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Transport through quantum system is usually investigated in thermodynamic equilibrium. As systems shrink in size fluctuations get ever more important and may even dominate the electronic properties of quantum devices. A charge detector capacitively coupled to a semiconductor quantum dot can be used to measure the passing of individual electrons through the systems, i.e. to measure the current on the level of individual charge carriers. The tunneling barriers as well as the dot occupation can be tuned on time scales faster than typical relaxation times in order to measure level degeneracies, energy dependent tunneling rates and decay times. For situations far from equilibrium the Jarzynski relation gives a clear prediction how out-of-equilibrium properties can be related to equilibrium properties, such as the free energy of a system. These relations can be probed experimentally using time-dependent electron transport through semiconductor quantum dots. As an introduction to clean semiconductor systems I will review recent results on Fermionic cavities.

: I will review a set of biologically inspired NeuroImaging methods (i.e. methods that take into consideration the brain topography, neuronal adaptation and population receptive fields, brain functional connectivity and so on), that we developed and/or refined to shed light on maps and computations in the human brain. Starting from retinotopy, we used partial correlations resting-state functional connectivity analysis to show that the large-scale topographical biases in all 3 dimensions of retinotopy are preserved in individuals without any visual experience. I will discuss how this result challenges classical views of retinotopy as the key organizational principle for computations in the visual system, and further suggest plasticity principles beyond classical Hebbian learning. Next, we use virtual environments to show that key retinotopic regions (mainly in the dorsal visual stream) are recruited not only during vision-based navigation but even when early-blind and sighted-blindfolded learn to navigate these same environments using audition. I will then show how such approaches can be applied to study the whole-body somatosensory-motor system, and demonstrate that topographical gradients are far more widespread than previously known. These findings help to bridge gaps between animal and human studies, and have clinical relevance to improve and refine deep-brain-stimulation and imaging-based diagnostics. Finally, I will briefly present the development of crossmodal adaptation and multiphase spectral analysis to study topographical binding and crossmodal integration. Based on all of these results I will discuss the intriguing hypothesis that our brain is topographically organized for high-order cognitive functions as well, and discuss our plans to combine the aforementioned approaches with the use of the high-field imaging (7T) that is required to test it. I will conclude by summarizing the wide set of tools that enable us to investigate and gain novel insights into the nature of the Topographical Multisensory Human Brain mind.

(Most relevant papers for the talk: Striem-Amit et al. Neuron 2012; Cerbral Cortex 2012; Curr Biol 2014; Brain 2015; Zeharia et al. PNAS 2012; J Neurosci 2015; Saadon-Grosman et al. PNAS 2015; Murray, et al. Trends Neurosci 2016 (cond. accepted); Maidenbaum et al. (in preparation)); Siuda-Krzywicka et al. Elife 2016; Sabbah et al. NeuroImage 2016 (accepted).

A tangent vector field on a surface is the generator of a smooth family of maps from the surface to itself, known as the flow. Given a scalar function on the surface, it can be transported, or advected, by composing it with a vector field's flow. Such transport is exhibited by many physical phenomena, e.g., in fluid dynamics. In this paper, we are interested in the inverse problem: given source and target functions, compute a vector field whose flow advects the source to the target. We propose a method for addressing this problem, by minimizing an energy given by the advection constraint together with a regularizing term for the vector field. Our approach is inspired by a similar method in computational anatomy, known as LDDMM, yet leverages the recent framework of functional vector fields for discretizing the advection and the flow as operators on scalar functions. The latter allows us to efficiently generalize LDDMM to curved surfaces, without explicitly computing the flow lines of the vector field we are optimizing for. We show two approaches for the solution: using linear advection with multiple vector fields, and using non-linear advection with a single vector field. We additionally derive an approximated gradient of the corresponding energy, which is based on a novel vector field transport operator. Finally, we demonstrate applications of our machinery to intrinsic symmetry analysis, function interpolation and map improvement.

: Recurrent neural networks are an important class of models for explaining neural computations. Recently, there has been progress both in training these networks to perform various tasks, and in relating their activity to that recorded in the brain. Despite this progress, there are many fundamental gaps towards a theory of these networks. Neither the conditions for successful learning, nor the dynamics of trained networks are fully understood. I will present the rationale for using such networks for neuroscience research, and a detailed analysis of very simple tasks as an approach to build a theory of general trained recurrent neural networks.