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Zachary Wilson

Publications and source records attributed to Zachary Wilson.

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Constructing X-ray Spectral Models of Galaxies: Varying Contributions from X-ray Binary Populations with Host Galaxy Properties

Recent work has shown that the emission from X-ray binary (XRB) populations in galaxies varies with stellar mass ($M_\star$), star formation rate (SFR), and metallicity ($Z$). Such scaling relations are widely used to predict the XRB contributions to galaxy-integrated X-ray luminosities including studies focused on dwarf active galactic nuclei (AGN) and the X-ray radiation field during the epoch of heating in the early ($z \geq 8$) universe. However, as galaxies approach low SFR and low $Z$, the relatively shallow slope of the XRB luminosity function (XLF) can yield very large stochastic variations in the total X-ray luminosity expected from the XRB population, for fixed values of $M_\star$, SFR, and $Z$. We have created a procedure to statistically sample any XLF and model total X-ray spectra for XRB populations and their stochastic uncertainties. We demonstrate the accuracy of this procedure using data for galaxies ranging from high to low $M_\star$, SFR, and $Z$ and generating X-ray spectral models consistent with Chandra observations. For galaxies that lie on the galactic main-sequence, we can relate SFR and $Z$ to $M_\star$ using established $M_\star$-SFR and $M_\star$-$Z$ relations. Applying these relations, we construct main-sequence (MS) XRB spectral models, which provide typical XRB spectral shapes, normalizations, and uncertainties as a function of $M_\star$. The spectral model library associated with this work is available at https://doi.org/10.5281/zenodo.20126734.

astro-ph.GA

A Novel Mixed-Integer Linear Programming Formulation for Continuous-Time Inventory Routing

Inventory management, vehicle routing, and delivery scheduling decisions are simultaneously considered in the context of the inventory routing problem. This paper focuses on the continuous-time version of this problem where, unlike its more traditional discrete-time counterpart, the distributor is required to guarantee that inventory levels are maintained within the desired intervals at any moment of the planning horizon. In this work, we develop a compact mixed-integer linear programming formulation to model the continuous-time inventory routing problem. We further discuss means to expedite its solution process, including the adaptation of well-known rounded capacity inequalities to tighten the formulation in the context of a branch-and-cut algorithm. Through extensive computational studies on a suite of 90 benchmark instances from the literature, we show that our branch-and-cut algorithm outperforms the state-of-the-art approach. We also consider a new set of 63 instances adapted from a real-life dataset and show our algorithm's practical value in solving instances with up to 20 customers to guaranteed optimality.

math.OC