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Case isolation, that is, detection and isolation of infected individuals in order to prevent spread, is a strategy to curb infectious disease epidemics. Here, we study the efficiency of a case isolation strategy subject to time delays in terms of its ability to stabilize the epidemic spread in heterogeneous contact networks. For an SIR epidemic model, we characterize the stability boundary analytically and show how it depends on the time delay between infection and isolation as well as the heterogeneity of the inter-individual contact network, quantified by the variance in contact rates. We show that network heterogeneity accounts for a restricting correction factor to previously derived stability results for homogeneous SIR models (with uniform contact rates), which are therefore too optimistic on the relevant time scales. We illustrate the results and the underlying mechanisms through insightful numerical examples., Comment: 6 pages, 3 figures

We present results from direct measurements of the $^{27}{\rm Al}(\alpha,n)$ thick target yield from laboratory incident energies $E_{\alpha}\approx$ 3$-$5~MeV, performed with the $^{3}$HeBF$_{3}$ Giant Barrel (HeBGB) neutron detector at the Edwards Accelerator Laboratory. Our measurements have a small energy cadence in order to address discrepancies and sparseness of thick-target yield data sets existing for this energy region. We find general agreement with existing data sets, including yields derived from cross section data, while resolving a discrepancy between existing thick-target yield data sets for $E_{\alpha}\approx4-5$~MeV. However, for $E_{\alpha}<3.5$~MeV, our results are substantially lower than previous thick-target yield data and somewhat larger than yields calculated from existing cross section data. Our data complete the energy-range needed for estimates of the $^{27}{\rm Al}(\alpha,n)$ contribution to neutrino and dark matter detector backgrounds and result in increased viability of $^{27}{\rm Al}(\alpha,n)$ as a plasma diagnostic tool at fusion facilities such as the National Ignition Facility., Comment: Accepted to Nuclear Science and Engineering

The reaction $^{96}$Zr($\alpha$,n)$^{99}$Mo plays an important role in $\nu$-driven wind nucleosynthesis in core-collapse supernovae and is a possible avenue for medical isotope production. Cross section measurements were performed using the activation technique at the Edwards Accelerator Laboratory. Results were analyzed along with world data on the $^{96}{\rm Zr}(\alpha,n)$ cross section and $^{96}{\rm Zr}(\alpha,\alpha)$ differential cross section using large-scale Hauser-Feshbach calculations. We compare our data, previous measurements, and a statistical description of the reaction. We find a larger cross section at low energies compared to prior experimental results, allowing for a larger astrophysical reaction rate. This may impact results of core-collapse supernova $\nu$-driven wind nucleosynthesis calculations, but does not significantly alter prior conclusions about $^{99}{\rm Mo}$ production for medical physics applications. The results from our large-scale Hauser-Feshbach calculations demonstrate that phenomenological optical potentials may yet be adequate to describe $(\alpha,n)$ reactions of interest for $\nu$-driven wind nucleosynthesis, albeit with regionally-adjusted model parameters., Comment: accepted to PRC

We measured the $^{57}$Zn $\beta$-delayed proton ($\beta$p) and $\gamma$ emission at the National Superconducting Cyclotron Laboratory. We find a $^{57}$Zn half-life of 43.6 $\pm$ 0.2 ms, $\beta$p branching ratio of (84.7 $\pm$ 1.4)%, and identify four transitions corresponding to the exotic $\beta$-$\gamma$-$p$ decay mode, the second such identification in the $f p$-shell. The $p/\gamma$ ratio was used to correct for isospin mixing while determining the $^{57}$Zn mass via the isobaric multiplet mass equation. Previously, it was uncertain as to whether the rp-process flow could bypass the textbook waiting point $^{56}$Ni for astrophysical conditions relevant to Type-I X-ray bursts. Our results definitively establish the existence of the $^{56}$Ni bypass, with 14-17% of the $rp$-process flow taking this route.

$(\alpha,n)$ reactions play an important role in nuclear astrophysics and applications and are an important background source in neutrino and dark matter detectors. Measurements of total $(\alpha,n)$ cross sections employing direct neutron detection often have a considerable systematic uncertainty associated with the energy-dependent neutron detection efficiency and the unknown initial neutron energy distribution. The $^{3}{\rm He}\,{\rm BF}_{3}$ Giant Barrel (HeBGB) neutron detector was built at the Edwards Accelerator Laboratory at Ohio University to overcome this challenge. HeBGB offers a near-constant neutron detection efficiency of ($7.5\pm 1.2$) \% over the neutron energy range 0.01 MeV -- 9.00 MeV, removing a significant source of systematic uncertainty present in earlier $(\alpha,n)$ cross section measurements.

An efficient neutron detection system with good energy resolution is required to correctly characterize decays of neutron-rich nuclei where $\beta-$delayed neutron emission is a dominant decay mode. The Neutron dEtector with Xn Tracking (NEXT) has been designed to measure $\beta$-delayed neutron emitters. By segmenting the detector along the neutron flight path, NEXT reduces the associated uncertainties in neutron time-of-flight measurements, improving energy resolution while maintaining detection efficiency. Detector prototypes are comprised of optically separated segments of a neutron-gamma discriminating plastic scintillator coupled to position-sensitive photomultiplier tubes. The first performance studies of this detector showed that high intrinsic neutron detection efficiency could be achieved while retaining good energy resolution. The results from the efficiency measurements using neutrons from direct reactions are presented., Comment: 8 pages, 9 figures

Nuclear reactions of interest for astrophysics and applications often rely on statistical model calculations for nuclear reaction rates, particularly for nuclei far from $\beta$-stability. However, statistical model parameters are often poorly constrained, where experimental constraints are particularly sparse for exotic nuclides. For example, our understanding of the breakout from the NiCu cycle in the astrophysical rp-process is currently limited by uncertainties in the statistical properties of the proton-rich nucleus $^{60}$Zn. We have determined the nuclear level density of $^{60}$Zn using neutron evaporation spectra from $^{58}$Ni($^3$He, n) measured at the Edwards Accelerator Laboratory. We compare our results to a number of theoretical predictions, including phenomenological, microscopic, and shell model based approaches. Notably, we find the $^{60}$Zn level density is somewhat lower than expected for excitation energies populated in the $^{59}$Cu(p,$\gamma$)$^{60}$Zn reaction under rp-process conditions. This includes a level density plateau from roughly 5-6 MeV excitation energy, which is counter to the usual expectation of exponential growth and all theoretical predictions that we explore. A determination of the spin-distribution at the relevant excitation energies in $^{60}$Zn is needed to confirm that the Hauser-Feshbach formalism is appropriate for the $^{59}$Cu(p,$\gamma$)$^{60}$Zn reaction rate at X-ray burst temperatures., Comment: 10 pages, 8 figures

40K plays a significant role in the radiogenic heating of earth-like exoplanets, which can affect the development of a habitable environment on their surfaces. The initial amount of 40K in the interior of these planets depends on the composition of the interstellar clouds from which they formed. Within this context, nuclear reactions that regulate the production of 40K during stellar evolution can play a critical role. In this study, we constrain for the first time the astrophysical reaction rate of 40K(n,p)40Ar, which is responsible for the destruction of 40K during stellar nucleosynthesis. We performed differential cross-section measurements on the 40Ar(p,n)40K reaction, for six energies in the center-of-mass between 3.2 and 4.0 MeV and various angles between 0-deg and 135-deg. The experiment took place at the Edwards Accelerator Laboratory at Ohio University using the beam swinger target location and a standard neutron time-of-flight technique. The total and partial cross-sections varied with energy due to the contribution from isobaric analog states and Ericson type fluctuations. The energy-averaged neutron angular distributions were symmetrical relative to 90-deg and consistent with the theoretical predictions of the statistical model. Based on the experimental data, local transmission coefficients were extracted and were used to calculate the astrophysical reaction rates of 40Ar(p,n)40K and 40K(n,p)40Ar reactions. Our results support that the destruction rate of 40K in massive stars via the 40K(n,p)40Ar reaction is larger compared to previous estimates. This result directly affects the predicted stellar yields of 40K from nucleosynthesis, which is a critical input parameter for the galactic chemical evolution models that are currently employed for the study of significant properties of exoplanets., Comment: 20 pages, 16 figures, submitted to PRC (revised manuscript after referee's review)

One of the simplest methods of generating a random graph with a given degree sequence is provided by the Monte Carlo Markov Chain method using switches. The switch Markov chain converges to the uniform distribution, but generally the rate of convergence is not known. After a number of results concerning various degree sequences, rapid mixing was established for so-called $P$-stable degree sequences (including that of directed graphs), which covers every previously known rapidly mixing region of degree sequences. In this paper we give a non-trivial family of degree sequences that are not $P$-stable and the switch Markov chain is still rapidly mixing on them. This family has an intimate connection to Tyshkevich-decompositions and strong stability as well., Comment: Generalized the main theorem, paper extended with a number of corroborating results

We say that two graphs on the same vertex set are $G$-creating if their union (the union of their edges) contains $G$ as a subgraph. Let $H_n(G)$ be the maximum number of pairwise $G$-creating Hamiltonian paths of $K_n$. Cohen, Fachini and K\"orner proved \[n^{\frac{1}{2}n-o(n)}\leq H_n(C_4) \leq n^{\frac{3}{4}n+o(n)}.\] In this paper we close the superexponential gap between their lower and upper bounds by proving \[n^{\frac{1}{2}n-\frac{1}{2}\frac{n}{\log{n}}-O(1)}\leq H_n(C_4) \leq n^{\frac{1}{2}n+o\left(\frac{n}{\log{n}} \right)}.\] We also improve the previously established upper bounds on $H_n(C_{2k})$ for $k>3$, and we present a small improvement on the lower bound of F\"uredi, Kantor, Monti and Sinaimeri on the maximum number of so-called pairwise reversing permutations. One of our main tools is a theorem of Krivelevich, which roughly states that (certain kinds of) good expanders contain many Hamiltonian paths., Comment: 14 pages, LaTeX2e; v2: updated Footnote 1 on Page 5; v3: revised version incorporating suggestions by the referees (the changes are mainly in Section 5); v4: final version to appear in Combinatorica

Since 1997 a considerable effort has been spent to study the mixing time of switch Markov chains on the realizations of graphic degree sequences of simple graphs. Several results were proved on rapidly mixing Markov chains on unconstrained, bipartite, and directed sequences, using different mechanisms. The aim of this paper is to unify these approaches. We will illustrate the strength of the unified method by showing that on any $P$-stable family of unconstrained/bipartite/directed degree sequences the switch Markov chain is rapidly mixing. This is a common generalization of every known result that shows the rapid mixing nature of the switch Markov chain on a region of degree sequences. Two applications of this general result will be presented. One is an almost uniform sampler for power-law degree sequences with exponent $\gamma>1+\sqrt{3}$. The other one shows that the switch Markov chain on the degree sequence of an Erd\H{o}s-R\'enyi random graph $G(n,p)$ is asymptotically almost surely rapidly mixing if $p$ is bounded away from 0 and 1 by at least $\frac{5\log n}{n-1}$., Comment: final review

We state a number of related questions on the structure of perfect matchings. Those questions are inspired by and directly connected to Quantum Physics. In particular, they concern the constructability of general quantum states using modern photonic technology. For that we introduce a new concept, denoted as inherited vertex coloring. It is a vertex coloring for every perfect matching. The colors are inherited from the color of the incident edge for each perfect matching. First, we formulate the concepts and questions in pure graph-theoretical language, and finally we explain the physical context of every mathematical object that we use. Importantly, every progress towards answering these questions can directly be translated into new understanding in quantum physics., Comment: 10 pages, 4 figures, 6 questions (added suggestions from peer-review)

We say that two graphs $H_1,H_2$ on the same vertex set are $G$-creating ($G$-different in other papers, this difference is explained in the introduction) if the union of the two graphs contains $G$ as a subgraph. Let $H(n,k)$ be the maximal number of pairwise $C_k$-creating paths (of arbitrary length) on $n$ vertices. The behaviour of $H(n,2k+1)$ is much better understood than the behaviour of $H(n,2k)$, the former is an exponential function of $n$ while the latter is larger than exponential, for every fixed $k$. We study $H(n,k)$ for fixed $k$ and $n$ tending to infinity. The only non trivial upper bound on $H(n,2k)$ was in the case where $k=2$ $$H(n,4)\leq n^{\left(1-\frac{1}{4} \right) n-o(n)}, $$ this was proved by Cohen, Fachini and K\"orner. In this paper, we generalize their method to prove that for every $k \geq 2$, $$H(n,2k) \leq n^{\left( 1- \frac{2}{3k^2-2k} \right)n-o(n)}. $$ Our proof uses constructions of bipartite, regular, $C_{2k}$-free graphs with many edges by Reiman, Benson, Lazebnik, Ustimenko and Woldar. For some special values of $k$ we can have slightly denser such bipartite graphs than for general $k$, this results in having better upper bounds on $H(n,2k)$ than stated above for these special values of $k$.