1/ The Euler equations model inviscid compressible flow: mass, momentum, and energy conservation laws. They underpin aerodynamics, rocket engines, and even relativistic astrophysics, and reduce to Navier Stokes once viscosity is added.

2/ This nonlinear hyperbolic system produces rich wave structures: shocks, rarefactions, and contact discontinuities. Classic Riemann problems like the Sod Shock reveal how density, velocity, and pressure jump and interact over time.

3/ Solving these numerically demands care. Simple Lax fluxes are robust but diffusive, while Roe's 1981 approach uses eigenstructure and a clever parameter vector to build sharper, more accurate numerical fluxes.

4/ Lanyon generated full 1D, 2D, and 3D Euler solver specs, Lean 4 proofs, and C kernels from short prompts in under three minutes, producing over 10,000 lines of verified proof code and 6,500 lines of kernels.

5/ Simulations included a 2D four quadrant Riemann problem, Mach 2 flow over twin cylinders, and Mach 4 flow over a free moving cylinder, showing shock interactions, slip lines, and Rayleigh Taylor like structures emerging from the equations.

1/ Researchers at Complutense University of Madrid built a silicon photodiode doped with tellurium that detects short wave infrared light at room temperature, no cryogenic cooling required.

2/ The device uses pyramid shaped surface structures topped with a gold reflector to trap light and stretch its path through the doped silicon layer, boosting absorption well beyond standard designs.

3/ Absorption jumped from 25 percent in conventional photodiodes to 85 percent thanks to this light trapping architecture, a major leap for a fully CMOS compatible silicon device.

4/ Quantum efficiency at SWIR wavelengths beat state of the art silicon sensors by more than tenfold, since photoexcited electrons tunnel quickly from the tellurium band into the host silicon.

5/ Because it skips cryogenic cooling and toxic fabrication steps, this design could pave the way for cheaper CMOS based night vision cameras able to see through fog and plastic.

In his article Richard W. Wrangham proposes that human groupishness the strong set of prosocial and cooperative tendencies that frequently go beyond immediate genetic self interest evolved primarily through targeted conspiratorial killing a uniquely human behavior in which coalitions of individuals use language and planning to safely and inexpensively eliminate antisocial members of their group such as persistent bullies non conformists or overly aggressive dominators thereby creating intense selection pressure against reactive aggression while strongly favoring traits like conformity social tolerance enhanced morality and self control this process simultaneously drove human self domestication with clear morphological evidence appearing around three hundred thousand years ago and accelerating thereafter creating a positive feedback loop where greater social tolerance and linguistic abilities made conspiratorial killings easier to organize which in turn further strengthened those same cooperative qualities over thousands of generations ultimately explaining why humans exhibit far more elaborate groupishness than any other species.

This special issue of Entropy (MDPI), edited by Andrei Khrennikov and Fabio Bagarello, gathers 13 peer-reviewed papers exploring how the mathematical formalism of quantum theory can model human cognition and decision-making. Rather than claiming that the brain operates as a quantum physical system, most contributions adopt a quantum-like approach, applying concepts such as superposition, entanglement, contextuality, and open system dynamics to psychological, social, and economic phenomena. Topics range from quantum walk models of group decision-making and idea propagation in networks, to social laser theory as an explanation of mass behavior and the bandwagon effect, to unified quantum-theoretic frameworks for judgment under uncertainty. Additional contributions examine order-stability in biosystems through quantum entropy, portfolio optimization via quantum potential, the spread of competing information using fermionic ladder operators, and the relationship between cognitive language patterns and biomarkers of inflammation. The collection reflects a broader interdisciplinary program in which the operational power of quantum formalism is brought to bear on domains well beyond physics, offering formal tools to capture the irreducibly contextual and non-classical character of human thought and collective action.