Non-Linear Employment Effects of Tax Policy

We study the non-linear propagation mechanism of tax policy in a heterogeneous agent equilibrium business cycle model with search frictions in the labor market and an extensive margin of employment adjustment. The model exhibits endogenous job destruction and endogenous hiring standards in the form of occasionally-binding zero-surplus constraints. After parameterizing the model using U.S. data, we find that the dynamic response of employment to a temporary change in the labor income tax is highly non-linear, displaying sizable asymmetries and state-dependence. Notably, the response to a tax rate cut is at least twice as large in a recession as in an expansion.

Correlation and Power Distribution of Intercore Crosstalk Field Components of Polarization-Coupled Weakly Coupled Single-Mode Multicore Fibres

The correlation and power distribution of intercore crosstalk (ICXT) field components of weakly coupled multicore fibers (WC-MCFs) are important properties that determine the statistics of the ICXT and ultimately impact the performance of WC-MCF optical communication systems. Using intensive numerical simulation of the coupled mode equations describing ICXT of a single-mode WC-MCF with intracore birefringence and linear propagation, we assess the mean, correlation, and power distribution of the four ICXT field components of unmodulated polarization-coupled homogeneous and quasi-homogeneous WC-MCFs with a single interfering core in a wide range of birefringence conditions and power distribution among the field components at the interfering core input. It is shown that, for homogeneous and quasi-homogeneous WC-MCFs, zero mean uncorrelated ICXT field components with similar power levels are observed for birefringence correlation length and birefringence beat length in the ranges of 0.5m,10m and 0.1m,10m, respectively, regardless of the distribution of power between the four field components at the interfering core input.

Efficient MILP Modelings for Sboxes and Linear Layers of SPN ciphers

Mixed Integer Linear Programming (MILP) solvers are regularly used by designers for providing security arguments and by cryptanalysts for searching for new distinguishers. For both applications, bitwise models are more refined and permit to analyze properties of primitives more accurately than word-oriented models. Yet, they are much heavier than these last ones. In this work, we first propose many new algorithms for efficiently modeling any subset of Fn2 with MILP inequalities. This permits, among others, to model differential or linear propagation through Sboxes. We manage notably to represent the differential behaviour of the AES Sbox with three times less inequalities than before. Then, we present two new algorithms inspired from coding theory to model complex linear layers without dummy variables. This permits us to represent many diffusion matrices, notably the ones of Skinny-128 and AES in a much more compact way. To demonstrate the impact of our new models on the solving time we ran experiments for both Skinny-128 and AES. Finally, our new models allowed us to computationally prove that there are no impossible differentials for 5-round AES and 13-round Skinny-128 with exactly one input and one output active byte, even if the details of both the Sbox and the linear layer are taken into account.

Comparison of Two Versions of the MNLS With the Full Water Wave Equations

Versions of the non-linear Schrödinger equation are frequently used for modelling the non-linear propagation of water waves. In this paper, we compare two models against the results of fully non-linear numerical simulations. We consider uni-directional versions of the non-linear Schrödinger equation of Dysthe et al. with the hybrid model of Trulsen et al. The model of Trulsen et al. is shown to have clear advantages in all situations considered including modelling wave crest statistics for highly non-linear cases. However, for very broad bandwidths this model does start to break down, presumably due to the inherent limitation of the envelope representation of water waves. This in turn leads to a small, non-physical, leakage of energy in nonlinear simulations, although, this leakage is much smaller than for the version with 5th order linear dispersion relationship.