##### Cutting Across Disciplines

##### REUVENI GROUP

# Welcome to

Basic Theoretical Research in the Mathematical & Natural Sciences

# THE REUVENI GROUP

#### New Paper: Constant gradient FEXSY: A time-efficient method for measuring exchange

December 16, 2019

Filter-Exchange NMR Spectroscopy (FEXSY) allows for non-invasive estimation of water exchange rates across membranes in biological tissues. We develop CG-FEXSY, a time-efficient constant-gradient variant of FEXSY. FEXSY and CG-FEXSY are then compared experimentally on a yeast cells sample and a fixed optic nerve. The methods are shown to be in agreement. Thus, CG-FEXSY can provide the same information in a significantly shorter scan time.

#### New Paper: Time-Dependent Density of Diffusion with Stochastic Resetting is Invariant to Return Speed

October 7, 2019

The canonical Evans-Majumdar model for diffusion with stochastic resetting assumes that resetting takes zero time: upon resetting the diffusing particle is teleported back to the origin to start its motion anew. We consider a situation where the particle returns to the origin at a finite (rather than infinite) speed. This creates a coupling between the particle's random position at the moment of resetting and its return time. However, whether returns are slow or fast, we always find that the time-dependent distribution of the particle's position is identical to that obtained for instantaneous returns.

#### New Paper: Invariants of Motion with Stochastic Resetting and Space-Time Coupled Returns

October 28, 2019

Motion under stochastic resetting serves to model a myriad of processes in physics and beyond, but in most cases studied to date resetting was assumed to take zero time or a time decoupled from the spatial position at the resetting moment. However, in our world, getting from one place to another always takes time; and places that are further away take more time to be reached. We extend the theory to account for this inherent spatio-temporal coupling and discover key invariants of motion with stochastic resetting and space-time coupled returns.

#### New Paper: Gumbel Central Limit Theorem for Max-Min and Min-Max

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August 21, 2019

The max-min and min-max of matrices arise prevalently in science and engineering. However, in many real-world situations the computation of the max-min and min-max is challenging as matrices are large and full information about their entries is lacking. We take a statistical-physics approach and establish a Gumbel limit law—akin to the central limit theorem—for the max-min and min-max of large random matrices. See also: Poisson-process limit laws yield Gumbel max-min and min-max.

#### New Paper: Occupancy Correlations in the Asymmetric Simple Inclusion Process

October 8, 2019

The asymmetric simple inclusion process (ASIP) is a lattice-gas model for unidirectional transport with irreversible aggregation. To date, the analytical tractability of the model has been rather limited: while the average particle density is easy to compute, very little is known about the joint occupancy distribution. To partially bridge this gap, we study occupancy correlations in the ASIP. An exact formula for the covariance matrix of the occupancy vector at the steady-state is derived and corroborated against numerical simulations.

#### Reuveni Group Wins ISF Grant

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July 16, 2019

The Israel Science Foundation is the main body supporting breakthrough basic science in Israel, based on scientific excellence within the different fields of knowledge, in a wide variety of funding opportunities. We are thankful for their supportā.