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The stochastic exploration of the configuration space and the exploitation of functional states underlie many biological processes. The evolutionary dynamics stands out as a remarkable example. Here, we introduce a novel formalism that…
Analysing how neural networks represent data features in their activations can help interpret how they perform tasks. Hence, a long line of work has focused on mathematically characterising the geometry of such "neural representations." In…
The schooling behavior of fish can be studied through simulations involving a large number of interacting particles. In such systems, each individual particle is guided by behavior rules, which include aggregation towards a centroid,…
Spatially-embedded complex networks, such as nervous systems, the Internet and transportation networks, generally have non-trivial topological patterns of connections combined with nearly minimal wiring costs. However the growth rules…
One of the major resource requirements of computers - ranging from biological cells to human brains to high-performance (engineered) computers - is the energy used to run them. Those costs of performing a computation have long been a focus…
Understanding how the brain learns to compute functions reliably, efficiently and robustly with noisy spiking activity is a fundamental challenge in neuroscience. Most sensory and motor tasks can be described as dynamical systems and could…
Recent years have seen dramatic progress in the development of techniques for measuring the activity and connectivity of large populations of neurons in the brain. However, as these techniques grow ever more powerful---allowing us to even…
Biological organisms must perform computation as they grow, reproduce, and evolve. Moreover, ever since Landauer's bound was proposed it has been known that all computation has some thermodynamic cost -- and that the same computation can be…
Heterogeneity is a ubiquitous property of many biological systems and has profound implications for computation. While it is conceivable to optimize neuronal and synaptic heterogeneity for a specific task, such top-down optimization is…
Habituation - a phenomenon in which a dynamical system exhibits a diminishing response to repeated stimulations that eventually recovers when the stimulus is withheld - is universally observed in living systems from animals to unicellular…
Animal and robotic collective behaviours can exhibit complex dynamics that require multi-level descriptions. Here, we are interested in developing a multi-level modeling framework for the use of robots in studies about animal collective…
Simulating dynamics of physical systems is a key application of quantum computing, with potential impact in fields such as condensed matter physics and quantum chemistry. However, current quantum algorithms for Hamiltonian simulation yield…
We present results from an experiment similar to one performed by Packard (1988), in which a genetic algorithm is used to evolve cellular automata (CA) to perform a particular computational task. Packard examined the frequency of evolved CA…
Quantifying the neural signatures of consciousness remains a major challenge in neuroscience and AI. Although many theories link consciousness to rich, multiscale, and flexible neural organisation, robust quantitative measures are still…
In the fields of computation and neuroscience, much is still unknown about the underlying computations that enable key cognitive functions including learning, memory, abstraction and behavior. This paper proposes a mathematical and…
This paper proposes a neural network hybrid modeling framework for dynamics learning to promote an interpretable, computationally efficient way of dynamics learning and system identification. First, a low-level model will be trained to…
Modern computational neuroscience strives to develop complex network models to explain dynamics and function of brains in health and disease. This process goes hand in hand with advancements in the theory of neuronal networks and increasing…
To scrutinize notions of computation and time complexity, we introduce and formally define an interactive model for computation that we call it the \emph{computation environment}. A computation environment consists of two main parts: i) a…
Computational feasibility is a widespread concern that guides the framing and modeling of biological and artificial intelligence. The specification of cognitive system capacities is often shaped by unexamined intuitive assumptions about the…
The chapter presents some new approaches to describing the collective behavior of complex systems of mathematical biology based on the evolution equations of observables such as open systems. This representation of kinetic evolution has…