Neuronal morphologies: the shapes of thoughts

The mammalian brain, one of the most fascinating systems in nature, is a complex biological structure that has kept scientists busy for over a century. Many of the brain's mysteries have been unraveled due to the enormous efforts of the scientific community, but yet many questions remain unsolved. The detailed drawings of Ramon y Cajal revealed the hidden structure of the brain, identifying the neurons as its fundamental structural and functional units. Although a significant amount of experimental reconstructions have been gathered over the past years, neuronal morphologies still remain one of the unsolved riddles of the brain. Why is neuronal diversity important for the functionality of the brain and how do neuronal morphologies ''shape'' our thoughts? To address these questions one needs to characterize the various shapes of neuronal morphologies. Traditionally, this task has been performed by using a set of morphological features, such as total length, branch orders and asymmetry. However, these features focus on a specific morphological aspect thereby causing a significant information loss from the original structure. Inspired by algebraic topology, I have conceived a topological descriptor of neuronal trees that couples the topology of a tree with the geometric features of its structure, retaining more details of the original morphology than traditional morphometrics. This descriptor has proved to be very powerful in discriminating several neuronal types into concrete groups based on morphological grounds, and has lead to the discovery of two distinct classes of pyramidal cells in the human cortex. In addition, the Topological Morphology Descriptor is important for the generation of artificial cells whose morphologies remain faithful to the biological ones. Neurons of the same morphological type have similar topological and geometric characteristics, therefore appearing to be highly structured. However, it is still unknown to what extent the complex neuronal morphology is shaped by the genetic information of an organism and to what extent it arises from stochastic processes. To study the impact of randomness and structure of neuronal morphologies on the connectivity of the network they form, I compared the properties of networks that arise from different artificially generated morphologies, ranging from random walks to constrained branching structures, against those of biological networks and computational reconstructions built from biological morphologies. Surprisingly, networks that are generated from almost random morphologies share a lot of common properties with biological networks, such as the spatial clustering of connections and the common neighbor effect, indicating that stochastic processes that take place during development, contribute significantly to the observed neuronal shapes. This thesis resolves a number of the mysteries of neuronal morphologies and questions our beliefs about the role of randomness in the formation of the brain. Thus, it brings us closer to understanding the fundamental differences among morphologies, and how randomness and structure are combined together to generate one of the most complex biological systems

A Topological Representation of Branching Neuronal Morphologies

The online version of this article (https://doi.org/10.1007/s12021-017-9341-1) contains supplementary material, which is available to authorized users. Among others, we thank Athanassia Chalimourda and Katherine Turner for helpful conversations in various stages of this research and Jay Coggan for a critical reading of the manuscript. We also thank Hanchuan Peng and Xiaoxiao Liu for providing and curating the BigNeuron datasets. This work was supported by funding for the Blue Brain Project (BBP) from the ETH Domain. P.D. and R.L. were supported part by the Blue Brain Project and by the start-up grant of KH. Partial support for P.D. has been provided by the Advanced Grant of the European Research Council GUDHI (Geometric Understanding in Higher Dimensions). MS was supported by the SNF NCCR “Synapsy”.Peer reviewedPublisher PD

Reconstruction and simulation of neocortical microcircuitry

We present a first-draft digital reconstruction of the microcircuitry of somatosensory cortex of juvenile rat. The reconstruction uses cellular and synaptic organizing principles to algorithmically reconstruct detailed anatomy and physiology from sparse experimental data. An objective anatomical method defines a neocortical volume of 0.29 ± 0.01 mm3 containing ∼31,000 neurons, and patch-clamp studies identify 55 layer-specific morphological and 207 morpho-electrical neuron subtypes. When digitally reconstructed neurons are positioned in the volume and synapse formation is restricted to biological bouton densities and numbers of synapses per connection, their overlapping arbors form ∼8 million connections with ∼37 million synapses. Simulations reproduce an array of in vitro and in vivo experiments without parameter tuning. Additionally, we find a spectrum of network states with a sharp transition from synchronous to asynchronous activity, modulated by physiological mechanisms. The spectrum of network states, dynamically reconfigured around this transition, supports diverse information processing strategies

26th Annual Computational Neuroscience Meeting (CNS*2017): Part 3 - Meeting Abstracts - Antwerp, Belgium. 15–20 July 2017

This work was produced as part of the activities of FAPESP Research,\ud Disseminations and Innovation Center for Neuromathematics (grant\ud 2013/07699-0, S. Paulo Research Foundation). NLK is supported by a\ud FAPESP postdoctoral fellowship (grant 2016/03855-5). ACR is partially\ud supported by a CNPq fellowship (grant 306251/2014-0)

Biomechanics of rabbit femur bone: 3D reconstruction of femur bone and comparative evaluation of bending experimental setups

151 σ.Εθνικό Μετσόβιο Πολυτεχνείο--Μεταπτυχιακή Εργασία. Διεπιστημονικό-Διατμηματικό Πρόγραμμα Μεταπτυχιακών Σπουδών (Δ.Π.Μ.Σ.) “Υπολογιστική Μηχανική”Η παρούσα εργασία εξετάζει την αποτελεσματικότητα τόσο των καινοτόμων όσο και των παραδοσιακών πειραματικών τεχνικών στον τομέα της εμβιομηχανικής των οστών, με την κατασκευή των αντίστοιχων υπολογιστικών μοντέλων. Θα χρησιμοποιηθούν υπολογιστικές μέθοδοι για τη σύγκριση και την αξιολόγηση διαφορετικών πειραματικών τεχνικών, που αποσκοπούν στον προσδιορισμό των μηχανικών ιδιοτήτων των οστών, με βασικό στόχο την ανάδειξη των προτερημάτων και των αδυναμιών της εκάστοτε τεχνικής.The current thesis studies the effectiveness of innovative but also traditional experimental techniques in the field of bone biomechanics, through the construction of computational models. Computational methods will be used for the comparison and the evaluation of different experimental methods, which are used for the determination of bone mechanical properties, in order to illustrate the benefits and the diffculties of each method. The science of biomechanics is becoming more and more part of the clinical practice, especially in the field of orthopaedics. The introduction of modern techniques, contributes to the improvement of the diagnostic methods as well as of the therapeutic procedure, in order to eliminate the postoperative complications and the possibility of a failure of the clinical treatment. The development of more effective and radical treatment techniques leads to the decrease of the recovery time, when the patience should stay immobilized, with multiple benefits. However, the major problem of the above convenient approach, is the imposed restrictions of experimental biomechanical techniques, which render the application of those techniques in clinical practice unattainable. Those restrictions concern, first of all, the weakness of utilizing the appropriate specimen, for example human bones, in order to export results corresponding to reality rather than to insufficient approaches. The major problem of experimental methods is introduced by the inability of their direct application in patients during the clinical procedure, due to the destruction of experimental specimen and the lack of reproducibility of the procedure. The computational methods attempt to solve the above weaknesses of the experimental biomechanical methods, by substituting the parts of the procedure, which cannot be transferred in the clinical practice. The computational simulations use the information of the experimental data, in order to extract important results concerning the bone's mechanical properties and their response to certain loadings. Those results would require the application of biomechanical techniques in patients in order to be collected experimentally. In the current thesis, a femur rabbit bone is tested under different loading procedures. The first step of the procedure, contains the use of computed tomography in order to receive accurate data for the bone geometry. Those information will be used for the construction of the three dimensional model of the femur bone. The computational model will be compared with experimental data for the confirmation of its accuracy. In the next step, the created model will be subjected in computational tests that simulate the experimental procedure. The study contains three and four point bending tests applied in both free and embedded bone specimen. The computational results will be compared with respective experimental results and will be used for the evaluation of each experimental technique. The purpose of the study is to illustrate the advantages of each test in different cases, in order to contribute to the optimization of the experimental techniques for the optimum use of the resources.Λήδα Δ. Κανάρ

From Trees to Barcodes and Back Again: Theoretical and Statistical Perspectives

Methods of topological data analysis have been successfully applied in a wide range of fields to provide useful summaries of the structure of complex data sets in terms of topological descriptors, such as persistence diagrams. While there are many powerful techniques for computing topological descriptors, the inverse problem, i.e., recovering the input data from topological descriptors, has proved to be challenging. In this article, we study in detail the Topological Morphology Descriptor (TMD), which assigns a persistence diagram to any tree embedded in Euclidean space, and a sort of stochastic inverse to the TMD, the Topological Neuron Synthesis (TNS) algorithm, gaining both theoretical and computational insights into the relation between the two. We propose a new approach to classify barcodes using symmetric groups, which provides a concrete language to formulate our results. We investigate to what extent the TNS recovers a geometric tree from its TMD and describe the effect of different types of noise on the process of tree generation from persistence diagrams. We prove moreover that the TNS algorithm is stable with respect to specific types of noise

Vacuum Dynamics: schwinger effect

98 σ.Μόνο ένα μικρό ποσοστό του σύμπαντος, γύρω στο 4\%, αποτελείται από τη γνωστή μας ύλη. Το υπόλοιπο 96\% του χώρου μπορεί να χαρακτηριστεί ως κενό. Ο γερμανός φιλόσοφος Hegel ταύτιζε τόσο τη "Μονάδα" όσο και το "Μηδέν" με το "Απόλυτο", καταλήγοντας στο συμπέρασμα ότι η ύπαρξη και η ανυπαρξία αποτελούν διαφορετικές εκφάνσεις της ίδιας κατάστασης. Πράγματι, σύμφωνα με την κβαντομηχανική θεώρηση, το κενό μπορεί να ταυτιστεί με τα ζεύγη σωματιδίων - αντισωματιδίων, που συνεχώς δημιουργούνται και καταστρέφονται. Το χρονικό διάστημα της ύπαρξής τους είναι απειροελάχιστα μικρό, με αποτέλεσμα να μην προλαβαίνουν να καταστούν παρατηρήσιμα. Επομένως, κάθε σημείο του χώρου, ακόμη κι αν δεν περιέχει υλικά σωματίδια, αποτελείται από ζεύγη δυνητικών σωματιδίων. Στην παρούσα εργασία μελετάται η απόκριση του δυναμικού αυτού κενού, στην εφαρμογή ενός εξωτερικού ηλεκτρομαγνητικού πεδίου. Το μαγνητικό πεδίο προσανατολίζει τα σωματίδια, καθορίζοντας τις περιστροφικές τους κινήσεις, χωρίς όμως να είναι σε θέση να διαχωρίσει τα ζεύγη. Το ηλεκτρικό πεδίο, όμως, ωθεί τα θετικά φορτισμένα σωματίδια να κινηθούν παράλληλα με τη διεύθυνσή του, ενώ τα αρνητικά φορτισμένα σωματίδια προς την αντίθετη κατεύθυνση. Επομένως, πολώνει τα δυνητικά μόρια του κενού, παραμορφώνοντας τη σφαιρικά συμμετρική δομή τους, σε ελλειψοειδή. Όταν η ένταση του ηλεκτρικού πεδίου ξεπεράσει μια κατώτερη τιμή, αναμένεται η θραύση των δεσμών που κρατάνε ένα σωματίδιο δεσμευμένο με το αντισωματίδιό του. Αναζητείται, λοιπόν, η τιμή του ηλεκτρικού πεδίου, για την οποία θα αρχίσει να παρατηρείται η δημιουργία σωματιδίων. Εξ' αιτίας της κβαντομηχανικής φύσης του μηχανισμού παραγωγής ζευγών σωματιδίων ύλης - αντιύλης, το παραπάνω φαινόμενο έχει μη ντετερμινιστικό χαρακτήρα. Επομένως δεν είναι δυνατός ο υπολογισμός μιας μονοσήμαντης τιμής για το κατώφλι του ηλεκτρικού πεδίου. Στην πραγματικότητα, ο υπολογισμός αφορά στην εύρεση της πιθανότητας εμφάνισης σωματιδίων συναρτήσει της τιμής του πεδίου, που θα ασκηθεί στον κενό από ύλη χώρο. Το παραπάνω φαινόμενο και ο υπολογισμός της πιθανότητας μελετήθηκαν από τον Αμερικανό φυσικό Julian Seymour Schwinger , στο άρθρο που δημοσίευσε το 1951 "On Gauge Invariance and Vacuum Polarization", στο πανεπιστήμιο του Cambridge. Στην παρούσα διπλωματική θα επιχειρηθεί η επαλήθευση της φόρμουλας του Schwinger , με τον υπολογισμό της πιθανότητας παραγωγής ενός ζεύγους ηλεκτρονίου - ποζιτρονίου συναρτήσει της έντασης του ηλεκτρικού πεδίου. Αρχικά θα αναλυθούν τα βασικά στοιχεία της Θεωρίας της Σχετικότητας και της Κβαντομηχανικής, οι οποίες θα χρησιμοποιηθούν για την εύρεση της εξίσωσης του Dirac, που περιγράφει σωματίδια με σπιν 1/2. Στο επόμενο κεφάλαιο, θα μελετηθεί η φύση της αλληλεπίδρασης των QED σωματιδίων με ένα εξωτερικό βαθμωτό πεδίο. Από την εξίσωση αλληλεπίδρασης που θα προκύψει, μπορεί να υπολογιστεί ο πίνακας μετάβασης S από μια αρχική κατάσταση με μηδενικό αριθμό σωματιδίων, που περιγράφει το κενό, σε μια τελική κατάσταση όπου θα δημιουργηθεί τουλάχιστον ένα ζεύγος σωματιδίων. Μ' αυτό τον τρόπο μπορεί να υπολογιστεί η ζητούμενη πιθανότητα ως το τετράγωνο του πίνακα μετάβασης. Η εργασία θα ολοκληρωθεί με τις παρατηρήσεις που θα εξαχθούν όσον αφορά στη μορφή της υπολογισμένης πιθανότητας. Θα επιχειρηθεί επίσης να τεκμηριωθεί η έλλειψη πειραματικών δεδομένων, παρόλη τη σπουδαιότητα του φαινομένου.The universe is filled with particles only in 4\% of its space. The rest 96\% of space can be considered as empty. The german philosopher Hegel claimed that " The Absolute is Unity " and "The Absolute is Nothing" reaching the conclusion that being and not being could be considered as different states of the same situation. Indeed, according to the Theory of Quantum Mechanics, the vacuum can be identified to a pair of a particle and an antiparticle, which are formed and destroyed continuously. The period of their existence is so infinitesimally small that they can't be observed. Therefore, every point in space, even if it is devoid of particles, contains pairs of potential particles. In the current essay, the response of this potential vacuum is examined, if an external electric field is applied. The magnetic field orientates the particles causing their rotation, but it cannot cause the separation of the particle from the antiparticle. On the other hand, the electric field, urges the positive particles to move at the direction of the field and the negative particles to move at the opposite direction. As a result, the electric field causes the polarization of those potential molecules, deforming their spherically symmetric shape, in an elliptic shape. When the intensity of the electric field overcomes a threshold, it is expected to observe the fracture of those bonds and thus the creation of particles and antiparticles, moving in opposite directions. Because of the Quantum Mechanical nature of pair production process, the phenomenon cannot be described deterministically. Therefore, it is not possible to calculate unambiguously the threshold of the elctric field mentioned. Indeed, the calculation refers to the determination of the possibility of producing pairs of particles as a function of the intensity of the electric field. The phenomenon described and the number of this possibility were first studied by the American physicist Julian Seymour Schwinger in the article published in 1951 "On Gauge Invariance and Vacuum Polarization" at the university of Cambridge. In the current thesis, it will be attempted to extract the Schwinger formula by calculating the number of the possibility for the creation of an electron - positron pair as a function of the intensity of the electric field. At first, the basic principles of the Theory of Relativity and of Quantum Mechanics will be analyzed. This study will lead to the Dirac equation, which describes spin 1/2 particles. In the next section, the interaction between QED particles and an external scalar field will be studied. From the equation of the interaction, it is possible to measure the transition matrix S from the vacuum, which contains zero pairs of particles, to the situation where at least a single pair of particles can be observed. The requested possibility can then be measured from the square of the transition matrix. The essay will be completed with the observations made over the calculated possibility.Λήδα Δ. Κανάρ

From Trees to Barcodes and Back Again: Theoretical and Statistical Perspectives

Methods of topological data analysis have been successfully applied in a wide range of fields to provide useful summaries of the structure of complex data sets in terms of topological descriptors, such as persistence diagrams. While there are many powerful techniques for computing topological descriptors, the inverse problem, i.e., recovering the input data from topological descriptors, has proved to be challenging. In this article, we study in detail the Topological Morphology Descriptor (TMD), which assigns a persistence diagram to any tree embedded in Euclidean space, and a sort of stochastic inverse to the TMD, the Topological Neuron Synthesis (TNS) algorithm, gaining both theoretical and computational insights into the relation between the two. We propose a new approach to classify barcodes using symmetric groups, which provides a concrete language to formulate our results. We investigate to what extent the TNS recovers a geometric tree from its TMD and describe the effect of different types of noise on the process of tree generation from persistence diagrams. We prove moreover that the TNS algorithm is stable with respect to specific types of noise

Framework for efficient synthesis of spatially embedded morphologies

Many problems in science and engineering require the ability to grow tubular or polymeric structures up to large volume fractions within a bounded region of three-dimensional space. Examples range from the construction of fibrous materials and biological cells such as neurons, to the creation of initial configurations for molecular simulations. A common feature of these problems is the need for the growing structures to wind throughout space without intersecting. At any time, the growth of a morphology depends on the current state of all the others, as well as the environment it is growing in, which makes the problem computationally intensive. Neuron synthesis has the additional constraint that the morphologies should reliably resemble biological cells, which possess nonlocal structural correlations, exhibit high packing fractions, and whose growth responds to anatomical boundaries in the synthesis volume. We present a spatial framework for simultaneous growth of an arbitrary number of nonintersecting morphologies that presents the growing structures with information on anisotropic and inhomogeneous properties of the space. The framework is computationally efficient because intersection detection is linear in the mass of growing elements up to high volume fractions and versatile because it provides functionality for environmental growth cues to be accessed by the growing morphologies. We demonstrate the framework by growing morphologies of various complexity