241 research outputs found
STRATIGRAPHY AND FUSULINIDS OF THE KASIMOVIAN AND LOWER GZHELIAN(UPPER CARBONIFEROUS) IN THE SOUTHWESTERN DARVAZ (PAMIR)
A detailed fusulinid biostratigraphic zonation of the Kasimovian and lowermost Gzhelian in southwestern Darvaz is proposed. Based on the investigation of five stratigraphic sections, five local fusulinid zones were established. These zones correlate with their chronostratigraphic equivalents in the East-European Platform and in the Urals, Arctic and Carnic Alps regions. Eighty-seven species and subspecies, which belong to 18 genera and 7 families of fusulinids, were identified in the Kasimovian and lowermost Gzhelian of Darvaz. Among them, two genera (Kushanella and Darvasoschwagerina), one subgenus (Tumefactus), and 24 species are new ( i. e. Fusiella segyrdashtiensis, Quasifusulina pseudotenuissima, Protriticites putrjai, P. compactus, Obsoletes darvasicus, Schwagerinoides (Schwagerinoides) pamiricus, Schw. (Tumefactus) oblisus, Montiparus kushanicus, M. rauserae, M. pigmaeus, M. memorabilis, M. citreum, M. hirsutus, M. dubius, M. stuckenbergiformis, M. desinens, Triticites umbonoplicatiformis, T. licis, Rauserites concinnus, R. jucundus, R. darvasicus, Kushanella globosa, K. insueta, Darvasoschwagerina donbasica)
Development of an Advanced Force Field for Water using Variational Energy Decomposition Analysis
Given the piecewise approach to modeling intermolecular interactions for
force fields, they can be difficult to parameterize since they are fit to data
like total energies that only indirectly connect to their separable functional
forms. Furthermore, by neglecting certain types of molecular interactions such
as charge penetration and charge transfer, most classical force fields must
rely on, but do not always demonstrate, how cancellation of errors occurs among
the remaining molecular interactions accounted for such as exchange repulsion,
electrostatics, and polarization. In this work we present the first generation
of the (many-body) MB-UCB force field that explicitly accounts for the
decomposed molecular interactions commensurate with a variational energy
decomposition analysis, including charge transfer, with force field design
choices that reduce the computational expense of the MB-UCB potential while
remaining accurate. We optimize parameters using only single water molecule and
water cluster data up through pentamers, with no fitting to condensed phase
data, and we demonstrate that high accuracy is maintained when the force field
is subsequently validated against conformational energies of larger water
cluster data sets, radial distribution functions of the liquid phase, and the
temperature dependence of thermodynamic and transport water properties. We
conclude that MB-UCB is comparable in performance to MB-Pol, but is less
expensive and more transferable by eliminating the need to represent
short-ranged interactions through large parameter fits to high order
polynomials
Approximately coloring graphs without long induced paths
It is an open problem whether the 3-coloring problem can be solved in
polynomial time in the class of graphs that do not contain an induced path on
vertices, for fixed . We propose an algorithm that, given a 3-colorable
graph without an induced path on vertices, computes a coloring with
many colors. If the input graph is
triangle-free, we only need many
colors. The running time of our algorithm is if the input
graph has vertices and edges
Complexity of Coloring Graphs without Paths and Cycles
Let and denote a path on vertices and a cycle on
vertices, respectively. In this paper we study the -coloring problem for
-free graphs. Maffray and Morel, and Bruce, Hoang and Sawada,
have proved that 3-colorability of -free graphs has a finite forbidden
induced subgraphs characterization, while Hoang, Moore, Recoskie, Sawada, and
Vatshelle have shown that -colorability of -free graphs for
does not. These authors have also shown, aided by a computer search, that
4-colorability of -free graphs does have a finite forbidden induced
subgraph characterization. We prove that for any , the -colorability of
-free graphs has a finite forbidden induced subgraph
characterization. We provide the full lists of forbidden induced subgraphs for
and . As an application, we obtain certifying polynomial time
algorithms for 3-coloring and 4-coloring -free graphs. (Polynomial
time algorithms have been previously obtained by Golovach, Paulusma, and Song,
but those algorithms are not certifying); To complement these results we show
that in most other cases the -coloring problem for -free
graphs is NP-complete. Specifically, for we show that -coloring is
NP-complete for -free graphs when and ; for we show that -coloring is NP-complete for -free graphs
when , ; and additionally, for , we show that
-coloring is also NP-complete for -free graphs if and
. This is the first systematic study of the complexity of the
-coloring problem for -free graphs. We almost completely
classify the complexity for the cases when , and
identify the last three open cases
Exhaustive generation of -critical -free graphs
We describe an algorithm for generating all -critical -free
graphs, based on a method of Ho\`{a}ng et al. Using this algorithm, we prove
that there are only finitely many -critical -free graphs, for
both and . We also show that there are only finitely many
-critical graphs -free graphs. For each case of these cases we
also give the complete lists of critical graphs and vertex-critical graphs.
These results generalize previous work by Hell and Huang, and yield certifying
algorithms for the -colorability problem in the respective classes.
Moreover, we prove that for every , the class of 4-critical planar
-free graphs is finite. We also determine all 27 4-critical planar
-free graphs.
We also prove that every -free graph of girth at least five is
3-colorable, and determine the smallest 4-chromatic -free graph of
girth five. Moreover, we show that every -free graph of girth at least
six and every -free graph of girth at least seven is 3-colorable. This
strengthens results of Golovach et al.Comment: 17 pages, improved girth results. arXiv admin note: text overlap with
arXiv:1504.0697
List coloring in the absence of a linear forest.
The k-Coloring problem is to decide whether a graph can be colored with at most k colors such that no two adjacent vertices receive the same color. The Listk-Coloring problem requires in addition that every vertex u must receive a color from some given set L(u)⊆{1,…,k}. Let Pn denote the path on n vertices, and G+H and rH the disjoint union of two graphs G and H and r copies of H, respectively. For any two fixed integers k and r, we show that Listk-Coloring can be solved in polynomial time for graphs with no induced rP1+P5, hereby extending the result of Hoàng, Kamiński, Lozin, Sawada and Shu for graphs with no induced P5. Our result is tight; we prove that for any graph H that is a supergraph of P1+P5 with at least 5 edges, already List 5-Coloring is NP-complete for graphs with no induced H
Parameterized Complexity of Maximum Edge Colorable Subgraph
A graph is {\em -edge colorable} if there is a coloring , such that for distinct , we have
. The {\sc Maximum Edge-Colorable Subgraph} problem
takes as input a graph and integers and , and the objective is to
find a subgraph of and a -edge-coloring of , such that . We study the above problem from the viewpoint of Parameterized
Complexity. We obtain \FPT\ algorithms when parameterized by: the vertex
cover number of , by using {\sc Integer Linear Programming}, and ,
a randomized algorithm via a reduction to \textsc{Rainbow Matching}, and a
deterministic algorithm by using color coding, and divide and color. With
respect to the parameters , where is one of the following: the
solution size, , the vertex cover number of , and l -
{\mm}(G), where {\mm}(G) is the size of a maximum matching in ; we show
that the (decision version of the) problem admits a kernel with vertices. Furthermore, we show that there is no kernel of size
, for any and computable
function , unless \NP \subseteq \CONPpoly
Resonant scattering of spin waves from a region of inhomogeneous magnetic field in a ferromagnetic film
The transmission of a dipole-dominated spin wave in a ferromagnetic film
through a localised inhomogeneity in the form of a magnetic field produced by a
dc current through a wire placed on the film surface was studied experimentally
and theoretically. It was shown that the amplitude and phase of the transmitted
wave can be simultaneously affected by the current induced field, a feature
that will be relevant for logic based on spin wave transport.
The direction of the current creates either a barrier or well for spin wave
transmission. The main observation is that the current dependence of the
amplitude of the spin wave transmitted through the well inhomogeneity is
non-monotonic. The dependence has a minimum and an additional maximum. A theory
was constructed to clarify the nature of the maximum. It shows that the
transmission of spin waves through the inhomogeneity can be considered as a
scattering process and that the additional maximum is a scattering resonance
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