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The merger of dark matter halos and the gaseous structures embedded in them, such as proto-galaxies, galaxies, and groups and clusters of galaxies, results in strong shocks that are capable of accelerating cosmic rays (CRs) to $\sim10~\rm PeV$. These shocks will produce high-energy neutrinos and $\gamma$-rays through inelastic $pp$ collisions with ambient gaseous environments. In this work, we study the contributions of these halo mergers to the diffuse neutrino flux measured in IceCube and to the non-blazar portion of the extragalactic $\gamma$-ray background measured by $Fermi$. In order to calculate them, we formulate the redshift dependence of the shock velocity, galactic radius, halo gas content and galactic/intergalactic magnetic fields over the dark matter halo distribution up to a redshift $z=10$. We find that high-redshift mergers contribute a significant amount of the cosmic-ray energy luminosity density, and the resulting neutrino spectra could explain a large part of the observed diffuse neutrino flux above 0.1 PeV up to several PeV. We also show that our model can somewhat alleviate tensions with the extragalactic $\gamma$-ray background. First, since a larger fraction of the CR energy luminosity density comes from high redshifts, the accompanying $\gamma$-rays are more strongly suppressed through $\gamma\gamma$ annihilations with the cosmic microwave background (CMB) and the extragalactic background light (EBL). Second, mildly radiative-cooled shocks may lead to a harder CR spectrum with spectral indices of $1.5\lesssim s\lesssim2.0$. Our study suggests that halo mergers, a fraction of which may also induce starbursts in the merged galaxies, can be promising neutrino emitters without violating the existing $Fermi$ $\gamma$-ray constraints on the non-blazar component of the extragalactic $\gamma$-ray background., Comment: 13 pages, 7 figures, ApJ accepted

Recent results from the Pierre Auger Collaboration have shown that the composition of ultrahigh-energy cosmic rays (UHECRs) becomes gradually heavier with increasing energy. Although gamma-ray bursts (GRBs) have been promising sources of UHECRs, it is still unclear whether they can account for the Auger results because of their unknown nuclear composition of ejected UHECRs. In this work, we revisit the possibility that low-luminosity GRBs (LL GRBs) act as the sources of UHECR nuclei, and give new predictions based on the intrajet nuclear composition models considering progenitor dependencies. We find that the nuclear component in the jet can be divided into two groups according to the mass fraction of silicon nuclei, Si-free and Si-rich. Motivated by the connection between LL GRBs and transrelativistic supernovae, we also consider the hypernova ejecta composition. Then, we discuss the survivability of UHECR nuclei in the jet base and internal shocks of the jets, and show that it is easier for nuclei to survive for typical LL GRBs. Finally, we numerically propagate UHECR nuclei ejected from LL GRBs with different composition models and compare the resulting spectra and composition to Auger data. Our results show that both the Si-rich progenitor and hypernova ejecta models match the Auger data well, while the Si-free progenitor models have more difficulty in fitting the spectrum. We argue that our model is consistent with the newly reported cross correlation between the UHECRs and starburst galaxies, since both LL GRBs and hypernovae are expected to be tracers of the star-formation activity. LL GRBs have also been suggested as the dominant origin of IceCube neutrinos in the PeV range, and the LL GRB origin of UHECRs can be critically tested by near-future multimessenger observations., Comment: 17 pages, 16 figures, minor corrections, added the discussion about the possible correlation with starburst galaxies, version accepted by PRD

In this paper we describe the photometric and spectroscopic properties of multiple populations in seven northern globular clusters. In this study we employ precise ground based photometry from the private collection of Stetson, space photometry from the Hubble Space Telescope, literature abundances of Na and O, and APOGEE survey abundances for Mg, Al, C, and N. Multiple populations are identified by their position in the CU,B,I -V pseudo-CMD and confirmed with their chemical composition determined using abundances. We confirm the expectation from previous studies that the RGB in all seven clusters are split and the different branches have different chemical compositions. The Mg-Al anti-correlations were well explored by the APOGEE and Gaia-ESO surveys for most globular clusters, some clusters showing bimodal distributions, while others continuous distributions. Even though the structure (i.e., bimodal vs. continuous) of Mg-Al can greatly vary, the Al-rich and Al-poor populations do not seem to have very different photometric properties, agreeing with theoretical calculations. There is no one-to-one correspondence between the Mg-Al anticorrelation shape (bimodal vs. continuous) and the structure of the RGB seen in the HST pseudo-CMDs, with the HST photometric information usually implying more complex formation/evolution histories than the spectroscopic ones. We report on finding two second generation HB stars in M5, and five second generation AGB stars in M92, which is the most metal-poor cluster to date in which second generation AGB stars have been observed., Comment: Accepted for publication in MNRAS, 13 pages, 7 figures, 5 tables

We discuss the self-enrichment scenario by AGB stars for the formation of multiple populations in globular clusters (GCs) by analyzing data set of giant stars observed in 9 Galactic GCs, covering a wide range of metallicities and for which the simultaneous measurements of C, N, O, Mg, Al, Si are available. To this aim we calculated 6 sets of AGB models, with the same chemical composition as the stars belonging to the first generation of each GC. We find that the AGB yields can reproduce the set of observations available, not only in terms of the degree of contamination shown by stars in each GC but, more important, also the observed trend with metallicity, which agrees well with the predictions from AGB evolution modelling. While further observational evidences are required to definitively fix the main actors in the pollution of the interstellar medium from which new generation of stars formed in GCs, the present results confirm that the gas ejected by stars of mass in the range $4~\rm M_{\odot} \leq \rm M \leq 8~\rm M_{\odot}$ during the AGB phase share the same chemical patterns traced by stars in GCs., Comment: 22 pages and 11 figures; accepted for publication in MNRAS

The Apache Point Observatory Galactic Evolution Experiment (APOGEE) provides spectroscopic information of regions of the inner Milky Way inaccessible to optical surveys. We present the first large study of the metallicity distribution of the innermost Galactic regions based on homogeneous measurements from the SDSS Data Release 12 for 7545 red giant stars within 4.5 kpc of the Galactic center, with the goal to shed light on the structure and origin of the Galactic bulge. Stellar metallicities are found, through multiple-Gaussian decompositions, to be distributed in several components indicative of the presence of various stellar populations such as the bar, or the thin and the thick disk. A super-solar ([Fe/H]=+0.32) and a solar ([Fe/H]=+0.00) metallicity components, tentatively associated with the thin disk and the Galactic bar, respectively, seem to be the major contributors near the midplane. The solar-metallicity component extends outwards in the midplane but is not observed in the innermost regions. The central regions (within 3 kpc of the Galactic center) reveal, on the other hand, the presence of a significant metal-poor population ([Fe/H] =-0.46), tentatively associated with the thick disk, and which becomes the dominant component far from the midplane ($|Z| > +0.75 kpc). Varying contributions from these different components produce a transition region at +0.5 kpc < |Z| < +1.0 kpc characterized by a significant vertical metallicity gradient., Comment: 15 pages, 11 figures

Carbon isotope ratios, along with carbon and nitrogen abundances, are derived in a sample of 11 red-giant members of one of the most metal-rich clusters in the Milky Way, NGC 6791. The selected red-giants have a mean metallicity and standard deviation of [Fe/H]=+0.39+-0.06 (Cunha et al. 2015). We used high resolution H-band spectra obtained by the SDSS-IV Apache Point Observatory Galactic Evolution Experiment (APOGEE). The advantage of using high-resolution spectra in the H-band is that lines of CO are well represented and their line profiles are sensitive to the variation of 12C/13C. Values of the 12C/13C ratio were obtained from a spectrum synthesis analysis. The derived 12C/13C ratios varied between 6.3 and 10.6 in NGC 6791, in agreement with the final isotopic ratios from thermohaline-induced mixing models. The ratios derived here are combined with those obtained for more metal poor red-giants from the literature to examine the correlation between 12C/13C, mass, metallicity and evolutionary status., Comment: Accepted for publication in MNRAS, 9 pages, 4 figures, 2 tables

Solid inflation is a cosmological model where inflation is driven by fields which enter the Lagrangian in the same way as body coordinates of a solid matter enter the equation of state, spontaneously breaking spatial translational and rotational symmetry. We construct a simple generalization of this model by adding a scalar field with standard kinetic term to the action. In our model the scalar power spectrum and the tensor-to-scalar ratio do not differ from the ones predicted by the solid inflation qualitatively, if the scalar field does not dominate the solid matter. The same applies also for the size of the scalar bispectrum measured by the non-linearity parameter, although our model allows it to have different shapes. The tensor bispectra predicted by the two models do not differ from each other in the leading order of the slow-roll approximation. In the case when contribution of the solid matter to the stress-energy tensor is much smaller than the contribution from the scalar field, the tensor-to-scalar ratio and the non-linearity parameter are amplified by factors $\epsilon^{-1}$ and $\epsilon^{-2}$ respectively., Comment: 23 pages, 3 figures

We discuss the electromagnetic radiation from newborn binary black holes (BBHs). As a consequence of the evolution of massive stellar binaries, a binary consisting of a primary black hole (BH) and a secondary Wolf-Rayet star is expected as a BBH progenitor system. We investigate optical transients from the birth of BBHs powered by the Bondi-Hoyle-Lyttleton accretion onto the primary BH, which occur $\sim1-10$ Gyr earlier than gravitational wave signals at the BH-BH merger. When the secondary massive star collapses into a BH, it may eject a fraction of its outer material and may form a disk around the primary BH and induces a powerful disk wind. These primary-induced winds can lead to optical transients with a kinetic energy of $\sim10^{47}-3\times10^{48}$ erg, an ejecta velocity of $10^8-10^9\rm~cm~s^{-1}$, a duration of a few days, and an absolute magnitude ranging from about $-11$ to $-14$. The light curves and late-time spectra of these transients are distinctive from those of ordinary supernovae, and detection of this type of transient is possible by future optical transient surveys if the event rate of this transient is comparable to the merger rate of BBHs. This paper focuses on the emissions from disk-driven transients induced by the primary BH, different from the first paper that focuses on wind-driven transients from the tidally-locked secondary massive star., Comment: 9 pages, 3 figures, accepted for publication in ApJ, arXiv:1702.07337v2 was split into two papers according to referee's suggestion. This is Paper II. See also arXiv:1702.07337v3 for Paper I

The recent detection of gravitational waves and electromagnetic counterparts from the double neutron star merger event GW+EM170817, supports the standard paradigm of short gamma-ray bursts (SGRBs) and kilonovae/macronovae. It is important to reveal the nature of the compact remnant left after the merger, either a black hole or neutron star, and their physical link to the origin of the long-lasting emission observed in SGRBs. The diversity of the merger remnants may also lead to different kinds of transients that can be detected in future. Here we study the high-energy emission from the long-lasting central engine left after the coalescence, under certain assumptions. In particular, we consider the X-ray emission from a remnant disk and the non-thermal nebular emission from disk-driven outflows or pulsar winds. We demonstrate that late-time X-ray and high-frequency radio emission can provide useful constraints on properties of the hidden compact remnants and their connections to long-lasting SGRB emission, and we discuss the detectability of nearby merger events through late-time observations at $\sim30-100$ d after the coalescence. We also investigate the GeV-TeV gamma-ray emission that occurs in the presence of long-lasting central engines, and show the importance of external inverse-Compton radiation due to up-scattering of X-ray photons by relativistic electrons in the jet. We also search for high-energy gamma-rays from GW170817 in the Fermi-LAT data, and report upper limits on such long-lasting emission. Finally, we consider the implications of GW+EM170817 and discuss the constraints placed by X-ray and high-frequency radio observations., Comment: 16 pages, 12 figures, accepted for publication in ApJ, minor changes

First we consider families in the hypercube $Q_n$ with bounded VC dimension. Frankl raised the problem of estimating the number $m(n,k)$ of maximal families of VC dimension $k$. Alon, Moran and Yehudayoff showed that $$n^{(1+o(1))\frac{1}{k+1}\binom{n}{k}}\leq m(n,k)\leq n^{(1+o(1))\binom{n}{k}}.$$ We close the gap by showing that $\log \left(m(n,k)\right)= {(1+o(1))\binom{n}{k}}\log n$ and show how a tight asymptotic for the logarithm of the number of induced matchings between two adjacent small layers of $Q_n$ follows as a corollary. Next, we consider the integrity $I(Q_n)$ of the hypercube, defined as $$I(Q_n) = \min\{ |S| +m(Q_n \setminus S) : S \subseteq V (Q_n) \},$$ where $m(H)$ denotes the number of vertices in the largest connected component of $H$. Beineke, Goddard, Hamburger, Kleitman, Lipman and Pippert showed that $c\frac{2^n}{\sqrt{n}} \leq I(Q_n)\leq C\frac{2^n}{\sqrt{n}}\log n$ and suspected that their upper bound is the right value. We prove that the truth lies below the upper bound by showing that $I(Q_n)\leq C \frac{2^n}{\sqrt{n}}\sqrt{\log n}$., Comment: 7 pages

The coincident detection of a gravitational-wave (GW) event GW170817 with electromagnetic (EM) signals (e.g., a short gamma-ray burst SGRB 170817A or a macronova) from a binary neutron star merger within the nearby galaxy NGC 4933 provides a new, multimessenger test of the weak equivalence principle (WEP), extending the WEP test with GWs and photons. Assuming that the arrival time delay between the GW signals from GW170817 and the photons from SGRB 170817A or the macronova is mainly attributed to the gravitational potential of the Milky Way, we demonstrate that the strict upper limits on the deviation from the WEP are $\Delta \gamma<1.4\times10^{-3}$ for GW170817/macronova and $\Delta \gamma <5.9\times10^{-8}$ for GW170817/SGRB 170817A. A much more severe constraint on the WEP accuracy can be achieved ($\sim0.9\times10^{-10}$) for GW170817/SGRB 170817A when we consider the gravitational potential of the Virgo Cluster, rather than the Milky Way's gravity. This provides the tightest limit to date on the WEP through the relative differential variations of the $\gamma$ parameter for two different species of particles. Compared with other multimessenger (photons and neutrinos) results, our limit is 7 orders of magnitude tighter than that placed by the neutrinos and photons from supernova 1987A, and is almost as good as or is an improvement of 6 orders of magnitude over the limits obtained by the low-significance neutrinos correlated with GRBs and a blazar flare., Comment: 10 pages, no figures. Accepted by JCAP on Nov 8, 2017

We say that a set system $\mathcal{F}\subseteq 2^{[n]}$ shatters a given set $S\subseteq [n]$ if $2^S= \{F~\cap~S:~F~\in~\mathcal{F}\}$. The Sauer-Shelah lemma states that in general, a set system $\mathcal{F}$ shatters at least $|\mathcal{F}|$ sets. Here we concentrate on the case of equality. A set system is called \emph{shattering-extremal} if it shatters exactly $|\mathcal{F}|$ sets. A conjecture of R\'onyai and the second author and of Litman and Moran states that if a family is shattering-extremal then one can add a set to it and the resulting family is still shattering-extremal. Here we prove this conjecture for a class of set systems defined from Sperner families., Comment: 15 pages

The Lidskii formula for the type $A_n$ root system expresses the volume and Ehrhart polynomial of the flow polytope of the complete graph with nonnegative integer netflows in terms of Kostant partition functions. For every integer polytope the volume is the leading coefficient of the Ehrhart polynomial. The beauty of the Lidskii formula is the revelation that for these polytopes its Ehrhart polynomial function can be deduced from its volume function! Baldoni and Vergne generalized Lidskii's result for flow polytopes of arbitrary graphs $G$ and nonnegative integer netflows. While their formulas are combinatorial in nature, their proofs are based on residue computations. In this paper we construct canonical polytopal subdivisions of flow polytopes which we use to prove the Baldoni-Vergne-Lidskii formulas. In contrast with the original computational proof of these formulas, our proof reveal their geometry and combinatorics. We conclude by exhibiting enumerative properties of the Lidskii formulas via our canonical polytopal subdivisions., Comment: 28 pages, 10 figures, v2. includes proof of a second formula for the lattice points and an appendix with examples

SiC based metal-oxide-semiconductor field-effect transistors (MOSFETs) have gained a significant importance in power electronics applications. However, electrically active defects at the SiC/SiO$_2$ interface degrade the ideal behavior of the devices. The relevant microscopic defects can be identified by electron paramagnetic resonance (EPR) or electrically detected magnetic resonance (EDMR). This helps to decide which changes to the fabrication process will likely lead to further increases of device performance and reliability. EDMR measurements have shown very similar dominant hyperfine (HF) spectra in differently processed MOSFETs although some discrepancies were observed in the measured $g$-factors. Here, the HF spectra measured of different SiC MOSFETs are compared and it is argued that the same dominant defect is present in all devices. A comparison of the data with simulated spectra of the C dangling bond (P$_\textrm{bC}$) center and the silicon vacancy (V$_\textrm{Si}$) demonstrates that the P$_\textrm{bC}$ center is a more suitable candidate to explain the observed HF spectra., Comment: Accepted for publication in the Journal of Applied Physics

We investigate current and future prospects for coincident detection of high-energy neutrinos and gravitational waves (GWs). Short gamma-ray bursts (SGRBs) are believed to originate from mergers of compact star binaries involving neutron stars. We estimate high-energy neutrino fluences from prompt emission, extended emission, X-ray flares, and plateau emission, and show that neutrino signals associated with the extended emission are the most promising. Assuming that the cosmic-ray loading factor is $\sim10$ and the Lorentz factor distribution is lognormal, we calculate the probability of neutrino detection from extended emission by current and future neutrino detectors, and find that the quasi-simultaneous detection of high-energy neutrinos, gamma rays, and GWs is possible with future instruments or even with current instruments for nearby SGRBs having extended emission. We also discuss stacking analyses that will also be useful with future experiments such as IceCube-Gen2., Comment: 8 pages, 2 figures, 3 tables, accepted for publication in ApJL

A graph $G$ is terminal-pairable with respect to a demand multigraph $D$ on the same vertex set as $G$, if there exists edge-disjoint paths joining the end vertices of every demand edge of $D$. In this short note, we improve the upper bound on the largest $\Delta(n)$ with the property that the complete graph on $n$ vertices is terminal-pairable with respect to any demand multigraph of maximum degree at most $\Delta(n)$. This disproves a conjecture originally stated by Csaba, Faudree, Gy\'arf\'as, Lehel and Schelp., Comment: 4 pages

In this paper we obtain Sobolev estimates for weak solutions of first oder variational Mean Field Game systems with coupling terms that are local function of the density variable. Under some coercivity condition on the coupling, we obtain first order Sobolev estimates for the density variable, while under similar coercivity condition on the Hamiltonian we obtain second order Sobolev estimates for the value function. These results are valid both for stationary and time-dependent problems. In the latter case the estimates are fully global in time, thus we resolve a question which was left open in [PS17]. Our methods apply to a large class of Hamiltonians and coupling functions., Comment: to appear in Ann. Inst. H. Poincar\'e Anal. Non Lin\'eaire

High energy neutrino astrophysics has come of age with the discovery by IceCube of neutrinos in the TeV to PeV energy range attributable to extragalactic sources at cosmological distances. At such energies, astrophysical neutrinos must have their origin in cosmic ray interactions, providing information about the sources of high energy cosmic rays, as well as leading to the co-production of high energy gamma-rays. The intimate link with these latter two independently observed types of radiation provides important tools in the search for identifying and understanding the nature of their astrophysical sources. These neutrinons can provide important constraints about the cosmic ray acceleration process, and since they travel essentially unimpeded they can probe our Universe out to the farthest cosmological distances., Comment: 26 pages, 8 figures; accepted in Annual Review of Nuclear and Particle Science; to appear in vol. 67 (2017)

We compute the CMB angular power spectrum in the presence of the radiation-like solid with the same pressure to energy density ratio as for the radiation but with nonzero shear modulus. The effect can be observable not only for large-angle anisotropies as shown by Balek and \v{S}kovran [2015] but also for very small-angle ones., Comment: 7 pages, 1 figure, conference: Week of Doctoral Students 2016, Prague

APOGEE-2 is a high-resolution, near-infrared spectroscopic survey observing roughly 300,000 stars across the entire sky. It is the successor to APOGEE and is part of the Sloan Digital Sky Survey IV (SDSS-IV). APOGEE-2 is expanding upon APOGEE's goals of addressing critical questions of stellar astrophysics, stellar populations, and Galactic chemodynamical evolution using (1) an enhanced set of target types and (2) a second spectrograph at Las Campanas Observatory in Chile. APOGEE-2 is targeting red giant branch (RGB) and red clump (RC) stars, RR Lyrae, low-mass dwarf stars, young stellar objects, and numerous other Milky Way and Local Group sources across the entire sky from both hemispheres. In this paper, we describe the APOGEE-2 observational design, target selection catalogs and algorithms, and the targeting-related documentation included in the SDSS data releases., Comment: 19 pages, 6 figures. Accepted to AJ

The fourth generation of the Sloan Digital Sky Survey (SDSS-IV) has been in operation since July 2014. This paper describes the second data release from this phase, and the fourteenth from SDSS overall (making this, Data Release Fourteen or DR14). This release makes public data taken by SDSS-IV in its first two years of operation (July 2014-2016). Like all previous SDSS releases, DR14 is cumulative, including the most recent reductions and calibrations of all data taken by SDSS since the first phase began operations in 2000. New in DR14 is the first public release of data from the extended Baryon Oscillation Spectroscopic Survey (eBOSS); the first data from the second phase of the Apache Point Observatory (APO) Galactic Evolution Experiment (APOGEE-2), including stellar parameter estimates from an innovative data driven machine learning algorithm known as "The Cannon"; and almost twice as many data cubes from the Mapping Nearby Galaxies at APO (MaNGA) survey as were in the previous release (N = 2812 in total). This paper describes the location and format of the publicly available data from SDSS-IV surveys. We provide references to the important technical papers describing how these data have been taken (both targeting and observation details) and processed for scientific use. The SDSS website (www.sdss.org) has been updated for this release, and provides links to data downloads, as well as tutorials and examples of data use. SDSS-IV is planning to continue to collect astronomical data until 2020, and will be followed by SDSS-V., Comment: SDSS-IV collaboration alphabetical author data release paper. DR14 happened on 31st July 2017. 19 pages, 5 figures. Accepted by ApJS on 28th Nov 2017 (this is the "post-print" and "post-proofs" version; minor corrections only from v1, and most of errors found in proofs corrected)

The dimension is a key measure of complexity of partially ordered sets. Small dimension allows succinct encoding. Indeed if $P$ has dimension $d$, then to know whether $x \leq y$ in $P$ it is enough to check whether $x\leq y$ in each of the $d$ linear extensions of a witnessing realizer. Focusing on the encoding aspect Ne\v{s}et\v{r}il and Pudl\'{a}k defined a more expressive version of dimension. A poset $P$ has boolean dimension at most $d$ if it is possible to decide whether $x \leq y$ in $P$ by looking at the relative position of $x$ and $y$ in only $d$ permutations of the elements of $P$. We prove that posets with cover graphs of bounded tree-width have bounded boolean dimension. This stays in contrast with the fact that there are posets with cover graphs of tree-width three and arbitrarily large dimension. This result might be a step towards a resolution of the long-standing open problem: Do planar posets have bounded boolean dimension?, Comment: one more reference added; paper revised along the suggestion of three reviewers

A graph is path-pairable if for any pairing of its vertices there exist edge disjoint paths joining the vertices in each pair. We obtain sharp bounds on the maximum possible diameter of path-pairable graphs which either have a given number of edges, or are c- degenerate. Along the way we show that a large family of graphs obtained by blowing up a path is path-pairable, which may be of independent interest., Comment: 8 pages

We report the peculiar chemical abundance patterns of eleven atypical Milky Way (MW) field red giant stars observed by the Apache Point Observatory Galactic Evolution Experiment (APOGEE). These atypical giants exhibit strong Al and N enhancements accompanied by C and Mg depletions, strikingly similar to those observed in the so-called second-generation (SG) stars of globular clusters (GCs). Remarkably, we find low-Mg abundances ([Mg/Fe]$<$0.0) together with strong Al and N overabundances in the majority (5/7) of the metal-rich ([Fe/H]$\gtrsim - 1.0$) sample stars, which is at odds with actual observations of SG stars in Galactic CGs of similar metallicities. This chemical pattern is unique and unprecedented among MW stars, posing urgent questions about its origin. These atypical stars could be former SG stars of dissolved GCs formed with intrinsically lower abundances of Mg and enriched Al (subsequently self-polluted by massive AGB stars) or the result of exotic binary systems. We speculate that the stars Mg-deficiency as well as the orbital properties suggest that they could have an extragalactic origin. This discovery should guide future dedicated spectroscopic searches of atypical stellar chemical patterns in our Galaxy; a fundamental step forward to understand the Galactic formation and evolution., Comment: Accepted for publication in ApJ Letters, 11 pages, 2 Figures, 2 Tables

Recent progress on flow polytopes indicates many interesting families with product formulas for their volume. These product formulas are all proved using analytic techniques. Our work breaks from this pattern. We define a family of closely related flow polytopes $\mathcal{F}_{(\lambda, {\bf a})}$ for each partition shape $\lambda$ and netflow vector ${\bf a}\in \mathbb{Z}^n_{> 0}$. In each such family, we prove that there is a polytope (the limiting one in a sense) which is a product of scaled simplices, explaining their product volumes. We also show that the combinatorial type of all polytopes in a fixed family $\mathcal{F}_{(\lambda, {\bf a})}$ is the same. When $\lambda$ is a staircase shape and ${\bf a}$ is the all ones vector the latter result specializes to a theorem of the first author with Morales and Rhoades, which shows that the combinatorial type of the Tesler polytope is a product of simplices.

We identify six new CEMP stars ([C/Fe]>+0.7 and [Fe/H]< -1.8) and another seven likely candidates within the APOGEE database following Data Release 12. These stars have chemical compositions typical of metal-poor halo stars, e.g., mean [$\alpha$/Fe] = +0.24$\pm$0.24, based on the ASPCAP pipeline results. A lack of heavy element spectral lines impedes further sub-classification of these CEMP stars, however, based on radial velocity scatter, we predict most are not CEMP-s stars which are typically found in binary systems. Only one object, 2M15312547+4220551, may be in a binary since it exhibits a scatter in its radial velocity of 1.7 $\pm$0.6 km s$^{-1}$ based on three visits over a 25.98 day baseline. Optical observations are now necessary to confirm the stellar parameters and low metallicities of these stars, to determine the heavy-element abundance ratios and improve the precision in the derived abundances, and to examine their CEMP sub-classifications., Comment: 20 pages, 9 tables, 9 figures: Accepted for publication in MNRAS

We show that the dual character of the flagged Weyl module of any diagram is a positively weighted integer point transform of a generalized permutahedron. In particular, Schubert and key polynomials are positively weighted integer point transforms of generalized permutahedra. This implies several recent conjectures of Monical, Tokcan and Yong., Comment: 8 pages. Corrected title in arXiv metadata (d'oh); no change to manuscript

There are indications that $\gamma$-ray dark objects such as supernovae (SNe) with choked jets, and the cores of active galactic nuclei may contribute to the diffuse flux of astrophysical neutrinos measured by the IceCube observatory. In particular, stripped-envelope SNe have received much attention since they are capable of producing relativistic jets and could explain the diversity in observations of collapsar explosions (e.g., gamma-ray bursts (GRBs), low-luminosity GRBs, and Type Ibc SNe). We use an unbinned maximum likelihood method to search for spatial and temporal coincidences between Type Ibc core-collapse SNe, which may harbor a choked jet, and muon neutrinos from a sample of IceCube up-going track-like events measured from May 2011-May 2012. In this stacking analysis, we find no significant deviation from a background-only hypothesis using one year of data, and are able to place upper limits on the total amount of isotropic equivalent energy that choked jet core-collapse SNe deposit in cosmic rays ${\mathcal E}_{\rm cr}$ and the fraction of core-collapse SNe which have a jet pointed towards Earth $f_{\rm jet}$. This analysis can be extended with yet to be made public IceCube data, and the increased amount of optically detected core-collapse SNe discovered by wide field-of-view surveys such as the Palomar Transient Factory and All-Sky Automated Survey for Supernovae. The choked jet SNe/high-energy cosmic neutrino connection can be more tightly constrained in the near future., Comment: 21 pages, 7 figures, 1 table, accepted for publication in JCAP

High-energy neutrinos are expected to originate from different stages in a gamma-ray burst (GRB) event. In this work we revisit the dissipative photospheric scenario, in which the GRB prompt emission is produced around the photospheric radius. Meanwhile, possible dissipation mechanisms (e.g., internal shocks or magnetic reconnection) could accelerate cosmic-rays (CRs) to ultra-high energies and then produce neutrinos via hadronuclear and photohadronic processes, which are referred to as prompt neutrinos. In this paper, we obtain the prompt neutrino spectrum of a single GRB within a self-consistent analytical framework, in which the jet-cocoon structure and possible collimation effects are included. We investigate a possible neutrino signal from the cocoon, which has been ignored in the previous studies. We show that if a GRB event happens at a distance of the order of Mpc, there is a great chance to observe the neutrino emission from the cocoon by IceCube, which is even more promising than jet neutrinos since the opening angle of the cocoon is much larger. We also figure out the diffuse neutrino flux of GRB cocoons and find that it could be comparable with that of the jets. Our results are consistent with the latest result reported by the IceCube collaboration that no significant correlation between neutrino events and observed GRBs is seen in the new data (Aartsen et al. 2017)., Comment: 6 pages, 6 figures, accepted for publication in ApJ

The measurement of the structure of stellar populations in the Milky Way disk places fundamental constraints on models of galaxy formation and evolution. Previously, the disk's structure has been studied in terms of populations defined geometrically and/or chemically, but a decomposition based on stellar ages provides a more direct connection to the history of the disk, and stronger constraint on theory. Here, we use positions, abundances and ages for 31,244 red giant branch stars from the SDSS-APOGEE survey, spanning $3 < R_{\mathrm{gc}} < 15$ kpc, to dissect the disk into mono-age and mono-[Fe/H] populations at low and high [$\alpha$/Fe]. For each population, with $\Delta \mathrm{age} < 2$ Gyr and $\Delta \mathrm{[Fe/H]} < 0.1$ dex, we measure the structure and surface-mass density contribution. We find that low [$\alpha$/Fe] mono-age populations are fit well by a broken exponential, which increases to a peak radius and decreases thereafter. We show that this profile becomes broader with age, interpreted here as a new signal of disk heating and radial migration. High [$\alpha$/Fe] populations are well fit as single exponentials within the radial range considered, with an average scale length of $1.9\pm 0.1$ kpc. We find that the relative contribution of high to low [$\alpha$/Fe] populations at $R_0$ is $f_\Sigma = 18\% \pm 5\%$; high [$\alpha$/Fe] contributes most of the mass at old ages, and low [$\alpha$/Fe] at young ages. The low and high [$\alpha$/Fe] populations overlap in age at intermediate [Fe/H], although both contribute mass at $R_{0}$ across the full range of [Fe/H]. The mass weighted scale height $h_Z$ distribution is a smoothly declining exponential function. High [$\alpha$/Fe] populations are thicker than low [$\alpha$/Fe], and the average $h_Z$ increases steadily with age, between 200 and 600 pc., Comment: Submitted to MNRAS. Revised version following comments from the referee. 24 Pages, 18 Figures

A graph is path-pairable if for any pairing of its vertices there exist edge-disjoint paths joining the vertices in each pair. We investigate the behaviour of the maximum degree in path-pairable planar graphs. We show that any $n$-vertex path-pairable planar graph must contain a vertex of degree linear in $n$.

A simple and fast analysis method to sort large data sets into groups with shared distinguishing characteristics is described, and applied to single molecular break junction conductance versus electrode displacement data. The method, based on principal component analysis, successfully sorted data sets based on the projection of the data onto the first or second principal component of the correlation matrix without the need to assert any specific hypothesis about the expected features within the data. This was an improvement on the current correlation matrix analysis approach because it sorted data automatically, making it more objective and less time consuming, and our method is applicable to a wide range of multivariate data sets. Here the method was demonstrated on two systems. First, it was demonstrated on mixtures of two molecules with identical anchor groups, similar lengths, but either a $\pi$ (high conductance) or $\sigma$ (low conductance) bridge. The mixed data was automatically sorted into two groups containing one molecule or the other. Second, it was demonstrated on break junction data measured with the $\pi$ bridged molecule alone. Again the method distinguished between two groups. These groups were tentatively assigned to different geometries of the molecule in the junction., Comment: Maths in SM; NMR in SM

We study a nonlinear, degenerate cross-diffusion model which involves two densities with two different drift velocities. A general framework is introduced based on its gradient flow structure in Wasserstein space to derive a notion of discrete-time solutions. Its continuum limit, due to the possible mixing of the densities, only solves a weaker version of the original system. In one space dimension, where the densities are guaranteed to be segregated, a stable interface appears between the two densities, and a stronger convergence result, in particular derivation of a standard weak solution to the system, is available. We also study the incompressible limit of the system, which addresses transport under a height constraint on the total density. In one space dimension we show that the problem leads to a two-phase Hele-Shaw type flow., Comment: improved version; some well-known results shortened

We study a family of dissections of flow polytopes arising from the subdivision algebra. To each dissection of a flow polytope, we associate a polynomial, called the left-degree polynomial, which we show is invariant of the dissection considered (proven independently by Grinberg). We prove that left-degree polynomials encode integer points of generalized permutahedra. Using that certain left-degree polynomials are related to Grothendieck polynomials, we resolve special cases of conjectures by Monical, Tokcan, and Yong regarding the saturated Newton polytope property of Grothendieck polynomials., Comment: 33 pages; Multiple improvements to exposition. Result numbers may have changed

Violations of Lorentz invariance can lead to an energy-dependent vacuum dispersion of light, which results in arrival-time differences of photons arising with different energies from a given transient source. In this work, direction-dependent dispersion constraints are obtained on nonbirefringent Lorentz-violating effects, using the observed spectral lags of the gamma-ray burst GRB 160625B. This burst has unusually large high-energy photon statistics, so we can obtain constraints from the true spectral time lags of bunches of high-energy photons rather than from the rough time lag of a single highest-energy photon. Also, GRB 160625B is the only burst to date having a well-defined transition from positive lags to negative lags, which provides a unique opportunity to distinguish Lorentz-violating effects from any source-intrinsic time lag in the emission of photons of different energy bands. Our results place comparatively robust two-sided constraints on a variety of isotropic and anisotropic coefficients for Lorentz violation, including first bounds on Lorentz-violating effects from operators of mass dimension ten in the photon sector., Comment: 6 pages, 3 figures, 1 table. Accepted for publication in ApJ

The normalized volume of the Chan-Robbins-Yuen polytope ($CRY_n$) is the product of consecutive Catalan numbers. The polytope $CRY_n$ has captivated combinatorial audiences for over a decade, as there is no combinatorial proof for its volume formula. In their quest to understand $CRY_n$ better, the third author and Morales introduced two natural generalizations of it and conjectured that their volumes are certain powers of $2$ multiplied by a product of consecutive Catalan numbers. Zeilberger proved one of these conjectures. In this paper we present proofs of both conjectures., Comment: 15 pages, 3 figures

We consider the variational approach to prove the existence of solutions of second order stationary Mean Field Games on a bounded domain $\Omega\subseteq \mathbb{R}^{d}$, with Neumann boundary conditions, and with and without density constraints. We consider Hamiltonians which growth as $|\cdot|^{q'}$, where $q'=q/(q-1)$ and $q>d$. Despite this restriction, our approach allows us to prove the existence of solutions in the case of rather general coupling terms. When density constraints are taken into account, our results improve those in \cite{MesSil}. Furthermore, our approach can be used to obtain solutions of systems with multiple populations.

In the updated APOGEE-Kepler catalog, we have asteroseismic and spectroscopic data for over 3000 first ascent red giants. Given the size and accuracy of this sample, these data offer an unprecedented test of the accuracy of stellar models on the post-main-sequence. When we compare these data to theoretical predictions, we find a metallicity dependent temperature offset with a slope of around 100 K per dex in metallicity. We find that this effect is present in all model grids tested and that theoretical uncertainties in the models, correlated spectroscopic errors, and shifts in the asteroseismic mass scale are insufficient to explain this effect. Stellar models can be brought into agreement with the data if a metallicity dependent convective mixing length is used, with $ \Delta\alpha_{\rm ML, YREC} \sim 0.2$ per dex in metallicity, a trend inconsistent with the predictions of three dimensional stellar convection simulations. If this effect is not taken into account, isochrone ages for red giants from the Gaia data will be off by as much as a factor of 2 even at modest deviations from solar metallicity ([Fe/H]=$-$0.5)., Comment: 13 pages, 10 figures. Accepted for publication in the Astrophysical Journal. For a brief video discussing key results from this paper see https://www.youtube.com/watch?v=cV_0AhPAIRo . The data and models used in this paper are available at http://www.astronomy.ohio-state.edu/~tayar/MixingLength.htm

The Space Telescope Imaging Spectrograph (STIS) has measured the spectral energy distributions (SEDs) for several stars of types O, B, A, F, and G. These absolute fluxes from the CALSPEC database are fit with a new spectral grid computed from the ATLAS-APOGEE ATLAS9 model atmosphere database using a chi-square minimization technique in four parameters. The quality of the fits are compared for complete LTE grids by Castelli & Kurucz (CK04) and our new comprehensive LTE grid (BOSZ). For the cooler stars, the fits with the MARCS LTE grid are also evaluated, while the hottest stars are also fit with the NLTE Lanz & Hubeny OB star grids. Unfortunately, these NLTE models do not transition smoothly in the infrared to agree with our new BOSZ LTE grid at the NLTE lower limit of Teff =15,000K. The new BOSZ grid is available via the Space Telescope Institute MAST archive and has a much finer sampled IR wavelength scale than CK04, which will facilitate the modeling of stars observed by the James Webb Space Telescope (JWST). Our result for the angular diameter of Sirius agrees with the ground- based interferometric value., Comment: 11 figures

Einstein's weak equivalence principle (WEP) states that any freely falling, uncharged test particle follows the same identical trajectory independent of its internal structure and composition. Since the polarization of a photon is considered to be part of its internal structure, we propose that polarized photons from astrophysical transients, such as gamma-ray bursts (GRBs) and fast radio bursts (FRBs), can be used to constrain the accuracy of the WEP through the Shapiro time delay effect. Assuming that the arrival time delays of photons with different polarizations are mainly attributed to the gravitational potential of the Laniakea supercluster of galaxies, we show that a strict upper limit on the differences of the parametrized post-Newtonian parameter $\gamma$ value for the polarized optical emission of GRB 120308A is $\Delta\gamma<1.2\times10^{-10}$, for the polarized gamma-ray emission of GRB 100826A is $\Delta\gamma<1.2\times10^{-10}$, and for the polarized radio emission of FRB 150807 is $\Delta\gamma<2.2\times10^{-16}$. These are the first direct verifications of the WEP for multiband photons with different polarizations. In particular, the result from FRB 150807 provides the most stringent limit to date on a deviation from the WEP, improving by one order of magnitude the previous best result based on Crab pulsar photons with different energies., Comment: 7 pages, 1 table. Updated to match the published version

Given a set $S$ of $v \ge 2$ symbols, and integers $k \ge t \ge 2$ and $N \ge 1$, an $N \times k$ array $A \in S^{N \times k}$ is an $(N; t, k, v)$-covering array if all sequences in $S^t$ appear as rows in every $N \times t$ subarray of $A$. These arrays have a wide variety of applications, driving the search for small covering arrays. The covering array number, $\mathrm{CAN}(t,k,v)$, is the smallest $N$ for which an $(N; t,k,v)$-covering array exists. In this paper, we combine probabilistic and linear algebraic constructions to improve the upper bounds on $\mathrm{CAN}(t,k,v)$ by a factor of $\ln v$, showing that for prime powers $v$, $\mathrm{CAN}(t,k,v) \le (1 + o(1)) \left( (t-1) v^t / (2 \log_2 v - \log_2 (v+1)) \right)\log_2 k$, which also offers improvements for large $v$ that are not prime powers. Our main tool, which may be of independent interest, is a construction of an array with $v^t$ rows that covers the maximum possible number of subsets of size $t$., Comment: 20 pages. This version subsumes the results in the previous version, "Families of Mass Destruction," generalising the results from set systems to covering arrays over larger alphabets

We apply Ramsey theoretic tools to show that there is a family of graphs which have tree-chromatic number at most~$2$ while the path-chromatic number is unbounded. This resolves a problem posed by Seymour., Comment: reviewers comments included

We discuss likely sources of cosmic rays in the $10^{15}-10^{20}$ eV range and their possible very high energy neutrino and gamma-ray signatures which could serve to identify these sources and constrain their physics. Among these sources we discuss in particular low luminosity gamma-ray bursts, including choked and shock-breakout objects, tidal disruption events and white dwarf mergers. Among efforts aimed at simultaneous secondary multi-messenger detections we discuss the AMON program., Comment: 9 pages; Based on a talk given at the Origin of Cosmic Rays: Beyond the Standard Model 2016 conference in San Vito di Cadore, Dolomites; This is not a comprehensive review; it is weighted towards work the author has been more personally involved with. Fig 3 has been updated to reflect the published work

We describe the Sloan Digital Sky Survey IV (SDSS-IV), a project encompassing three major spectroscopic programs. The Apache Point Observatory Galactic Evolution Experiment 2 (APOGEE-2) is observing hundreds of thousands of Milky Way stars at high resolution and high signal-to-noise ratio in the near-infrared. The Mapping Nearby Galaxies at Apache Point Observatory (MaNGA) survey is obtaining spatially-resolved spectroscopy for thousands of nearby galaxies (median redshift of z = 0.03). The extended Baryon Oscillation Spectroscopic Survey (eBOSS) is mapping the galaxy, quasar, and neutral gas distributions between redshifts z = 0.6 and 3.5 to constrain cosmology using baryon acoustic oscillations, redshift space distortions, and the shape of the power spectrum. Within eBOSS, we are conducting two major subprograms: the SPectroscopic IDentification of eROSITA Sources (SPIDERS), investigating X-ray AGN and galaxies in X-ray clusters, and the Time Domain Spectroscopic Survey (TDSS), obtaining spectra of variable sources. All programs use the 2.5-meter Sloan Foundation Telescope at Apache Point Observatory; observations there began in Summer 2014. APOGEE-2 also operates a second near-infrared spectrograph at the 2.5-meter du Pont Telescope at Las Campanas Observatory, with observations beginning in early 2017. Observations at both facilities are scheduled to continue through 2020. In keeping with previous SDSS policy, SDSS-IV provides regularly scheduled public data releases; the first one, Data Release 13, was made available in July 2016., Comment: Published in Astronomical Journal

We propose a new type of electromagnetic transients associated with the birth of binary black holes (BBHs), which may lead to merger events accompanied by gravitational waves in $\sim0.1-1$ Gyr. We consider the newborn BBHs formed through the evolution of isolated massive stellar binaries. For a close massive binary, consisting of a primary black hole (BH) and a secondary Wolf-Rayet (WR) star that are orbiting around each other, the spin period of the WR star can be tidally synchronized to its orbital period. Then, the angular momentum of the outer material of the WR star is large enough to form an accretion disk around a newborn, secondary BH, following its core-collapse. This disk may produce an energetic outflow with a kinetic energy of $\sim10^{50}-10^{52}$ erg and an outflow velocity of $\sim10^{10}\rm~cm~s^{-1}$, resulting in an optical transient with an absolute magnitude from $\sim -14$ to $\sim-17$ with a duration of around a day. This type of transient also produces detectable radio signals $\sim1-10$ years after the birth of BBHs, via synchrotron emission from non-thermal electrons accelerated at external shocks. The predicted optical transients have a shorter duration than ordinary core-collapse supernovae. Dedicated optical transient surveys can detect them, and distinguish it from ordinary SNe using the different features of its light curve and late-time spectrum. In the paper I, we investigate disk-driven outflows from the secondary BH, whereas possible signals from the primary BH will be discussed in the paper II., Comment: v3: 8 pages, 3 figures, accepted for publication in ApJ. arXiv:1702.07337v2 was split into two papers according to referee's suggestion. This is Paper I. See also arXiv:1711.01015 for Paper II

On February 17 2016, the IceCube real-time neutrino search identified, for the first time, three muon neutrino candidates arriving within 100 s of one another, consistent with coming from the same point in the sky. Such a triplet is expected once every 13.7 years as a random coincidence of background events. However, considering the lifetime of the follow-up program the probability of detecting at least one triplet from atmospheric background is 32%. Follow-up observatories were notified in order to search for an electromagnetic counterpart. Observations were obtained by Swift's X-ray telescope, by ASAS-SN, LCO and MASTER at optical wavelengths, and by VERITAS in the very-high-energy gamma-ray regime. Moreover, the Swift BAT serendipitously observed the location 100 s after the first neutrino was detected, and data from the Fermi LAT and HAWC observatory were analyzed. We present details of the neutrino triplet and the follow-up observations. No likely electromagnetic counterpart was detected, and we discuss the implications of these constraints on candidate neutrino sources such as gamma-ray bursts, core-collapse supernovae and active galactic nucleus flares. This study illustrates the potential of and challenges for future follow-up campaigns., Comment: 23 pages, 13 figures, accepted by A&A on July 30 2017

We present arguments to support the existence of weight spaces for supersymmetric field theories and identify the calculations of information about supermultiplets to define such spaces via the concept of "holoraumy." For the first time this is extended to the complex linear supermultiplet by a calculation of the commutator of supercovariant derivatives on all of its component fields., Comment: 27 pages, five figures, three tables, LaTeX twice, latest version include coding descriptions and on-line access to codes, complete `crystal' description, Univ. of Maryland Preprint #: UMDEPP--017-020, Brown Univ. Preprint #: HET-1711

We compute the CMB angular power spectrum in the presence of a radiation-like solid - elastic matter with the same pressure to energy density ratio as radiation but with nonzero shear modulus. For the values of shear modulus that are close enough to zero, so that the effect of the solid on large-scale anisotropies remains within cosmic variance, we find that there is an observable effect of the solid on small-scale anisotropies., Comment: 16 pages, 3 figures

We review the physics of GRB production by relativistic jets that start highly opaque near the central source and then expand to transparency. We discuss dissipative and radiative processes in the jet and how radiative transfer shapes the observed nonthermal spectrum released at the photosphere. A comparison of recent detailed models with observations gives estimates for important parameters of GRB jets, such as the Lorentz factor and magnetization. We also discuss predictions for GRB polarization and neutrino emission., Comment: 29 pages, 10 figures, accepted to Space Science Reviews, chapter in ISSI book "Jets and Winds in Pulsar Wind Nebulae and Gamma-ray Bursts"

We examine values of the Adinkra Holoraumy-induced Gadget representation space metric over all possible four-color, four-open node, and four-closed node adinkras. Of the 1,358,954,496 gadget matrix elements, only 226,492,416 are non-vanishing and take on one of three values: $-1/3$, $1/3$, or $1$ and thus a subspace isomorphic to a description of a body-centered tetrahedral molecule emerges., Comment: LaTeX twice, 56pp, 30 tables, 5 figures, latest version includes link to updated code, minor corrections, and additional support about inequivalent representations and tetrahedral geometry comments added along with observations about similarity with results previously found by Nekrasov