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  1. Drăgoi, C. ; Mukherjee, S. ; Namjoshi, K. (Ed.)
    This paper studies the problem of range analysis for feedforward neural networks, which is a basic primitive for applications such as robustness of neural networks, compliance to specifications and reachability analysis of neural-network feedback systems. Our approach focuses on ReLU (rectified linear unit) feedforward neural nets that present specific difficulties: approaches that exploit derivatives do not apply in general, the number of patterns of neuron activations can be quite large even for small networks, and convex approximations are generally too coarse. In this paper, we employ set-based methods and abstract interpretation that have been very successful in coping with similar difficulties in classical program verification. We present an approach that abstracts ReLU feedforward neural networks using tropical polyhedra. We show that tropical polyhedra can efficiently abstract ReLU activation function, while being able to control the loss of precision due to linear computations. We show how the connection between ReLU networks and tropical rational functions can provide approaches for range analysis of ReLU neural networks. We report on a preliminary evaluation of our approach using a prototype implementation.
  2. Mukherjee, S. (Ed.)
    Described is a one-flask, two-step method for the synthesis of highly functionalized piperidines. The process involves formal [4 + 2] cycloadditions of Schiff bases and Nazarov reagents, followed by facile elaborations of the initial cycloadducts. Notably, these aza-annulations are facilitated by protic solvents and proceed smoothly under ambient conditions, without other additives. The synthetic utility of this annulation protocol is further showcased through a concise, convergent synthesis of (±)-tetrabenazine.
  3. David, G. ; Garg, P. ; Kalweit, A. ; Mukherjee, S. ; Ullrich, T. ; Xu, Z. ; Yoo, I.-K. (Ed.)
    Recent theory progress in (3+1)D dynamical descriptions of relativistic nuclear collisions at finite baryon density are reviewed. Heavy-ion collisions at different collision energies produce strongly coupled nuclear matter to probe the phase structure of Quantum Chromodynamics (QCD). Dynamical frameworks serve as a quantitative tool to study properties of hot QCD matter and map collisions to the QCD phase diagram. Outstanding challenges are highlighted when confronting theoretical models with the current and forthcoming experimental measurements from the RHIC beam energy scan program.
  4. David, G. ; Garg, P. ; Kalweit, A. ; Mukherjee, S. ; Ullrich, T. ; Xu, Z. ; Yoo, I.-K. (Ed.)
    The yields, mean transverse momenta, and flow of K *0 , ρ 0 , Λ(1520) resonances provide an evidence of a late stage hadronic rescattering in ultrarelativistic central heavy ion collisions [1]. Using hydrodynamic + hadronic afterburner simulations of Pb+Pb collisions at 5.02 TeV we achieve a reasonable description of resonance yields and spectra as a function of collision centrality. We demonstrate that the measurements of Λ(1520)’s mean transverse momentum allow to constrain the unknown branching ratios of Σ* → Λ(1520)π decays. Hadronic dynamics leads to an enhanced ∆(1232) production in central collisions.
  5. David, G. ; Garg, P. ; Kalweit, A. ; Mukherjee, S. ; Ullrich, T. ; Xu, Z. ; Yoo, I.-K. (Ed.)
    Utilizing viscous hydrodynamic simulations of heavy-ion collisions, we study the behavior of cumulants of (net-)(anti)proton number distributions at RHIC beam energy scan energies, incorporating non-critical contributions like baryon conservation and excluded volume. The experimental data on net-proton cumulants at √ S NN > 20 GeV are consistent with simultaneous effects of global baryon conservation and repulsive interactions in baryon sector, whereas the data at lower collision energies show possible indications for sizable attractive interactions among baryons. We discuss the behavior of factorial cumulants in addition to the ordinary cumulants, and also address the quantitative difference between proton and baryon number cumulants.
  6. David, G. ; Garg, P. ; Kalweit, A. ; Mukherjee, S. ; Ullrich, T. ; Xu, Z. ; Yoo, I.-K. (Ed.)
    In this conference proceeding, we review important theoretical developments related to the production of strangeness in astrophysics. This includes its effects in supernova explosions, neutron stars, and compact-star mergers. We also discuss in detail how the presence of net strangeness affects the deconfinement to quark matter, expected to take place at large densities and/or temperatures. We conclude that a complete description of dense matter containing hyperons and strange quarks is fundamental for the understanding of modern high-energy astrophysics.
  7. David, G. ; Garg, P. ; Kalweit, A. ; Mukherjee, S. ; Ullrich, T. ; Xu, Z. ; Yoo, I.-K. (Ed.)
    The Beam Energy Scan program at the Relativistic Heavy Ion Collider (RHIC) is searching for the QCD critical point. The main signal for the critical point is the kurtosis of the distribution of proton yields obtained on an event by event basis where one expects a peak at the critical point. However, its exact behavior is still an open question due to out-of-equilibrium effects and uncertainty in the equation of state. Here we use a simplistic hydrodynamic model that enforces strangeness-neutrality, selecting trajectories that pass close to the critical point. We vary the initial conditions to estimate the effect of out-of-equilibrium hydrodynamics on the kurtosis signal.
  8. David, G. ; Garg, P. ; Kalweit, A. ; Mukherjee, S. ; Ullrich, T. ; Xu, Z. ; Yoo, I.-K. (Ed.)
    The Taylor expansion approach to the equation of state of QCD at finite chemical potential struggles to reach large chemical potential μ B . This is primarily due to the intrinsic diffculty in precisely determining higher order Taylor coefficients, as well as the structure of the temperature dependence of such observables. In these proceedings, we illustrate a novel scheme [1] that allows us to extrapolate the equation of state of QCD without suffering from the poor convergence typical of the Taylor expansion approach. We continuum extrapolate the coefficients of our new expansion scheme and show the thermodynamic observables up to μ B / T ≤ 3.5.
  9. David, G. ; Garg, P. ; Kalweit, A. ; Mukherjee, S. ; Ullrich, T. ; Xu, Z. ; Yoo, I.-K. (Ed.)
    We investigate the chemical freeze-out in heavy-ion collisions (HICs) and the impact of the hadronic spectrum on thermal model analyses [1, 2]. Detailed knowledge of the hadronic spectrum is still an open question, which has phenomenological consequences on the study of HICs. By varying the number of resonances included in Hadron Resonance Gas (HRG) Model calculations, we can shed light on which particles may be produced. Furthermore, we study the influence of the number of states on the so-called two flavor freezeout scenario, in which strange and light particles can freeze-out separately. We consider results for the chemical freeze-out parameters obtained from thermal model fits and from calculating net-particle fluctuations. We will show the effect of using one global temperature to fit all particles and alternatively, allowing particles with and without strange quarks to freeze-out separately.
  10. David, G. ; Garg, P. ; Kalweit, A. ; Mukherjee, S. ; Ullrich, T. ; Xu, Z. ; Yoo, I.-K. (Ed.)
    We use the excluded volume Hadron Resonance Gas (HRG) model with the most up-to-date hadron list to calculate η T/w at low temperatures and at finite baryon densities ρ B . This η T/w is then matched to a QCD-based shear viscosity calculation of the QGP for different profiles of η T/w across T,μ B including cross-over and critical point transitions. When compared to ideal hydrodynamic trajectories across T,μ B , we find that the η T/w (T,μ B ) profiles would require initial conditions at much larger baryon density to reach the same freeze-out point.