Quantum work and information geometry of a quantum Myers-Perry black hole

In this paper, we will obtain quantum work for a quantum scale five dimensional Myers-Perry black hole. Unlike heat represented by Hawking radiation, the quantum work is represented by a unitary information preserving process, and becomes important for black holes only at small quantum scales. It will be observed that at such short distances, the quantum work will be corrected by non-perturbative quantum gravitational corrections. We will use the Jarzynski equality to obtain this quantum work modified by non-perturbative quantum gravitational corrections. These non-perturbative corrections will also modify the stability of a quantum Myers-Perry black hole. We will define a quantum corrected information geometry by incorporating the non-perturbative quantum corrections in the information geometry of a Myers-Perry black hole. We will use several different quantum corrected effective information metrics to analyze the stability of a quantum Myers-Perry black hole.

Adaptive Radar Waveform Design Based on Weighted MI and the Difference of Two Mutual Information Metrics

This study deals with the problem of radar waveform design based on the weighted mutual information (MI) and the difference of two mutual information metrics (DMI) in signal-dependent interference. Since the target and clutter information are included in the received signal at the beginning of the design, DMI-based waveform is designed according to the following criterion: maximizing the MI between the received signal and target impulse response while minimizing the MI between the received signal and the clutter impulse response. This criterion is equivalent to maximizing the difference between the first MI and the second MI. Then maximizing the difference of two types of MI is used as the objective function, and the optimization model with the transmitted waveform energy constraint is established. In order to solve it, we resort to maximum marginal allocation (MMA) method to find the DMI-based waveform. Since DMI-based waveform does not allocate energy to the frequency band where the clutter power spectral density (PSD) is greater than the target PSD, we propose to weight the MI-based waveform and DMI-based waveform to synthesize the final optimal waveform. It could provide different trade-offs between two types of MI. Simulation results show the proposed algorithm is valid.

Reduced Perplexity

This chapter introduces a simple, intuitive approach to the assessment of probabilistic inferences. The Shannon information metrics are translated to the probability domain. The translation shows that the negative logarithmic score and the geometric mean are equivalent measures of the accuracy of a probabilistic inference. The geometric mean of forecasted probabilities is thus a measure of forecast accuracy and represents the central tendency of the forecasts. The reciprocal of the geometric mean is referred to as the perplexity and defines the number of independent choices needed to resolve the uncertainty. The assessment method introduced in this chapter is intended to reduce the ‘qualitative’ perplexity relative to the potpourri of scoring rules currently used to evaluate machine learning and other probabilistic algorithms. Utilization of this assessment will provide insight into designing algorithms with reduced the ‘quantitative’ perplexity and thus improved the accuracy of probabilistic forecasts. The translation of information metrics to the probability domain is incorporating the generalized entropy functions developed Rényi and Tsallis. Both generalizations translate to the weighted generalized mean. The generalized mean of probabilistic forecasts forms a spectrum of performance metrics referred to as a Risk Profile. The arithmetic mean is used to measure the decisiveness, while the –2/3 mean is used to measure the robustness.

Information theoretic approaches to deciphering the neural code with functional fluorescence imaging

Information theoretic metrics have proven highly useful to quantify the relationship between behaviorally relevant parameters and neuronal activity with relatively few assumptions. However, such metrics are typically applied to action potential recordings and were not designed for the slow timescales and variable amplitudes typical of functional fluorescence recordings (e.g. calcium imaging). Therefore, the power of information theoretic metrics has yet to be fully exploited by the neuroscience community due to a lack of understanding for how to apply and interpret the metrics with such fluorescence traces. Here, we used computational methods to create mock action potential traces with known amounts of information and from them generated fluorescence traces to examine the ability of different information metrics to recover the known information values. We provide guidelines for the use of information metrics when applied to functional fluorescence and demonstrate their appropriate application to GCaMP6f population recordings from hippocampal neurons imaged during virtual navigation.

A simple analysis of the mixed-state information metric in AdS3/CFT2

We compute the quantum information metrics of a thermal CFT on [Formula: see text] perturbed by the scalar primary operators of conformal dimensions [Formula: see text] = 3, 4, 5, 6. In particular, we assume that the Hamiltonians of the mixed states commute with each other and the temperature is fixed. Under these conditions, the evaluation is analogous to the pure state case. Then we apply the method of A. Trivella [Class. Quantum Grav. 34, 105003 (2017)] to calculate the mixed state information metric for the scalar primary operator of conformal dimension [Formula: see text] = 4 holographically, and reproduce exactly the result in the CFT2 by our approach.

On Mautner-Type Probability of Capture of Intergalactic Meteor Particles by Habitable Exoplanets

Both macro and microprojectiles (e.g., interplanetary, interstellar and even intergalactic material) are seen as important vehicles for the exchange of potential (bio)material within our solar system as well as between stellar systems in our Galaxy. Accordingly, this requires estimates of the impact probabilities for different source populations of projectiles, including for intergalactic meteor particles which have received relatively little attention since considered as rare events (discrete occurrences that are statistically improbable due to their very infrequent appearance). We employ the simple but comprehensive model of intergalactic microprojectile capture by the gravity of exoplanets which enables us to estimate the map of collisional probabilities for an available sample of exoplanets in habitable zones around host stars. The model includes a dynamical description of the capture adopted from Mautner model of interstellar exchange of microparticles and changed for our purposes. We use statistical and information metrics to calculate probability map of intergalactic meteorite particle capture. Moreover, by calculating the entropy index map we estimate the concentration of these rare events. We further adopted a model from immigration theory, to show that the time dependent distribution of single molecule immigration of material indicates high survivability of the immigrated material taking into account birth and death processes on our planet. At present immigration of material can not be observationally constrained but it seems reasonable to think that it will be possible in the near future, and to use it along other proposed parameters for life sustainability on some planet.

Comparing Information Metrics for a Coupled Ornstein–Uhlenbeck Process

It is often the case when studying complex dynamical systems that a statistical formulation can provide the greatest insight into the underlying dynamics. When discussing the behavior of such a system which is evolving in time, it is useful to have the notion of a metric between two given states. A popular measure of information change in a system under perturbation has been the relative entropy of the states, as this notion allows us to quantify the difference between states of a system at different times. In this paper, we investigate the relaxation problem given by a single and coupled Ornstein–Uhlenbeck (O-U) process and compare the information length with entropy-based metrics (relative entropy, Jensen divergence) as well as others. By measuring the total information length in the long time limit, we show that it is only the information length that preserves the linear geometry of the O-U process. In the coupled O-U process, the information length is shown to be capable of detecting changes in both components of the system even when other metrics would detect almost nothing in one of the components. We show in detail that the information length is sensitive to the evolution of subsystems.