Federico Stella

The project will focus on the computational investigation of the role of neural reactivations in memory. Since their discovery neural reactivations happening during sleep have emerged as an exceptional tool to investigate the process of memory formation in the brain. This phenomenon has been mostly associated with the hippocampus, an area known for its role in the processing of new memories and their initial storage. Continuous advancements in data acquisition techniques are giving us an unprecedented access to the activity of large-scale networks during sleep, in the hippocampus and in other cortical regions. At the same time, our theoretical understanding of the computations underlying neural reactivations and more in general memory representations, has only began to take shape. Combining mathematical modeling of neural networks and analysis of existing dataset, we will address some key aspects of this phenomenon such as: 1) The role of different sleep phases in regulating the reactivation process and in modulating the evolution of a memory trace. 2) The relationship of hippocampal reactivations to the process of (semantic) learning and knowledge generalization. 3) The relevance of reactivation statistical properties for learning in cortico-hippocampal networks.

“Brain theory, what is it or what should it be?”

n the neurosciences the need for some 'overarching' theory is sometimes expressed, but it is not always obvious what is meant by this. One can perhaps agree that in modern science observation and experimentation is normally complemented by 'theory', i.e. the development of theoretical concepts that help guiding and evaluating experiments and measurements. A deeper discussion of 'brain theory' will require the clarification of some further distictions, in particular: theory vs. model and brain research (and its theory) vs. neuroscience. Other questions are: Does a theory require mathematics? Or even differential equations? Today it is often taken for granted that the whole universe including everything in it, for example humans, animals, and plants, can be adequately treated by physics and therefore theoretical physics is the overarching theory. Even if this is the case, it has turned out that in some particular parts of physics (the historical example is thermodynamics) it may be useful to simplify the theory by introducing additional theoretical concepts that can in principle be 'reduced' to more complex descriptions on the 'microscopic' level of basic physical particals and forces. In this sense, brain theory may be regarded as part of theoretical neuroscience, which is inside biophysics and therefore inside physics, or theoretical physics. Still, in neuroscience and brain research, additional concepts are typically used to describe results and help guiding experimentation that are 'outside' physics, beginning with neurons and synapses, names of brain parts and areas, up to concepts like 'learning', 'motivation', 'attention'. Certainly, we do not yet have one theory that includes all these concepts. So 'brain theory' is still in a 'pre-newtonian' state. However, it may still be useful to understand in general the relations between a larger theory and its 'parts', or between microscopic and macroscopic theories, or between theories at different 'levels' of description. This is what I plan to do.

Computational modelling of ocular pharmacokinetics

Pharmacokinetics in the eye is an important factor for the success of ocular drug delivery and treatment. Pharmacokinetic features determine the feasible routes of drug administration, dosing levels and intervals, and it has impact on eventual drug responses. Several physical, biochemical, and flow-related barriers limit drug exposure of anterior and posterior ocular target tissues during treatment during local (topical, subconjunctival, intravitreal) and systemic administration (intravenous, per oral). Mathematical models integrate joint impact of various barriers on ocular pharmacokinetics (PKs) thereby helping drug development. The models are useful in describing (top-down) and predicting (bottom-up) pharmacokinetics of ocular drugs. This is useful also in the design and development of new drug molecules and drug delivery systems. Furthermore, the models can be used for interspecies translation and probing of disease effects on pharmacokinetics. In this lecture, ocular pharmacokinetics and current modelling methods (noncompartmental analyses, compartmental, physiologically based, and finite element models) are introduced. Future challenges are also highlighted (e.g. intra-tissue distribution, prediction of drug responses, active transport).

Predicting traveling waves: a new mathematical technique to link the structure of a network to the specific patterns of neural activity

Why age-related macular degeneration is a mathematically tractable disease

Among all prevalent diseases with a central neurodegeneration, AMD can be considered the most promising in terms of prevention and early intervention, due to several factors surrounding the neural geometry of the foveal singularity. • Steep gradients of cell density, deployed in a radially symmetric fashion, can be modeled with a difference of Gaussian curves. • These steep gradients give rise to huge, spatially aligned biologic effects, summarized as the Center of Cone Resilience, Surround of Rod Vulnerability. • Widely used clinical imaging technology provides cellular and subcellular level information. • Data are now available at all timelines: clinical, lifespan, evolutionary • Snapshots are available from tissues (histology, analytic chemistry, gene expression) • A viable biogenesis model exists for drusen, the largest population-level intraocular risk factor for progression. • The biogenesis model shares molecular commonality with atherosclerotic cardiovascular disease, for which there has been decades of public health success. • Animal and cell model systems are emerging to test these ideas.

Roles of inhibition in stabilizing and shaping the response of cortical networks

Inhibition has long been thought to stabilize the activity of cortical networks at low rates, and to shape significantly their response to sensory inputs. In this talk, I will describe three recent collaborative projects that shed light on these issues. (1) I will show how optogenetic excitation of inhibition neurons is consistent with cortex being inhibition stabilized even in the absence of sensory inputs, and how this data can constrain the coupling strengths of E-I cortical network models. (2) Recent analysis of the effects of optogenetic excitation of pyramidal cells in V1 of mice and monkeys shows that in some cases this optogenetic input reshuffles the firing rates of neurons of the network, leaving the distribution of rates unaffected. I will show how this surprising effect can be reproduced in sufficiently strongly coupled E-I networks. (3) Another puzzle has been to understand the respective roles of different inhibitory subtypes in network stabilization. Recent data reveal a novel, state dependent, paradoxical effect of weakening AMPAR mediated synaptic currents onto SST cells. Mathematical analysis of a network model with multiple inhibitory cell types shows that this effect tells us in which conditions SST cells are required for network stabilization.

Learning produces a hippocampal cognitive map in the form of an orthogonalized state machine

Cognitive maps confer animals with flexible intelligence by representing spatial, temporal, and abstract relationships that can be used to shape thought, planning, and behavior. Cognitive maps have been observed in the hippocampus, but their algorithmic form and the processes by which they are learned remain obscure. Here, we employed large-scale, longitudinal two-photon calcium imaging to record activity from thousands of neurons in the CA1 region of the hippocampus while mice learned to efficiently collect rewards from two subtly different versions of linear tracks in virtual reality. The results provide a detailed view of the formation of a cognitive map in the hippocampus. Throughout learning, both the animal behavior and hippocampal neural activity progressed through multiple intermediate stages, gradually revealing improved task representation that mirrored improved behavioral efficiency. The learning process led to progressive decorrelations in initially similar hippocampal neural activity within and across tracks, ultimately resulting in orthogonalized representations resembling a state machine capturing the inherent struture of the task. We show that a Hidden Markov Model (HMM) and a biologically plausible recurrent neural network trained using Hebbian learning can both capture core aspects of the learning dynamics and the orthogonalized representational structure in neural activity. In contrast, we show that gradient-based learning of sequence models such as Long Short-Term Memory networks (LSTMs) and Transformers do not naturally produce such orthogonalized representations. We further demonstrate that mice exhibited adaptive behavior in novel task settings, with neural activity reflecting flexible deployment of the state machine. These findings shed light on the mathematical form of cognitive maps, the learning rules that sculpt them, and the algorithms that promote adaptive behavior in animals. The work thus charts a course toward a deeper understanding of biological intelligence and offers insights toward developing more robust learning algorithms in artificial intelligence.

Where Cognitive Neuroscience Meets Industry: Navigating the Intersections of Academia and Industry

In this talk, Mirta will share her journey from her education a mathematically-focused high school to her currently unconventional career in London, emphasizing the evolution from a local education in Croatia to international experiences in the US and UK. We will explore the concept of interdisciplinary careers in the modern world, viewing them through the framework of increasing demand, flexibility, and dynamism in the current workplace. We will underscore the significance of interdisciplinary research for launching careers outside of academia, and bolstering those within. I will challenge the conventional norm of working either in academia or industry, and encourage discussion about the opportunities for combining the two in a myriad of career opportunities. I’ll use examples from my own and others’ research to highlight opportunities for early career researchers to extend their work into practical applications. Such an approach leverages the strengths of both sectors, fostering innovation and practical applications of research findings. I hope these insights can offer valuable perspectives for those looking to navigate the evolving demands of the global job market, illustrating the advantages of a versatile skill set that spans multiple disciplines and allows extensions into exciting career options.

Unifying the mechanisms of hippocampal episodic memory and prefrontal working memory

Remembering events in the past is crucial to intelligent behaviour. Flexible memory retrieval, beyond simple recall, requires a model of how events relate to one another. Two key brain systems are implicated in this process: the hippocampal episodic memory (EM) system and the prefrontal working memory (WM) system. While an understanding of the hippocampal system, from computation to algorithm and representation, is emerging, less is understood about how the prefrontal WM system can give rise to flexible computations beyond simple memory retrieval, and even less is understood about how the two systems relate to each other. Here we develop a mathematical theory relating the algorithms and representations of EM and WM by showing a duality between storing memories in synapses versus neural activity. In doing so, we develop a formal theory of the algorithm and representation of prefrontal WM as structured, and controllable, neural subspaces (termed activity slots). By building models using this formalism, we elucidate the differences, similarities, and trade-offs between the hippocampal and prefrontal algorithms. Lastly, we show that several prefrontal representations in tasks ranging from list learning to cue dependent recall are unified as controllable activity slots. Our results unify frontal and temporal representations of memory, and offer a new basis for understanding the prefrontal representation of WM

Mathematical and computational modelling of ocular hemodynamics: from theory to applications

Changes in ocular hemodynamics may be indicative of pathological conditions in the eye (e.g. glaucoma, age-related macular degeneration), but also elsewhere in the body (e.g. systemic hypertension, diabetes, neurodegenerative disorders). Thanks to its transparent fluids and structures that allow the light to go through, the eye offers a unique window on the circulation from large to small vessels, and from arteries to veins. Deciphering the causes that lead to changes in ocular hemodynamics in a specific individual could help prevent vision loss as well as aid in the diagnosis and management of diseases beyond the eye. In this talk, we will discuss how mathematical and computational modelling can help in this regard. We will focus on two main factors, namely blood pressure (BP), which drives the blood flow through the vessels, and intraocular pressure (IOP), which compresses the vessels and may impede the flow. Mechanism-driven models translates fundamental principles of physics and physiology into computable equations that allow for identification of cause-to-effect relationships among interplaying factors (e.g. BP, IOP, blood flow). While invaluable for causality, mechanism-driven models are often based on simplifying assumptions to make them tractable for analysis and simulation; however, this often brings into question their relevance beyond theoretical explorations. Data-driven models offer a natural remedy to address these short-comings. Data-driven methods may be supervised (based on labelled training data) or unsupervised (clustering and other data analytics) and they include models based on statistics, machine learning, deep learning and neural networks. Data-driven models naturally thrive on large datasets, making them scalable to a plethora of applications. While invaluable for scalability, data-driven models are often perceived as black- boxes, as their outcomes are difficult to explain in terms of fundamental principles of physics and physiology and this limits the delivery of actionable insights. The combination of mechanism-driven and data-driven models allows us to harness the advantages of both, as mechanism-driven models excel at interpretability but suffer from a lack of scalability, while data-driven models are excellent at scale but suffer in terms of generalizability and insights for hypothesis generation. This combined, integrative approach represents the pillar of the interdisciplinary approach to data science that will be discussed in this talk, with application to ocular hemodynamics and specific examples in glaucoma research.

Virtual Brain Twins for Brain Medicine and Epilepsy

Over the past decade we have demonstrated that the fusion of subject-specific structural information of the human brain with mathematical dynamic models allows building biologically realistic brain network models, which have a predictive value, beyond the explanatory power of each approach independently. The network nodes hold neural population models, which are derived using mean field techniques from statistical physics expressing ensemble activity via collective variables. Our hybrid approach fuses data-driven with forward-modeling-based techniques and has been successfully applied to explain healthy brain function and clinical translation including aging, stroke and epilepsy. Here we illustrate the workflow along the example of epilepsy: we reconstruct personalized connectivity matrices of human epileptic patients using Diffusion Tensor weighted Imaging (DTI). Subsets of brain regions generating seizures in patients with refractory partial epilepsy are referred to as the epileptogenic zone (EZ). During a seizure, paroxysmal activity is not restricted to the EZ, but may recruit other healthy brain regions and propagate activity through large brain networks. The identification of the EZ is crucial for the success of neurosurgery and presents one of the historically difficult questions in clinical neuroscience. The application of latest techniques in Bayesian inference and model inversion, in particular Hamiltonian Monte Carlo, allows the estimation of the EZ, including estimates of confidence and diagnostics of performance of the inference. The example of epilepsy nicely underwrites the predictive value of personalized large-scale brain network models. The workflow of end-to-end modeling is an integral part of the European neuroinformatics platform EBRAINS and enables neuroscientists worldwide to build and estimate personalized virtual brains.

Brain network communication: concepts, models and applications

Understanding communication and information processing in nervous systems is a central goal of neuroscience. Over the past two decades, advances in connectomics and network neuroscience have opened new avenues for investigating polysynaptic communication in complex brain networks. Recent work has brought into question the mainstay assumption that connectome signalling occurs exclusively via shortest paths, resulting in a sprawling constellation of alternative network communication models. This Review surveys the latest developments in models of brain network communication. We begin by drawing a conceptual link between the mathematics of graph theory and biological aspects of neural signalling such as transmission delays and metabolic cost. We organize key network communication models and measures into a taxonomy, aimed at helping researchers navigate the growing number of concepts and methods in the literature. The taxonomy highlights the pros, cons and interpretations of different conceptualizations of connectome signalling. We showcase the utility of network communication models as a flexible, interpretable and tractable framework to study brain function by reviewing prominent applications in basic, cognitive and clinical neurosciences. Finally, we provide recommendations to guide the future development, application and validation of network communication models.

Computational and mathematical approaches to myopigenesis

Myopia is predicted to affect 50% of all people worldwide by 2050, and is a risk factor for significant, potentially blinding ocular pathologies, such as retinal detachment and glaucoma. Thus, there is significant motivation to better understand the process of myopigenesis and to develop effective anti-myopigenic treatments. In nearly all cases of human myopia, scleral remodeling is an obligate step in the axial elongation that characterizes the condition. Here I will describe the development of a biomechanical assay based on transient unconfined compression of scleral samples. By treating the scleral as a poroelastic material, one can determine scleral biomechanical properties from extremely small samples, such as obtained from the mouse eye. These properties provide proxy measures of scleral remodeling, and have allowed us to identify all-trans retinoic acid (atRA) as a myopigenic stimulus in mice. I will also describe nascent collaborative work on modeling the transport of atRA in the eye.

Diverse applications of artificial intelligence and mathematical approaches in ophthalmology

Ophthalmology is ideally placed to benefit from recent advances in artificial intelligence. It is a highly image-based specialty and provides unique access to the microvascular circulation and the central nervous system. This talk will demonstrate diverse applications of machine learning and deep learning techniques in ophthalmology, including in age-related macular degeneration (AMD), the leading cause of blindness in industrialized countries, and cataract, the leading cause of blindness worldwide. This will include deep learning approaches to automated diagnosis, quantitative severity classification, and prognostic prediction of disease progression, both from images alone and accompanied by demographic and genetic information. The approaches discussed will include deep feature extraction, label transfer, and multi-modal, multi-task training. Cluster analysis, an unsupervised machine learning approach to data classification, will be demonstrated by its application to geographic atrophy in AMD, including exploration of genotype-phenotype relationships. Finally, mediation analysis will be discussed, with the aim of dissecting complex relationships between AMD disease features, genotype, and progression.

Computational models and experimental methods for the human cornea

The eye is a multi-component biological system, where mechanics, optics, transport phenomena and chemical reactions are strictly interlaced, characterized by the typical bio-variability in sizes and material properties. The eye’s response to external action is patient-specific and it can be predicted only by a customized approach, that accounts for the multiple physics and for the intrinsic microstructure of the tissues, developed with the aid of forefront means of computational biomechanics. Our activity in the last years has been devoted to the development of a comprehensive model of the cornea that aims at being entirely patient-specific. While the geometrical aspects are fully under control, given the sophisticated diagnostic machinery able to provide a fully three-dimensional images of the eye, the major difficulties are related to the characterization of the tissues, which require the setup of in-vivo tests to complement the well documented results of in-vitro tests. The interpretation of in-vivo tests is very complex, since the entire structure of the eye is involved and the characterization of the single tissue is not trivial. The availability of micromechanical models constructed from detailed images of the eye represents an important support for the characterization of the corneal tissues, especially in the case of pathologic conditions. In this presentation I will provide an overview of the research developed in our group in terms of computational models and experimental approaches developed for the human cornea.

Relations and Predictions in Brains and Machines

Humans and animals learn and plan with flexibility and efficiency well beyond that of modern Machine Learning methods. This is hypothesized to owe in part to the ability of animals to build structured representations of their environments, and modulate these representations to rapidly adapt to new settings. In the first part of this talk, I will discuss theoretical work describing how learned representations in hippocampus enable rapid adaptation to new goals by learning predictive representations, while entorhinal cortex compresses these predictive representations with spectral methods that support smooth generalization among related states. I will also cover recent work extending this account, in which we show how the predictive model can be adapted to the probabilistic setting to describe a broader array of generalization results in humans and animals, and how entorhinal representations can be modulated to support sample generation optimized for different behavioral states. In the second part of the talk, I will overview some of the ways in which we have combined many of the same mathematical concepts with state-of-the-art deep learning methods to improve efficiency and performance in machine learning applications like physical simulation, relational reasoning, and design.

Autopoiesis and Enaction in the Game of Life

Enaction plays a central role in the broader fabric of so-called 4E (embodied, embedded, extended, enactive) cognition. Although the origin of the enactive approach is widely dated to the 1991 publication of the book "The Embodied Mind" by Varela, Thompson and Rosch, many of the central ideas trace to much earlier work. Over 40 years ago, the Chilean biologists Humberto Maturana and Francisco Varela put forward the notion of autopoiesis as a way to understand living systems and the phenomena that they generate, including cognition. Varela and others subsequently extended this framework to an enactive approach that places biological autonomy at the foundation of situated and embodied behavior and cognition. I will describe an attempt to place Maturana and Varela's original ideas on a firmer foundation by studying them within the context of a toy model universe, John Conway's Game of Life (GoL) cellular automata. This work has both pedagogical and theoretical goals. Simple concrete models provide an excellent vehicle for introducing some of the core concepts of autopoiesis and enaction and explaining how these concepts fit together into a broader whole. In addition, a careful analysis of such toy models can hone our intuitions about these concepts, probe their strengths and weaknesses, and move the entire enterprise in the direction of a more mathematically rigorous theory. In particular, I will identify the primitive processes that can occur in GoL, show how these can be linked together into mutually-supporting networks that underlie persistent bounded entities, map the responses of such entities to environmental perturbations, and investigate the paths of mutual perturbation that these entities and their environments can undergo.

How Children Design by Analogy: The Role of Spatial Thinking

Analogical reasoning is a common reasoning tool for learning and problem-solving. Existing research has extensively studied children’s reasoning when comparing, or choosing from ready-made analogies. Relatively less is known about how children come up with analogies in authentic learning environments. Design education provides a suitable context to investigate how children generate analogies for creative learning purposes. Meanwhile, the frequent use of visual analogies in design provides an additional opportunity to understand the role of spatial reasoning in design-by-analogy. Spatial reasoning is one of the most studied human cognitive factors and is critical to the learning of science, technology, engineering, arts, and mathematics (STEAM). There is growing interest in exploring the interplay between analogical reasoning and spatial reasoning. In this talk, I will share qualitative findings from a case study, where a class of 11-to-12-year-olds in the Netherlands participated in a biomimicry design project. These findings illustrate (1) practical ways to support children’s analogical reasoning in the ideation process and (2) the potential role of spatial reasoning as seen in children mapping form-function relationships in nature analogically and adaptively to those in human designs.

Cognitive supports for analogical reasoning in rational number understanding

In cognitive development, learning more than the input provides is a central challenge. This challenge is especially evident in learning the meaning of numbers. Integers – and the quantities they denote – are potentially infinite, as are the fractional values between every integer. Yet children’s experiences of numbers are necessarily finite. Analogy is a powerful learning mechanism for children to learn novel, abstract concepts from only limited input. However, retrieving proper analogy requires cognitive supports. In this talk, I seek to propose and examine number lines as a mathematical schema of the number system to facilitate both the development of rational number understanding and analogical reasoning. To examine these hypotheses, I will present a series of educational intervention studies with third-to-fifth graders. Results showed that a short, unsupervised intervention of spatial alignment between integers and fractions on number lines produced broad and durable gains in fractional magnitudes. Additionally, training on conceptual knowledge of fractions – that fractions denote magnitude and can be placed on number lines – facilitates explicit analogical reasoning. Together, these studies indicate that analogies can play an important role in rational number learning with the help of number lines as schemas. These studies shed light on helpful practices in STEM education curricula and instructions.

A Better Method to Quantify Perceptual Thresholds : Parameter-free, Model-free, Adaptive procedures

The ‘quantification’ of perception is arguably both one of the most important and most difficult aspects of perception study. This is particularly true in visual perception, in which the evaluation of the perceptual threshold is a pillar of the experimental process. The choice of the correct adaptive psychometric procedure, as well as the selection of the proper parameters, is a difficult but key aspect of the experimental protocol. For instance, Bayesian methods such as QUEST, require the a priori choice of a family of functions (e.g. Gaussian), which is rarely known before the experiment, as well as the specification of multiple parameters. Importantly, the choice of an ill-fitted function or parameters will induce costly mistakes and errors in the experimental process. In this talk we discuss the existing methods and introduce a new adaptive procedure to solve this problem, named, ZOOM (Zooming Optimistic Optimization of Models), based on recent advances in optimization and statistical learning. Compared to existing approaches, ZOOM is completely parameter free and model-free, i.e. can be applied on any arbitrary psychometric problem. Moreover, ZOOM parameters are self-tuned, thus do not need to be manually chosen using heuristics (eg. step size in the Staircase method), preventing further errors. Finally, ZOOM is based on state-of-the-art optimization theory, providing strong mathematical guarantees that are missing from many of its alternatives, while being the most accurate and robust in real life conditions. In our experiments and simulations, ZOOM was found to be significantly better than its alternative, in particular for difficult psychometric functions or when the parameters when not properly chosen. ZOOM is open source, and its implementation is freely available on the web. Given these advantages and its ease of use, we argue that ZOOM can improve the process of many psychophysics experiments.

Fidelity and Replication: Modelling the Impact of Protocol Deviations on Effect Size

Cognitive science and cognitive neuroscience researchers have agreed that the replication of findings is important for establishing which ideas (or theories) are integral to the study of cognition across the lifespan. Recently, high-profile papers have called into question findings that were once thought to be unassailable. Much attention has been paid to how p-hacking, publication bias, and sample size are responsible for failed replications. However, much less attention has been paid to the fidelity by which researchers enact study protocols. Researchers conducting education or clinical trials are aware of the importance in fidelity – or the extent to which the protocols are delivered in the same way across participants. Nevertheless, this idea has not been applied to cognitive contexts. This seminar discusses factors that impact the replicability of findings alongside recent models suggesting that even small fidelity deviations have real impacts on the data collected.

Analogical inference in mathematics: from epistemology to the classroom (and back)

In this presentation, we will discuss adaptations of historical examples of mathematical research to bring out some of the intuitive judgments that accompany the working practice of mathematicians when reasoning by analogy. The main epistemological claim that we will aim to illustrate is that a central part of mathematical training consists in developing a quasi-perceptual capacity to distinguish superficial from deep analogies. We think of this capacity as an instance of Hadamard’s (1954) discriminating faculty of the mathematical mind, whereby one is led to distinguish between mere “hookings” (77) and “relay-results” (80): on the one hand, suggestions or ‘hints’, useful to raise questions but not to back up conjectures; on the other, more significant discoveries, which can be used as an evidentiary source in further mathematical inquiry. In the second part of the presentation, we will present some recent applications of this epistemological framework to mathematics education projects for middle and high schools in Italy.

Unique features of oxygen delivery to the mammalian retina

Like all neural tissue, the retina has a high metabolic demand, and requires a constant supply of oxygen. Second and third order neurons are supplied by the retinal circulation, whose characteristics are similar to brain circulation. However, the photoreceptor region, which occupies half of the retinal thickness, is avascular, and relies on diffusion of oxygen from the choroidal circulation, whose properties are very different, as well as the retinal circulation. By fitting diffusion models to oxygen measurements made with oxygen microelectrodes, it is possible to understand the relative roles of the two circulations under normal conditions of light and darkness, and what happens if the retina is detached or the retinal circulation is occluded. Most of this work has been done in vivo in rat, cat, and monkey, but recent work in the isolated mouse retina will also be discussed.

Geometry of concept learning

Understanding Human ability to learn novel concepts from just a few sensory experiences is a fundamental problem in cognitive neuroscience. I will describe a recent work with Ben Sorcher and Surya Ganguli (PNAS, October 2022) in which we propose a simple, biologically plausible, and mathematically tractable neural mechanism for few-shot learning of naturalistic concepts. We posit that the concepts that can be learned from few examples are defined by tightly circumscribed manifolds in the neural firing-rate space of higher-order sensory areas. Discrimination between novel concepts is performed by downstream neurons implementing ‘prototype’ decision rule, in which a test example is classified according to the nearest prototype constructed from the few training examples. We show that prototype few-shot learning achieves high few-shot learning accuracy on natural visual concepts using both macaque inferotemporal cortex representations and deep neural network (DNN) models of these representations. We develop a mathematical theory that links few-shot learning to the geometric properties of the neural concept manifolds and demonstrate its agreement with our numerical simulations across different DNNs as well as different layers. Intriguingly, we observe striking mismatches between the geometry of manifolds in intermediate stages of the primate visual pathway and in trained DNNs. Finally, we show that linguistic descriptors of visual concepts can be used to discriminate images belonging to novel concepts, without any prior visual experience of these concepts (a task known as ‘zero-shot’ learning), indicated a remarkable alignment of manifold representations of concepts in visual and language modalities. I will discuss ongoing effort to extend this work to other high level cognitive tasks.

Maths, AI and Neuroscience Meeting Stockholm

To understand brain function and develop artificial general intelligence it has become abundantly clear that there should be a close interaction among Neuroscience, machine learning and mathematics. There is a general hope that understanding the brain function will provide us with more powerful machine learning algorithms. On the other hand advances in machine learning are now providing the much needed tools to not only analyse brain activity data but also to design better experiments to expose brain function. Both neuroscience and machine learning explicitly or implicitly deal with high dimensional data and systems. Mathematics can provide powerful new tools to understand and quantify the dynamics of biological and artificial systems as they generate behavior that may be perceived as intelligent.

The impact of analogical learning approaches on mathematics education

Learning by Analogy in Mathematics

Analogies between old and new concepts are common during classroom instruction. While previous studies of transfer focus on how features of initial learning guide later transfer to new problem solving, less is known about how to best support analogical transfer from previous learning while children are engaged in new learning episodes. Such research may have important implications for teaching and learning in mathematics, which often includes analogies between old and new information. Some existing research promotes supporting learners' explicit connections across old and new information within an analogy. In this talk, I will present evidence that instructors can invite implicit analogical reasoning through warm-up activities designed to activate relevant prior knowledge. Warm-up activities "close the transfer space" between old and new learning without additional direct instruction.

Multi-level theory of neural representations in the era of large-scale neural recordings: Task-efficiency, representation geometry, and single neuron properties

A central goal in neuroscience is to understand how orchestrated computations in the brain arise from the properties of single neurons and networks of such neurons. Answering this question requires theoretical advances that shine light into the ‘black box’ of representations in neural circuits. In this talk, we will demonstrate theoretical approaches that help describe how cognitive and behavioral task implementations emerge from the structure in neural populations and from biologically plausible neural networks. First, we will introduce an analytic theory that connects geometric structures that arise from neural responses (i.e., neural manifolds) to the neural population’s efficiency in implementing a task. In particular, this theory describes a perceptron’s capacity for linearly classifying object categories based on the underlying neural manifolds’ structural properties. Next, we will describe how such methods can, in fact, open the ‘black box’ of distributed neuronal circuits in a range of experimental neural datasets. In particular, our method overcomes the limitations of traditional dimensionality reduction techniques, as it operates directly on the high-dimensional representations, rather than relying on low-dimensionality assumptions for visualization. Furthermore, this method allows for simultaneous multi-level analysis, by measuring geometric properties in neural population data, and estimating the amount of task information embedded in the same population. These geometric frameworks are general and can be used across different brain areas and task modalities, as demonstrated in the work of ours and others, ranging from the visual cortex to parietal cortex to hippocampus, and from calcium imaging to electrophysiology to fMRI datasets. Finally, we will discuss our recent efforts to fully extend this multi-level description of neural populations, by (1) investigating how single neuron properties shape the representation geometry in early sensory areas, and by (2) understanding how task-efficient neural manifolds emerge in biologically-constrained neural networks. By extending our mathematical toolkit for analyzing representations underlying complex neuronal networks, we hope to contribute to the long-term challenge of understanding the neuronal basis of tasks and behaviors.

A Framework for a Conscious AI: Viewing Consciousness through a Theoretical Computer Science Lens

We examine consciousness from the perspective of theoretical computer science (TCS), a branch of mathematics concerned with understanding the underlying principles of computation and complexity, including the implications and surprising consequences of resource limitations. We propose a formal TCS model, the Conscious Turing Machine (CTM). The CTM is influenced by Alan Turing's simple yet powerful model of computation, the Turing machine (TM), and by the global workspace theory (GWT) of consciousness originated by cognitive neuroscientist Bernard Baars and further developed by him, Stanislas Dehaene, Jean-Pierre Changeux, George Mashour, and others. However, the CTM is not a standard Turing Machine. It’s not the input-output map that gives the CTM its feeling of consciousness, but what’s under the hood. Nor is the CTM a standard GW model. In addition to its architecture, what gives the CTM its feeling of consciousness is its predictive dynamics (cycles of prediction, feedback and learning), its internal multi-modal language Brainish, and certain special Long Term Memory (LTM) processors, including its Inner Speech and Model of the World processors. Phenomena generally associated with consciousness, such as blindsight, inattentional blindness, change blindness, dream creation, and free will, are considered. Explanations derived from the model draw confirmation from consistencies at a high level, well above the level of neurons, with the cognitive neuroscience literature. Reference. L. Blum and M. Blum, "A theory of consciousness from a theoretical computer science perspective: Insights from the Conscious Turing Machine," PNAS, vol. 119, no. 21, 24 May 2022. https://www.pnas.org/doi/epdf/10.1073/pnas.2115934119

How Children Discover Mathematical Structure through Relational Mapping

A core question in human development is how we bring meaning to conventional symbols. This question is deeply connected to understanding how children learn mathematics—a symbol system with unique vocabularies, syntaxes, and written forms. In this talk, I will present findings from a program of research focused on children’s acquisition of place value symbols (i.e., multidigit number meanings). The base-10 symbol system presents a variety of obstacles to children, particularly in English. Children who cannot overcome these obstacles face years of struggle as they progress through the mathematics curriculum of the upper elementary and middle school grades. Through a combination of longitudinal, cross-sectional, and pretest-training-posttest approaches, I aim to illuminate relational learning mechanisms by which children sometimes succeed in mastering the place value system, as well as instructional techniques we might use to help those who do not.

Optimal information loading into working memory in prefrontal cortex

Working memory involves the short-term maintenance of information and is critical in many tasks. The neural circuit dynamics underlying working memory remain poorly understood, with different aspects of prefrontal cortical (PFC) responses explained by different putative mechanisms. By mathematical analysis, numerical simulations, and using recordings from monkey PFC, we investigate a critical but hitherto ignored aspect of working memory dynamics: information loading. We find that, contrary to common assumptions, optimal information loading involves inputs that are largely orthogonal, rather than similar, to the persistent activities observed during memory maintenance. Using a novel, theoretically principled metric, we show that PFC exhibits the hallmarks of optimal information loading and we find that such dynamics emerge naturally as a dynamical strategy in task-optimized recurrent neural networks. Our theory unifies previous, seemingly conflicting theories of memory maintenance based on attractor or purely sequential dynamics, and reveals a normative principle underlying the widely observed phenomenon of dynamic coding in PFC.

Membrane mechanics meet minimal manifolds

Changes in the geometry and topology of self-assembled membranes underlie diverse processes across cellular biology and engineering. Similar to lipid bilayers, monolayer colloidal membranes studied by the Sharma (IISc Bangalore) and Dogic (UCSB) Labs have in-plane fluid-like dynamics and out-of-plane bending elasticity, but their open edges and micron length scale provide a tractable system to study the equilibrium energetics and dynamic pathways of membrane assembly and reconfiguration. First, we discuss how doping colloidal membranes with short miscible rods transforms disk-shaped membranes into saddle-shaped minimal surfaces with complex edge structures. Theoretical modeling demonstrates that their formation is driven by increasing positive Gaussian modulus, which in turn is controlled by the fraction of short rods. Further coalescence of saddle-shaped surfaces leads to exotic topologically distinct structures, including shapes similar to catenoids, tri-noids, four-noids, and higher order structures. We then mathematically explore the mechanics of these catenoid-like structures subject to an external axial force and elucidate their intimate connection to two problems whose solutions date back to Euler: the shape of an area-minimizing soap film and the buckling of a slender rod under compression. A perturbation theory argument directly relates the tensions of membranes to the stability properties of minimal surfaces. We also investigate the effects of including a Gaussian curvature modulus, which, for small enough membranes, causes the axial force to diverge as the ring separation approaches its maximal value.

How communication networks promote cross-cultural similarities: The case of category formation

Individuals vary widely in how they categorize novel phenomena. This individual variation has led canonical theories in cognitive and social science to suggest that communication in large social networks leads populations to construct divergent category systems. Yet, anthropological data indicates that large, independent societies consistently arrive at similar categories across a range of topics. How is it possible for diverse populations, consisting of individuals with significant variation in how they view the world, to independently construct similar categories? Through a series of online experiments, I show how large communication networks within cultures can promote the formation of similar categories across cultures. For this investigation, I designed an online “Grouping Game” to observe how people construct categories in both small and large populations when tasked with grouping together the same novel and ambiguous images. I replicated this design for English-speaking subjects in the U.S. and Mandarin-speaking subjects in China. In both cultures, solitary individuals and small social groups produced highly divergent category systems. Yet, large social groups separately and consistently arrived at highly similar categories both within and across cultures. These findings are accurately predicted by a simple mathematical model of critical mass dynamics. Altogether, I show how large communication networks can filter lexical diversity among individuals to produce replicable society-level patterns, yielding unexpected implications for cultural evolution. In particular, I discuss how participants in both cultures readily harnessed analogies when categorizing novel stimuli, and I examine the role of communication networks in promoting cross-cultural similarities in analogy-making as the key engine of category formation.

It’s not over our heads: Why human language needs a body

n the ‘orthodox’ view, cognition has been seen as manipulation of symbolic, mental representations, separate from the body. This dualist Cartesian approach characterised much of twentieth-century thought and is still taken for granted by many people today. Language, too, has for a long time been treated across scientific domains as a system operating largely independently from perception, action, and the body (articulatory-perceptual organs notwithstanding). This could lead one into believing that to emulate linguistic behaviour, it would suffice to develop ‘software’ operating on abstract representations that would work on any computational machine. Yet the brain is not the sole problem-solving resource we have at our disposal. The disembodied picture is inaccurate for numerous reasons, which will be presented addressing the issue of the indissoluble link between cognition, language, body, and environment in understanding and learning. The talk will conclude with implications and suggestions for pedagogy, relevant for disciplines as diverse as instruction in language, mathematics, and sports.

Population coding in the cerebellum: a machine learning perspective

The cerebellum resembles a feedforward, three-layer network of neurons in which the “hidden layer” consists of Purkinje cells (P-cells) and the output layer consists of deep cerebellar nucleus (DCN) neurons. In this analogy, the output of each DCN neuron is a prediction that is compared with the actual observation, resulting in an error signal that originates in the inferior olive. Efficient learning requires that the error signal reach the DCN neurons, as well as the P-cells that project onto them. However, this basic rule of learning is violated in the cerebellum: the olivary projections to the DCN are weak, particularly in adulthood. Instead, an extraordinarily strong signal is sent from the olive to the P-cells, producing complex spikes. Curiously, P-cells are grouped into small populations that converge onto single DCN neurons. Why are the P-cells organized in this way, and what is the membership criterion of each population? Here, I apply elementary mathematics from machine learning and consider the fact that P-cells that form a population exhibit a special property: they can synchronize their complex spikes, which in turn suppress activity of DCN neuron they project to. Thus complex spikes cannot only act as a teaching signal for a P-cell, but through complex spike synchrony, a P-cell population may act as a surrogate teacher for the DCN neuron that produced the erroneous output. It appears that grouping of P-cells into small populations that share a preference for error satisfies a critical requirement of efficient learning: providing error information to the output layer neuron (DCN) that was responsible for the error, as well as the hidden layer neurons (P-cells) that contributed to it. This population coding may account for several remarkable features of behavior during learning, including multiple timescales, protection from erasure, and spontaneous recovery of memory.

Network science and network medicine: New strategies for understanding and treating the biological basis of mental ill-health

The last twenty years have witnessed extraordinarily rapid progress in basic neuroscience, including breakthrough technologies such as optogenetics, and the collection of unprecedented amounts of neuroimaging, genetic and other data relevant to neuroscience and mental health. However, the translation of this progress into improved understanding of brain function and dysfunction has been comparatively slow. As a result, the development of therapeutics for mental health has stagnated too. One central challenge has been to extract meaning from these large, complex, multivariate datasets, which requires a shift towards systems-level mathematical and computational approaches. A second challenge has been reconciling different scales of investigation, from genes and molecules to cells, circuits, tissue, whole-brain, and ultimately behaviour. In this talk I will describe several strands of work using mathematical, statistical, and bioinformatic methods to bridge these gaps. Topics will include: using artificial neural networks to link the organization of large-scale brain connectivity to cognitive function; using multivariate statistical methods to link disease-related changes in brain networks to the underlying biological processes; and using network-based approaches to move from genetic insights towards drug discovey. Finally, I will discuss how simple organisms such as C. elegans can serve to inspire, test, and validate new methods and insights in networks neuroscience.

4D Chromosome Organization: Combining Polymer Physics, Knot Theory and High Performance Computing

Self-organization is a universal concept spanning numerous disciplines including mathematics, physics and biology. Chromosomes are self-organizing polymers that fold into orderly, hierarchical and yet dynamic structures. In the past decade, advances in experimental biology have provided a means to reveal information about chromosome connectivity, allowing us to directly use this information from experiments to generate 3D models of individual genes, chromosomes and even genomes. In this talk I will present a novel data-driven modeling approach and discuss a number of possibilities that this method holds. I will discuss a detailed study of the time-evolution of X chromosome inactivation, highlighting both global and local properties of chromosomes that result in topology-driven dynamical arrest and present and characterize a novel type of motion we discovered in knots that may have applications to nanoscale materials and machines.

Structure, Function, and Learning in Distributed Neuronal Networks

A central goal in neuroscience is to understand how orchestrated computations in the brain arise from the properties of single neurons and networks of such neurons. Answering this question requires theoretical advances that shine light into the ‘black box’ of neuronal networks. In this talk, I will demonstrate theoretical approaches that help describe how cognitive and behavioral task implementations emerge from structure in neural populations and from biologically plausible learning rules. First, I will introduce an analytic theory that connects geometric structures that arise from neural responses (i.e., neural manifolds) to the neural population’s efficiency in implementing a task. In particular, this theory describes how easy or hard it is to discriminate between object categories based on the underlying neural manifolds’ structural properties. Next, I will describe how such methods can, in fact, open the ‘black box’ of neuronal networks, by showing how we can understand a) the role of network motifs in task implementation in neural networks and b) the role of neural noise in adversarial robustness in vision and audition. Finally, I will discuss my recent efforts to develop biologically plausible learning rules for neuronal networks, inspired by recent experimental findings in synaptic plasticity. By extending our mathematical toolkit for analyzing representations and learning rules underlying complex neuronal networks, I hope to contribute toward the long-term challenge of understanding the neuronal basis of behaviors.

Neural correlates of temporal processing in humans

Estimating intervals is essential for adaptive behavior and decision-making. Although several theoretical models have been proposed to explain how the brain keeps track of time, there is still no evidence toward a single one. It is often hard to compare different models due to their overlap in behavioral predictions. For this reason, several studies have looked for neural signatures of temporal processing using methods such as electrophysiological recordings (EEG). However, for this strategy to work, it is essential to have consistent EEG markers of temporal processing. In this talk, I'll present results from several studies investigating how temporal information is encoded in the EEG signal. Specifically, across different experiments, we have investigated whether different neural signatures of temporal processing (such as the CNV, the LPC, and early ERPs): 1. Depend on the task to be executed (whether or not it is a temporal task or different types of temporal tasks); 2. Are encoding the physical duration of an interval or how much longer/shorter an interval is relative to a reference. Lastly, I will discuss how these results are consistent with recent proposals that approximate temporal processing with decisional models.

A novel form of retinotopy in area V2 highlights location-dependent feature selectivity in the visual system

Topographic maps are a prominent feature of brain organization, reflecting local and large-scale representation of the sensory surface. ​​Traditionally, such representations in early visual areas are conceived as retinotopic maps preserving ego-centric retinal spatial location while ensuring that other features of visual input are uniformly represented for every location in space. I will discuss our recent findings of a striking departure from this simple mapping in the secondary visual area (V2) of the tree shrew that is best described as a sinusoidal transformation of the visual field. This sinusoidal topography is ideal for achieving uniform coverage in an elongated area like V2 as predicted by mathematical models designed for wiring minimization, and provides a novel explanation for stripe-like patterns of intra-cortical connections and functional response properties in V2. Our findings suggest that cortical circuits flexibly implement solutions to sensory surface representation, with dramatic consequences for large-scale cortical organization. Furthermore our work challenges the framework of relatively independent encoding of location and features in the visual system, showing instead location-dependent feature sensitivity produced by specialized processing of different features in different spatial locations. In the second part of the talk, I will propose that location-dependent feature sensitivity is a fundamental organizing principle of the visual system that achieves efficient representation of positional regularities in visual input, and reflects the evolutionary selection of sensory and motor circuits to optimally represent behaviorally relevant information. The relevant papers can be found here: V2 retinotopy (Sedigh-Sarvestani et al. Neuron, 2021) Location-dependent feature sensitivity (Sedigh-Sarvestani et al. Under Review, 2022)

Human memory: mathematical models and experiments

I will present my recent work on mathematical modeling of human memory. I will argue that memory recall of random lists of items is governed by the universal algorithm resulting in the analytical relation between the number of items in memory and the number of items that can be successfully recalled. The retention of items in memory on the other hand is not universal and differs for different types of items being remembered, in particular retention curves for words and sketches is different even when sketches are made to only carry information about an object being drawn. I will discuss the putative reasons for these observations and introduce the phenomenological model predicting retention curves.

A precise and adaptive neural mechanism for predictive temporal processing in the frontal cortex

The theory of predictive processing posits that the brain computes expectations to process information predictively. Empirical evidence in support of this theory, however, is scarce and largely limited to sensory areas. Here, we report a precise and adaptive mechanism in the frontal cortex of non-human primates consistent with predictive processing of temporal events. We found that the speed of neural dynamics is precisely adjusted according to the average time of an expected stimulus. This speed adjustment, in turn, enables neurons to encode stimuli in terms of deviations from expectation. This lawful relationship was evident across multiple experiments and held true during learning: when temporal statistics underwent covert changes, neural responses underwent predictable changes that reflected the new mean. Together, these results highlight a precise mathematical relationship between temporal statistics in the environment and neural activity in the frontal cortex that may serve as a mechanism for predictive temporal processing.

Maths, AI and Neuroscience meeting

To understand brain function and develop artificial general intelligence it has become abundantly clear that there should be a close interaction among Neuroscience, machine learning and mathematics. There is a general hope that understanding the brain function will provide us with more powerful machine learning algorithms. On the other hand advances in machine learning are now providing the much needed tools to not only analyse brain activity data but also to design better experiments to expose brain function. Both neuroscience and machine learning explicitly or implicitly deal with high dimensional data and systems. Mathematics can provide powerful new tools to understand and quantify the dynamics of biological and artificial systems as they generate behavior that may be perceived as intelligent. In this meeting we bring together experts from Mathematics, Artificial Intelligence and Neuroscience for a three day long hybrid meeting. We will have talks on mathematical tools in particular Topology to understand high dimensional data, explainable AI, how AI can help neuroscience and to what extent the brain may be using algorithms similar to the ones used in modern machine learning. Finally we will wrap up with a discussion on some aspects of neural hardware that may not have been considered in machine learning.

Inferring informational structures in neural recordings of drosophila with epsilon-machines

Measuring the degree of consciousness an organism possesses has remained a longstanding challenge in Neuroscience. In part, this is due to the difficulty of finding the appropriate mathematical tools for describing such a subjective phenomenon. Current methods relate the level of consciousness to the complexity of neural activity, i.e., using the information contained in a stream of recorded signals they can tell whether the subject might be awake, asleep, or anaesthetised. Usually, the signals stemming from a complex system are correlated in time; the behaviour of the future depends on the patterns in the neural activity of the past. However these past-future relationships remain either hidden to, or not taken into account in the current measures of consciousness. These past-future correlations are likely to contain more information and thus can reveal a richer understanding about the behaviour of complex systems like a brain. Our work employs the "epsilon-machines” framework to account for the time correlations in neural recordings. In a nutshell, epsilon-machines reveal how much of the past neural activity is needed in order to accurately predict how the activity in the future will behave, and this is summarised in a single number called "statistical complexity". If a lot of past neural activity is required to predict the future behaviour, then can we say that the brain was more “awake" at the time of recording? Furthermore, if we read the recordings in reverse, does the difference between forward and reverse-time statistical complexity allow us to quantify the level of time asymmetry in the brain? Neuroscience predicts that there should be a degree of time asymmetry in the brain. However, this has never been measured. To test this, we used neural recordings measured from the brains of fruit flies and inferred the epsilon-machines. We found that the nature of the past and future correlations of neural activity in the brain, drastically changes depending on whether the fly was awake or anaesthetised. Not only does our study find that wakeful and anaesthetised fly brains are distinguished by how statistically complex they are, but that the amount of correlations in wakeful fly brains was much more sensitive to whether the neural recordings were read forward vs. backwards in time, compared to anaesthetised brains. In other words, wakeful fly brains were more complex, and time asymmetric than anaesthetised ones.

A nonlinear shot noise model for calcium-based synaptic plasticity

Activity dependent synaptic plasticity is considered to be a primary mechanism underlying learning and memory. Yet it is unclear whether plasticity rules such as STDP measured in vitro apply in vivo. Network models with STDP predict that activity patterns (e.g., place-cell spatial selectivity) should change much faster than observed experimentally. We address this gap by investigating a nonlinear calcium-based plasticity rule fit to experiments done in physiological conditions. In this model, LTP and LTD result from intracellular calcium transients arising almost exclusively from synchronous coactivation of pre- and postsynaptic neurons. We analytically approximate the full distribution of nonlinear calcium transients as a function of pre- and postsynaptic firing rates, and temporal correlations. This analysis directly relates activity statistics that can be measured in vivo to the changes in synaptic efficacy they cause. Our results highlight that both high-firing rates and temporal correlations can lead to significant changes to synaptic efficacy. Using a mean-field theory, we show that the nonlinear plasticity rule, without any fine-tuning, gives a stable, unimodal synaptic weight distribution characterized by many strong synapses which remain stable over long periods of time, consistent with electrophysiological and behavioral studies. Moreover, our theory explains how memories encoded by strong synapses can be preferentially stabilized by the plasticity rule. We confirmed our analytical results in a spiking recurrent network. Interestingly, although most synapses are weak and undergo rapid turnover, the fraction of strong synapses are sufficient for supporting realistic spiking dynamics and serve to maintain the network’s cluster structure. Our results provide a mechanistic understanding of how stable memories may emerge on the behavioral level from an STDP rule measured in physiological conditions. Furthermore, the plasticity rule we investigate is mathematically equivalent to other learning rules which rely on the statistics of coincidences, so we expect that our formalism will be useful to study other learning processes beyond the calcium-based plasticity rule.

NMC4 Short Talk: Two-Photon Imaging of Norepinephrine in the Prefrontal Cortex Shows that Norepinephrine Structures Cell Firing Through Local Release

Norepinephrine (NE) is a neuromodulator that is released from projections of the locus coeruleus via extra-synaptic vesicle exocytosis. Tonic fluctuations in NE are involved in brain states, such as sleep, arousal, and attention. Previously, NE in the PFC was thought to be a homogenous field created by bulk release, but it remains unknown whether phasic (fast, short-term) fluctuations in NE can produce a spatially heterogeneous field, which could then structure cell firing at a fine spatial scale. To understand how spatiotemporal dynamics of norepinephrine (NE) release in the prefrontal cortex affect neuronal firing, we performed a novel in-vivo two-photon imaging experiment in layer ⅔ of the prefrontal cortex using a green fluorescent NE sensor and a red fluorescent Ca2+ sensor, which allowed us to simultaneously observe fine-scale neuronal and NE dynamics in the form of spatially localized fluorescence time series. Using generalized linear modeling, we found that the local NE field differs from the global NE field in transient periods of decorrelation, which are influenced by proximal NE release events. We used optical flow and pattern analysis to show that release and reuptake events can occur at the same location but at different times, and differential recruitment of release and reuptake sites over time is a potential mechanism for creating a heterogeneous NE field. Our generalized linear models predicting cellular dynamics show that the heterogeneous local NE field, and not the global field, drives cell firing dynamics. These results point to the importance of local, small-scale, phasic NE fluctuations for structuring cell firing. Prior research suggests that these phasic NE fluctuations in the PFC may play a role in attentional shifts, orienting to sensory stimuli in the environment, and in the selective gain of priority representations during stress (Mather, Clewett et al. 2016) (Aston-Jones and Bloom 1981).

NMC4 Short Talk: Resilience through diversity: Loss of neuronal heterogeneity in epileptogenic human tissue impairs network resilience to sudden changes in synchrony

A myriad of pathological changes associated with epilepsy, including the loss of specific cell types, improper expression of individual ion channels, and synaptic sprouting, can be recast as decreases in cell and circuit heterogeneity. In recent experimental work, we demonstrated that biophysical diversity is a key characteristic of human cortical pyramidal cells, and past theoretical work has shown that neuronal heterogeneity improves a neural circuit’s ability to encode information. Viewed alongside the fact that seizure is an information-poor brain state, these findings motivate the hypothesis that epileptogenesis can be recontextualized as a process where reduction in cellular heterogeneity renders neural circuits less resilient to seizure onset. By comparing whole-cell patch clamp recordings from layer 5 (L5) human cortical pyramidal neurons from epileptogenic and non-epileptogenic tissue, we present the first direct experimental evidence that a significant reduction in neural heterogeneity accompanies epilepsy. We directly implement experimentally-obtained heterogeneity levels in cortical excitatory-inhibitory (E-I) stochastic spiking network models. Low heterogeneity networks display unique dynamics typified by a sudden transition into a hyper-active and synchronous state paralleling ictogenesis. Mean-field analysis reveals a distinct mathematical structure in these networks distinguished by multi-stability. Furthermore, the mathematically characterized linearizing effect of heterogeneity on input-output response functions explains the counter-intuitive experimentally observed reduction in single-cell excitability in epileptogenic neurons. This joint experimental, computational, and mathematical study showcases that decreased neuronal heterogeneity exists in epileptogenic human cortical tissue, that this difference yields dynamical changes in neural networks paralleling ictogenesis, and that there is a fundamental explanation for these dynamics based in mathematically characterized effects of heterogeneity. These interdisciplinary results provide convincing evidence that biophysical diversity imbues neural circuits with resilience to seizure and a new lens through which to view epilepsy, the most common serious neurological disorder in the world, that could reveal new targets for clinical treatment.

Refuting the unfolding-argument on the irrelevance of causal structure to consciousness

I will build from Niccolo's discussion of the Blockhead argument to argue that having an FeedForward Network (FN) responding like an recurrent network (RN) in a consciousness experiment is not enough to convince us the two are the same with regards to the posession of mental states and conscious experience. I will then argue that a robust functional equivalence between FFN and RN is akso not supported by the mathematical work on the Universal Approximator theorem, and is also unlikely to hold, as a conjecture, given data in cognitive neuroscience; I will argue that an equivalence of RN and FFN may only apply to static functions between input/output layers and not to the temporal patterns or to the network's reactions to structural perturbations. Finally, I review data indicating that consciousness has functional characteristics, such as a flexible control of behavior, and that cognitive/brain dynamics reveal interacting top-down and bottom-up processes, which are necessary for the mediation of such control processes.

Advancing Brain-Computer Interfaces by adopting a neural population approach

Brain-computer interfaces (BCIs) have afforded paralysed users “mental control” of computer cursors and robots, and even of electrical stimulators that reanimate their own limbs. Most existing BCIs map the activity of hundreds of motor cortical neurons recorded with implanted electrodes into control signals to drive these devices. Despite these impressive advances, the field is facing a number of challenges that need to be overcome in order for BCIs to become widely used during daily living. In this talk, I will focus on two such challenges: 1) having BCIs that allow performing a broad range of actions; and 2) having BCIs whose performance is robust over long time periods. I will present recent studies from our group in which we apply neuroscientific findings to address both issues. This research is based on an emerging view about how the brain works. Our proposal is that brain function is not based on the independent modulation of the activity of single neurons, but rather on specific population-wide activity patters —which mathematically define a “neural manifold”. I will provide evidence in favour of such a neural manifold view of brain function, and illustrate how advances in systems neuroscience may be critical for the clinical success of BCIs.

“Mind reading” with brain scanners: Facts versus science fiction

Every thought is associated with a unique pattern of brain activity. Thus, in principle, it should be possible to use these activity patterns as "brain fingerprints" for different thoughts and to read out what a person is thinking based on their brain activity alone. Indeed, using machine learning considerable progress has been made in such "brainreading" in recent years. It is now possible to decode which image a person is viewing, which film sequence they are watching, which emotional state they are in or which intentions they hold in mind. This talk will provide an overview of the current state of the art in brain reading. It will also highlight the main challenges and limitations of this research field. For example, mathematical models are needed to cope with the high dimensionality of potential mental states. Furthermore, the ethical concerns raised by (often premature) commercial applications of brain reading will also be discussed.

When and (maybe) why do high-dimensional neural networks produce low-dimensional dynamics?

There is an avalanche of new data on activity in neural networks and the biological brain, revealing the collective dynamics of vast numbers of neurons. In principle, these collective dynamics can be of almost arbitrarily high dimension, with many independent degrees of freedom — and this may reflect powerful capacities for general computing or information. In practice, neural datasets reveal a range of outcomes, including collective dynamics of much lower dimension — and this may reflect other desiderata for neural codes. For what networks does each case occur? We begin by exploring bottom-up mechanistic ideas that link tractable statistical properties of network connectivity with the dimension of the activity that they produce. We then cover “top-down” ideas that describe how features of connectivity and dynamics that impact dimension arise as networks learn to perform fundamental computational tasks.

Qualitative Structure, Automorphism Groups and Private Language

It is generally agreed upon that qualities of conscious experience instantiate structural properties, usually called relations. They furnish a representation of qualities (or qualia, in fact) in terms of a mathematical space Q (rather than a set), which is crucial to both modelling and measuring of conscious experience." "What is usually disregarded is that “only such structural properties generalize across individuals” (Austen Clark), but that qualities themselves as differentiated by stimulus specifications, behavior or reports do not. We show that this implies that only the part of Q which is invariant with respect to the automorphism group has a well-defined referent, while individual elements do not. This poses a prima facie limitation of any theory or experiment that aims to address individual qualities. We show how mathematical theories of consciousness can overcome this limitation via symmetry groups and group actions, making accessible to science what is properly called private language.

3 Reasons Why You Should Care About Category Theory

Category theory is a branch of mathematics which have been used to organize various regions of mathematics and related sciences from a radical “relation-first” point of view. Why consciousness researchers should care about category theory? " "There are (at least) 3 reasons:" "1 Everything is relational" "2 Everything is relation" "3 Relation is everything" "In this talk we explain the reasons above more concretely and introduce the ideas to utilize basic concepts in category theory for consciousness studies.

Physical Computation in Insect Swarms

Our world is full of living creatures that must share information to survive and reproduce. As humans, we easily forget how hard it is to communicate within natural environments. So how do organisms solve this challenge, using only natural resources? Ideas from computer science, physics and mathematics, such as energetic cost, compression, and detectability, define universal criteria that almost all communication systems must meet. We use insect swarms as a model system for identifying how organisms harness the dynamics of communication signals, perform spatiotemporal integration of these signals, and propagate those signals to neighboring organisms. In this talk I will focus on two types of communication in insect swarms: visual communication, in which fireflies communicate over long distances using light signals, and chemical communication, in which bees serve as signal amplifiers to propagate pheromone-based information about the queen’s location.

Credit Assignment in Neural Networks through Deep Feedback Control

The success of deep learning sparked interest in whether the brain learns by using similar techniques for assigning credit to each synaptic weight for its contribution to the network output. However, the majority of current attempts at biologically-plausible learning methods are either non-local in time, require highly specific connectivity motives, or have no clear link to any known mathematical optimization method. Here, we introduce Deep Feedback Control (DFC), a new learning method that uses a feedback controller to drive a deep neural network to match a desired output target and whose control signal can be used for credit assignment. The resulting learning rule is fully local in space and time and approximates Gauss-Newton optimization for a wide range of feedback connectivity patterns. To further underline its biological plausibility, we relate DFC to a multi-compartment model of cortical pyramidal neurons with a local voltage-dependent synaptic plasticity rule, consistent with recent theories of dendritic processing. By combining dynamical system theory with mathematical optimization theory, we provide a strong theoretical foundation for DFC that we corroborate with detailed results on toy experiments and standard computer-vision benchmarks.

Learning the structure and investigating the geometry of complex networks

Networks are widely used as mathematical models of complex systems across many scientific disciplines, and in particular within neuroscience. In this talk, we introduce two aspects of our collaborative research: (1) machine learning and networks, and (2) graph dimensionality. Machine learning and networks. Decades of work have produced a vast corpus of research characterising the topological, combinatorial, statistical and spectral properties of graphs. Each graph property can be thought of as a feature that captures important (and sometimes overlapping) characteristics of a network. We have developed hcga, a framework for highly comparative analysis of graph data sets that computes several thousands of graph features from any given network. Taking inspiration from hctsa, hcga offers a suite of statistical learning and data analysis tools for automated identification and selection of important and interpretable features underpinning the characterisation of graph data sets. We show that hcga outperforms other methodologies (including deep learning) on supervised classification tasks on benchmark data sets whilst retaining the interpretability of network features, which we exemplify on a dataset of neuronal morphologies images. Graph dimensionality. Dimension is a fundamental property of objects and the space in which they are embedded. Yet ideal notions of dimension, as in Euclidean spaces, do not always translate to physical spaces, which can be constrained by boundaries and distorted by inhomogeneities, or to intrinsically discrete systems such as networks. Deviating from approaches based on fractals, here, we present a new framework to define intrinsic notions of dimension on networks, the relative, local and global dimension. We showcase our method on various physical systems.

Bacterial rheotaxis in bulk and at surfaces

Individual bacteria transported in viscous flows, show complex interactions with flows and bounding surfaces resulting from their complex shape as well as their activity. Understanding these transport dynamics is crucial, as they impact soil contamination, transport in biological conducts or catheters, and constitute thus a serious health threat. Here we investigate the trajectories of individual E-coli bacteria in confined geometries under flow, using microfluidic model systems in bulk flows as well as close to surfaces using a novel Langrangian 3D tracking method. Combining experimental observations and modelling we elucidate the origin of upstream swimming, lateral drift or persistent transport along corners. [1] Junot et al, EPL, 126 (2019) 44003 [2] Mathijssen et al. 10:3 (2019) Nature Comm. [3] Figueroa-Morales et al., Soft Matter, 2015,11, 6284-6293 [4] Darnige et al. Review of Scientific Instruments 88, 055106 (2017) [5] Jing et al, Science Advances, 2020; 6 : eabb2012 [6] Figueroa-Morales et al, Sci. Adv. 2020; 6 : eaay0155, 2020, 10.1126/sciadv.aay0155

The quest for the cortical algorithm

The cortical algorithm hypothesis states that there is one common computational framework to solve diverse cognitive problems such as vision, voice recognition and motion control. In my talk, I propose a strategy to guide the search for this algorithm and I present a few ideas on how some of its components might look like. I'll explain why a highly interdisciplinary approach is needed from neuroscience, computer science, mathematics and physics to make further progress in this important question.

Generative models of the human connectome

The human brain is a complex network of neuronal connections. The precise arrangement of these connections, otherwise known as the topology of the network, is crucial to its functioning. Recent efforts to understand how the complex topology of the brain has emerged have used generative mathematical models, which grow synthetic networks according to specific wiring rules. Evidence suggests that a wiring rule which emulates a trade-off between connection costs and functional benefits can produce networks that capture essential topological properties of brain networks. In this webinar, Professor Alex Fornito and Dr Stuart Oldham will discuss these previous findings, as well as their own efforts in creating more physiologically constrained generative models. Professor Alex Fornito is Head of the Brain Mapping and Modelling Research Program at the Turner Institute for Brain and Mental Health. His research focuses on developing new imaging techniques for mapping human brain connectivity and applying these methods to shed light on brain function in health and disease. Dr Stuart Oldham is a Research Fellow at the Turner Institute for Brain and Mental Health and a Research Officer at the Murdoch Children’s Research Institute. He is interested in characterising the organisation of human brain networks, with particular focus on how this organisation develops, using neuroimaging and computational tools.

Distinct patterns of default mode network activity differentially represent divergent thinking and mathematical reasoning.

Bernstein Conference 2024

Event-related brain potentials reveal math anxiety effects in a numerical Go/NoGo task

FENS Forum 2024

Mathematical modelling of ATP-induced Ca2+ transients in Deiters cells considering the tonotopic axis

FENS Forum 2024

Simple mathematical model for replicating the ATP-induced Ca2+ transients in different types of cochlear supporting cells

FENS Forum 2024

Towards a mathematical model of microtubules in neurites

FENS Forum 2024

Mathematical Models of Visual-Vestibular Integration in a Speed Accuracy Task

Neuromatch 5

Parallels between Intuitionistic Mathematics and Neurophenomenology

Neuromatch 5

Predicting Math and Story-Related Auditory Tasks Completed in fMRI using a Logistic Regression Machine Learning Model

Neuromatch 5