5,153 research outputs found
FIGURE 1. Myristica beddomei subsp. beddomei A. Twig with leaves and fruit. B. Male inflorescence. C. Female inflorescence. D. Male flower. E. Androecium, exposed. F. Female flower. G. Gynoecium exposed. H. Fruits. I. Arillate seed. J in Status of the subspecies of Myristica beddomei (Myristicaceae), endemic to the Western Ghats, India
No full textFIGURE 1. Myristica beddomei subsp. beddomei A. Twig with leaves and fruit. B. Male inflorescence. C. Female inflorescence. D. Male flower. E. Androecium, exposed. F. Female flower. G. Gynoecium exposed. H. Fruits. I. Arillate seed. J. Bark exudate.Published as part of Govind, Murugan Govindakurup & Dan, Mathew, 2022, Status of the subspecies of Myristica beddomei (Myristicaceae), endemic to the Western Ghats, India, pp. 261-269 in Phytotaxa 541 (3) on page 264, DOI: 10.11646/phytotaxa.541.3.5, http://zenodo.org/record/639264
On the Kernel and Related Problems in Interval Digraphs
No full textGiven a digraph G, a set X ⊆ V(G) is said to be an absorbing set (resp. dominating set) if every vertex in the graph is either in X or is an in-neighbour (resp. out-neighbour) of a vertex in X. A set S ⊆ V(G) is said to be an independent set if no two vertices in S are adjacent in G. A kernel (resp. solution) of G is an independent and absorbing (resp. dominating) set in G. The problem of deciding if there is a kernel (or solution) in an input digraph is known to be NP-complete. Similarly, the problems of computing a minimum cardinality kernel, absorbing set (or dominating set) and the problems of computing a maximum cardinality kernel, independent set are all known to be NP-hard for general digraphs. We explore the algorithmic complexity of these problems in the well known class of interval digraphs. A digraph G is an interval digraph if a pair of intervals (S_u,T_u) can be assigned to each vertex u of G such that (u,v) ∈ E(G) if and only if S_u ∩ T_v ≠ ∅. Many different subclasses of interval digraphs have been defined and studied in the literature by restricting the kinds of pairs of intervals that can be assigned to the vertices. We observe that several of these classes, like interval catch digraphs, interval nest digraphs, adjusted interval digraphs and chronological interval digraphs, are subclasses of the more general class of reflexive interval digraphs - which arise when we require that the two intervals assigned to a vertex have to intersect. We see as our main contribution the identification of the class of reflexive interval digraphs as an important class of digraphs. We show that all the problems mentioned above are efficiently solvable, in most of the cases even linear-time solvable, in the class of reflexive interval digraphs, but are APX-hard on even the very restricted class of interval digraphs called point-point digraphs, where the two intervals assigned to each vertex are required to be degenerate, i.e. they consist of a single point each. The results we obtain improve and generalize several existing algorithms and structural results for reflexive interval digraphs. We also obtain some new results for undirected graphs along the way: (a) We get an O(n(n+m)) time algorithm for computing a minimum cardinality (undirected) independent dominating set in cocomparability graphs, which slightly improves the existing O(n³) time algorithm for the same problem by Kratsch and Stewart; and (b) We show that the Red Blue Dominating Set problem, which is NP-complete even for planar bipartite graphs, is linear-time solvable on interval bigraphs, which is a class of bipartite (undirected) graphs closely related to interval digraphs
Cubicity, Degeneracy, and Crossing Number
No full textA k-box B=(R_1,R_2,...,R_k), where each R_i is a closed interval on the real line, is defined to be the Cartesian product R_1 X R_2 X ... X R_k. If each R_i is a unit length interval, we call B a k-cube. Boxicity of a graph G, denoted as box(G), is the minimum integer k such that G is an intersection graph of k-boxes. Similarly, the cubicity of G, denoted as cub(G), is the minimum integer k such that G is an intersection graph of k-cubes.
It was shown in [L. Sunil Chandran, Mathew C. Francis, and Naveen Sivadasan. Representing graphs as the intersection of axis-parallel cubes. MCDES-2008, IISc Centenary Conference, available at CoRR, abs/cs/0607092, 2006.] that, for a graph G with maximum degree \Delta, cub(G) <= \lceil 4(\Delta +1) ln n\rceil. In this paper we show that, for a k-degenerate graph G, cub(G) <= (k+2) \lceil 2e log n \rceil. Since k is at most \Delta and can be much lower, this clearly is a stronger result. We also give an efficient deterministic algorithm that runs in O(n^2k) time to output a 8k(\lceil 2.42 log n\rceil + 1) dimensional cube representation for G.
The crossing number of a graph G, denoted as CR(G), is the minimum number of crossing pairs of edges, over all drawings of G in the plane. An important consequence of the above result is that if the crossing number of a graph G is t, then box(G) is O(t^{1/4}{\lceil log t\rceil}^{3/4}) . This bound is tight upto a factor of O((log t)^{3/4}).
Let (P,\leq) be a partially ordered set and let G_{P} denote its underlying comparability graph. Let dim(P) denote the poset dimension of P. Another interesting consequence of our result is to show that dim(P) \leq 2(k+2) \lceil 2e \log n \rceil, where k denotes the degeneracy of G_{P}. Also, we get a deterministic algorithm that runs in O(n^2k) time to construct a 16k(\lceil 2.42 log n\rceil + 1) sized realizer for P. As far as we know, though very good upper bounds exist for poset dimension in terms of maximum degree of its underlying comparability graph, no upper bounds in terms of the degeneracy of the underlying comparability graph is seen in the literature
Correction to: The role of resection in hepatocellular carcinoma BCLC stage B: A multi-institutional patient-level meta-analysis and systematic review (Langenbeck's Archives of Surgery, (2024), 409, 1, (277), 10.1007/s00423-024-03466-x)
No full textCorrection to: Langenbeck’s Archives of Surgery (2024) 409:277. https://doi.org/10.1007/s00423-024-03466-x. This article unfortunately contained a mistake. The author name ‘Mathew Vithayathil’ was incorrectly written as ‘Vithayathil Mathew K.’. The original article has been corrected
[Samuel G. Goodrich, head-and-shoulders portrait, three-quarters to the left, wearing spectacles]
No full textAuthor, editor, publisher, known as Peter Parley.Identification from engraving by Bannister in Memorial History of Hartford County, Conn., 1866, 1:162.Scratched on back of plate: 166.Hallmark: Rinhart 9.DAG no. 217 is a reversed copy of this image.Original served by appointment only.Produced by Mathew Brady's studio.Transfer; U.S. War College; 1920; (DLC/PP-1920:46153).Forms part of: Daguerreotype collection (Library of Congress)
[Samuel G. Goodrich, head-and-shoulders portrait, three-quarters to the right]
No full textAuthor, editor, publisher, known as Peter Parley.Identification from engraving by Bannister in Memorial History of Hartford County, Conn., 1886, 1:162.Scratched on back of plate: 217.Hallmark: [asterisk paschal lamb] Brevite 40.Copy of DAG no. 166.Original served by appointment only.Produced by Mathew Brady's studio.Transfer; U.S. War College; 1920; (DLC/PP-1920:46153).Forms part of: Daguerreotype collection (Library of Congress)
A new and accurate map of New South Wales [cartographic material] with Norfolk and Lord Howe's Islands Port Jackson &c. from actual surveys /
No full textEngraved map of the East coast of Australia from the Furneaux Islands to Endeavour Islands, and of the South Pacific Ocean and islands including the Solomon Islands and New Caledonia.; Insets: Ld. Howe's Island. Scale [ca. 1:250 000] -- An accurate survey of Norfolk Island. Scale [ca. 1:50 000] -- Port Jackson, Botany Bay &c. Scale ca.1:600 000.; Plate 55 from: Carey's General atlas. Philadelphia : M. Carey and Son, 1817.; Philips, 4311.; Tooley, Printed maps of New South Wales 1773-1873 (Map Collectors Circle no. 44), 32.Carey's General atla
The two-loop QCD correction to massive spin-2 resonance → qq ̄ g
No full textThe two-loop QCD correction to massive spin-2 graviton decaying to q+ q ̄ + g is presented considering a generic universal spin-2 coupling to the SM through the conserved energy-momentum tensor. Such a massive spin-2 particle can arise in extra-dimensional models. The ultraviolet and infrared structure of the QCD amplitudes are studied. In dimensional regularization, the infrared pole structure is in agreement with Catani’s proposal, confirming the universal factorization property of QCD amplitudes, even with the spin-2 tensorial coupling
Mutation analysis of the Fanconi Anaemia group A, C, E, F and G genes in sporadic acute myeloid leukaemia
No full textIsothermal diffusion coefficients for sodium chloride-magnesium chloride-water at 25°C. 3. Low magnesium chloride concentrations with a wide range of sodium chloride concentrations
No full textIsothermal interdiffusion coeffs. have been measured by Gouy interferometry for the system NaCl(1)-MgCl2(2)-H2O at 25 °C. Diffusion coeffs. have been obtained for 5 sets of total mean concns. of C1 + C2 = 0.536, 1.053, 2.05, 3.05, and 3.80 mol dm-3, for which the concns. C2 of MgCl2 are kept small. The main-term diffusion coeffs. D11 and D22 vary modestly from their values at infinite diln. as the NaCl concn. is increased. However, the cross-term diffusion coeff. is D12, Which relates the coupled flow of NaCl to the concn. gradient of MgCl2, increases sharply as the total concn. increases. It becomes even larger than both main-term diffusion coeffs. at higher NaCl concns. Thus, a gradient of MgCl2 will cause a greater flow of NaCl than will the same gradient of NaCl itself. Also a gradient of MgCl2 will cause NaCl to diffuse faster than MgCl2 itself. When combined with diffusion data for other salt ratios, yield the tracer-diffusion coeff. of Mg2+ in NaCl solns. Densities were also obtained in this study. These diffusion and d. data are part of a systematic study of this system at LLNL
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