Task-specific effects of reward on task switching

Although cognitive control and reinforcement learning have been researched extensively over the last few decades, only recently have studies investigated their interrelationship. An important unanswered question concerns how the control system decides what task to execute and how vigorously to carry out the task once selected. Based on a recent theory of control formulated according to principles of hierarchical reinforcement learning, we asked whether rewards can affect top-down control over task performance at the level of task representation. Participants were rewarded for correctly performing only one of two tasks in a standard task-switching experiment. Reaction times and error rates were lower for the reinforced task compared to the non-reinforced task. Moreover, the switch cost in error rates for the non-reinforced task was significantly larger compared to the reinforced task, especially for trials in which the imperative stimulus afforded different responses for the two tasks, resulting in a "non-paradoxical" asymmetric switch cost. These findings suggest that reinforcement at the task level resulted in greater application of top-down control rather than in stronger stimulus-response pathways for the rewarded task

Towards an Entanglement Measure for Mixed States in CFTs Based on Relative Entropy

Relative entropy of entanglement (REE) is an entanglement measure of bipartite mixed states, defined by the minimum of the relative entropy $S(\rho_{AB}|| \sigma_{AB})$ between a given mixed state $\rho_{AB}$ and an arbitrary separable state $\sigma_{AB}$. The REE is always bounded by the mutual information $I_{AB}=S(\rho_{AB} || \rho_{A}\otimes \rho_{B})$ because the latter measures not only quantum entanglement but also classical correlations. In this paper we address the question of to what extent REE can be small compared to the mutual information in conformal field theories (CFTs). For this purpose, we perturbatively compute the relative entropy between the vacuum reduced density matrix $\rho^{0}_{AB}$ on disjoint subsystems $A \cup B$ and arbitrarily separable state $\sigma_{AB}$ in the limit where two subsystems A and B are well separated, then minimize the relative entropy with respect to the separable states. We argue that the result highly depends on the spectrum of CFT on the subsystems. When we have a few low energy spectrum of operators as in the case where the subsystems consist of a finite number of spins in spin chain models, the REE is considerably smaller than the mutual information. However in general our perturbative scheme breaks down, and the REE can be as large as the mutual information.Comment: 35 pages, 2 figure

Electrophysiological indices of anterior cingulate cortex function reveal changing levels of cognitive effort and reward valuation that sustain task performance

Successful execution of goal-directed behaviors often requires the deployment of cognitive control, which is thought to require cognitive effort. Recent theories have proposed that anterior cingulate cortex (ACC) regulates control levels by weighing the reward-related benefits of control against its effort-related costs. However, given that the sensations of cognitive effort and reward valuation are available only to introspection, this hypothesis is difficult to investigate empirically. We have proposed that two electrophysiological indices of ACC function, frontal midline theta and the reward positivity (RewP), provide objective measures of these functions. To explore this issue, we recorded the electroencephalogram (EEG) from participants engaged in an extended, cognitively-demanding task. Participants performed a time estimation task for 2 h in which they received reward and error feedback according to their task performance. We observed that the amplitude of the RewP, a feedback-locked component of the event related brain potential associated with reward processing, decreased with time-on-task. Conversely, frontal midline theta power, which consists of 4-8 Hz EEG oscillations associated with cognitive effort, increased with time-on-task. We also explored how these phenomena changed over time by conducting within-participant multi-level modeling analyses. Our results suggest that extended execution of a cognitively-demanding task is characterized by an early phase in which high control levels foster rapid improvements in task performance, and a later phase in which high control levels were necessary to maintain stable task performance, perhaps counteracting waning reward valuation

Chemical Variation in Molecular Cloud Cores in the Orion A Cloud

We have observed molecular cloud cores in the Orion A giant molecular cloud (GMC) in CCS, HC3N, DNC, and HN13C to study their chemical characteristics. We have detected CCS in the Orion A GMC for the first time. CCS was detected in about a third of the observed cores. The cores detected in CCS are not localized but are widely distributed over the Orion A GMC. The CCS peak intensity of the core tends to be high in the southern region of the Orion A GMC. The HC3N peak intensity of the core also tends to be high in the southern region, while there are HC3N intense cores near Orion KL, which is not seen in CCS. The core associated with Orion KL shows broad HC3N line profile, and star formation activity near Orion KL seems to enhance the HC3N emission. The column density ratio of NH3 to CCS is lower near the middle of the filament, and is higher toward the northern and southern regions along the Orion A GMC filament. This ratio is known to trace the chemical evolution in nearby dark cloud cores, but seems to be affected by core gas temperature in the Orion A GMC: cores with low NH3 to CCS column density ratios tend to have warmer gas temperature. The value of the column density ratio of DNC to HN13C is generally similar to that in dark cloud cores, but becomes lower around Orion KL due to higher gas temperature.Comment: 26 pages, 18 figures, to be published in Publications of the Astronomical Society of Japa

Holographic Entanglement of Purification from Conformal Field Theories

We explore a conformal field theoretic interpretation of the holographic entanglement of purification, which is defined as the minimal area of entanglement wedge cross section. We argue that in AdS3/CFT2, the holographic entanglement of purification agrees with the entanglement entropy for a purified state, obtained from a special Weyl transformation, called path-integral optimizations. By definition, this special purified state has the minimal path-integral complexity. We confirm this claim in several examples.Comment: 7 pages, Revtex, 5 figure