1,016 research outputs found

    Entropy function from the Einstein boundary term

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    We show using the entropy function formalism developed by Sen \cite{Sen:2005wa} that the boundary term which arises from the Einstein-Hilbert action is sufficient to yield the Bekenstein-Hawking entropy of a static extremal black hole which is asymptotically flat. However, for asymptotically AdSAdS black holes, the bulk term also plays an important role due to the presence of the cosmological constant. Further, we show that for extremal rotating black holes, both the boundary and the bulk terms contribute non-vanishing pieces to the entropy.Comment: v1: 9 pages LaTex, v2: 10 pages LaTex (to appear in Europhysics Letters

    The role of mutual information in the Page curve

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    In this work, we give two proposals regarding the status of connectivity of entanglement wedges and the associated saturation of mutual information. The first proposal has been given for the scenario before the Page time depicting the fact that at a particular value of the observer's time tb=tRt_b=t_R (where tRβt_R\ll\beta), the mutual information I(R+:R)I(R_+:R_-) vanishes representing the disconnected phase of the radiation entanglement wedge. We argue that this time is the Hartman-Maldacena time at which the fine-grained entropy of radiation goes as S(R)log(β)S(R)\sim \log(\beta), where β\beta is the inverse of Hawking temperature of the black hole. On the other hand, the second proposal probes the crucial role played by the mutual information of black hole subsystems in obtaining the correct Page curve of radiation.Comment: v1: 7 pages LaTex, 2 figures, v2: 9 pages LaTex, 2 figures. Accepted for publication in Physical Review

    Mutual information of subsystems and the Page curve for Schwarzschild de-Sitter black hole

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    In this work, we show that the two proposals associated to the mutual information of matter fields can be given for an eternal Schwarzschild black hole in de-Sitter spacetime. These proposals also depicts the status of associated entanglement wedges and their roleplay in obtaining the correct Page curve of radiation. The first proposal has been give for the before Page time scenario, which shows that the mutual information I(RH+:RH)I(R_{H}^{+}:R_{H}^{-}) vanishes at a certain value of the observer's time tbH=tHt_{b_{H}}=t_{H} (where tHβHt_{H}\ll \beta_{H}). We claim that this is the Hartman-Maldacena time at which the entanglement wedge associated to RH+RHR_{H}^{+}\cup R_{H}^{-} gets disconnected and the fine-grained radiation entropy has the form S(RH)log(βH)S(R_{H})\sim \log(\beta_{H}). The second proposal depicts the fact that just after the Page time, when the replica wormholes are the dominating saddle-points, the mutual information I(BH+:BH)I(B_{H}^{+}:B_{H}^{-}) vanishes as soon as the time difference taHtbHt_{a_{H}}-t_{b_{H}} equals the scrambling time. Holographically, this reflects that the entanglement wedge associated to BH+BHB_{H}^{+}\cup B_{H}^{-} jumps to the disconnected phase at this particular time-scale. Furthermore, these two proposals lead us to the correct time-evolution of the fine-grained entropy of radiation as portrayed by the Page curve. We have also shown that similar observations can be obtained for the radiation associated to the cosmological horizon.Comment: v1:18 pages LaTex with multiple figures, v2: matches with the accepted version; To appear in Physical Review

    Stability, quasinormal modes in a charged black hole in perfect fluid dark matter

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    In this work, we study time-like and null geodesics in a charged black hole background immersed in perfect fluid dark matter (PFDM). Using the condition for circular geodesics, we evaluate the energy (EE) and angular momentum (LL) in terms of the radius (rcr_c) of the circular orbits. The existence and finite-ness of EE and LL constrain the possible range of PFDM parameter (χ\chi) and the radius of the circular orbit (rcr_c). We then use the Lyapunov exponent (λ\lambda) to study the stability of the geodesics. Then we analyze the critical exponent (γ\gamma) useful for determining the possibility of detection of gravitational wave signals. After that, we study the perturbation due to a massless scalar field in such a background and calculate the quasinrmal mode (QNM) frequencies and their dependence on PFDM parameter χ\chi and black hole charge QQ. Also, we compare the obtained QNM frequencies both in the exact case and in the eikonal limit. We also calculate the quality factor of the oscillating system and study its dependence on χ\chi and QQ. Finally, we evaluate the black hole shadow radius RsR_s and graphically observe the effect of χ\chi and QQ on it.Comment: 29 pages, 18 Figures; Comments are welcom

    Mixed state information theoretic measures in boosted black brane

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    In this paper, we study various mixed state information theoretic quantities for a boosted black brane geometry. We have considered two set ups, namely, the subsystem taken parallel and perpendicular to the direction of the boost. The quantities that we calculate are the entanglement wedge cross-section, mutual information, entanglement negativity and mutual complexity. In particular, we study the dependence of these quantities on the boost parameter. We then proceed to calculate the asymmetry ratios of these quantities, and observe that they are independent of the subsystem size. Finally, we proceed to study an interesting limit of the boosted black brane geometry, which is the so called AdS wave geometry. We once again compute all the mixed state information theoretic quantities for this geometry.Comment: 32 pages LaTex and 9 figures, comments are welcom

    Deep Learning based Inter-subject Continuous Decoding of Motor Imagery for Practical Brain-Computer Interfaces

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    Inter-subject transfer learning is a long-standing problem in brain-computer interfaces (BCIs) and has not yet been fully realized due to high inter-subject variability in the brain signals related to motor imagery (MI). The recent success of deep learning-based algorithms in classifying different brain signals warrants further exploration to determine whether it is feasible for the inter-subject continuous decoding of MI signals to provide contingent neurofeedback which is important for neurorehabilitative BCI designs. In this paper, we have shown how a convolutional neural network (CNN) based deep learning framework can be used for inter-subject continuous decoding of MI related electroencephalographic (EEG) signals using the novel concept of Mega Blocks for adapting the network against inter-subject variabilities. These Mega Blocks have the capacity to repeat a specific architectural block several times such as one or more convolutional layers in a single Mega Block. The parameters of such Mega Blocks can be optimized using Bayesian hyperparameter optimization. The results, obtained on the publicly available BCI competition IV-2b dataset, yields an average inter-subject continuous decoding accuracy of 71.49% (kappa=0.42) and 70.84% (kappa =0.42) for two different training methods such as adaptive moment estimation (Adam) and stochastic gradient descent (SGDM) respectively in 7 out of 9 subjects. Our results show for the first time that it is feasible to use CNN based architectures for inter-subject continuous decoding with a sufficient level of accuracy for developing calibration-free MI-BCIs for practical purposes

    On Some Properties of Cylindrically Transformed Systems With R(?) Symmetry and Phase Dynamics

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    Nonlinear dynamical systems with R(p) symmetry are shown to behave in a very interesting manner under a new transformation of dynamical variables. Such property helps to identify the phase dynamics embedded in the system but preserves the basic property of the attractor intact. This is very similar to those phenomenon discussed with the help of covering transformation in the literature. The Poincare sections obtained are identical to those obtained through covering transformation and hence indicate to a similar topological structure and identical dynamical characteristics

    Assessing impact of channel selection on decoding of motor and cognitive imagery from MEG data

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    Objective: Magnetoencephalography (MEG) based Brain-Computer Interface (BCI) involves a large number of sensors allowing better spatiotemporal resolution for assessing brain activity patterns. There have been many efforts to develop BCI using MEG with high accuracy, though an increase in the number of channels means an increase in computational complexity. However, not all sensors necessarily contribute significantly to an increase in classification accuracy, and specifically in the case of MEG-based BCI no channel selection methodology has been performed. Therefore, this study investigates the effect of channel selection on the performance of MEG-based BCI. Approach: MEG data were recorded for two sessions from 15 healthy participants performing motor imagery, cognitive imagery and a mixed imagery task pair using a unique paradigm. Performance of four state-of-the-art channel selection methods (i.e. Class-Correlation (CC), ReliefF (RF), Random Forest (RandF), and Infinite Latent Feature Selection (ILFS) were applied across six binary tasks in three different frequency bands) was evaluated in this study on two state-of-the-art features i.e. bandpower and CSP. Main results: All four methods provided a statistically significant increase in classification accuracy (CA) compared to a baseline method using all gradiometer sensors, i.e. 204 channels with band-power features from alpha (8-12Hz), beta (13-30Hz), or broadband (alpha+beta ) (8-30Hz). It is also observed that the alpha frequency band performed better than the beta and broadband frequency bands. The performance of the beta band gave the lowest CA compared with the other two bands. Channel selection improved accuracy irrespective of feature types. Moreover, all the methods reduced the number of channels significantly, from 204 to a range of 1-25, using bandpower as a feature and from 15-105 for CSP. The optimal channel number also varied not only in each session but also for each participant. Reducing the number of channels will help to decrease the computation cost and maintain numerical stability in cases of low trial numbers. Significance: The study showed significant improvement in performance of MEG-BCI with channel selection irrespective of feature type and hence can be successfully applied for BCI applications

    Mapping & decoding cortical engagement during motor imagery, mental arithmetic, and silent word generation using MEG

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    Accurate quantification of cortical engagement during mental imagery tasks remains a challenging brain-imaging problem with immediate relevance to developing brain–computer interfaces. We analyzed magnetoencephalography (MEG) data from 18 individuals completing cued motor imagery, mental arithmetic, and silent word generation tasks. Participants imagined movements of both hands (HANDS) and both feet (FEET), subtracted two numbers (SUB), and silently generated words (WORD). The task-related cortical engagement was inferred from beta band (17–25 Hz) power decrements estimated using a frequency-resolved beamforming method. In the hands and feet motor imagery tasks, beta power consistently decreased in premotor and motor areas. In the word and subtraction tasks, beta-power decrements showed engagements in language and arithmetic processing within the temporal, parietal, and inferior frontal regions. A support vector machine classification of beta power decrements yielded high accuracy rates of 74 and 68% for classifying motor-imagery (HANDS vs. FEET) and cognitive (WORD vs. SUB) tasks, respectively. From the motor-versus-nonmotor contrasts, excellent accuracy rates of 85 and 80% were observed for hands-versus-word and hands-versus-sub, respectively. A multivariate Gaussian-process classifier provided an accuracy rate of 60% for the four-way (HANDS-FEET-WORD-SUB) classification problem. Individual task performance was revealed by within-subject correlations of beta-decrements. Beta-power decrements are helpful metrics for mapping and decoding cortical engagement during mental processes in the absence of sensory stimuli or overt behavioral outputs. Markers derived based on beta decrements may be suitable for rehabilitation purposes, to characterize motor or cognitive impairments, or to treat patients recovering from a cerebral stroke
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