Optimal neural inference of stimulus intensities

Martingales and the fixation time of evolutionary graphs with arbitrary dimensionality

Evolutionary graph theory (EGT) investigates the Moran birth-death process constrained by graphs. Its two principal goals are to find the fixation probability and time for some initial population of mutants on the graph. The fixation probability of graphs has received considerable attention. Less is known about the distribution of fixation time. We derive clean, exact expressions for the full conditional characteristic functions (CCFs) of a close proxy to fixation and extinction times. That proxy is the number of times that the mutant population size changes before fixation or extinction. We derive these CCFs from a product martingale that we identify for an evolutionary graph with any number of partitions. The existence of that martingale only requires that the connections between those partitions are of a certain type. Our results are the first expressions for the CCFs of any proxy to fixation time on a graph with any number of partitions. The parameter dependence of our CCFs is explicit, so we can explore how they depend on graph structure. Martingales are a powerful approach to study principal problems of EGT. Their applicability is invariant to the number of partitions in a graph, so we can study entire families of graphs simultaneously.

Noise-robust text-dependent speaker identification using cochlear models

One challenging issue in speaker identification (SID) is to achieve noise-robust performance. Humans can accurately identify speakers, even in noisy environments. We can leverage our knowledge of the function and anatomy of the human auditory pathway to design SID systems that achieve better noise-robust performance than conventional approaches. We propose a text-dependent SID system based on a real-time cochlear model called cascade of asymmetric resonators with fast-acting compression (CARFAC). We investigate the SID performance of CARFAC on signals corrupted by noise of various types and levels. We compare its performance with conventional auditory feature generators including mel-frequency cepstrum coefficients, frequency domain linear predictions, as well as another biologically inspired model called the auditory nerve model. We show that CARFAC outperforms other approaches when signals are corrupted by noise. Our results are consistent across datasets, types and levels of noise, different speaking speeds, and back-end classifiers. We show that the noise-robust SID performance of CARFAC is largely due to its nonlinear processing of auditory input signals. Presumably, the human auditory system achieves noise-robust performance via inherent nonlinearities as well.

Wald’s martingale and the conditional distributions of absorption time in the Moran process

Many models of evolution are stochastic processes, where some quantity of interest fluctuates randomly in time. One classic example is the Moranbirth–death process, where that quantity is the number of mutants in a population. In such processes, we are often interested in their absorption (i.e. fixation) probabilities and the conditional distributions of absorption time. Those conditional time distributions can be very difficult to calculate, even for relatively simple processes like the Moran birth–death model. Instead of considering the time to absorption, we consider a closely related quantity: the number of mutant population size changes before absorption. We use Wald’s martingale to obtain the conditional characteristic functions of that quantity in the Moran process. Our expressions are novel, analytical and exact, and their parameter dependence is explicit. We use our results to approximate the conditional characteristic functions of absorption time. We state the conditions under which that approximation is particularly accurate. Martingales are an elegant framework to solve principal problems of evolutionary stochastic processes. They do not require us to evaluate recursion relations, so when they are applicable, we can quickly and tractably obtain absorption probabilities and times of evolutionary models.

Neuroregeneration and plasticity: a review of the physiological mechanisms for achieving functional recovery postinjury

Neuronal networks, especially those in the central nervous system (CNS), evolved to support extensive functional capabilities while ensuring stability. Several physiological "brakes" that maintain the stability of the neuronal networks in a healthy state quickly become a hinderance postinjury. These "brakes" include inhibition from the extracellular environment, intrinsic factors of neurons and the control of neuronal plasticity. There are distinct differences between the neuronal networks in the peripheral nervous system (PNS) and the CNS. Underpinning these differences is the trade-off between reduced functional capabilities with increased adaptability through the formation of new connections and new neurons. The PNS has "facilitators" that stimulate neuroregeneration and plasticity, while the CNS has "brakes" that limit them. By studying how these "facilitators" and "brakes" work and identifying the key processes and molecules involved, we can attempt to apply these theories to the neuronal networks of the CNS to increase its adaptability. The difference in adaptability between the CNS and PNS leads to a difference in neuroregenerative properties and plasticity. Plasticity ensures quick functional recovery of abilities in the short and medium term. Neuroregeneration involves synthesizing new neurons and connections, providing extra resources in the long term to replace those damaged by the injury, and achieving a lasting functional recovery. Therefore, by understanding the factors that affect neuroregeneration and plasticity, we can combine their advantages and develop rehabilitation techniques. Rehabilitation training methods, coordinated with pharmacological interventions and/or electrical stimulation, contributes to a precise, holistic treatment plan that achieves functional recovery from nervous system injuries. Furthermore, these techniques are not limited to limb movement, as other functions lost as a result of brain injury, such as speech, can also be recovered with an appropriate training program.

The self-organized learning of noisy environmental stimuli requires distinct phases of plasticity

Along sensory pathways, representations of environmental stimuli become increasingly sparse and expanded. If additionally the feed-forward synaptic weights are structured according to the inherent organization of stimuli, the increase in sparseness and expansion leads to a reduction of sensory noise. However, it is unknown how the synapses in the brain form the required structure, especially given the omnipresent noise of environmental stimuli. Here, we employ a combination of synaptic plasticity and intrinsic plasticity—adapting the excitability of each neuron individually—and present stimuli with an inherent organization to a feed-forward network. We observe that intrinsic plasticity maintains the sparseness of the neural code and thereby allows synaptic plasticity to learn the organization of stimuli in low-noise environments. Nevertheless, even high levels of noise can be handled after a subsequent phase of readaptation of the neuronal excitabilities by intrinsic plasticity. Interestingly, during this phase the synaptic structure has to be maintained. These results demonstrate that learning and recalling in the presence of noise requires the coordinated interplay between plasticity mechanisms adapting different properties of the neuronal circuit.

Everyday life requires living beings to continuously recognize and categorize perceived stimuli from the environment. To master this task, the representations of these stimuli become increasingly sparse and expanded along the sensory pathways of the brain. In addition, the underlying neuronal network has to be structured according to the inherent organization of the environmental stimuli. However, how the neuronal network learns the required structure even in the presence of noise remains unknown. In this theoretical study, we show that the interplay between synaptic plasticity—controlling the synaptic efficacies—and intrinsic plasticity—adapting the neuronal excitabilities—enables the network to encode the organization of environmental stimuli. It thereby structures the network to correctly categorize stimuli even in the presence of noise. After having encoded the stimuli’s organization, consolidating the synaptic structure while keeping the neuronal excitabilities dynamic enables the neuronal system to readapt to arbitrary levels of noise resulting in a near-optimal classification performance for all noise levels. These results provide new insights into the interplay between different plasticity mechanisms and how this interplay enables sensory systems to reliably learn and categorize stimuli from the surrounding environment.