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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.
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.
Uniform sampling from the set G(d) of graphs with a given degree-sequence d=(d1,…,dn)∈Nn is a classical problem in the study of random graphs. We consider an analogue for temporal graphs in which the edges are labeled with integer timestamps. The input to this generation problem is a tuple D=(d,T)∈Nn×N>0 and the task is to output a uniform random sample from the set G(D) of temporal graphs with degree-sequence d and timestamps in the interval [1,T]. By allowing repeated edges with distinct timestamps, G(D) can be non-empty even if G(d) is, and as a consequence, existing algorithms are difficult to apply.
We describe an algorithm for this generation problem which runs in expected time O(M) if Δ2+ϵ=O(M) for some constant ϵ>0 and T−Δ=Ω(T) where M=∑idi and Δ=maxidi. Our algorithm applies the switching method of McKay and Wormald [1] to temporal graphs: we first generate a random temporal multigraph and then remove self-loops and duplicated edges with switching operations which rewire the edges in a degree-preserving manner.
Uniform sampling from the set G(d) of graphs with a given degree-sequence d=(d1,…,dn)∈Nn is a classical problem in the study of random graphs. We consider an analogue for temporal graphs in which the edges are labeled with integer timestamps. The input to this generation problem is a tuple D=(d,T)∈Nn×N>0 and the task is to output a uniform random sample from the set G(D) of temporal graphs with degree-sequence d and timestamps in the interval [1,T]. By allowing repeated edges with distinct timestamps, G(D) can be non-empty even if G(d) is, and as a consequence, existing algorithms are difficult to apply.
We describe an algorithm for this generation problem which runs in expected time O(M) if Δ2+ϵ=O(M) for some constant ϵ>0 and T−Δ=Ω(T) where M=∑idi and Δ=maxidi. Our algorithm applies the switching method of McKay and Wormald [1] to temporal graphs: we first generate a random temporal multigraph and then remove self-loops and duplicated edges with switching operations which rewire the edges in a degree-preserving manner.
n this paper we study invasion probabilities and invasion times of cooperative parasites spreading in spatially structured host populations. The spatial structure of the host population is given by a random geometric graph on [0,1]n, n∈N, with a Poisson(N)-distributed number of vertices and in which vertices are connected over an edge when they have a distance of at most rN∈Θ(Nβ−1n) for some 0<β<1 and N→∞. At a host infection many parasites are generated and parasites move along edges to neighbouring hosts. We assume that parasites have to cooperate to infect hosts, in the sense that at least two parasites need to attack a host simultaneously. We find lower and upper bounds on the invasion probability of the parasites in terms of survival probabilities of branching processes with cooperation. Furthermore, we characterize the asymptotic invasion time.
An important ingredient of the proofs is a comparison with infection dynamics of cooperative parasites in host populations structured according to a complete graph, i.e. in well-mixed host populations. For these infection processes we can show that invasion probabilities are asymptotically equal to survival probabilities of branching processes with cooperation.
Furthermore, we build in the proofs on techniques developed in [BP22], where an analogous invasion process has been studied for host populations structured according to a configuration model.
We substantiate our results with simulations.
Parallel global edge switching for the uniform sampling of simple graphs with prescribed degrees
(2023)
The uniform sampling of simple graphs matching a prescribed degree sequence is an important tool in network science, e.g. to construct graph generators or null-models. Here, the Edge Switching Markov Chain (ES-MC) is a common choice. Given an arbitrary simple graph with the required degree sequence, ES-MC carries out a large number of small changes, called edge switches, to eventually obtain a uniform sample. In practice, reasonably short runs efficiently yield approximate uniform samples.
In this work, we study the problem of executing edge switches in parallel. We discuss parallelizations of ES-MC, but find that this approach suffers from complex dependencies between edge switches. For this reason, we propose the Global Edge Switching Markov Chain (G-ES-MC), an ES-MC variant with simpler dependencies. We show that G-ES-MC converges to the uniform distribution and design shared-memory parallel algorithms for ES-MC and G-ES-MC. In an empirical evaluation, we provide evidence that G-ES-MC requires not more switches than ES-MC (and often fewer), and demonstrate the efficiency and scalability of our parallel G-ES-MC implementation.
Stimulated emission depletion (STED) microscopy is a super-resolution technique that surpasses the diffraction limit and has contributed to the study of dynamic processes in living cells. However, high laser intensities induce fluorophore photobleaching and sample phototoxicity, limiting the number of fluorescence images obtainable from a living cell. Here, we address these challenges by using ultra-low irradiation intensities and a neural network for image restoration, enabling extensive imaging of single living cells. The endoplasmic reticulum (ER) was chosen as the target structure due to its dynamic nature over short and long timescales. The reduced irradiation intensity combined with denoising permitted continuous ER dynamics observation in living cells for up to 7 hours with a temporal resolution of seconds. This allowed for quantitative analysis of ER structural features over short (seconds) and long (hours) timescales within the same cell, and enabled fast 3D live-cell STED microscopy. Overall, the combination of ultra-low irradiation with image restoration enables comprehensive analysis of organelle dynamics over extended periods in living cells.
Heavy quarks are useful probes to investigate the properties of the Quark-Gluon Plasma (QGP) produced in heavy-ion collisions at the LHC, since they are produced in initial hard scattering processes. To single out the signals that are characteristic of the QGP, it is nevertheless crucial to understand the primordial heavy-quark production in vacuum, and to disentangle hot from cold nuclear matter effects. Moreover, observations of collective effects in high-multiplicity pp and p-Pb collisions show surprising similarities with those in heavy-ion collisions. Heavy-flavour production in such collisions could give further insight into the underlying processes. The heavy-flavour production can be studied with e+e− pairs from correlated semileptonic decays of heavy-flavour hadrons. Compared to single heavy-flavour measurements, the dielectron yield contains information about the initial kinematical correlations between the charm and anti-charm quarks, which is otherwise not accessible, and is sensitive to soft heavy-flavour production. We report results on correlated e+e− pairs in pp collisions recorded by the ALICE detector at different collision energies. The production of heavy quarks is discussed by comparing the yield of dielectrons from heavy-flavour hadron decays as a function of invariant mass, pair transverse momentum and distance of closest approach to the primary vertex with different Monte Carlo event generators. The heavy-flavour production cross sections are also presented. Results from high-multiplicity pp collisions at √s=13 TeV and the status of the p-Pb analysis at √sNN=5.02 TeV are reported as well.
The production yields of antideuterons and antiprotons are measured in pp collisions at a center-of-mass energy of √s=13 TeV, as a function of transverse momentum (pT) and rapidity (y), for the first time up to |y|=0.7. The measured spectra are used to study the pT and rapidity dependence of the coalescence parameter B2, which quantifies the coalescence probability of antideuterons. The pT and rapidity dependence of the obtained B2 is extrapolated for pT>1.7 GeV/c and |y|>0.7 using the phenomenological antideuteron production model implemented in PYTHIA 8.3 as well as a baryon coalescence afterburner model based on EPOS 3. Such measurements are of interest to the astrophysics community, since they can be used for the calculation of the flux of antinuclei from cosmic rays, in combination with coalescence models.
