Fold bifurcation entangled surfaces for one-dimensional Kitaev lattice model

In this paper, we investigate a feasible holography with the Kitaev model using dilatonic gravity in AdS2. We propose a generic dual theory of gravity in the AdS2 and suggest that this bulk action is a suitable toy model in studying quantum mechanics in Kitaev model using gauge/gravity duality. This gives a possible equivalent description for the Kitaev model in the dual gravity bulk. Scalar and tensor perturbations are investigated in details. In the case of near AdS perturbation, we show that the geometry still “freezes” as is AdS, while the dilation perturbation decays at the AdS boundary safely. The time-dependent part of the perturbation is an oscillatory model. We discover that the dual gravity induces an effective and renormalizable quantum action. The entanglement entropy for bulk theory is computed using extremal surfaces. We prove that these surfaces have a fold bifurcation regime of criticality.

Beyond Rescorla-Wagner: the ups and downs of learning

We check the robustness of a recently proposed dynamical model of associative Pavlovian learning that extends the Rescorla-Wagner (RW) model in a natural way and predicts progressively damped oscillations in the response of the subjects. Using the data of two experiments, we compare the dynamical oscillatory model (DOM) with a non-associative oscillatory model (NAOM) made of the superposition of the RW learning curve and oscillations. Not only do data clearly show an oscillatory pattern, but they also favour the DOM over the NAOM, thus pointing out that these oscillations are the manifestation of an associative process. The latter is interpreted as the fact that subjects make predictions on trial outcomes more extended in time than in the RW model, but with more uncertainty.

An oscillator model better predicts cortical entrainment to music

A body of research demonstrates convincingly a role for synchronization of auditory cortex to rhythmic structure in sounds including speech and music. Some studies hypothesize that an oscillator in auditory cortex could underlie important temporal processes such as segmentation and prediction. An important critique of these findings raises the plausible concern that what is measured is perhaps not an oscillator but is instead a sequence of evoked responses. The two distinct mechanisms could look very similar in the case of rhythmic input, but an oscillator might better provide the computational roles mentioned above (i.e., segmentation and prediction). We advance an approach to adjudicate between the two models: analyzing the phase lag between stimulus and neural signal across different stimulation rates. We ran numerical simulations of evoked and oscillatory computational models, showing that in the evoked case,phase lag is heavily rate-dependent, while the oscillatory model displays marked phase concentration across stimulation rates. Next, we compared these model predictions with magnetoencephalography data recorded while participants listened to music of varying note rates. Our results show that the phase concentration of the experimental data is more in line with the oscillatory model than with the evoked model. This finding supports an auditory cortical signal that (i) contains components of both bottom-up evoked responses and internal oscillatory synchronization whose strengths are weighted by their appropriateness for particular stimulus types and (ii) cannot be explained by evoked responses alone.

The Impact of the Dollar Rate on Fluctuations of Ruble Liquidity in Russia

The influence of both the absolute values of the dollar/ruble exchange rate (rate) and its changes per day on the balance of the Bank of Russia operations for ruble liquidity provision and absorption (saldo) was investigated. Daily data were used from January 2015 to April 2018. It was found that the change in the rate 6 days ago is the cause (according to Granger) of the saldo value. For the saldo dynamics, an oscillatory model with an external force - a change in the rate - is proposed. Using the Kalman filter, the model parameters were estimated and saldo forecasted. Found period of self-oscillation is 4.218 days and attenuation of the amplitude for a day in 2.179 times. The rate growth of 1 RUB, after 6 days, causes saldo increase of approximately 20 billion rubles. In fact, the changes in rate cause the variability of the saldo not more than for found coefficient of determination (26.7%), but the "change in the rate-liquidity saldo" system during the crisis-free period has a high "Q-factor," and changes in the rate, repeated with a period close to self-one, can cause large-amplitude fluctuations in saldo.

Behavior stability and individual differences in Pavlovian extended conditioning

How stable and general is behavior once maximum learning is reached? To answer this question and understand post-acquisition behavior and its related individual differences, we propose a psychological principle that naturally extends associative models of Pavlovian conditioning to a dynamical oscillatory model where subjects have a greater memory capacity than usually postulated, but with greater forecast uncertainty. This results in a greater resistance to learning in the first few sessions followed by an over-optimal response peak and a sequence of progressively damped response oscillations. We detected the first peak and trough of the new learning curve in our data, but their dispersion was too large to also check the presence of oscillations with smaller amplitude. We ran an unusually long experiment with 32 rats over 3960 trials, where we excluded habituation and other well-known phenomena as sources of variability in the subjects' performance. Using the data of this and another Pavlovian experiment by Harris et al. (2015), as an illustration of the principle we tested the theory against the basic associative single-cue Rescorla-Wagner (RW) model. We found evidence that the RW model is the best nonlinear regression to data only for a minority of the subjects, while its dynamical extension can explain the almost totality of data with strong to very strong evidence. Finally, an analysis of short-scale fluctuations of individual responses showed that they are described by random white noise, in contrast with the colored-noise findings in human performance.