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We use the quantum null energy condition in strongly coupled two-dimensional field theories (QNEC2) as diagnostic tool to study a variety of phase structures, including crossover, second and first order phase transitions. We find a universal QNEC2 constraint for first order phase transitions with kinked entanglement entropy and discuss in general the relation between the QNEC2-inequality and monotonicity of the Casini-Huerta c-function. We then focus on a specific example, the holographic dual of which is modelled by three-dimensional Einstein gravity plus a massive scalar field with one free parameter in the self-interaction potential. We study translation invariant stationary states dual to domain walls and black branes. Depending on the value of the free parameter we find crossover, second and first order phase transitions between such states, and the c-function either flows to zero or to a finite value in the infrared. Strikingly, evaluating QNEC2 for ground state solutions allows to predict the existence of phase transitions at finite temperature.
We use the quantum null energy condition in strongly coupled two-dimensional field theories (QNEC2) as diagnostic tool to study a variety of phase structures, including crossover, second and first order phase transitions. We find a universal QNEC2 constraint for first order phase transitions with kinked entanglement entropy and discuss in general the relation between the QNEC2-inequality and monotonicity of the Casini-Huerta c-function. We then focus on a specific example, the holographic dual of which is modelled by three-dimensional Einstein gravity plus a massive scalar field with one free parameter in the self-interaction potential. We study translation invariant stationary states dual to domain walls and black branes. Depending on the value of the free parameter we find crossover, second and first order phase transitions between such states, and the c-function either flows to zero or to a finite value in the infrared. Strikingly, evaluating QNEC2 for ground state solutions allows to predict the existence of phase transitions at finite temperature.
We use holography to study the dynamics of a strongly-coupled gauge theory in four-dimensional de Sitter space with Hubble rate H. The gauge theory is non-conformal with a characteristic mass scale M. We solve Einstein’s equations numerically and determine the time evolution of homogeneous gauge theory states. If their initial energy density is high compared with H4 then the early-time evolution is well described by viscous hydrodynamics with a non-zero bulk viscosity. At late times the dynamics is always far from equilibrium. The asymptotic late-time state preserves the full de Sitter symmetry group and its dual geometry is a domain-wall in AdS5. The approach to this state is characterised by an emergent relation of the form P = w E that is different from the equilibrium equation of state in flat space. The constant w does not depend on the initial conditions but only on H/M and is negative if the ratio H/M is close to unity. The event and the apparent horizons of the late-time solution do not coincide with one another, reflecting its non-equilibrium nature. In between them lies an “entanglement horizon” that cannot be penetrated by extremal surfaces anchored at the boundary, which we use to compute the entanglement entropy of boundary regions. If the entangling region equals the observable universe then the extremal surface coincides with a bulk cosmological horizon that just touches the event horizon, while for larger regions the extremal surface probes behind the event horizon.
Cryo electron tomography (cryo-ET) combined with subtomogram averaging (StA) enables structural determination of macromolecules in their native context. A few structures were reported by StA at resolution higher than 4.5 Å, however all of these are from viral structural proteins or vesicle coats. Reaching high resolution for a broader range of samples is uncommon due to beam-induced sample drift, poor signal-to-noise ratio (SNR) of images, challenges in CTF correction, limited number of particles. Here we propose a strategy to address these issues, which consists of a tomographic data collection scheme and a processing workflow. Tilt series are collected with higher electron dose at zero-degree tilt in order to increase SNR. Next, after performing StA conventionally, we extract 2D projections of the particles of interest from the higher SNR images and use the single particle analysis tools to refine the particle alignment and generate a reconstruction. We benchmarked our proposed hybrid StA (hStA) workflow and improved the resolution for tobacco mosaic virus from 7.2 to 5.2 Å and the resolution for the ion channel RyR1 in crowded native membranes from 12.9 to 9.1 Å. We demonstrate that hStA can improve the resolution obtained by conventional StA and promises to be a useful tool for StA projects aiming at subnanometer resolution or higher.
Relationship between regional white matter hyperintensities and alpha oscillations in older adults
(2020)
Objective: To investigate whether regional white matter hyperintensities (WMHs) relate to alpha oscillations (AO) in a large population-based sample of elderly individuals.
Methods: We associated voxel-wise WMHs from high-resolution 3-Tesla MRI with neuronal alpha oscillations (AO) from resting-state multichannel EEG at sensor (N=907) and source space (N=855) in older participants of the LIFE-Adult study (60–80 years). In EEG, we computed relative alpha power (AP), individual alpha peak frequency (IAPF), as well as long-range temporal correlations (LRTC) that represent dynamic properties of the signal. We implemented whole-brain voxel-wise regression models to identify regions where parameters of AO were linked to probability of WMH occurrence. We further used mediation analyses to examine whether WMH volume mediated the relationship between age and AO.
Results: Higher prevalence of WMHs in the superior and posterior corona radiata was related to elevated relative AP, with strongest correlations in the bilateral occipital cortex, even after controlling for potential confounding factors. The age-related increase of relative AP in the right temporal brain region was shown to be mediated by total WMH volume.
Conclusion: A high relative AP corresponding to increased regional WMHs was not associated with age per se, in fact, this relationship was mediated by WMHs. We argue that the WMH-associated increase of AP reflects a generalized and likely compensatory spread of AO leading to a larger number of synchronously recruited neurons. Our findings thus suggest that longitudinal EEG recordings might be sensitive to detect functional changes due to WMHs.
Relationship between regional white matter hyperintensities and alpha oscillations in older adults
(2020)
White matter hyperintensities (WMHs) in the cerebral white matter and attenuation of alpha oscillations (AO; 7–13 Hz) occur with the advancing age. However, a crucial question remains, whether changes in AO relate to aging per se or they rather reflect the impact of age-related neuropathology like WMHs. In this study, using a large cohort (N=907) of elderly participants (60-80 years), we assessed relative alpha power (AP), individual alpha peak frequency (IAPF) and long-range temporal correlations (LRTC) from resting-state EEG. We further associated these parameters with voxel-wise WMHs from 3T MRI. We found that higher prevalence of WMHs in the superior and posterior corona radiata was related to elevated relative AP, with strongest correlations in the bilateral occipital cortex, even after controlling for potential confounding factors. In contrast, we observed no significant relation of probability of WMH occurrence with IAPF and LRTC. We argue that the WMH-associated increase of AP reflects generalized and likely compensatory changes of AO leading to a larger number of synchronously recruited neurons.
Understanding effects of emotional valence and stress on children’s memory is important for educational and legal contexts. This study disentangles the effects of emotional content of to-be-remembered information (i.e., items differing in emotional valence and arousal), stress exposure, and associated cortisol secretion on children’s memory. We also examine whether girls’ memory is more affected by stress induction. 143 6-to-7-year-old children were randomly allocated to the Trier Social Stress Test for Children (n = 103) or a control condition (n = 40). 25 minutes after stressor onset, children incidentally encoded 75 objects varying in emotional valence (crossed with arousal) together with neutral scene backgrounds. We found that response-bias corrected memory was worse for low arousing negative items than neutral and positive items, with the latter two categories not being different from each other. Whilst boys’ memory was largely unaffected by stress, girls in the stress condition showed worse memory for negative items, especially the low arousing ones, than girls in the control condition. Girls, compared to boys, reported higher subjective stress increases following stress exposure, and had higher cortisol stress responses. Whilst a higher cortisol stress response was associated with better emotional memory in girls in the stress condition, boys’ memory was not associated with their cortisol secretion. Taken together, our study suggests that 6-to-7-year-old children, more so girls, show memory suppression for negative information. Girls’ memory for negative information, compared to boys, is also more strongly modulated by stress experience and the associated cortisol response.
Recurrent cortical network dynamics plays a crucial role for sequential information processing in the brain. While the theoretical framework of reservoir computing provides a conceptual basis for the understanding of recurrent neural computation, it often requires manual adjustments of global network parameters, in particular of the spectral radius of the recurrent synaptic weight matrix. Being a mathematical and relatively complex quantity, the spectral radius is not readily accessible to biological neural networks, which generally adhere to the principle that information about the network state should either be encoded in local intrinsic dynamical quantities (e.g. membrane potentials), or transmitted via synaptic connectivity. We present two synaptic scaling rules for echo state networks that solely rely on locally accessible variables. Both rules work online, in the presence of a continuous stream of input signals. The first rule, termed flow control, is based on a local comparison between the mean squared recurrent membrane potential and the mean squared activity of the neuron itself. It is derived from a global scaling condition on the dynamic flow of neural activities and requires the separability of external and recurrent input currents. We gained further insight into the adaptation dynamics of flow control by using a mean field approximation on the variances of neural activities that allowed us to describe the interplay between network activity and adaptation as a two-dimensional dynamical system. The second rule that we considered, variance control, directly regulates the variance of neural activities by locally scaling the recurrent synaptic weights. The target set point of this homeostatic mechanism is dynamically determined as a function of the variance of the locally measured external input. This functional relation was derived from the same mean-field approach that was used to describe the approximate dynamics of flow control.
The effectiveness of the presented mechanisms was tested numerically using different external input protocols. The network performance after adaptation was evaluated by training the network to perform a time delayed XOR operation on binary sequences. As our main result, we found that flow control can reliably regulate the spectral radius under different input statistics, but precise tuning is negatively affected by interneural correlations. Furthermore, flow control showed a consistent task performance over a wide range of input strengths/variances. Variance control, on the other side, did not yield the desired spectral radii with the same precision. Moreover, task performance was less consistent across different input strengths.
Given the better performance and simpler mathematical form of flow control, we concluded that a local control of the spectral radius via an implicit adaptation scheme is a realistic alternative to approaches using classical “set point” homeostatic feedback controls of neural firing.
Author summary How can a neural network control its recurrent synaptic strengths such that network dynamics are optimal for sequential information processing? An important quantity in this respect, the spectral radius of the recurrent synaptic weight matrix, is a non-local quantity. Therefore, a direct calculation of the spectral radius is not feasible for biological networks. However, we show that there exist a local and biologically plausible adaptation mechanism, flow control, which allows to control the recurrent weight spectral radius while the network is operating under the influence of external inputs. Flow control is based on a theorem of random matrix theory, which is applicable if inter-synaptic correlations are weak. We apply the new adaption rule to echo-state networks having the task to perform a time-delayed XOR operation on random binary input sequences. We find that flow-controlled networks can adapt to a wide range of input strengths while retaining essentially constant task performance.
Recurrent cortical network dynamics plays a crucial role for sequential information processing in the brain. While the theoretical framework of reservoir computing provides a conceptual basis for the understanding of recurrent neural computation, it often requires manual adjustments of global network parameters, in particular of the spectral radius of the recurrent synaptic weight matrix. Being a mathematical and relatively complex quantity, the spectral radius is not readily accessible to biological neural networks, which generally adhere to the principle that information about the network state should either be encoded in local intrinsic dynamical quantities (e.g. membrane potentials), or transmitted via synaptic connectivity. We present two synaptic scaling rules for echo state networks that solely rely on locally accessible variables. Both rules work online, in the presence of a continuous stream of input signals. The first rule, termed flow control, is based on a local comparison between the mean squared recurrent membrane potential and the mean squared activity of the neuron itself. It is derived from a global scaling condition on the dynamic flow of neural activities and requires the separability of external and recurrent input currents. We gained further insight into the adaptation dynamics of flow control by using a mean field approximation on the variances of neural activities that allowed us to describe the interplay between network activity and adaptation as a two-dimensional dynamical system. The second rule that we considered, variance control, directly regulates the variance of neural activities by locally scaling the recurrent synaptic weights. The target set point of this homeostatic mechanism is dynamically determined as a function of the variance of the locally measured external input. This functional relation was derived from the same mean-field approach that was used to describe the approximate dynamics of flow control.
The effectiveness of the presented mechanisms was tested numerically using different external input protocols. The network performance after adaptation was evaluated by training the network to perform a time delayed XOR operation on binary sequences. As our main result, we found that flow control can reliably regulate the spectral radius under different input statistics, but precise tuning is negatively affected by interneural correlations. Furthermore, flow control showed a consistent task performance over a wide range of input strengths/variances. Variance control, on the other side, did not yield the desired spectral radii with the same precision. Moreover, task performance was less consistent across different input strengths.
Given the better performance and simpler mathematical form of flow control, we concluded that a local control of the spectral radius via an implicit adaptation scheme is a realistic alternative to approaches using classical “set point” homeostatic feedback controls of neural firing.
Author summary How can a neural network control its recurrent synaptic strengths such that network dynamics are optimal for sequential information processing? An important quantity in this respect, the spectral radius of the recurrent synaptic weight matrix, is a non-local quantity. Therefore, a direct calculation of the spectral radius is not feasible for biological networks. However, we show that there exist a local and biologically plausible adaptation mechanism, flow control, which allows to control the recurrent weight spectral radius while the network is operating under the influence of external inputs. Flow control is based on a theorem of random matrix theory, which is applicable if inter-synaptic correlations are weak. We apply the new adaption rule to echo-state networks having the task to perform a time-delayed XOR operation on random binary input sequences. We find that flow-controlled networks can adapt to a wide range of input strengths while retaining essentially constant task performance.
Evolution of nematic fluctuations in CaK(Fe1−xNix)4As4 with spin-vortex crystal magnetic order
(2020)
The CaK(Fe1−xNix)4As4 superconductors resemble the archetypal 122-type iron-based materials but have a crystal structure with distinctly lower symmetry. This family hosts one of the few examples of the so-called spin-vortex crystal magnetic order, a non-collinear magnetic configuration that preserves tetragonal symmetry, in contrast to the orthorhombic collinear stripe-type magnetic configuration common to the 122-type systems. Thus, nematic order is completely absent from its phase diagram. To investigate the evolution of nematic fluctuations in such a case, we present elastoresistance and elastic modulus measurements in CaK(Fe1−xNix)4As4 (x=0−0.05) combined with phenomenological modeling and density functional theory. We find clear experimental signatures of considerable nematic fluctuations, including softening of the Young's modulus Y[110] and a Curie-Weiss type divergence of the B2g elastoresistance coefficient in CaK(Fe0.951Ni0.049)4As4. Overall, nematic fluctuations within this series bear strong similarities to the hole-doped Ba1−xKxFe2As2 series, including a substitution-induced sign change. Our theoretical analysis addresses the effect of the specific crystal symmetry of the 1144-type structure in determining its magnetic ground state and on the nematic fluctuations.