, and we found it in the "sample degree correlation" (SDC), or the correlation coefficient between in- and out-degrees in small groups of neurons. The analysis of the SDC in real data suggests that cortical microcircuits are heterogeneous in structure and possibly shaped through a mixture of distance-dependent and non-symmetrical organizational principles. We finally explored some of the dynamical consequences of imposing a heterogeneous structure in models of neuronal activity. This heterogeneity appears through an arbitrary joint in/out-degree distribution in the entire network. By means of both mean-field approximations and spectral analysis, we demonstrate that broad and positively correlated degree distributions can have an important effect on neuronal dynamics, which suggests that this particular type of structural heterogeneity might allow for richer network computations as compared to standard random models.L'estructura té un paper fonamental a l'hora de determinar els tipus d'operacions que els circuits neuronals poden dur a terme. Entendre les lleis que defineixen la connectivitat de les xarxes del cervell i les seves implicacions en la dinàmica neuronal és, per tant, un pas important en la comprensió del funcionament d'aquestes xarxes. Els circuits locals del còrtex, que es creu suporten les computacions essencials i bàsiques de la funció cerebral, estan organitzats de manera altament ordenada i estereotipada, i aquesta arquitectura, en termes molt generals, s'ha conservat al llarg de les diferents espècies, de les diverses àrees cerebrals i dels individus. Una bona manera de representar matemàticament aquesta família de xarxes és mitjançant models definits per una sèrie de lleis de connectivitat que inclouen un cert grau d'aleatorietat. Les lleis reflecteixen el patró estructural comú, mentre que l'aleatorietat ha de ser interpretada com la variabilitat quan es comparen diferents xarxes del conjunt. Cada vegada hi ha més evidència experimental que els circuits locals del còrtex estan lluny del model aleatori més simple, segons el qual les connexions apareixen de manera independent amb una probabilitat fixada. Aquesta troballa es fonamenta en un conjunt d'observacions a les quals ens referim col·lectivament com la ?no aleatorietat? dels circuits corticals. En aquesta tesi hem explorat fins a quin punt diverses arquitectures alternatives (xarxes amb agrupació, xarxes amb connectivitat dependent de la distància i xarxes definides a través d'una certa distribució de graus d'entrada i de sortida) podrien ser compatibles amb les propietats de no aleatorietat. Hem mostrat que tots els models estructurals alternatius que havíem proposat poden explicar les observacions esmentades, per tant aquestes propietats no aporten gaire informació sobre el tipus d'organització subjacent. Això es deu principalment al fet que les dades reals provenen d'anàlisis molt restringides, en les quals l'estructura s'estudia a partir de mostres locals formades per poques neurones. Vam buscar un estadístic local que permetés, malgrat aquestes dificultats, distingir entre les diverses estructures alternatives, i l'hem trobat en el coeficient de correlació entre els graus d'entrada i de sortida en mostres petites, que hem anomenat "sample degree correlation" (SDC) en anglès. L'anàlisi d'aquesta mesura en dades reals suggereix que els microcircuits corticals tenen una configuració heterogènia -en el sentit que semblen diferir dels models simples proposats- i estan modelats possiblement per factors dependents de la distància física entre neurones però també per principis addicionals que actuen de manera no simètrica. Finalment, hem estudiat algunes de les conseqüències dinàmiques d'imposar una estructura heterogènia en models d'activitat neuronal. Aquesta heterogeneïtat apareix en els nostres models a través de la distribució conjunta de graus d'entrada i de sortida a la xarxa completa. Fent ús d'aproximacions de camp mitjà i de l'anàlisi espectral, hem mostrat que les distribucions de grau amb elevada variància i correlació positiva poden tenir un efecte rellevant en la dinàmica neuronal, fet que suggereix que aquest tipus d'heterogeneïtat estructural podria facilitar uns modes de computació més rics en comparació dels models aleatoris estàndard.Postprint (published version

A study of cortical network models with realistic connectivity

Structure is fundamental in shaping the types of computations that neuronal circuits can perform. Explaining the laws that determine the connectivity properties of brain networks and their implications in neuronal dynamics is therefore an important step in the understanding of how brains operate. The local circuits of cortex, which are considered to carry out the basic and essential computations for brain functioning, exhibit a highly stereotyped and organized architecture, which is, in very general terms, conserved across different species, brain areas and individuals. An appropriate way to mathematically represent this family of networks is by means of models defined by a set of connectivity laws that include a certain degree of randomness. These laws reflect the common structural scaffold, whereas the randomness should be interpreted as the variability across the different networks in the ensemble. There is growing experimental evidence that the local circuits of cerebral cortex are far from the simplest random model, according to which connections appear independently with a fixed probability. This evidence is based on a set of observed features that have been collectively called the "nonrandomness" of the cortical circuitry. In this thesis we have explored to what extent several alternative architectures (clustered networks, networks with distance-dependent connectivity and networks that exhibit a given in/out-degree distribution) could be compatible with the reported nonrandom features. We showed that all these structural models can explain the experimental observations, which implies that these nonrandom properties do not provide much information about the underlying organization. This is mainly due to the fact that real data are collected from sparse neuronal samples due to experimental limitations. We sought a local measure that can nevertheless help to distinguish between different alternatives, and we found it in the "sample degree correlation" (SDC), or the correlation coefficient between in- and out-degrees in small groups of neurons. The analysis of the SDC in real data suggests that cortical microcircuits are heterogeneous in structure and possibly shaped through a mixture of distance-dependent and non-symmetrical organizational principles. We finally explored some of the dynamical consequences of imposing a heterogeneous structure in models of neuronal activity. This heterogeneity appears through an arbitrary joint in/out-degree distribution in the entire network. By means of both mean-field approximations and spectral analysis, we demonstrate that broad and positively correlated degree distributions can have an important effect on neuronal dynamics, which suggests that this particular type of structural heterogeneity might allow for richer network computations as compared to standard random models.L'estructura té un paper fonamental a l'hora de determinar els tipus d'operacions que els circuits neuronals poden dur a terme. Entendre les lleis que defineixen la connectivitat de les xarxes del cervell i les seves implicacions en la dinàmica neuronal és, per tant, un pas important en la comprensió del funcionament d'aquestes xarxes. Els circuits locals del còrtex, que es creu suporten les computacions essencials i bàsiques de la funció cerebral, estan organitzats de manera altament ordenada i estereotipada, i aquesta arquitectura, en termes molt generals, s'ha conservat al llarg de les diferents espècies, de les diverses àrees cerebrals i dels individus. Una bona manera de representar matemàticament aquesta família de xarxes és mitjançant models definits per una sèrie de lleis de connectivitat que inclouen un cert grau d'aleatorietat. Les lleis reflecteixen el patró estructural comú, mentre que l'aleatorietat ha de ser interpretada com la variabilitat quan es comparen diferents xarxes del conjunt. Cada vegada hi ha més evidència experimental que els circuits locals del còrtex estan lluny del model aleatori més simple, segons el qual les connexions apareixen de manera independent amb una probabilitat fixada. Aquesta troballa es fonamenta en un conjunt d'observacions a les quals ens referim col·lectivament com la ?no aleatorietat? dels circuits corticals. En aquesta tesi hem explorat fins a quin punt diverses arquitectures alternatives (xarxes amb agrupació, xarxes amb connectivitat dependent de la distància i xarxes definides a través d'una certa distribució de graus d'entrada i de sortida) podrien ser compatibles amb les propietats de no aleatorietat. Hem mostrat que tots els models estructurals alternatius que havíem proposat poden explicar les observacions esmentades, per tant aquestes propietats no aporten gaire informació sobre el tipus d'organització subjacent. Això es deu principalment al fet que les dades reals provenen d'anàlisis molt restringides, en les quals l'estructura s'estudia a partir de mostres locals formades per poques neurones. Vam buscar un estadístic local que permetés, malgrat aquestes dificultats, distingir entre les diverses estructures alternatives, i l'hem trobat en el coeficient de correlació entre els graus d'entrada i de sortida en mostres petites, que hem anomenat "sample degree correlation" (SDC) en anglès. L'anàlisi d'aquesta mesura en dades reals suggereix que els microcircuits corticals tenen una configuració heterogènia -en el sentit que semblen diferir dels models simples proposats- i estan modelats possiblement per factors dependents de la distància física entre neurones però també per principis addicionals que actuen de manera no simètrica. Finalment, hem estudiat algunes de les conseqüències dinàmiques d'imposar una estructura heterogènia en models d'activitat neuronal. Aquesta heterogeneïtat apareix en els nostres models a través de la distribució conjunta de graus d'entrada i de sortida a la xarxa completa. Fent ús d'aproximacions de camp mitjà i de l'anàlisi espectral, hem mostrat que les distribucions de grau amb elevada variància i correlació positiva poden tenir un efecte rellevant en la dinàmica neuronal, fet que suggereix que aquest tipus d'heterogeneïtat estructural podria facilitar uns modes de computació més rics en comparació dels models aleatoris estàndard

A systems approach to analyze the robustness of infrastructure networks to complex spatial hazards

Ph. D. ThesisInfrastructure networks such as water supply systems, power networks, railway networks, and road networks provide essential services that underpin modern society’s health, wealth, security, and wellbeing. However, infrastructures are susceptible to damage and disruption caused by extreme weather events such as floods and windstorms. For instance, in 2007, extensive disruption was caused by floods affecting a number of electricity substations in the United Kingdom, resulting in an estimated damage of GBP£3.18bn (US$4bn). In 2017, Hurricane Harvey hit the Southern United States, causing an approximated US$125bn (GBP£99.35bn) in damage due to the resulting floods and high winds. The magnitude of these impacts is at risk of being compounded by the effects of Climate Change, which is projected to increase the frequency of extreme weather events. As a result, it is anticipated that an estimated US$3.7tn (GBP£2.9tn) in investment will be required, per year, to meet the expected need between 2019 and 2035. A key reason for the susceptibility of infrastructure networks to extreme weather events is the wide area that needs to be covered to provide essential services. For example, in the United Kingdom alone there are over 800,000 km of overhead electricity cables, suggesting that the footprint of infrastructure networks can be as extended as that of an entire Country. These networks possess different spatial structures and attributes, as a result of their evolution over long timeframes, and respond to damage and disruption in different and complex ways. Existing approaches to understanding the impact of hazards on infrastructure networks typically either (i) use computationally expensive models, which are unable to support the investigation of enough events and scenarios to draw general insights, or (ii) use low complexity representations of hazards, with little or no consideration of their spatial properties. Consequently, this has limited the understanding of the relationship between spatial hazards, the spatial form and connectivity of infrastructure networks, and infrastructure reliability. This thesis investigates these aspects through a systemic modelling approach, applied to a synthetic and a real case study, to evaluate the response of infrastructure networks to spatially complex hazards against a series of robustness metrics. In the first case study, non-deterministic spatial hazards are generated by a fractal method which allows to control their spatial variability, resulting in spatial configurations that very closely resemble natural phenomena such as floods or windstorms. These hazards are then superimposed on a range of synthetic network layouts, which have spatial structures consistent with real infrastructure networks reported in the literature. Failure of network components is initially determined as a function of hazard intensity, and cascading failure of further components is also investigated. The performance of different infrastructure configurations is captured by an array of metrics which cover different aspects of robustness, ranging from the proneness to partitioning to the ability to process flows in the face of disruptions. Whereas analyses to date have largely adopted low complexity representations of hazards, this thesis shows that consideration of a high complexity representation which includes hazard spatial variability can reduce the robustness of the infrastructure network by nearly 40%. A “small-world” network, in which each node is within a limited number of steps from any other node, is shown to be the most robust of all the modelled networks to the different structures of spatial hazard. The second case study uses real data to assess the robustness of a power supply network operating in the Hull region in the United Kingdom, which is split in high and low voltage lines. The spatial hazard is represented by a high-resolution wind gust model and tested under current and future climate scenarios. The analysis reveals how the high and low voltage lines interact with each other in the event of faults, which lines would benefit the most from increased robustness, and which are most exposed to cascading failures. The second case study also reveals the importance of the spatial footprint of the hazard relative to the location of the infrastructure, and how particular hazard patterns can affect low voltage lines that are more often located in exposed areas at the edge of the network. The impact of Climate Change on windstorms is highly uncertain, although it could further reduce network robustness due to more severe events. Overall the two case studies provide important insights for infrastructure designers, asset managers, the academic sector, and practitioners in general. In fact, in the first case study, this thesis defines important design principles, such as the adoption of a small-world network layout, that can integrate the traditional design drivers of demand, efficiency, and cost. In the second case study, this thesis lays out a methodology that can help identify assets requiring increased robustness and protection against cascading failures, resulting in more effective prioritized infrastructure investments and adaptation plans

Handbook of Vascular Biometrics

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Second International Conference on Sustainable Futures: Environmental, Technological, Social and Economic Matters (ICSF 2021). Kryvyi Rih, Ukraine, May 19-21, 2021.Друга міжнародна конференція зі сталого майбутнього: екологічні, технологічні, соціальні та економічні питання (ICSF 2021). Кривий Ріг, Україна, 19-21 травня 2021 року

Матеріали 1-го симпозіуму з передових освітніх технологій - Том 1: AET

Матеріали 1-го симпозіуму з передових освітніх технологій.Proceedings of the 1st Symposium on Advances in Educational Technology