Information transfer with a gravitating bath

Late-time dominance of entanglement islands plays a critical role in addressing the information paradox for black holes in AdS coupled to an asymptotic non-gravitational bath. A natural question is how this observation can be extended to gravitational systems. To gain insight into this question, we explore how this story is modified within the context of Karch-Randall braneworlds when we allow the asymptotic bath to couple to dynamical gravity. We find that because of the inability to separate degrees of freedom by spatial location when defining the radiation region, the entanglement entropy of radiation emitted into the bath is a time-independent constant, consistent with recent work on black hole information in asymptotically flat space. If we instead consider an entanglement entropy between two sectors of a specific division of the Hilbert space, we then find non-trivial time-dependence, with the Page time a monotonically decreasing function of the brane angle---provided both branes are below a particular angle. However, the properties of the entropy depend discontinuously on this angle, which is the first example of such discontinuous behavior for an AdS brane in AdS space.

Software Methodology for Estimating the Efficiency of the Hardware Composition of Deep Packet Inspection System Using the Modernized Hooke ‒ Jeeves Method

Deep packet inspection systems on communication networks are used to identify the application generating a specific traffic flow. The issues related to modeling and design of deep packet inspection systems remain poorly understood. In this paper, a software technique for evaluating the effectiveness of the hardware composition of the servers of the deep packet inspection system is presented, using a mathematical model of such a system and software search methods. The description of the program search by the maximum element method and the Hook - Jeeves method is given. A modernization of the Hook-Jeeves method for a monotonically decreasing function is proposed. Comparison of the methods by the number of search steps is performed.

Quenched free energy from spacetime D-branes

We propose a useful integral representation of the quenched free energy which is applicable to any random systems. Our formula involves the generating function of multi-boundary correlators, which can be interpreted on the bulk gravity side as spacetime D-branes introduced by Marolf and Maxfield in [arXiv:2002.08950]. As an example, we apply our formalism to the Airy limit of the random matrix model and compute its quenched free energy under certain approximations of the generating function of correlators. It turns out that the resulting quenched free energy is a monotonically decreasing function of the temperature, as expected.

About magnetic AdS black holes

There has recently been a strong revival of interest in quasi-extremal magnetically charged black holes. In the asymptotically flat case, it is possible to choose the magnetic charge of such an object in such a manner that the black hole is surrounded by a corona in which electroweak symmetry is restored on macroscopic scales, a result of very considerable interest. We argue that holographic duality indicates that the asymptotically AdS analogues of these black holes have several interesting properties: the dual theory is only physical if the black hole is required to rotate; in the rotating case, the magnetic field at the poles does not attain its maximum on the event horizon, but rather somewhat outside it; the magnetic field at the equator is not a monotonically decreasing function of the magnetic charge; the electric fields induced by the rotation, while smaller than their magnetic counterparts, are by no means negligible; the maximal electric field often occurs neither at the poles nor at the equator; and so on. Most importantly, in the magnetically charged case it is possible to avoid the superradiant instability to which neutral AdS-Kerr black holes are subject; but the need to avoid this instability imposes upper bounds on the magnetic and electric fields. In some circumstances, therefore, the corona may not exist in the asymptotically AdS case.

Effects of cell cycle variability on lineage and population measurements of messenger RNA abundance

Many models of gene expression do not explicitly incorporate a cell cycle description. Here, we derive a theory describing how messenger RNA (mRNA) fluctuations for constitutive and bursty gene expression are influenced by stochasticity in the duration of the cell cycle and the timing of DNA replication. Analytical expressions for the moments show that omitting cell cycle duration introduces an error in the predicted mean number of mRNAs that is a monotonically decreasing function of η , which is proportional to the ratio of the mean cell cycle duration and the mRNA lifetime. By contrast, the error in the variance of the mRNA distribution is highest for intermediate values of η consistent with genome-wide measurements in many organisms. Using eukaryotic cell data, we estimate the errors in the mean and variance to be at most 3% and 25%, respectively. Furthermore, we derive an accurate negative binomial mixture approximation to the mRNA distribution. This indicates that stochasticity in the cell cycle can introduce fluctuations in mRNA numbers that are similar to the effect of bursty transcription. Finally, we show that for real experimental data, disregarding cell cycle stochasticity can introduce errors in the inference of transcription rates larger than 10%.

Effects of cell cycle variability on lineage and population measurements of mRNA abundance

Many models of gene expression do not explicitly incorporate a cell cycle description. Here we derive a theory describing how mRNA fluctuations for constitutive and bursty gene expression are influenced by stochasticity in the duration of the cell cycle and the timing of DNA replication. Analytical expressions for the moments show that omitting cell cycle duration introduces an error in the predicted mean number of mRNAs that is a monotonically decreasing function of η, which is proportional to the ratio of the mean cell cycle duration and the mRNA lifetime. By contrast, the error in the variance of the mRNA distribution is highest for intermediate values of η consistent with genome-wide measurements in many organisms. Using eukaryotic cell data, we estimate the errors in the mean and variance to be at most 3% and 25%, respectively. Furthermore, we derive an accurate negative binomial mixture approximation to the mRNA distribution. This indicates that stochasticity in the cell cycle can introduce fluctuations in mRNA numbers that are similar to the effect of bursty transcription. Finally, we show that for real experimental data, disregarding cell cycle stochasticity can introduce errors in the inference of transcription rates larger than 10%.

Orbital dynamics of circumbinary planets

ABSTRACT We investigate the dynamics of a non-zero mass, circular orbit planet around an eccentric orbit binary for various values of the binary eccentricity, binary mass fraction, planet mass, and planet semimajor axis by means of numerical simulations. Previous studies investigated the secular dynamics mainly by approximate analytic methods. In the stationary inclination state, the planet and binary precess together with no change in relative tilt. For both prograde and retrograde planetary orbits, we explore the conditions for planetary orbital libration versus circulation and the conditions for stationary inclination. As was predicted by analytic models, for sufficiently high initial inclination, a prograde planet’s orbit librates about the stationary tilted state. For a fixed binary eccentricity, the stationary angle is a monotonically decreasing function of the ratio of the planet-to-binary angular momentum j. The larger j, the stronger the evolutionary changes in the binary eccentricity and inclination. We also calculate the critical tilt angle that separates the circulating from the librating orbits for both prograde and retrograde planet orbits. The properties of the librating orbits and stationary angles are quite different for prograde versus retrograde orbits. The results of the numerical simulations are in very good quantitative agreement with the analytic models. Our results have implications for circumbinary planet formation and evolution.

How We Solve the Weights in Our Surrogate Models Matters

The construction of surrogate models, such as radial basis function (RBF) and Kriging-based surrogates, requires an invertible (square and full rank matrix) or pseudoinvertible (overdetermined) linear system to be solved. This study demonstrates that the method used to solve this linear system may result in up to five orders of magnitude difference in the accuracy of the constructed surrogate model using exactly the same information. Hence, this paper makes the canonic and important point toward reproducible science: the details of solving the linear system when constructing a surrogate model must be communicated. This point is clearly illustrated on a single function, namely the Styblinski–Tang test function by constructing over 200 RBF surrogate models from 128 Latin Hypercubed sampled points. The linear system in the construction of each surrogate model was solved using LU, QR, Cholesky, Singular-Value Decomposition, and the Moore–Penrose pseudoinverse. As we show, the decomposition method influences the utility of the surrogate model, which depends on the application, i.e., whether an accurate approximation of a surrogate is required or whether the ability to optimize the surrogate and capture the optimal design is pertinent. Evidently the selection of the optimal hyperparameters based on the cross validation error also significantly impacts the utility of the constructed surrogate. For our problem, it turns out that selecting the hyperparameters at the lowest cross validation error favors function approximation but adversely affects the ability to optimize the surrogate model. This is demonstrated by optimizing each constructed surrogate model from 16 fixed initial starting points and recording the optimal designs. For our problem, selecting the optimal hyperparameter that coincides with the lowest monotonically decreasing function value significantly improves the ability to optimize the surrogate for most solution strategies.

Thermodynamic properties of coherent photons in self-focusing nonlinear waveguides

We study the thermodynamic properties of coherent photons in self-focusing nonlinear waveguides. The equation of the superfluid state of photons has been derived. There is a transition temperature [Formula: see text], above which the photon gas is in the coherent state, but below which the photon gas is in the superfluid state. At [Formula: see text], the photon system undergoes a first-order phase transition from the coherent to the superfluid state. To determine the fugacity [Formula: see text] and the transition temperature [Formula: see text] of the photon gas, we numerically solve the equation of the superfluid state of photons. The fugacity [Formula: see text] is a monotonically decreasing function of temperature [Formula: see text] and light intensity [Formula: see text]. The transition temperature [Formula: see text] is a monotonically decreasing function of light intensity [Formula: see text].

Buoyancy-driven bubbly flows: ordered and free rise at small and intermediate volume fraction

Various expressions have been proposed previously for the rise velocity of gas bubbles in homogeneous steady bubbly flows, generally a monotonically decreasing function of the bubble volume fraction. For suspensions of freely moving bubbles, some of these are of the form expected for ordered arrays of bubbles, and vice versa, as they do not reduce to the behaviour expected theoretically in the dilute limit. The microstructure of weakly inhomogeneous bubbly flows not being known generally, the effect of microstructure is an important consideration. We revisit this problem here for bubbly flows at small to moderate Reynolds number values for deformable bubbles, using direct numerical simulation and analysis. For ordered suspensions, the rise velocity is demonstrated not to be monotonically decreasing with volume fraction due to cooperative wake interactions. The fore-and-aft asymmetry of an isolated ellipsoidal bubble is reversed upon increasing the volume fraction, and the bubble aspect ratio approaches unity. Recent work on rising bubble pairs is used to explain most of these results; the present work therefore forms a platform of extending the former to suspensions of many bubbles. We adopt this new strategy also to support the existence of the oblique rise of ordered suspensions, the possibility of which is also demonstrated analytically. Finally, we demonstrate that most of the trends observed in ordered systems also appear in freely evolving suspensions. These similarities are supported by prior experimental measurements and attributed to the fact that free bubbles keep the same neighbours for extended periods of time.