This work is motivated from error-correcting codes in the brain. To counteract the effect of representation noise, a large number of neurons participate in encoding even low-dimensional variables. In many brain areas, the mean firing rates of neurons as a function of represented variable, called the tuning curve, have unimodal shape centered at different values, defining a unary code. This dissertation focuses on a new type of neural code where neurons have periodic tuning curves, with a diversity of periods. Neurons that exhibit this tuning are grid cells of the entorhinal cortex, which represent self-location in two-dimensional space. First, we investigate mutual information between such multi-scale codes and the coded variable as a function of tuning curve width. For decoding, we consider maximum likelihood (ML) and plausible neural network (NN) based models. For unary neural codes, Fisher information increases with narrower tuning, regardless of the decoding method. By contrast, for the multi-scale neural code, the optimal tuning curve width depends on the decoding method. While narrow tuning is optimal for ML decoding, a finite width, matched to statistics of the noise, is optimal with a NN decoder. This finding may explain why actual neural tuning curves have relatively wide tuning. Next, motivated by the observation that multi-scale codes involve non-trivial decoding, we examine a decoding algorithm based on belief propagation (BP) because BP promises certain gains in decoding efficiency. The decoding problem is first formulated as a subset selection problem on a graph and then approximately solved by BP. Even though the graph has many cycles, BP converges to a fixed point after few iterations. The mean square error of BP approaches to that of ML at high signal-to-noise ratios. Finally, using the multi-scale code, we propose a joint source-channel coding scheme that allows separate senders to transmit complementary information over additive Gaussian noise channels without cooperation. The receiver decodes one sender's codeword using the other as side information and achieves a lower distortion using the same number of transmissions. The proposed scheme offers a new framework to design distributed joint source-channel codes for continuous variables. / text

Short-term synaptic plasticity (STP) is a phenomenon that has been closely associated with how neurons communicate with each other. I study communication between neurons tied to synapses endowed with short-term plasticity (dynamic synapses). This is achieved by using mathematical models of neural phenomena that align with those found in real neurons. In addition to dynamic synapses, a model of static synapses is created, on which control experiments are performed. The response of postsynaptic neurons, to spiking-sequences from presynaptic neurons, is examined in order to infer how information is transmitted across cells. During these computational experiments, it was found that the range of firing rates to which postsynaptic neurons responded, depends heavily on certain parameters of STP-processes. These parameters are the time constants for short-term synaptic depression and facilitation: the two time-dependent processes that define STP. Some results confirm those of the existing literature, while this work places an added emphasis on the sensitivity of the propagation of rate codes to the aforementioned parameters of synapses. This is relevant because it has been found that real synapses display a wide range of time constants in the nervous system. Hence, understanding how this variation carries a significant impact on rate-coding schemes is vital when engaging in further studies of neural rate codes. / Synaptisk plasticitet på kort sikt (STP) är ett fenomen som har blivit nära förknippat med hur nervceller kommunicerar med varandra. Jag studerar kommunikation mellan nervceller som är kopplade till synapser som är försedda med kortsiktig synaptisk plasticitet (dynamiska synapser). Detta har åstadkommits genom matematisk modellering av fenomen i nervsystemet som är konsekventa med de som är funna i verkliga nervceller. Utöver dynamiska synapser, så skapas även en modell av statiska synapser på vilka kontrollexperiment utövas. Gensvaret av postsynaptiska nervceller, på sekvenser av nervimpulser från presynaptiska nervceller, kartläggs för att studera hur information transmitteras mellan celler. I dessa beräkningsmässiga experiment så var det funnet att spannet av frekvenser för vilka postsynaptiska nervceller visade gensvar, var kraftigt beroende på specifika parametrar för STP-processer. Dessa parametrar är tidskonstanterna för synaptisk depression på kort sikt samt synaptisk facilitering på kort sikt: de två tidsberoende processerna som definierar STP. Vissa resultat bekräftade de som återfinns i den befintliga literaturen, samtidigt som detta arbete placerar adderad tyngd på känsligheten som frekvensmässiga koder uppvisar för ovannämnda synaptiska parametrar. Detta är relevant eftersom det är känt att verkliga synapser uppvisar ett brett spann av tidskonstanter i nervsystemet. Följdaktigen är det centralt att förstå hur denna variation innehar signifikant påverkan på frekvenskoder vid fortsatta studier inom frekvensmässiga neurala koder.