Zain H. Saleem

General black holes, untwisted

A bstractWe use solution-generating techniques to construct interpolating geometries between general asymptotically flat, charged, rotating, non-extremal black holes in four and five dimensions and their subtracted geometries. In the four-dimensional case, this is achieved by the use of Harrison transformations, whereas in the five-dimensional case we use STU transformations. We also give the interpretation of these solution-generating transformations in terms of string (pseudo)-dualities, showing that they correspond to combinations of T-dualities and Melvin twists. Upon uplift to one dimension higher, these dualities allow us to “untwist” general black holes to AdS3 times a sphere.

Quasinormal modes for subtracted rotating and magnetized geometries

We obtain explicit separable solutions of the wave equation of massless minimally coupled scalar fields in the subtracted geometry of four-dimensional rotating and Melvin (magnetised) four-charge black holes of the STU model, a consistent truncation of maximally supersymmetric supergravity with four types of electromagnetic fields. These backgrounds possess a hidden SL(2,R) x SL(2,R) x SO(3) symmetry and faithfully model the near horizon geometry of these black holes, but locate them in a confining asymptotically conical box. For each subtracted geometry we obtain two branches of quasi-normal modes, given in terms of hypergeometric functions and spherical harmonics. One branch is over-damped and the other under-damped and they exhibit rotational splitting. No black hole bomb is possible because the Killing field which co-rotates with the horizon is everywhere timelike outside the black hole. A five-dimensional lift of these geometries is given locally by the product of a BTZ black hole with a two-sphere. This allows an explicit analysis of the minimally coupled massive five-dimensional scalar field. Again, there are two branches, both damped, however now their oscillatory parts are shifted by the quantised wave number

Vacuum polarization of STU black holes and their subtracted geometry limit

k

Analytical result for the vacuum polarization of subtracted rotating black holes

along the fifth circle direction.

Theoretical analysis of the distribution of isolated particles in totally asymmetric exclusion processes: Application to mRNA translation rate estimation

A bstractWe study the vacuum polarization of a massless minimally coupled scalar field at the horizon of four-charge STU black holes. We compare the results for the standard asymptotically flat black holes and for the black holes obtained in the “subtracted limit”, both in the general static case and at the horizon pole for the general rotating case. The original and the subtracted results are identical only in the BPS limit, and have opposite sign in the extremal Kerr limit. We also compute the vacuum polarization on the static solutions that interpolate between both the original and the subtracted case through a solution-generating transformation and show that the vacuum polarization stays positive throughout the interpolating solution. In the appendix we provide a closed-form solution for the Green’s function on general (static or rotating) subtracted black hole geometries.

The curious case of large-N expansions on a (pseudo)sphere

We give an analytical formula for the vacuum polarization of a massless minimally coupled scalar field at the horizon of a rotating black hole with subtracted geometry. This is the first example of an exact, analytical result for a four-dimensional rotating black hole.

Theoretical quantification of interference in the TASEP: Application to mRNA translation shows near-optimality of termination rates

The Totally Asymmetric Exclusion Process (TASEP) is a classical stochastic model for describing the transport of interacting particles, such as ribosomes moving along the messenger ribonucleic acid (mRNA) during translation. Although this model has been widely studied in the past, the extent of collision between particles and the average distance between a particle to its nearest neighbor have not been quantified explicitly. We provide here a theoretical analysis of such quantities via the distribution of isolated particles. In the classical form of the model in which each particle occupies only a single site, we obtain an exact analytic solution using the matrix ansatz. We then employ a refined mean-field approach to extend the analysis to a generalized TASEP with particles of an arbitrary size. Our theoretical study has direct applications in mRNA translation and the interpretation of experimental ribosome profiling data. In particular, our analysis of data from Saccharomyces cerevisiae suggests a potential bias against the detection of nearby ribosomes with a gap distance of less than approximately three codons, which leads to some ambiguity in estimating the initiation rate and protein production flux for a substantial fraction of genes. Despite such ambiguity, however, we demonstrate theoretically that the interference rate associated with collisions can be robustly estimated and show that approximately 1% of the translating ribosomes get obstructed.

Erratum to: Entanglement entropy of subtracted geometry black holes

We elucidate the large-N dynamics of one-dimensional sigma models with spherical and hyperbolic target spaces and find a duality between the Lagrange multiplier and the angular momentum. In the hyperbolic model we propose a new class of operators based on the irreducible representations of hyperbolic space. We also uncover unexpected zero modes which lead to the double scaling of the 1/N expansion and explore these modes using Gelfand–Dikiy equations.

Thermodynamics of Asymptotically Conical Geometries

The Totally Asymmetric Exclusion Process (TASEP) is a classical stochastic model for describing the transport of interacting particles, such as ribosomes moving along the mRNA during translation. Applying this model to quantify translation dynamics from ribosome profiling data is not straightforward, however, and it requires characterizing the extent of interference, since the experimental protocol may be biased against nearby ribosomes. To evaluate and correct for this potential bias, we provide here a theoretical analysis of the distribution of isolated particles in the TASEP. In the classical form of the model in which each particle occupies only a single site, we obtain exact analytic solutions using the Matrix Ansatz. We then employ a refined mean field approach to extend the analysis to a generalized TASEP with particles of an arbitrary size. Our theoretical study has direct applications in mRNA translation and the interpretation of experimental ribosome profiling data. In particular, our analysis of data from S. cerevisiae suggests a potential bias against the detection of nearby ribosomes with gap distance less than ~3 codons, which leads to some ambiguity in estimating the initiation rate and protein production flux for a substantial fraction of genes. Despite such ambiguity, however, we demonstrate theoretically that the interference rate can be robustly estimated, and show that approximately 1% of the translating ribosomes get obstructed. Lastly, we find that, on average, the termination rate is near optimal in that it is close to the minimum value needed to not limit the ribosome flux.The Totally Asymmetric Exclusion Process (TASEP) is a classical stochastic model for describing the transport of interacting particles, such as ribosomes moving along the mRNA during translation. Although this model has been widely studied in the past, the extent of collision between particles and the average distance between a particle to its nearest neighbor have not been quantified explicitly. We provide here a theoretical analysis of such quantities via the distribution of isolated particles. In the classical form of the model in which each particle occupies only a single site, we obtain an exact analytic solution using the Matrix Ansatz. We then employ a refined mean field approach to extend the analysis to a generalized TASEP with particles of an arbitrary size. Our theoretical study has direct applications in mRNA translation and the interpretation of experimental ribosome profiling data. In particular, our analysis of data from S. cerevisiae suggests a potential bias against the detection of nearby ribosomes with gap distance less than ~ 3 codons, which leads to some ambiguity in estimating the initiation rate and protein production flux for a substantial fraction of genes. Despite such ambiguity, however, we demonstrate theoretically that the interference rate associated with collisions can be robustly estimated, and show that approximately 1% of the translating ribosomes get obstructed.