Mathematical Models
mathematical models
Eugenio Piasini
SISSA is an elite postgraduate research institution for Maths, Physics and Neuroscience, located in Trieste, Italy. The Cognitive Neuroscience Department hosts 7 research labs that study the neuronal bases of time and magnitude processing, visual perception, motivation and intelligence, language and reading, tactile perception and learning, and neural computation. The Department is highly interdisciplinary; our approaches include behavioural, psychophysics, and neurophysiological experiments with humans and animals, as well as computational, statistical and mathematical models.
Eugenio Piasini
Up to 6 PhD positions in Cognitive Neuroscience are available at SISSA, Trieste, starting October 2024. SISSA is an elite postgraduate research institution for Maths, Physics and Neuroscience, located in Trieste, Italy. SISSA operates in English, and its faculty and student community is diverse and strongly international. The Cognitive Neuroscience group hosts 7 research labs that study the neuronal bases of time and magnitude processing, visual perception, motivation and intelligence, language and reading, tactile perception and learning, and neural computation. Our research is highly interdisciplinary; our approaches include behavioural, psychophysics, and neurophysiological experiments with humans and animals, as well as computational, statistical and mathematical models. Students from a broad range of backgrounds (physics, maths, medicine, psychology, biology) are encouraged to apply. This year, one of the PhD scholarships is set aside for joint PhD projects across PhD programs within the Neuroscience department.
Paul Cisek
Doctoral studies in computational neuroscience, focusing on the neural mechanisms of embodied decision-making and action planning in humans and non-human primates. The research involves computational models of the nervous system integrated with behavioral experiments, transcranial magnetic stimulation, and multi-electrode recording in multiple regions of the cerebral cortex and basal ganglia. New projects will use virtual reality to study naturalistic behavior and develop theoretical models of distributed cortical and subcortical circuits.
Jean-Pascal Pfister
The Theoretical Neuroscience Group of the University of Bern is seeking applications for a PhD position, funded by a Swiss National Science Foundation grant titled “Why Spikes?”. This project aims at answering a nearly century-old question in Neuroscience: “What are spikes good for?”. Indeed, since the discovery of action potentials by Lord Adrian in 1926, it has remained largely unknown what the benefits of spiking neurons are, when compared to analog neurons. Traditionally, it has been argued that spikes are good for long-distance communication or for temporally precise computation. However, there is no systematic study that quantitatively compares the communication as well as the computational benefits of spiking neuron w.r.t analog neurons. The aim of the project is to systematically quantify the benefits of spiking at various levels by developing and analyzing appropriate mathematical models. The PhD student will be supervised by Prof. Jean-Pascal Pfister (Theoretical Neuroscience Group, Department of Physiology, University of Bern). The project will involve close collaborations within a highly motivated team as well as regular exchange of ideas with the other theory groups at the institute.
Mathew Diamond
Up to 2 PhD positions in Cognitive Neuroscience are available at SISSA, Trieste, starting October 2024. SISSA is an elite postgraduate research institution for Maths, Physics and Neuroscience, located in Trieste, Italy. SISSA operates in English, and its faculty and student community is diverse and strongly international. The Cognitive Neuroscience group (https://phdcns.sissa.it/) hosts 6 research labs that study the neuronal bases of time and magnitude processing, visual perception, motivation and intelligence, language, tactile perception and learning, and neural computation. Our research is highly interdisciplinary; our approaches include behavioural, psychophysics, and neurophysiological experiments with humans and animals, as well as computational, statistical and mathematical models. Students from a broad range of backgrounds (physics, maths, medicine, psychology, biology) are encouraged to apply. The selection procedure is now open. The application deadline is 27 August 2024. Please apply here (https://www.sissa.it/bandi/ammissione-ai-corsi-di-philosophiae-doctor-posizioni-cofinanziate-dal-fondo-sociale-europeo), and see the admission procedure page (https://phdcns.sissa.it/admission-procedure) for more information. Note that the positions available for current admission round are those funded by the 'Fondo Sociale Europeo Plus', accessible through the first link above.
Mathew Diamond
Up to 6 PhD positions in Cognitive Neuroscience are available at SISSA, Trieste, starting October 2025. SISSA is an elite postgraduate research institution for Maths, Physics and Neuroscience, located in Trieste, Italy. SISSA operates in English, and its faculty and student community is diverse and strongly international. The Cognitive Neuroscience group (https://phdcns.sissa.it/) hosts 6 research labs that study the neuronal bases of time and magnitude processing, neuronal foundations of perceptual experience and learning in various sensory modalities, motivation and intelligence, language, and neural computation. Our research is highly interdisciplinary; our approaches include behavioral, psychophysics, and neurophysiological experiments with humans and animals, as well as computational, statistical and mathematical models. Students from a broad range of backgrounds (physics, maths, medicine, psychology, biology) are encouraged to apply.
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).
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.
“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.
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.
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.
Mathematical models of neurodegenerative diseases
Neurodegenerative diseases such as Alzheimer’s or Parkinson’s are devastating conditions with poorly understood mechanisms and no cure. Yet, a striking feature of these conditions is the characteristic pattern of invasion throughout the brain, leading to well-codified disease stages associated with various cognitive deficits and pathologies. How can we use mathematical modelling to gain insight into this process and, doing so, gain understanding about how the brain works? In this talk, I will show that by linking new mathematical theories to recent progress in imaging, we can unravel some of the universal features associated with dementia and, more generally, brain functions.
Multimodal brain imaging to predict progression of Alzheimer’s disease
Cross-sectional and longitudinal multimodal brain imaging studies using positron emission tomography (PET) and magnetic resonance imaging (MRI) have provided detailed insight into the pathophysiological progression of Alzheimer’s disease. It starts at an asymptomatic stage with widespread gradual accumulation of beta-amyloid and spread of pathological tau deposits. Subsequently changes of functional connectivity and glucose metabolism associated with mild cognitive impairment and brain atrophy may develop. However, the rate of progression to a symptomatic stage and ultimately dementia varies considerably between individuals. Mathematical models have been developed to describe disease progression, which may be used to identify markers that determine the current stage and likely rate of progression. Both are very important to improve the efficacy of clinical trials. In this lecture, I will provide an overview on current research and future perspectives in this area.
Towards multipurpose biophysics-based mathematical models of cortical circuits
Starting with the work of Hodgkin and Huxley in the 1950s, we now have a fairly good understanding of how the spiking activity of neurons can be modelled mathematically. For cortical circuits the understanding is much more limited. Most network studies have considered stylized models with a single or a handful of neuronal populations consisting of identical neurons with statistically identical connection properties. However, real cortical networks have heterogeneous neural populations and much more structured synaptic connections. Unlike typical simplified cortical network models, real networks are also “multipurpose” in that they perform multiple functions. Historically the lack of computational resources has hampered the mathematical exploration of cortical networks. With the advent of modern supercomputers, however, simulations of networks comprising hundreds of thousands biologically detailed neurons are becoming feasible (Einevoll et al, Neuron, 2019). Further, a large-scale biologically network model of the mouse primary visual cortex comprising 230.000 neurons has recently been developed at the Allen Institute for Brain Science (Billeh et al, Neuron, 2020). Using this model as a starting point, I will discuss how we can move towards multipurpose models that incorporate the true biological complexity of cortical circuits and faithfully reproduce multiple experimental observables such as spiking activity, local field potentials or two-photon calcium imaging signals. Further, I will discuss how such validated comprehensive network models can be used to gain insights into the functioning of cortical circuits.
Mathematical Models of Visual-Vestibular Integration in a Speed Accuracy Task
Neuromatch 5