2,361 research outputs found
"Mississippi Territory."
No full textThe map was engraved by Francis Shallus for Philadelphia-based publisher Mathew Carey's "Carey's General Atlas, Improved and Enlarged: Being a Collection of Maps of the World and Quarters, Their Principal Empires, Kingdoms, &c.
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
Francis Celeste Le Blond CdV (from House Representatives, 38th Congress Album)
No full textThe photograph features a portrait of Francis C. Le Blond (United States Representatives from Ohio). On its verso, it has a Mathew Brady backmark. The CdV is included in an album containing CdVs of Lincoln\u27s cabinet members as well as senators and representatives from the 38th Congress.https://scholarsjunction.msstate.edu/fvw-cdv/1178/thumbnail.jp
Partially Polynomial Kernels for Set Cover and Test Cover
No full textIn a typical covering problem we are given a universe U of size n, a family S (S could be given implicitly) of size m and an integer k and the objective is to check whether there exists a subfamily S' \subseteq S of size at most k satisfying some desired properties. If S' is required to contain all the elements of U then it corresponds to the classical Set Cover problem. On the other hand if we require S' to satisfy the property that for every pair of elements x,y \in U there exists a set S \in S' such that |S \cap {x,y}|=1 then it corresponds to the Test Cover problem. In this paper we consider a natural parameterization of Set Cover and Test Cover. More precisely, we study the (n-k)-Set Cover and (n-k)-Test Cover problems, where the objective is to find a subfamily S' of size at most n-k satisfying the respective properties, from the kernelization perspective. It is known in the literature that both (n-k)-Set Cover and (n-k)-Test Cover do not admit polynomial kernels (under some well known complexity theoretic assumptions). However, in this paper we show that they do admit "partially polynomial kernels". More precisely, we give polynomial time algorithms that take as input an instance (U,S,k) of (n-k)-Set Cover (n-k)-Test Cover) and return an equivalent instance (~U,~S,~k) of (n-k)-Set Cover (respectively (n-k)-Test Cover) with ~k <= k and |~U|= O(k^2) (|~U|=O(k^7)). These results allow us to generalize, improve and unify several results known in the literature. For example, these immediately imply traditional kernels when input instances satisfy certain "sparsity properties". Using a part of our kernelization algorithm for (n-k)-Set Cover, we also get an improved FPT algorithm for this problem which runs in time O(4^k*k^{\O(1)}*(m+n)) improving over the previous best of O(8^{k+o(k)}*(m+n)^{O(1)}). On the other hand the partially polynomial kernel for (n-k)-Test Cover implies the first single exponential FPT algorithm, an algorithm with running time O(2^{O(k^2)}*(m+n)^{O(1)}). We believe such an approach will also be useful for other covering problems as well
CA_funding_options_report_UAR_RR2_submit – Supplemental material for Fiscal Secession: An Analysis of Special Assessment Financing in California
No full textSupplemental material, CA_funding_options_report_UAR_RR2_submit for Fiscal Secession: An Analysis of Special Assessment Financing in California by Mathew D. McCubbins and Ellen C. Seljan in Urban Affairs Review</p
Genetic diversity of Crocus antalyensis B. Mathew (Iridaceae) and a new subspecies from southern Anatolia
No full textCrocus antalyensis B. Mathew is a bulbous plant endemic to Turkey. It is morphologically variable within the western part of Anatolia. Amplified fragment length polymorphism (AFLP) marker system was used to detect genetic variation among the Crocus taxa. Twenty-two primer combinations were used to screen for polymorphism among the samples. Genetic variation ranged from 0.44 to 0.69. We demonstrated the efficiency of the AFLP marker system for discriminating between individual C. antalyensis specimens. A high level of genetic variation was present among C. antalyensis specimens collected from different locations in Turkey. We also observed that C. antalyensis subspp. are genetically distinct from their relative Crocus flavus Haw. subsp. dissectus Baytop & B. Mathew. A new subspecies of C. antalyensis B. Mathew from southern Turkey is described. It is characterized by striped outer perianth segments, waist-shaped flowers, and glabrous throat of the perianth. A composite image of the new subspecies is presented.Research Fund of Istanbul University, Istanbul, TurkeyIstanbul University [4155]; Turkish Research CouncilTurkiye Bilimsel ve Teknolojik Arastirma Kurumu (TUBITAK) [108G096]The first author appreciates Helmut Kerndorff and Eric Pasche for sharing of their knowledge of the genus Crocus. We are grateful to Prof. Dr. Neriman Ozhatay (ISTE) for her scientific advice. We also thank Mark Garland (Micanopy, Florida, USA) for Latin translation. This work was supported by the Research Fund of Istanbul University, Istanbul, Turkey (project number 4155). We also kindly thank the Turkish Research Council for supporting PhD student H. Betul Kaya's scholarship (project number 108G096)
On the Road to an Atomic- and Molecular-Level Understanding of Friction
No full textAbstractThe following article is an edited transcript based on the MRS Medal presentation given by C. Mathew Mate of IBM Almaden Research Center on November 29, 2001, at the Materials Research Society Fall Meeting in Boston. Mate received the Medal for his “pioneering studies of friction at the atomic and molecular levels.” This presentation describes some of his efforts at understanding friction at the atomic level. The starting point for the author was the invention of the friction force microscope and the first observation of atomic-scale friction in 1987. Soon afterward came other applications of force microscopy, leading toward a greater understanding of friction, lubrication, and wear. These studies also have had an impact on the understanding of lubricant films in disk drives and are now aiding the development of nanoscale devices such as the “molecular raft,” an 8-Å-thick island of squalane floating on a thicker squalane film that could potentially be used to transport nanoscale objects.</jats:p
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
A mediterranean passage by water, from London to Bristol, &c., and from Lynne to Yarmouth, and so consequently to the city of York for the great advancement of trade & traffique / by Francis Mathew, Esquire.
No full text- …
