ABSTRACT: Humans anticipate events signaled by sensory cues. It is commonly assumed that two uncertainty parameters modulate the brain's capacity to predict: the hazard rate (HR) of event probability and the uncertainty in time estimation which increases with elapsed time. We investigate both assumptions by presenting event probability density functions (PDFs) in each of three sensory modalities. We show that perceptual systems use the reciprocal PDF and not the HR to model event probability density. We also demonstrate that temporal uncertainty does not necessarily grow with elapsed time but can also diminish, depending on the event PDF. Previous research identified neuronal activity related to event probability in multiple levels of the cortical hierarchy (sensory (V4), association (LIP), motor and other areas) proposing the HR as an elementary neuronal computation. Our results-consistent across vision, audition, and somatosensation-suggest that the neurobiological implementation of event anticipation is based on a different, simpler and more stable computation than HR: the reciprocal PDF of events in time.
Project description:We develop a method for the evaluation of extreme event statistics associated with nonlinear dynamical systems from a small number of samples. From an initial dataset of design points, we formulate a sequential strategy that provides the "next-best" data point (set of parameters) that when evaluated results in improved estimates of the probability density function (pdf) for a scalar quantity of interest. The approach uses Gaussian process regression to perform Bayesian inference on the parameter-to-observation map describing the quantity of interest. We then approximate the desired pdf along with uncertainty bounds using the posterior distribution of the inferred map. The next-best design point is sequentially determined through an optimization procedure that selects the point in parameter space that maximally reduces uncertainty between the estimated bounds of the pdf prediction. Since the optimization process uses only information from the inferred map, it has minimal computational cost. Moreover, the special form of the metric emphasizes the tails of the pdf. The method is practical for systems where the dimensionality of the parameter space is of moderate size and for problems where each sample is very expensive to obtain. We apply the method to estimate the extreme event statistics for a very high-dimensional system with millions of degrees of freedom: an offshore platform subjected to 3D irregular waves. It is demonstrated that the developed approach can accurately determine the extreme event statistics using a limited number of samples.
Project description:To prepare for an impending event of unknown temporal distribution, humans internally increase the perceived probability of event onset as time elapses. This effect is termed the hazard rate of events. We tested how the neural encoding of hazard rate changes by providing human participants with prior information on temporal event probability. We recorded behavioral and electroencephalographic (EEG) data while participants listened to continuously repeating five-tone sequences, composed of four standard tones followed by a non-target deviant tone, delivered at slow (1.6 Hz) or fast (4 Hz) rates. The task was to detect a rare target tone, which equiprobably appeared at either position two, three or four of the repeating sequence. In this design, potential target position acts as a proxy for elapsed time. For participants uninformed about the target's distribution, elapsed time to uncertain target onset increased response speed, displaying a significant hazard rate effect at both slow and fast stimulus rates. However, only in fast sequences did prior information about the target's temporal distribution interact with elapsed time, suppressing the hazard rate. Importantly, in the fast, uninformed condition pre-stimulus power synchronization in the beta band (Beta 1, 15-19 Hz) predicted the hazard rate of response times. Prior information suppressed pre-stimulus power synchronization in the same band, while still significantly predicting response times. We conclude that Beta 1 power does not simply encode the hazard rate, but-more generally-internal estimates of temporal event probability based upon contextual information.
Project description:In the immediate aftermath of a strong earthquake and in the presence of an ongoing aftershock sequence, scientific advisories in terms of seismicity forecasts play quite a crucial role in emergency decision-making and risk mitigation. Epidemic Type Aftershock Sequence (ETAS) models are frequently used for forecasting the spatio-temporal evolution of seismicity in the short-term. We propose robust forecasting of seismicity based on ETAS model, by exploiting the link between Bayesian inference and Markov Chain Monte Carlo Simulation. The methodology considers the uncertainty not only in the model parameters, conditioned on the available catalogue of events occurred before the forecasting interval, but also the uncertainty in the sequence of events that are going to happen during the forecasting interval. We demonstrate the methodology by retrospective early forecasting of seismicity associated with the 2016 Amatrice seismic sequence activities in central Italy. We provide robust spatio-temporal short-term seismicity forecasts with various time intervals in the first few days elapsed after each of the three main events within the sequence, which can predict the seismicity within plus/minus two standard deviations from the mean estimate within the few hours elapsed after the main event.
Project description:The pharmacokinetic parameters derived from dynamic contrast-enhanced (DCE) MRI have been used in more than 100 phase I trials and investigator led studies. A comparison of the absolute values of these quantities requires an estimation of their respective probability distribution function (PDF). The statistical variation of the DCE-MRI measurement is analyzed by considering the fundamental sources of error in the MR signal intensity acquired with the spoiled gradient-echo (SPGR) pulse sequence.The variance in the SPGR signal intensity arises from quadrature detection and excitation flip angle inconsistency. The noise power was measured in 11 phantoms of contrast agent concentration in the range [0-1] mM (in steps of 0.1 mM) and in onein vivo acquisition of a tumor-bearing mouse. The distribution of the flip angle was determined in a uniform 10 mM CuSO4 phantom using the spin echo double angle method. The PDF of a wide range of T1 values measured with the varying flip angle (VFA) technique was estimated through numerical simulations of the SPGR equation. The resultant uncertainty in contrast agent concentration was incorporated in the most common model of tracer exchange kinetics and the PDF of the derived pharmacokinetic parameters was studied numerically.The VFA method is an unbiased technique for measuringT1 only in the absence of bias in excitation flip angle. The time-dependent concentration of the contrast agent measured in vivo is within the theoretically predicted uncertainty. The uncertainty in measuring K(trans) with SPGR pulse sequences is of the same order, but always higher than, the uncertainty in measuring the pre-injection longitudinal relaxation time (T10). The lowest achievable bias/uncertainty in estimating this parameter is approximately 20%-70% higher than the bias/uncertainty in the measurement of the pre-injection T1 map. The fractional volume parameters derived from the extended Tofts model were found to be extremely sensitive to the variance in signal intensity. The SNR of the pre-injection T1 map indicates the limiting precision with which K(trans) can be calculated.Current small-animal imaging systems and pulse sequences robust to motion artifacts have the capacity for reproducible quantitative acquisitions with DCE-MRI. In these circumstances, it is feasible to achieve a level of precision limited only by physiologic variability.
Project description:Bayesian theories of neural coding propose that sensory uncertainty is represented by a probability distribution encoded in neural population activity, but direct neural evidence supporting this hypothesis is currently lacking. Using fMRI in combination with a generative model-based analysis, we found that probability distributions reflecting sensory uncertainty could reliably be estimated from human visual cortex and, moreover, that observers appeared to use knowledge of this uncertainty in their perceptual decisions.
Project description:Circadian clocks generate 24-hr rhythms in physiology and behavior. Despite numerous studies, it is still uncertain how circadian rhythms emerge from their molecular and neural constituents. Here, we demonstrate a tight connection between the molecular and neuronal circadian networks. Using fluorescent transcriptional reporters in a Drosophila ex vivo brain culture system, we identified a reciprocal negative regulation between the master circadian regulator CLK and expression of pdf, the main circadian neuropeptide. We show that PDF feedback is required for maintaining normal oscillation pattern in CLK-driven transcription. Interestingly, we found that CLK and neuronal firing suppresses pdf transcription, likely through a common pathway involving the transcription factors DHR38 and SR, establishing a direct link between electric activity and the circadian system. In sum, our work provides evidence for the existence of an uncharacterized CLK-PDF feedback loop that tightly wraps together the molecular oscillator with the circadian neuronal network in Drosophila.
Project description:The growth of a cell population from a large inoculum appears deterministic, although the division process is stochastic at the single-cell level. Microfluidic observations, however, display wide variations in the growth of small populations. Here we combine theory, simulations and experiments to explore the link between single-cell stochasticity and the growth of a population starting from a small number of individuals. The study yields descriptors of the probability distribution function (PDF) of the population size under three sources of stochasticity: cell-to-cell variability, uncertainty in the number of initial cells and generation-dependent division times. The PDF, rescaled to account for the exponential growth of the population, is found to converge to a stationary distribution. All moments of the PDF grow exponentially with the same growth rate, which depends solely on cell-to-cell variability. The shape of the PDF, however, contains the signature of all sources of stochasticity, and is dominated by the early stages of growth, and not by the cell-to-cell variability. Thus, probabilistic predictions of the growth of bacterial populations can be obtained with implications for both naturally occurring conditions and technological applications of single-cell microfluidics.
Project description:Objective. To estimate cause of death and to identify factors associated with risk of inhospital mortality among patients with T2D. Methods. Prospective cohort study performed in a referral public hospital in Lima, Peru. The outcome was time until event, elapsed from hospital admission to discharge or death, and the exposure was the cause of hospital admission. Cox regression was used to evaluate associations of interest reporting Hazard Ratios (HR) and 95% confidence intervals. Results. 499 patients were enrolled. Main causes of death were exacerbation of chronic renal failure (38.1%), respiratory infections (35.7%), and stroke (16.7%). During hospital stay, 42 (8.4%) patients died. In multivariable models, respiratory infections (HR = 6.55, p < 0.001), stroke (HR = 7.05, p = 0.003), and acute renal failure (HR = 16.9, p = 0.001) increased the risk of death. In addition, having 2+ (HR = 7.75, p < 0.001) and 3+ (HR = 21.1, p < 0.001) conditions increased the risk of dying. Conclusion. Respiratory infections, stroke, and acute renal disease increased the risk of inhospital mortality among hospitalized patients with T2D. Infections are not the only cause of inhospital mortality. Certain causes of hospitalization require standardized and aggressive management to decrease mortality.
Project description:Humans can meaningfully report their confidence in a perceptual or cognitive decision. It is widely believed that these reports reflect the Bayesian probability that the decision is correct, but this hypothesis has not been rigorously tested against non-Bayesian alternatives. We use two perceptual categorization tasks in which Bayesian confidence reporting requires subjects to take sensory uncertainty into account in a specific way. We find that subjects do take sensory uncertainty into account when reporting confidence, suggesting that brain areas involved in reporting confidence can access low-level representations of sensory uncertainty, a prerequisite of Bayesian inference. However, behavior is not fully consistent with the Bayesian hypothesis and is better described by simple heuristic models that use uncertainty in a non-Bayesian way. Both conclusions are robust to changes in the uncertainty manipulation, task, response modality, model comparison metric, and additional flexibility in the Bayesian model. Our results suggest that adhering to a rational account of confidence behavior may require incorporating implementational constraints.
Project description:There has been much uncertainty as to whether metastasis requires mutation at the time of spread. Here, we use clinical data to calculate the probability of the spread of melanoma and breast cancer cells. These calculations reveal that the probability of the spread of cancer cells is relatively high for small tumours (approximately 1 event of spread for every 500 cells for melanomas of 0.1 mm) and declines as tumours increase in size (approximately 1 event of spread for every 10(8) cells for melanomas of 12 mm). The probability of spread of breast cancer cells from the lymph nodes to the periphery is approximately 1 event of spread for every 10(8) cells in the nodal masses, which have a mean diameter of 5 mm, while the probability of spread of cancer cells from the breast to the periphery when the primary masses are 5 mm is also approximately 1 event of spread for every 10(8) cells. Thus, the occurrence of an event of spread from the breast to the lymph nodes appears not to increase the propensity of the progeny of those cells to spread from the lymph nodes to the periphery. These values indicate that the spread of human breast cancer and melanoma cells is unlikely to occur by a mechanism requiring mutation at the time of spread.