### Refine

#### Language

- English (4)

#### Has Fulltext

- yes (4)

#### Is part of the Bibliography

- no (4)

#### Keywords

#### Institute

- Informatik (3)
- Informatik und Mathematik (1)

Cone photoreceptor cells are wavelength-sensitive neurons in the retinas of vertebrate eyes and are responsible for color vision. The spatial distribution of these nerve cells is commonly referred to as the cone photoreceptor mosaic. By applying the principle of maximum entropy, we demonstrate the universality of retinal cone mosaics in vertebrate eyes by examining various species, namely, rodent, dog, monkey, human, fish, and bird. We introduce a parameter called retinal temperature, which is conserved across the retinas of vertebrates. The virial equation of state for two-dimensional cellular networks, known as Lemaître’s law, is also obtained as a special case of our formalism. We investigate the behavior of several artificially generated networks and the natural one of the retina concerning this universal, topological law.

We investigate the impact of non-Hermiticity on the thermodynamic properties of interacting fermions by examining bilinear extensions to the 3+1 dimensional SU(2)-symmetric Nambu--Jona-Lasinio (NJL) model of quantum chromodynamics at finite temperature and chemical potential. The system is modified through the anti-PT-symmetric pseudoscalar bilinear ψ¯γ5ψ and the PT-symmetric pseudovector bilinear iBνψ¯γ5γνψ, introduced with a coupling g. Beyond the possibility of dynamical fermion mass generation at finite temperature and chemical potential, our findings establish model-dependent changes in the position of the chiral phase transition and the critical end-point. These are tunable with respect to g in the former case, and both g and |B|/B0 in the latter case, for both lightlike and spacelike fields. Moreover, the behavior of the quark number, entropy, pressure and energy densities signal a potential fermion or antifermion excess compared to the standard NJL model, due to the pseudoscalar and pseudovector extension respectively. In both cases regions with negative interaction measure I=ϵ−3p are found. Future indications of such behaviors in strongly interacting fermion systems, for example in the context of neutron star physics, may point toward the presence of non-Hermitian contributions. These trends provide a first indication of curious potential mechanisms for producing non-Hermitian baryon asymmetry. In addition, the formalism described in this study is expected to apply more generally to other Hamiltonians with four-fermion interactions and thus the effects of the non-Hermitian bilinears are likely to be generic.

We investigate the impact of non-Hermiticity on the thermodynamic properties of interacting fermions by examining bilinear extensions to the 3+1 dimensional SU(2)-symmetric Nambu--Jona-Lasinio (NJL) model of quantum chromodynamics at finite temperature and chemical potential. The system is modified through the anti-PT-symmetric pseudoscalar bilinear ψ¯γ5ψ and the PT-symmetric pseudovector bilinear iBνψ¯γ5γνψ, introduced with a coupling g. Beyond the possibility of dynamical fermion mass generation at finite temperature and chemical potential, our findings establish model-dependent changes in the position of the chiral phase transition and the critical end-point. These are tunable with respect to g in the former case, and both g and |B|/B0 in the latter case, for both lightlike and spacelike fields. Moreover, the behavior of the quark number, entropy, pressure, and energy densities signal a potential fermion or antifermion excess compared to the standard NJL model, due to the pseudoscalar and pseudovector extension respectively. In both cases regions with negative interaction measure I=ϵ−3p are found. Future indications of such behaviors in strongly interacting fermion systems, for example in the context of neutron star physics, may point toward the presence of non-Hermitian contributions. These trends provide a first indication of curious potential mechanisms for producing non-Hermitian baryon asymmetry. In addition, the formalism described in this study is expected to apply more generally to other Hamiltonians with four-fermion interactions and thus the effects of the non-Hermitian bilinears are likely to be generic.