15,791 research outputs found
D-branes at Toric Singularities: Model Building, Yukawa Couplings and Flavour Physics
We discuss general properties of D-brane model building at toric
singularities. Using dimer techniques to obtain the gauge theory from the
structure of the singularity, we extract results on the matter sector and
superpotential of the corresponding gauge theory. We show that the number of
families in toric phases is always less than or equal to three, with a unique
exception being the zeroth Hirzebruch surface. With the physical input of three
generations we find that the lightest family of quarks is massless and the
masses of the other two can be hierarchically separated. We compute the CKM
matrix for explicit models in this setting and find the singularities possess
sufficient structure to allow for realistic mixing between generations and CP
violation.Comment: 55 pages, v2: typos corrected, minor comments adde
1-String CZ-Representation of Planar Graphs
In this paper, we prove that every planar 4-connected graph has a
CZ-representation---a string representation using paths in a rectangular grid
that contain at most one vertical segment. Furthermore, two paths representing
vertices intersect precisely once whenever there is an edge between
and . The required size of the grid is
Optimally fast incremental Manhattan plane embedding and planar tight span construction
We describe a data structure, a rectangular complex, that can be used to
represent hyperconvex metric spaces that have the same topology (although not
necessarily the same distance function) as subsets of the plane. We show how to
use this data structure to construct the tight span of a metric space given as
an n x n distance matrix, when the tight span is homeomorphic to a subset of
the plane, in time O(n^2), and to add a single point to a planar tight span in
time O(n). As an application of this construction, we show how to test whether
a given finite metric space embeds isometrically into the Manhattan plane in
time O(n^2), and add a single point to the space and re-test whether it has
such an embedding in time O(n).Comment: 39 pages, 15 figure
Hamiltonicity and -hypergraphs
We define and study a special type of hypergraph. A -hypergraph ), where is a partition of , is an
-uniform hypergraph having vertices partitioned into classes of
vertices each. If the classes are denoted by , ,...,, then a
subset of of size is an edge if the partition of formed by
the non-zero cardinalities , ,
is . The non-empty intersections are called the parts
of , and denotes the number of parts. We consider various types
of cycles in hypergraphs such as Berge cycles and sharp cycles in which only
consecutive edges have a nonempty intersection. We show that most
-hypergraphs contain a Hamiltonian Berge cycle and that, for and , a -hypergraph always contains a sharp
Hamiltonian cycle. We also extend this result to -intersecting cycles
Bypasses for rectangular diagrams. Proof of Jones' conjecture and related questions
In the present paper a criteria for a rectangular diagram to admit a
simplification is given in terms of Legendrian knots. It is shown that there
are two types of simplifications which are mutually independent in a sense. A
new proof of the monotonic simplification theorem for the unknot is given. It
is shown that a minimal rectangular diagram maximizes the Thurston--Bennequin
number for the corresponding Legendrian links. Jones' conjecture about the
invariance of the algebraic number of intersections of a minimal braid
representing a fixed link type is proved.Comment: 50 pages, 62 Figures, numerous minor correction
Exact algorithms for the order picking problem
Order picking is the problem of collecting a set of products in a warehouse
in a minimum amount of time. It is currently a major bottleneck in supply-chain
because of its cost in time and labor force. This article presents two exact
and effective algorithms for this problem. Firstly, a sparse formulation in
mixed-integer programming is strengthened by preprocessing and valid
inequalities. Secondly, a dynamic programming approach generalizing known
algorithms for two or three cross-aisles is proposed and evaluated
experimentally. Performances of these algorithms are reported and compared with
the Traveling Salesman Problem (TSP) solver Concorde
A Simplification of Combinatorial Link Floer Homology
We define a new combinatorial complex computing the hat version of link Floer
homology over Z/2Z, which turns out to be significantly smaller than the
Manolescu-Ozsvath-Sarkar one.Comment: 20 pages with figures, final version printed in JKTR, v.3 of
Oberwolfach Proceeding
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