Statistical population

Résumé

In statistics, a population is a set of similar items or events which is of interest for some question or experiment. A statistical population can be a group of existing objects (e.g. the set of all stars within the Milky Way galaxy) or a hypothetical and potentially infinite group of objects conceived as a generalization from experience (e.g. the set of all possible hands in a game of poker). A common aim of statistical analysis is to produce information about some chosen population. In statistical inference, a subset of the population (a statistical sample) is chosen to represent the population in a statistical analysis. Moreover, the statistical sample must be unbiased and accurately model the population (every unit of the population has an equal chance of selection). The ratio of the size of this statistical sample to the size of the population is called a sampling fraction. It is then possible to estimate the population parameters using the appropriate sample statistics. The population mean, or population expected value, is a measure of the central tendency either of a probability distribution or of a random variable characterized by that distribution. In a discrete probability distribution of a random variable X, the mean is equal to the sum over every possible value weighted by the probability of that value; that is, it is computed by taking the product of each possible value x of X and its probability p(x), and then adding all these products together, giving . An analogous formula applies to the case of a continuous probability distribution. Not every probability distribution has a defined mean (see the Cauchy distribution for an example). Moreover, the mean can be infinite for some distributions. For a finite population, the population mean of a property is equal to the arithmetic mean of the given property, while considering every member of the population. For example, the population mean height is equal to the sum of the heights of every individual—divided by the total number of individuals.

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https://en.wikipedia.org/wiki/Statistical_population

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Publications associées (3)

Concepts associés (40)

Cours associés (15)

Séances de cours associées (144)

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The medial amygdala (MeA) receives pheromone information about conspecifics and has crucial functions in social behaviors. A previous study showed that activation of GABA neurons in the postero-dorsal MeA (MeApd) with channelrhodopsin-2(H)(134R) (ChR2) stimulates inter-male aggression. When performing these experiments using the faster channelrhodopsin(H134R)(,)(E123T) (ChETA), we find the opposite behavioral outcome. A systematic comparison between the two channelrhodopsin variants reveals that optogenetic activation of MeApd GABA neurons with ChETA suppresses aggression, whereas activation under ChR2 increases aggression. Although the mechanism for this paradoxical difference is not understood, we observe that activation of MeApd GABA neurons with ChR2 causes larger plateau depolarizations, smaller action potentials, and larger local inhibition than with ChETA. Thus, the channelrhodopsin variant used for in vivo optogenetic experiments can radically influence the behavioral outcome. Future work should continue to study the role of specific sub-populations of MeApd GABA neurons in aggression control.

CELL PRESS2022

Animals are capable of evaluating sensory cues for possible threats and adapting their behaviours accordingly. Fear learning is an evolutionarily conserved behaviour crucial for animal survival, during which sensory percepts with a negative reinforcing quality, also called unconditioned stimuli (US), influence the valence of initially neutral sensory cues (conditioned stimulus, CS). The lateral amygdala (LA) is thought to integrate information about sensory cues like tones (the CS), and information about primary reinforcers like painful stimuli (the US). Nevertheless, synaptic afferents to the LA and upstream brain areas remain understudied in fear learning. The posterior insular cortex (pInsCx) has been shown to project to the LA and is known to be a multimodal sensory area which processes auditory, somatosensory-nociceptive, and interoceptive information, making it an interesting brain area with a putative role in fear learning. My PhD thesis therefore aimed to investigate a possible connection from the pInsCx to the LA, and the role of this pathway in the fear learning circuitry. I first used anatomical anterograde and retrograde tracing strategies in the mouse to study the afferents to the LA. Besides previously known inputs, I found that the granular (GI) and the dysgranular (DI) areas of the pInsCx strongly project to the anterior LA. With optogenetically-assisted circuit mapping (OACM), I found a glutamatergic monosynaptic connection from the pInsCx to LA principal neurons that, in agreement with the anatomical findings, was localized more to the anterior LA. In comparison, a well-studied auditory thalamic (MGm/PIN) input was localized more to the posterior LA. Despite this regional input specificity, ~30% LA principal neurons received projections from both areas. Thus, in the first part, using anatomical tracing and OACM, I have unambiguously shown a robust functional excitatory connection from the pInsCx (GI/DI) to the LA.In the second part of my thesis, I aimed to characterize the role of the pInsCx and the pInsCx-LA pathway in fear learning. Using archaerhodopsin-mediated optogenetic inhibition, I found that silencing of footshock-driven activity of pInsCx neurons in-vivo, partially blocks auditory-cued fear memory. These results were also supported by chemogenetic silencing of the pInsCx during the training day, which led to a modest impairment of fear retrieval a day later. Next, to investigate the role of the pInsCx-LA projection more specifically, I used a retrograde expression approach to silence LA-projectors during the footshock, which again, suppressed fear memory one day later. In further ex-vivo experiments, I found that EPSCs at the pInsCx-LA connection exhibited an increased AMPA/NMDA ratio following fear learning, indicating that plasticity occurs at this pathway during fear learning. Finally, miniature microscopic Ca2+ imaging of LA neurons combined with halorhodopsin-mediated axon inhibition, showed that the pInsCx-LA excitatory synapse contributes to transmitting footshock information to a sub-population of LA neurons. This study unravels the relationship between two serial nodes, the pInsCx and the LA, in the fear learning network. Thus, the pInsCx-LA connection is a novel pathway in auditory-cued fear memory that is strengthened with learning and that partly provides aversive information to the amygdala.

EPFL2022

A multi-class framework for a pedestrian cell transmission model accounting for population heterogeneity

Guy Alexander Cooper

This work is an extension of PedCTM, an aggregate and transient cell transmission model for multidirectional pedestrian flows in which pedestrian characteristics are assumed to be homogeneous across the population considered. Critically, one fundamental diagram relating pedestrian speed and flow to local pedestrian density is employed across the entire population. This work extends the model to population heterogeneity with a multi-class approach wherein each sub-population is assigned its own characteristic fundamental diagram. The model presented requires the implementation of an update cycle to minimize numerical dis- persion of pedestrians across all classes. In addition, multi-class dynamics introduces an element of competition in determining the flow constraints of the various classes. A priority scheme is implemented that allows for static, dynamic and stochastic determination of flow priorities throughout the network over the course of simulation. An attempt was made to base the class-specific fundamental diagrams off of inference from a dataset related to the PedFlux collaboration. Ultimately, however, the implementation made use of the Kladek formula for the speed-density relation. Preliminary simulations and results are presented to serve as a proof of concept.

2014

EPFL2022