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1. Sampling Multiple Edges Efficiently

   Eden, T.; Mossel, S.; Rubinfeld, R. (January 2021, Random)

   We present a sublinear time algorithm that allows one to sample multiple edges from a distribution that is pointwise ϵ-close to the uniform distribution, in an amortized-efficient fashion. We consider the adjacency list query model, where access to a graph G is given via degree and neighbor queries. The problem of sampling a single edge in this model has been raised by Eden and Rosenbaum (SOSA 18). Let n and m denote the number of vertices and edges of G, respectively. Eden and Rosenbaum provided upper and lower bounds of Θ∗(n/ √ m) for sampling a single edge in general graphs (where O ∗(·) suppresses poly(1/ϵ) and poly(log n) dependencies). We ask whether the query complexity lower bound for sampling a single edge can be circumvented when multiple samples are required. That is, can we get an improved amortized per-sample cost if we allow a preprocessing phase? We answer in the affirmative. We present an algorithm that, if one knows the number of required samples q in advance, has an overall cost that is sublinear in q, namely, O∗(√ q · (n/ √ m)), which is strictly preferable to O∗(q · (n/ √ m)) cost resulting from q invocations of the algorithm by Eden and Rosenbaum. Subsequent to a preliminary version of this work, Tětek and Thorup (arXiv, preprint) proved that this bound is essentially optimal. 

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2. Calculating QCD Phase Diagram Trajectories of Nuclear Collisions using a Semi-analytical Model

   https://doi.org/10.1051/epjconf/202327601012  

   Mendenhall, Todd; Lin, Zi-Wei (January 2023, EPJ Web of Conferences)

   Kim, Y.; Moon, D.H. (Ed.)

   At low to moderate collision energies where the parton formation time τ F is not small compared to the nuclear crossing time, the finite nuclear thickness significantly affects the energy density ϵ( t ) and net conserved-charge densities such as the net-baryon density n B ( t ) produced in heavy ion collisions. As a result, at low to moderate energies the trajectory in the QCD phase diagram is also affected by the finite nuclear thickness. Here, we first discuss our semi-analytical model and its results on ϵ( f ), n R ( t ), n Q ( t ), and n s ( t ) in central Au+Au collisions. We then compare the T ( t ), μ B ( t ), μ Q ( t ), and μ S ( t ) extracted with the ideal gas equation of state (EoS) with quantum statistics to those extracted with a lattice QCD-based EoS. We also compare the T -μ B trajectories with the RHIC chemical freezeout data. Finally, we discuss the effect of transverse flow on the trajectories. 

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3. Evolution of gas disc–embedded intermediate mass ratio inspirals in the LISA band

   https://doi.org/10.1093/mnras/staa3976  

   Derdzinski, A; D’Orazio, D; Duffell, P; Haiman, Z; MacFadyen, A (March 2021, Monthly Notices of the Royal Astronomical Society)

   null (Ed.)

   Abstract Among the potential milliHz gravitational wave (GW) sources for the upcoming space-based interferometer LISA are extreme- or intermediate-mass ratio inspirals (EMRI/IMRIs). These events involve the coalescence of supermassive black holes in the mass range 105M⊙ ≲ M ≲ 107M⊙ with companion BHs of much lower masses. A subset of E/IMRIs are expected to occur in the accretion discs of active galactic nuclei (AGN), where torques exerted by the disc can interfere with the inspiral and cause a phase shift in the GW waveform. Here we use a suite of two-dimensional hydrodynamical simulations with the moving-mesh code DISCO to present a systematic study of disc torques. We measure torques on an inspiraling BH and compute the corresponding waveform deviations as a function of the binary mass ratio q ≡ M2/M1, the disc viscosity (α), and gas temperature (or equivalently Mach number; $$\mathcal {M}$$). We find that the absolute value of the gas torques is within an order of magnitude of previously determined planetary migration torques, but their precise value and sign depends non-trivially on the combination of these parameters. The gas imprint is detectable by LISA for binaries embedded in AGN discs with surface densities above $$\Sigma _0\ge 10^{4-6} \rm \, g cm^{-2}$$, depending on q, α and $$\mathcal {M}$$. Deviations are most pronounced in discs with higher viscosities, and for E/IMRIs detected at frequencies where LISA is most sensitive. Torques in colder discs exhibit a noticeable dependence on the GW-driven inspiral rate as well as strong fluctuations at late stages of the inspiral. Our results further suggest that LISA may be able to place constraints on AGN disc parameters and the physics of disc-satellite interaction. 

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4. Antimatter Free-Fall Experiments and Charge Asymmetry

   https://doi.org/10.3390/sym13071192  

   Jentschura, Ulrich David (July 2021, Symmetry)

   null (Ed.)

   We propose a method by which one could use modified antimatter gravity experiments in order to perform a high-precision test of antimatter charge neutrality. The proposal is based on the application of a strong, external, vertically oriented electric field during an antimatter free-fall gravity experiment in the gravitational field of the Earth. The proposed experimental setup has the potential to drastically improve the limits on the charge-asymmetry parameter ϵ¯q of antimatter. On the theoretical side, we analyze possibilities to describe a putative charge-asymmetry of matter and antimatter, proportional to the parameters ϵq and ϵ¯q, by Lagrangian methods. We found that such an asymmetry could be described by four-dimensional Lorentz-invariant operators that break CPT without destroying the locality of the field theory. The mechanism involves an interaction Lagrangian with field operators decomposed into particle or antiparticle field contributions. Our Lagrangian is otherwise Lorentz, as well as PT invariant. Constraints to be derived on the parameter ϵ¯q do not depend on the assumed theoretical model. 

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5. Massless fermions in uniform flux background on $T^2\times R$ : Vacuum quantum numbers from single-particle filled modes using lattice regulator

   https://doi.org/10.1103/PhysRevD.111.014502  

   Karthik, Nikhil; Narayanan, Rajamani; Romero, Ray (January 2025, Physical Review D)

   The quantum numbers of monopoles in $R^3$in the presence of massless fermions have been analyzed using a uniform flux background in $S^2\times R$coupled to fermions. An analogous study in $T^2\times R$is performed by studying the discrete symmetries of the Dirac Hamiltonian in the presence of a static uniform field on $T^2$with a total flux of $Q$in the continuum. The degenerate ground states are classified based on their transformation properties under $\frac{\pi }{2}$rotations of $T^2$that leave the background field invariant. We find that the lattice analysis with overlap fermions exactly reproduces the transformation properties of the single-particle zero modes in the continuum. Whereas the transformation properties of the single-particle negative energy states can be studied in the continuum and the lattice, we are also able to study the transformation properties and the particle number (charge) of the many-body ground state on a finite lattice, and we show that the contributions from the fully filled single-particle states cannot be ignored. Published by the American Physical Society2025 

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