Edge-dominating cycles in graphs

AbstractA set S of vertices in a graph G is said to be an edge-dominating set if every edge in G is incident with a vertex in S. A cycle in G is said to be a dominating cycle if its vertex set is an edge-dominating set. Nash-Williams [Edge-disjoint hamiltonian circuits in graphs with vertices of large valency, Studies in Pure Mathematics, Academic Press, London, 1971, pp. 157–183] has proved that every longest cycle in a 2-connected graph of order n and minimum degree at least 13(n+2) is a dominating cycle. In this paper, we prove that for a prescribed positive integer k, under the same minimum degree condition, if n is sufficiently large and if we take k disjoint cycles so that they contain as many vertices as possible, then these cycles form an edge-dominating set. Nash-Williams’ Theorem corresponds to the case of k=1 of this result

Clustering Properties of Low-Luminosity Star-Forming galaxies at z = 0.24 and 0.40 in the Subaru Deep Field

We present our analysis on the clustering properties of star-forming galaxies selected by narrow-band excesses in the Subaru Deep Field. Specifically we focus on Halpha emitting galaxies at z = 0.24 and z = 0.40 in the same field, to investigate possible evolutionary signatures of clustering properties of star-forming galaxies. Based on the analysis on 228 Halpha emitting galaxies with 39.8 < log L(Halpha) < 40.8 at z = 0.40, we find that their two-point correlation function is estimated as xi = (r/1.62^{+0.64}_{-0.50} Mpc)^{-1.84 +/- 0.08}. This is similar to that of Halpha emitting galaxies in the same Halpha luminosity range at z = 0.24, xi = (r/1.88^{+0.60}_{-0.49} Mpc)^{-1.89 +/- 0.07}. These correlation lengths are smaller than those for the brighter galaxy sample studied by Meneux et al. (2006) in the same redshift range. The evolution of correlation length between z = 0.24 and z = 0.40 is interpreted by the gravitational growth of the dark matter halos.Comment: 16 pages, 7 figures, PASJ, Vol.60, No.6, in pres

Lyα view around a z = 2.84 hyperluminous QSO at a node of the cosmic web

We report on the results of deep and wide-field (1.1 deg²) narrow-band observations with Subaru/Hyper Suprime-Cam (HSC) of a field around a hyperluminous QSO (HLQSO), HS1549+1549+1919, residing in a protocluster at z = 2.84, to map the large-scale structure of Lyα emitters (LAEs). One HSC pointing enables us to detect 3490 LAEs and 76 extended Lyα blobs (LABs), probing diverse environments from voids to protoclusters. The HLQSO is found to be near the center of the protocluster, which corresponds to the intersection of ∼100 comoving Mpc-scale structures of LAEs. LABs are basically distributed along the large-scale structure, with larger ones particularly clustering around the HLQSO, confirming a previously noted tendency of LABs to prefer denser environments. Moreover, the shapes of LABs near the HLQSO appear to be aligned with the large-scale structure. Finally, a deep Lyα image reveals a diffuse Lyα nebula along a filamentary structure with no luminous UV/sub-mm counterpart. We suggest that the diffuse nebula is due to a cold filament with high clumping factor illuminated by the QSO, with the required high clumpiness provided by unresolved residing halos of mass ≤10⁹⁻¹⁰ M_⊙⁠

Assessment of biological dosimetric margin for stereotactic body radiation therapy

Purpose: To develop a novel biological dosimetric margin (BDM) and to create a biological conversion factor (BCF) that compensates for the difference between physical dosimetric margin (PDM) and BDM, which provides a novel scheme of a direct estimation of the BDM from the physical dose (PD) distribution. Methods: The offset to isocenter was applied in 1‐mm steps along left‐right (LR), anterior‐posterior (AP), and cranio‐caudal (CC) directions for 10 treatment plans of lung stereotactic body radiation therapy (SBRT) with a prescribed dose of 48 Gy. These plans were recalculated to biological equivalent dose (BED) by the linearquadratic model for the dose per fraction (DPF) of d = 3–20 Gy/fr and α/β= 3 - 10. BDM and PDM were defined so that the region that satisfied that the dose covering 95% (or 98%) of the clinical target volume was greater than or equal to the 90% of the prescribed PD and BED, respectively. An empirical formula of the BCF was created as a function of the DPF. Results: There was no significant difference between LR and AP directions for neither the PDM nor BDM. On the other hand, BDM and PDM in the CC direction were significantly larger than in the other directions. BCFs of D95% and D98% were derived for the transverse (LR and AP) and longitudinal (CC) directions. Conclusions: A novel scheme to directly estimate the BDM using the BCF was developed. This technique is expected to enable the BED‐based SBRT treatment planning using PD‐based treatment planning systems

The Voice Conversion Challenge 2018: Promoting Development of Parallel and Nonparallel Methods

We present the Voice Conversion Challenge 2018, designed as a follow up to the 2016 edition with the aim of providing a common framework for evaluating and comparing different state-of-the-art voice conversion (VC) systems. The objective of the challenge was to perform speaker conversion (i.e. transform the vocal identity) of a source speaker to a target speaker while maintaining linguistic information. As an update to the previous challenge, we considered both parallel and non-parallel data to form the Hub and Spoke tasks, respectively. A total of 23 teams from around the world submitted their systems, 11 of them additionally participated in the optional Spoke task. A large-scale crowdsourced perceptual evaluation was then carried out to rate the submitted converted speech in terms of naturalness and similarity to the target speaker identity. In this paper, we present a brief summary of the state-of-the-art techniques for VC, followed by a detailed explanation of the challenge tasks and the results that were obtained.Comment: Accepted for Speaker Odyssey 201

The Final Months of Massive Star Evolution from the Circumstellar Environment around SN Ic 2020oi

We present the results of Atacama Large Millimeter/submillimeter Array (ALMA) band 3 observations of the nearby type Ic supernova (SN) 2020oi. Under the standard assumptions on the SN-circumstellar medium (CSM) interaction and the synchrotron emission, the data indicate that the CSM structure deviates from a smooth distribution expected from the steady-state mass loss in the very vicinity of the SN (≲1015 cm), which is then connected to the outer smooth distribution (⪆1016 cm). This structure is further confirmed through the light-curve modeling of the whole radio data set as combined with the previously reported data at lower frequency. Because this is an explosion of a bare carbon-oxygen (C+O) star with a fast wind, we can trace the mass-loss history of the progenitor of SN 2020oi in the final year. The inferred nonsmooth CSM distribution corresponds to fluctuations on the subyear timescale in the mass-loss history toward the SN explosion. Our finding suggests that the pre-SN activity is likely driven by the accelerated change in the nuclear burning stage in the last moments just before the massive star´s demise. The structure of the CSM derived in this study is beyond the applicability of the other methods at optical wavelengths, highlighting the importance and uniqueness of quick follow-up observations of SNe by ALMA and other radio facilities.Fil: Maeda, Keiichi. Kyoto University; JapónFil: Chandra, Poonam. National Centre For Radio Astrophysics India; IndiaFil: Matsuoka, Tomoki. Kyoto University; JapónFil: Ryder, Stuart. Macquarie University; AustraliaFil: Moriya, Takashi J.. Monash University; AustraliaFil: Kuncarayakti, Hanindyo. University of Turku; FinlandiaFil: Lee, Shiu Hang. Kyoto University; JapónFil: Kundu, Esha. Curtin University; AustraliaFil: Patnaude, Daniel. Smithsonian Astrophysical Observatory; Estados UnidosFil: Saito, Tomoki. University Of Hyogo; JapónFil: Folatelli, Gaston. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Astrofísica La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas. Instituto de Astrofísica La Plata; Argentin

The final months of massive star evolution from the circumstellar environment around SN Ic 2020oi

We present the results of ALMA band 3 observations of a nearby type Ic supernova (SN) 2020oi. Under the standard assumptions on the SN-circumstellar medium (CSM) interaction and the synchrotron emission, the data indicate that the CSM structure deviates from a smooth distribution expected from the steady-state mass loss in the very vicinity of the SN (~10^{15} cm), which is then connected to the outer smooth distribution (~10^{16} cm). This structure is further confirmed through the light curve modeling of the whole radio data set as combined with data at lower frequency previously reported. Being an explosion of a bare carbon-oxygen (C+O) star having a fast wind, we can trace the mass-loss history of the progenitor of SN 2020oi in the final year. The inferred non-smooth CSM distribution corresponds to fluctuations on the sub-year time scale in the mass-loss history toward the SN explosion. Our finding suggests that the pre-SN activity is likely driven by the accelerated change in the nuclear burning stage in the last moments just before the massive star's demise. The structure of the CSM derived in this study is beyond the applicability of the other methods at optical wavelengths, highlighting an importance and uniqueness of quick follow-up observations of SNe by ALMA and other radio facilities.Comment: 20 pages, 8 figures, 1 table. Accepted for publication in Ap