Application of a unifying reward-prediction error (RPE)-based framework to explain underlying dynamic dopaminergic activity in timing tasks

SUMMARYThis manuscript is intended as a theoretical companion to Hamiloset al., 20201, in which we examined the role of dopaminergic neurons (DANs) in self-timed movements. In that study, we recorded DAN signals in mice trained to initiate a licking movement after a self-timed delay following a start-timing cue. DAN signals both before the start-timing cue and during the timing interval predicted the timing of movement onset, up to seconds before the movement itself. In particular, dopaminergic signals “ramped up” from the time of the cue to the time of the movement. On a given trial, the slope of the ramping was predictive of when the movement would occur, with steep slope associated with early movement and shallow slope with late movement, reminiscent of a ramp-to-threshold process.Ramping dopaminergic signals were recently proposed in a theoretical framework that examined temporal-difference learning under resolved state uncertainty (Mikhael et al., 20192; Mikhael & Gershman, 20193; Gershman, 20144). Here, we show that an adapted version of Mikhael et al.’s model recapitulates the ramping dopaminergic signaling observed in our self-timed movement task. We also applied the model to results reported in a recent temporal bisection study, in which mice categorized time intervals as relatively short or long compared to a criterion interval (Soares et al., 20165). The model successfully predicted the relative amplitude of dynamic DAN signals observed in the bisection task. These combined results suggest a common neural mechanism that broadly underlies timing behavior: trial-by-trial variation in the rate of the internal “pacemaker,” manifested in DAN signals that reflect stretching or compression of the derivative of the subjective value function relative to veridical time. In this view, faster pacemaking is associated with relatively high amplitude dopaminergic signaling, whereas slower pacemaking is associated with relatively low levels of dopaminergic signaling.

IDENTIFICATION AND INTERPRETATION OF THE THERMAL NETWORK RELIABILITY ASSESSMENT

A methodological approach to assessing the reliability of the thermal network is justified. It is presented in the form of a block diagram consisting of ten consecutive stages. Using the Sturgess formula and the confidence probability level of 0,95 set depending on the district’s thermal load criterion, interval estimates of the reliability of the heat network are developed with a brief description for each of them.– М.: Стройиздат, 2018. – 219 с.

An Analysis of the Temporal Patterning of Pecking in Chicks

In this paper aspects of the temporal and sequential patterning of pecks in the domestic chick are examined. To this end experiments were done in which young chicks were allowed to peck at pairs of coloured stimuli - the time of each peck being recorded automatically by a small computer. A particularly striking feature of the chicks' behaviour was the tendency of the pecks to occur in rapid bursts. Such bouts have been described (and quantified) for behaviours in a number of species, but the bout itself has proven to be a particularly difficult unit to define empirically. Accordingly a model is proposed which describes the order independent features of the intervals between pecks, and also objectively defines a bout criterion interval. This model assumes that not only do pecks tend to cluster into bouts but that the bouts themselves occur in clusters. Consequently two types of between bout intervals will be generated: "not pecking" intervals, whose mean length is long, and which separate bout clusters; and intervals of medium average length, separating bouts within a cluster. It is assumed that these between bout intervals are generated by two random (Poisson) processes of sharply differing rate constants. To test this model an Algol procedure was written which describes the survivorship curve of intervals between pecks in terms of components that can be adequately characterized as negative exponential. It is found that with large sample sizes three distributions are consistently delineated; the "not pecking" intervals are characterized by an exponential with a rate constant of order 10-3, the intervals within a cluster by one of 10-2 and the within bout intervals by one of 10-1 (if the latter generating process is assumed to have a dead time). In addition, a stable bout criterion ranging from 1.9 to 2.3 secs is defined. It is also argued that degeneracies in this model can occur when sample sizes are small - in particular that the intervals of medium length are either not distinguished from those belonging to the outer state of long intervals, or fail to be completely delineated from the two other components. Part II of this paper examines additional features of the pecking behaviour within the framework of this model. The question of how a colour is preferred is explored and it is found that preferred colours in these experiments receive from 1.6 to 3.2 times as many bouts, which are on average 1.1 to 1.3 times as long as those directed at the less preferred colour. Some information on sequencing of bouts is presented in which it is shown that there is a probability of about .60 of continuing to "bout" at the same position when the two stimuli are the same colour. This finding is combined with a measure of overall colour preference to allow fairly consistent predictions of the transition probabilities between bouts when the stimuli differ in colour. Upon examining the intervals within a bout it is found that although they peak strongly at .3 secs they can range between .1 and 2.3 secs. Through indirect evidence it is argued that the number of pecks within a bout also varies substantially. However, it is found that the distribution of intervals within a bout remains nearly invariant regardless of what colours the chicks are pecking. It is suggested that this invariance provides some objective verification for the concept of a "bout unit". However, upon closer examination, differences in the distribution of within bout intervals are found. These differences are interpreted as resulting from the rather surprising occurrence of mixed bouts, that is bouts during which pecks were elicited by both stimuli. Intervals within such mixed bouts were on average longer than those occurring in bouts where all pecks were directed at the same stimulus and consequently effected shifts in the mean and increased the spread in some of the within bout interval distributions. It is tentatively suggested that such mixed bouts are elicited when the chicks attend to cues upon which the stimuli cannot be distinguished. An important assumption of the model is that the interval distributions arising from the three generating processes overlap and that while a stable and obj ective bout criterion can be defined it does not provide a neat means of classifying intervals into either within or between bout intervals. Some intervals less than the bout criterion are assumed to belong to the processes generating between bout intervals. For this reason the total number of bouts defined by the criterion interval will underestimate the true number of bouts occurring - some bouts will be merged together when one of these very short between bout intervals occurs. The occurrence of mixed bouts, along with the substantial proportion of undetectable between bout intervals is shown to hinder extensive examination of the properties of the bouts defined by the criterion interval; it is argued that considerable ambiguity exists in the bouts so defined. The origin of this ambiguity is discussed within the framework of current studies in which bouts of behaviour, defined by a criterion interval, are used as a basic analytical unit.

SEISMOGEOLOGIC EXPERIENCE IN THE BEAUFORT SEA

Conventional seismic data processing was applied to 24‐fold airgun data acquired in the Liverpool and Mackenzie Bay areas of the Beaufort Sea. These data provided general indications of the regional geology and the types of structures present. A part of one line in each area was chosen on the basis of its geologic content and data quality for reprocessing through a velocity analysis package. The purpose was to establish velocity, particularly interval velocity, as the common ground between geology and the seismic section. The velocity package performs a continuous analysis for time and moveout as well as amplitude on all events present within a common‐depth‐point gather. Events are joined from depth point to depth point on the basis of similarity in time, moveout, amplitude, and polarity to yield a segment file. This file is statistically analyzed and sorted into two subsets, primary and nonprimary files, using segment velocity as the criterion. Interval velocities can be calculated between those segments that exhibit velocities characteristic of primary energy. The space‐variant velocity control derived from the data was used to correct it for moveout. A marked improvement in the interpretability of the data resulted on both lines. The data‐derived interval velocities give intriguing indications of lithology which can be correlated to acoustic logs on shore. Plausible hypotheses of offshore geology have been derived without the benefit of any offshore drilling.