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Uncertainty in various modalities (perceptual, motor, cognitive) is a fundamental problem that the brain must solve to ensure optimal responses to the demands of the environment. It has been shown theoretically that the optimal solution when faced with uncertainty is to represent and propagate full probability distributions over variables of interest and perform probabilistic inference according to Bayes' rule. Previous studies in humans and other animals have shown that the brain does indeed implement a version of Bayesian Inference. Several computational theories have proposed different models for the underlying representation of probability distributions that this requires. The most prominent of these are Probabilistic Population Codes (PPC) and Sampling-Based Codes (SBC). However, existing studies have been unable to prove or disprove these theories conclusively, especially due to the lack of neural population-level recordings concurrent with single-trial measures of uncertainty. In the present thesis, I investigated the representation of perceptual uncertainty in the brain, using the mouse primary visual cortex as a model system. I recorded the activity of large neuronal populations in vivo using two-photon calcium-imaging. I employed a variety of both passive (presentation of visual grating stimuli on a monitor) and active (visually-guided goal-directed behaviour) visual stimulation paradigms to manipulate the sensory uncertainty of the animals. Additionally, I derive a trial-by-trial behavioural uncertainty measure based on the licks that the animals make. My results show that: 1) repeated exposure to behaviourally-relevant (but not neutral) stimuli increases the precision of their representation in the cortex. 2) In a passive viewing setting, manipulation of visual contrast modulates neural responses in a manner partially consistent with both PPC and SBC, with higher contrasts evoking, in general, larger mean responses and larger response variance, and leading to more discriminable stimulus representations. 3) During a two-alternative forced choice task, mouse behavioural uncertainty was modulated in an asymmetrical way by stimulus uncertainty (contrast/aperture) and orientation. Behavioural responses were explained by similarity of neural population responses to two stimulus "archetypes".

This thesis presents a collection of studies which mainly focus on the population of high-redshift dusty star-forming galaxies (DSFGs) in the context of galaxy evolution. The sample of DSFGs that is used in this thesis was discovered as part of the Herschel-Astrophysical Terahertz Large Area Survey (HATLAS; Eales et al., 2010) which is the largest area extragalactic survey undertaken with the Herschel Space Telescope. One Chapter of this Thesis studies the clustering statistics, i.e. the angular correlation function (ACF), of this population demonstrating that when selected on the basis of their flux density (i.e. S250¹m È 30 mJy) they exhibit a higher clustering strength at high redshift (z È 1; r0 Æ 8¡14 Mpc/h) than at low redshfit (z Ç 0.3; r0 Æ 1¡2 Mpc/h). From a galaxy evolution point of view this it is evident that we are dealing with two different galaxy populations, where the later is consistent with being the progenitors of massive early-type galaxies in the local Universe. This study uses that largest sample of DSFGs (discovered in the H-ATLAS survey) that has even been used to perform the measurement of their ACF. Another Chapter of this Thesis studies the properties of the Interstellar medium (ISM) of one of these high redshift DSFGs (HATLAS J091043.0¡000322) using a suite of multiwavelength observations. As this object is strongly lensed, we combined the resolving power of (ALMA) with the enchanced resolution offered by strong lensing to probe scales down to 300¡700 pc. Our morphological and kinematical analysis of the ISM components led us to conclude that this object is more likely undergoing a major-merger event. Finally, another chapter of this thesis utilizes a sample of Herschel-selected strongly-lensed galaxies to study the density profiles of the lens population in a statistical manner. Using both numerically and analytically-derived density distributions we were able to reproduce the observed distribution of image separations. Although we were not able to distinguish between the two profiles, we showed that with a sample »200 lenses that would become possible, highlighting that the simplicity of our selection of our sample does not introduce any additional systematics.