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Schematic depictions for the analysis of neural population dynamics using PCA. A, Time series of a neural population activity projected into a regression subspace composed of probability and magnitude. A series of eigenvectors was obtained by applying PCA once to each of the four neural populations. PC1 and PC2 indicate the first and second principal components, respectively. The number of eigenvectors obtained by PCA was 2.7 s divided by the analysis window size for the probability and magnitude: 27, 54, and 135 eigenvectors in a 0.1, 0.05, or 0.02 s time window, respectively. B, Examples of eigenvectors at time of ith analysis window for probability and magnitude, whose direction indicates a signal characteristic at the time represented on the population ensemble activity. EV, 45°, 225°; M, magnitude (90°, 270°); P, probability (0°,180°); R-R, 135°, 315°. C, Characteristics of the eigenvectors evaluated quantitatively. Angle, Vector angle from the horizontal axis taken from 0° to 360°. Size, Eigenvector length; deviation, difference between vectors.
Source publication
Computation of expected values (i.e., probability × magnitude) seems to be a dynamic integrative process performed by the brain for efficient economic behavior. However, neural dynamics underlying this computation is largely unknown. Using lottery tasks in monkeys ( Macaca mulatta , male; Macaca fuscata , female), we examined (1) whether four core...
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... step determines the main feature of the neural population signal moment by moment in the space of probability and magnitude. Because activations are dynamic and change over time, the analysis identified whether and how signal transformations occurred to convert probability and magnitude into the expected value as a time series of eigenvectors (Fig. 4A). The directions of these eigenvectors capture the expected values as an angle moment by moment at the population level (Fig. ...
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... Because activations are dynamic and change over time, the analysis identified whether and how signal transformations occurred to convert probability and magnitude into the expected value as a time series of eigenvectors (Fig. 4A). The directions of these eigenvectors capture the expected values as an angle moment by moment at the population level (Fig. ...
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... evaluated eigenvector properties for PC1 and PC2 in each neural population in terms of vector angle, size, and deviation (Fig. 4C). A stable population signal is described as a small variation in eigenvector properties throughout a trial, whereas an unstable population signal is described as a large variation in eigenvector properties. It must be noted that our procedure is a variant of the state space analysis in line with the use of linear regression to identify ...
Citations
... In a previous study using a choice task, we showed that amygdala neurons do encode subjective values that reflected integrated reward probability and magnitude when these reward attributes were cued simultaneously 12 . Perhaps neurons in the prefrontal cortex, including the orbitofrontal cortex, and parietal cortex might be relatively more important in signaling to accumulate decision variables derived from sequential or otherwise complex cues 28,[63][64][65][66] . Some previous studies found largely similar coding of values and choices in the amygdala and orbitofrontal cortex 13,67 , while others emphasized differences in the time courses with which neurons in these structures track changing values 53,68 , and in the specificity with which single neurons encode complex, multisensory food rewards 69 . ...
The value of visual stimuli guides learning, decision-making, and motivation. Although stimulus values often depend on multiple attributes, how neurons extract and integrate distinct value components from separate cues remains unclear. Here we recorded the activity of amygdala neurons while two male monkeys viewed sequential cues indicating the probability and magnitude of expected rewards. Amygdala neurons frequently signaled reward probability in an abstract, stimulus-independent code that generalized across cue formats. While some probability-coding neurons were insensitive to magnitude information, signaling ‘pure’ probability rather than value, many neurons showed biphasic responses that signaled probability and magnitude in a dynamic (temporally-patterned) and flexible (reversible) value code. Specific amygdala neurons integrated these reward attributes into risk signals that quantified the variance of expected rewards, distinct from value. Population codes were accurate, mutually transferable between value components, and expressed differently across amygdala nuclei. Our findings identify amygdala neurons as a substrate for the sequential integration of multiple reward attributes into value and risk.
... The striatum and the OFC collaboratively encode expected value in economic decision-making in primates. Yamada et al. (2021) [18] showed that the central OFC (cOFC) and the ventral striatum (VS) had distinct roles in representing the expected value of a choice. In a visually cued lottery task, monkeys chose between two pie charts, each indicating a different probability and magnitude of a fluid reward. ...
... The striatum and the OFC collaboratively encode expected value in economic decision-making in primates. Yamada et al. (2021) [18] showed that the central OFC (cOFC) and the ventral striatum (VS) had distinct roles in representing the expected value of a choice. In a visually cued lottery task, monkeys chose between two pie charts, each indicating a different probability and magnitude of a fluid reward. ...
Decision-making is a behavior involving many neuronal processes that is crucial for animals to maximize benefits for survival. The orbitofrontal cortex (OFC) is a brain region known to play critical roles in decision-making in both rodents and primates, and it functions in conjunction with several other brain regions in both species to fulfill decision-making needs. Here we review studies on the specific roles of the OFC and related brain regions in decision-making in rodents and primates, to gain insights on how distinct neural activities in several brain regions functionally contribute to the complex processes required to make a choice. The prefrontal cortex (PFC), the anterior cingulate cortex (ACC), and the striatum work in combination with the OFC to perform the basic processes involved in decision-making, while the basolateral amygdala (BLA) and the hippocampus are implicated together with the OFC in specialized types of decision-making. The specific functions of these brain regions in rodents and primates reveal both preserved and evolved aspects of decision-making mechanisms along the evolutionary lineage.
... In general, we examine the outcome of our choice and adjust subsequent choice behavior using the outcome information to choose an appropriate action. Five significant studies on neurons (Kawai et al. (2015); Yamada et al. (2021); Imaizumi et al. (2022); Yang et al. (2022); Ferrari-Toniolo and Schultz (2023)) have examined neuronal responses to loss and gain. These studies suggest that two different neural systems may respond to loss and gain, resulting in a value function with a cusp as a reference point. ...
... In their studies on brain reward circuitry, Yamada et al. (2021) and Imaizumi et al. (2022) proposed a neuronal prospect theory model. Using theoretical accuracy equivalent to that of human neuroimaging studies from a gain perspective, they showed that single-neuron activity in four core reward-related cortical and subcortical regions represents a subjective assessment of risky gambles in monkeys. ...
... In the gain context, both monkeys were risk-seekers when the starting token number was low; however, both demonstrated risk-neutral or risk-averse behavior when the start token number increased. This result is consistent with Yamada et al. (2021) and Imaizumi et al. (2022). Moreover, Yang et al. (2022) showed, in monkey G, the utility functions (value functions) in monkey G were consistently steeper for losses than for gains. ...
In prospect theory, the value function is typically concave for gains and convex for losses, with losses usually having a steeper slope than gains. The neural system responds differently to losses and gains. Five new studies on neurons related to this issue have examined neuronal responses to losses, gains, and reference points. This study investigated a new concept of the value function. A value function with a neuronal cusp may exhibit variations and behavioral cusps associated with catastrophic events, potentially influencing a trader's decision to close a position. Additionally, we have conducted empirical studies on algorithmic trading strategies that employ different value function specifications.
... The same analyses were then carried out as replications in the second animal. The number of trials and sessions is within the range of previous literature (Yamada, Imaizumi, & Matsumoto, 2021;Padoa-Schioppa & Assad, 2006). Some trials were excluded because the animal failed to make a choice within 5 sec (Monkey D: 599, 1.04%, Monkey C: 1203, 1.8%). ...
... Among these, the OFC is particularly important, as damage or disruption consistently alters value-based choice behavior, suggesting that OFC neurons perform choice-relevant computations (Ballesta, Shi, Conen, & Padoa-Schioppa, 2020;Rudebeck, Saunders, Prescott, Chau, & Murray, 2013). Integrated value signals are commonly found within OFC, including in single-unit firing rates (Padoa-Schioppa & Assad, 2006;Wallis & Miller, 2003;Tremblay & Schultz, 1999), population codes (Yamada et al., 2021;Rich & Wallis, 2016), field potentials (Saez et al., 2018;Rich & Wallis, 2016, 2017, and fMRI BOLD signals (Chikazoe, Lee, Kriegeskorte, & Anderson, 2014;Plassmann, O'Doherty, & Rangel, 2007), and this has been taken as evidence that integrated value is the key decision variable in OFC. However, multiple laboratories consistently report neurons in monkey OFC (primarily Area 13) that encode the value of unique attributes (Pastor-Bernier, Stasiak, & Schultz, 2019;Setogawa et al., 2019;Blanchard, Hayden, & Bromberg-Martin, 2015;Raghuraman & Padoa-Schioppa, 2014;Hosokawa, Kennerley, Sloan, & Wallis, 2013;Padoa-Schioppa & Assad, 2006), and similar signals can be found in human fMRI BOLD (Howard, Gottfried, Tobler, & Kahnt, 2015). ...
In value-based decisions, there are frequently multiple attributes, such as cost, quality, or quantity, that contribute to the overall goodness of an option. Because one option may not be better in all attributes at once, the decision process should include a means of weighing relevant attributes. Most decision-making models solve this problem by computing an integrated value, or utility, for each option from a weighted combination of attributes. However, behavioral anomalies in decision-making, such as context effects, indicate that other attribute-specific computations might be taking place. Here, we tested whether rhesus macaques show evidence of attribute-specific processing in a value-based decision-making task. Monkeys made a series of decisions involving choice options comprising a sweetness and probability attribute. Each attribute was represented by a separate bar with one of two mappings between bar size and the magnitude of the attribute (i.e., bigger = better or bigger = worse). We found that translating across different mappings produced selective impairments in decision-making. Choices were less accurate and preferences were more variable when like attributes differed in mapping, suggesting that preventing monkeys from easily making direct attribute comparisons resulted in less accurate choice behavior. This was not the case when mappings of unalike attributes within the same option were different. Likewise, gaze patterns favored transitions between like attributes over transitions between unalike attributes of the same option, so that like attributes were sampled sequentially to support within-attribute comparisons. Together, these data demonstrate that value-based decisions rely, at least in part, on directly comparing like attributes of multiattribute options.
... This aforementioned limitation introduces several potential problems in neuroeconomic studies (Camerer et al., 2005;Glimcher et al., 2008;Yamada et al., 2021;Imaizumi et al., 2022;Tymula et al., 2023) that employ experimental testing of reward valuation systems for economic choices. When measuring neural activity in the reward circuitry, the subjective values of any reward depend on the physical state of the subject (Nakano et al., 1984;Critchley and Rolls, 1996;de Araujo et al., 2006;Pritchard et al., 2008), even for money (Symmonds et al., 2010). ...
Hunger and thirst drive animals’ consumption behavior and regulate their decision-making concerning rewards. We previously assessed the thirst states of monkeys by measuring blood osmolality under controlled water access and examined how these thirst states influenced their risk-taking behavior in decisions involving fluid rewards. However, hunger assessment in monkeys remains poorly performed. Moreover, the lack of precise measures for hunger states leads to another issue regarding how hunger and thirst states interact with each other in each individual. Thus, when controlling food access to motivate performance, it remains unclear how these two physiological needs are satisfied in captive monkeys. Here, we measured blood ghrelin and osmolality levels to respectively assess hunger and thirst in four captive macaques. Using an enzyme-linked immunosorbent assay, we identified that the levels of blood ghrelin, a widely measured hunger-related peptide hormone in humans, were high after 20 h of no food access (with ad libitum water). This reflects a typical controlled food access condition. One hour after consuming a regular dry meal, the blood ghrelin levels in three out of four monkeys decreased to within their baseline range. Additionally, blood osmolality measured from the same blood sample, the standard hematological index of hydration status, increased after consuming the regular dry meal with no water access. Thus, ghrelin and osmolality may reflect the physiological states of individual monkeys regarding hunger and thirst, suggesting that these indices can be used as tools for monitoring hunger and thirst levels that mediate an animal's decision to consume rewards.
... For example, multiple types of voltage-gated ion channels in Purkinje cells make complex spikes in neurons [4]. Recent research suggests that neurons perform complex computation such as detecting synchronized inputs [5], selecting inputs [6] and calculating expected values [7] by applying nonlinear spatiotemporal transformations to synaptic inputs in dendrites. Therefore, it is important to estimate spatial electrical properties of neurons for understanding information processing in the brain. ...
One of the neuron models that simulate the electrical activity of neurons, the multi-compartment model, has spatial electrical properties that control nonlinear spatiotemporal dynamics and can reproduce nonlinear electrical responses with high accuracy. However, it is difficult to determine the model parameters in multi-compartment models from membrane potentials, since unknown high dimensional parameters for spatial electrical property should be estimated using incomplete observation data. In this paper, we propose a data-driven method to estimate the spatial electrical properties in the multi-compartment model from membrane potentials observed incompletely. The proposed method employs the replica exchange method using prior information considering morphological smoothness to solve problems of the local optima in the solution space and incompleteness of observation data. We further verify the effectiveness of the proposed method by using simulation data obtained from realistic neuron models.
... To choose an appropriate action, we monitor the outcome of our choice and adjust subsequent choice behavior using the outcome information. Four important studies on neurons related to this issue have recently been published (Kawai et al. [2015], Yamada et al. [2021], Imaizumi et al. [2022], Yang et al. [2022]). These studies examine neuronal responses to loss and gain, respectively. ...
... In the gain context, both monkeys were risk-seeking when the start token number was low, but they became risk neutral or risk-averse when the start token number increased. This result is consistent with Yamada et al. [2021], Imaizumi et al. [2022]. Moreover, Yang et al. [2022] showed, in monkey G, the utility functions arXiv A PREPRINT (value functions) were consistently steeper for losses than for gains. ...
... To choose an appropriate action, we monitor the outcome of our choice and adjust subsequent choice behavior using the outcome information. Four important studies on neurons related to this issue have recently been published (Kawai et al. [2015], Yamada et al. [2021], Imaizumi et al. [2022], Yang et al. [2022]). These studies examine neuronal responses to losses, gains and reference points, respectively. ...
In the prospect theory, value function is typically concave for gains, commonly convex for losses, with losses usually having a steeper slope than gains. The neural system largely differs from the loss and gains sides. Five new studies on neurons related to this issue have examined neuronal responses to losses, gains, and reference points. This study investigates a new concept of the value function. A value function with a neuronal cusp may show variations and behavior cusps with catastrophe where a trader closes one's position.
... Then, according to the above equation (14), the P values of image skeleton line fitting for all subjects were calculated to be the maximum 99.72% and the minimum 99.35%, respectively. The expected probability [40,41] E P =99.61% is obtained by calculating the average value. The 3D skeleton extraction accuracy pairs under similar conditions are shown in Table 3. Table 3 Comparison of accuracy of 3D image skeleton extraction ID references methods accuracy 1 Lebre et al.,2018 [42] 3D erosion algorithm 0.97 2 Merveille et al.,2017 [43] 3D erosion algorithm 0.90 ...
INTRODUCTION: Analysis of magnetic resonance angiography image data is crucial for early detection and prevention of stroke patients. Extracting the 3D Skeleton of cerebral vessels is the focus and difficulty of analysis.OBJECTIVES: The objective is to remove other tissue components from the vascular tissue portion of the image with minimal loss by reading MRA image data and performing processing processes such as grayscale normalization, interpolation, breakpoint detection and repair, and image segmentation to facilitate 3D reconstruction of cerebral blood vessels and the reconstructed vascular tissues make extraction of the Skeleton easier.METHODS: Considering that most of the existing techniques for extracting the 3D vascular Skeleton are corrosion algorithms, machine learning algorithms require high hardware resources, a large number of learning and test cases, and the accuracy needs to be confirmed, an average plane center of mass computation method is proposed, which improves the average plane algorithm by combining the standard plane algorithm and the center of mass algorithm.RESULTS: Intersection points and skeleton breakpoints on the Skeleton are selected as critical points and manually labeled for experimental verification, and the algorithm has higher efficiency and accuracy than other algorithms in directly extracting the 3D Skeleton of blood vessels.CONCLUSION: The method has low hardware requirements, accurate and reliable image data, can be automatically modeled and calculated by Python program, and meets the needs of clinical applications under information technology conditions.
... Among these, the orbitofrontal cortex (OFC) is particularly important, as damage or disruption consistently alters value-based choice behavior, suggesting that OFC neurons perform choice-relevant computations (47,48). Integrated value signals are commonly found within OFC, including in single unit firing rates (7-9), population codes (49,50), field potentials (50-52), and fMRI BOLD signals (53,54), and this has been taken as evidence that integrated value is the key decision variable in OFC. However, multiple labs consistently report neurons in monkey OFC (primarily area 13) that encode the value of unique attributes (7,(55)(56)(57)(58)(59), and similar signals can be found in human fMRI BOLD (60). ...
In value-based decisions, there are frequently multiple attributes, such as cost, quality, or quantity, that contribute to the overall goodness of an option. Since one option may not be better in all attributes at once, the decision process should include a means of weighing relevant attributes. Most decision-making models solve this problem by computing an integrated value, or utility, for each option from a weighted combination of attributes. However, behavioral anomalies in decision-making, such as context effects, indicate that other attribute-specific computations might be taking place. Here, we tested whether rhesus macaques show evidence of attribute-specific processing in a value-based decision-making task. Monkeys made a series of decisions involving choice options comprising a sweetness and probability attribute. Each attribute was represented by a separate bar with one of two mappings between bar size and the magnitude of the attribute (i.e., bigger=better or bigger=worse). We found that translating across different mappings produced selective impairments in decision-making. When like attributes differed, monkeys were prevented from easily making direct attribute comparisons, and choices were less accurate and preferences were more variable. This was not the case when mappings of unalike attributes within the same option were different. Likewise, gaze patterns favored transitions between like attributes over transitions between unalike attributes of the same option, so that like attributes were sampled sequentially to support within-attribute comparisons. Together, these data demonstrate that value-based decisions rely, at least in part, on directly comparing like attributes of multi-attribute options.
Significance Statement
Value-based decision-making is a cognitive function impacted by a number of clinical conditions, including substance use disorder and mood disorders. Understanding the neural mechanisms, including online processing steps involved in decision formation, will provide critical insights into decision-making deficits characteristic of human psychiatric disorders. Using rhesus monkeys as a model species capable of complex decision-making, this study shows that decisions involve a process of comparing like features, or attributes, of multi-attribute options. This is contrary to popular models of decision-making in which attributes are first combined into an overall value, or utility, to make a choice. Therefore, these results serve as an important foundation for establishing a more complete understanding of the neural mechanisms involved in forming complex decisions.
... We previously developed a variant of state-space analysis for continuous parameters (Yamada et al., 2021) that describes how a neuronal population dynamically represents some cognitive task parameters in a regression subspace. This analysis simply extracts the temporal structures of neural modulations in the following two steps using standard statistical software: (1) an estimation of regression coefficients for neural modulations by task parameters across time and neurons, which provides a regression matrix representing the extent of neural modulation as a function of time in a neural population; and (2) application of PCA to the regression matrix, which provides neural dynamics in the regression subspace (i.e., temporal structures of neural modulations by the task parameters). ...
... Regarding Exp. 1, we previously reported that monkey behavior depends on expected values, defined as the probability time magnitude (Yamada et al., 2021). We described the analysis steps to check whether the behavior of the monkey reflected the task parameters, such as reward probability and magnitude. ...
... The regression coefficients for probability and magnitude were plotted as a time series for visual inspection. These results have been reported previously (Yamada et al., 2021). Based on linear regression, activity modulation patterns were categorized into the following several types: Probability type with a significant b p and without a significant b m ; Magnitude type without a significant b p and with a significant b m ; Both type with significant b p and b m . ...
Neural population dynamics provide a key computational framework for understanding information processing in the sensory, cognitive, and motor functions of the brain. They systematically depict complex neural population activity, dominated by strong temporal dynamics as trajectory geometry in a low-dimensional neural space. However, neural population dynamics are poorly related to the conventional analytical framework of single-neuron activity, the rate-coding regime that analyzes firing rate modulations using task parameters. To link the rate-coding and dynamic models, we developed a variant of state-space analysis in the regression subspace, which describes the temporal structures of neural modulations using continuous and categorical task parameters. In macaque monkeys, using two neural population datasets containing either of two standard task parameters, continuous and categorical, we revealed that neural modulation structures are reliably captured by these task parameters in the regression subspace as trajectory geometry in a lower dimension. Furthermore, we combined the classical optimal-stimulus response analysis (usually used in rate-coding analysis) with the dynamic model and found that the most prominent modulation dynamics in the lower dimension were derived from these optimal responses. Using those analyses, we successfully extracted geometries for both task parameters that formed a straight geometry, suggesting that their functional relevance is characterized as a unidimensional feature in their neural modulation dynamics. Collectively, our approach bridges neural modulation in the rate-coding model and the dynamic system, and provides researchers with a significant advantage in exploring the temporal structure of neural modulations for pre-existing datasets.
