Diverse processes rely on the viscous flow of polymer solutions through porous media. In many cases, the macroscopic flow resistance abruptly increases above a threshold flow rate in a porous

# On scalar products and form factors by Separation of Variables: the antiperiodic XXZ model. (arXiv:2011.06109v1 [math-ph])

We consider the XXZ spin-1/2 Heisenberg chain with antiperiodic boundary conditions. The inhomogeneous version of this model can be solved by Separation of Variables (SoV). We compute in this framework

# Space of initial conditions for the four-dimensional Fuji-Suzuki-Tsuda system. (arXiv:2011.06271v1 [nlin.SI])

A geometric study for an integrable 4-dimensional dynamical system so called the Fuji-Suzuki-Tsuda system is given. By the resolution of indeterminacy, the group of its B\”aklund transformations is lifted to

# Isomonodromic tau functions on a torus as Fredholm determinants, and charged partitions. (arXiv:2011.06292v1 [math-ph])

We prove that the isomonodromic tau function on a torus with Fuchsian singularities and generic monodromies in $GL(N,\mathbb{C})$ can be written in terms of a Fredholm determinant of Cauchy-Plemelj operators.

# Integrable Non-unitary Open Quantum Circuits. (arXiv:2011.06565v1 [cond-mat.stat-mech])

We explicitly construct an integrable interacting dissipative quantum circuit, via a trotterization of the Hubbard model with imaginary interaction strength. To prove integrability, we build an inhomogeneous transfer matrix, from

# Quantum algorithm for nonlinear differential equations. (arXiv:2011.06571v1 [quant-ph])

Quantum computers are known to provide an exponential advantage over classical computers for the solution of linear differential equations in high-dimensional spaces. Here, we present a quantum algorithm for the

# Aggression heuristics underlie animal dominance hierarchies and provide evidence of group-level social information. (arXiv:1810.07215v3 [q-bio.PE] UPDATED)

Members of a social species need to make appropriate decisions about who, how, and when to interact with others in their group. However, it has been difficult for researchers to

# Multi-scale structural complexity of natural patterns. (arXiv:2003.04632v2 [nlin.PS] UPDATED)

Complexity of patterns is a key information for human brain to differ objects of about the same size and shape. Like other innate human senses, the complexity perception cannot be

# Decay of two-dimensional quantum turbulence in binary Bose-Einstein condensates. (arXiv:2006.15239v2 [cond-mat.quant-gas] UPDATED)

We study two-dimensional quantum turbulence in miscible binary Bose-Einstein condensates in either a harmonic trap or a steep-wall trap through the numerical simulations of the Gross-Pitaevskii equations. The turbulence is

# On symmetries of the non-stationary $P_{II}^{(n)}$ hierarchy and their applications. (arXiv:2010.10617v2 [nlin.SI] UPDATED)

In the current paper we study auto-B\”acklund transformations of the non-stationary second Painlev\’e hierarchy $\text{P}_\text{II}^{(n)}$ depending on $n$ parameters: a parameter $\alpha_n$ and times $t_1, \dots, t_{n-1}$. Using generators $s^{(n)}$