Relative Entropy of Coherent States on General CCR Algebras

For a subalgebra of a generic CCR algebra, we consider the relative entropy between a general (not necessarily pure) quasifree state and a coherent excitationthereof. We give a unified formula for this entropy in terms of single-particle modular data. Further, we investigate changes of the relative entropy along subalgebras arising from an increasing family of symplectic subspaces; here convexity of the entropy (as usually considered for the Quantum Null Energy Condition) is replaced with lower estimates for the second derivative, composed of “bulk terms” and “boundary terms”. Our main assumption is that the subspaces are in differential modular position, a regularity condition that generalizes the usual notion of half-sided modular inclusions. We illustrate our results in relevant examples, including thermal states for the conformal U(1)-current.

Non-unitary TQFTs from 3D $$ \mathcal{N} $$ = 4 rank 0 SCFTs

We propose a novel procedure of assigning a pair of non-unitary topological quantum field theories (TQFTs), TFT±[$$ \mathcal{T} $$ T rank 0], to a (2+1)D interacting $$ \mathcal{N} $$ N = 4 superconformal field theory (SCFT) $$ \mathcal{T} $$ T rank 0 of rank 0, i.e. having no Coulomb and Higgs branches. The topological theories arise from particular degenerate limits of the SCFT. Modular data of the non-unitary TQFTs are extracted from the supersymmetric partition functions in the degenerate limits. As a non-trivial dictionary, we propose that F = maxα (− log|$$ {S}_{0\alpha}^{\left(+\right)} $$ S 0 α + |) = maxα (− log|$$ {S}_{0\alpha}^{\left(-\right)} $$ S 0 α − |), where F is the round three-sphere free energy of $$ \mathcal{T} $$ T rank 0 and $$ {S}_{0\alpha}^{\left(\pm \right)} $$ S 0 α ± is the first column in the modular S-matrix of TFT±. From the dictionary, we derive the lower bound on F, F ≥ − log $$ \left(\sqrt{\frac{5-\sqrt{5}}{10}}\right) $$ 5 − 5 10 ≃ 0.642965, which holds for any rank 0 SCFT. The bound is saturated by the minimal $$ \mathcal{N} $$ N = 4 SCFT proposed by Gang-Yamazaki, whose associated topological theories are both the Lee-Yang TQFT. We explicitly work out the (rank 0 SCFT)/(non-unitary TQFTs) correspondence for infinitely many examples.

Modular Data Acquisition System for Recording Activity and Electrical Stimulation of Brain Tissue Using Dedicated Electronics

In this paper, we present a modular Data Acquisition (DAQ) system for simultaneous electrical stimulation and recording of brain activity. The DAQ system is designed to work with custom-designed Application Specific Integrated Circuit (ASIC) called Neurostim-3 and a variety of commercially available Multi-Electrode Arrays (MEAs). The system can control simultaneously up to 512 independent bidirectional i.e., input-output channels. We present in-depth insight into both hardware and software architectures and discuss relationships between cooperating parts of that system. The particular focus of this study was the exploration of efficient software design so that it could perform all its tasks in real-time using a standard Personal Computer (PC) without the need for data precomputation even for the most demanding experiment scenarios. Not only do we show bare performance metrics, but we also used this software to characterise signal processing capabilities of Neurostim-3 (e.g., gain linearity, transmission band) so that to obtain information on how well it can handle neural signals in real-world applications. The results indicate that each Neurostim-3 channel exhibits signal gain linearity in a wide range of input signal amplitudes. Moreover, their high-pass cut-off frequency gets close to 0.6Hz making it suitable for recording both Local Field Potential (LFP) and spiking brain activity signals. Additionally, the current stimulation circuitry was checked in terms of the ability to reproduce complex patterns. Finally, we present data acquired using our system from the experiments on a living rat’s brain, which proved we obtained physiological data from non-stimulated and stimulated tissue. The presented results lead us to conclude that our hardware and software can work efficiently and effectively in tandem giving valuable insights into how information is being processed by the brain.

Wearable, Multimodal, Biosignal Acquisition System for Potential Critical and Emergency Applications

For emergency or intensive-care units (ICUs), patients with unclear consciousness or unstable hemodynamics often require aggressive monitoring by multiple monitors. Complicated pipelines or lines increase the burden on patients and inconvenience for medical personnel. Currently, many commercial devices provide related functionalities. However, most devices measure only one biological signal, which can increase the budget for users and cause difficulty in remote integration. In this study, we develop a wearable device that integrates electrocardiography (ECG), electroencephalography (EEG), and blood oxygen machines for medical applications with the hope that it can be applied in the future. We develop an integrated multiple-biosignal recording system based on a modular design. The developed system monitors and records EEG, ECG, and peripheral oxygen saturation (SpO2) signals for health purposes simultaneously in a single setting. We use a logic level converter to connect the developed EEG module (BR8), ECG module, and SpO2 module to a microcontroller (Arduino). The modular data are then smoothly encoded and decoded through consistent overhead byte stuffing (COBS). This developed system has passed simulation tests and exhibited proper functioning of all modules and subsystems. In the future, the functionalities of the proposed system can be expanded with additional modules to support various emergency or ICU applications.