1,817 research outputs found
Minimum Weight Resolving Sets of Grid Graphs
For a simple graph and for a pair of vertices , we say
that a vertex resolves and if the shortest path from to
is of a different length than the shortest path from to . A set of
vertices is a resolving set if for every pair of vertices
and in , there exists a vertex that resolves and . The
minimum weight resolving set problem is to find a resolving set for a
weighted graph such that is minimum, where is
the weight of vertex . In this paper, we explore the possible solutions of
this problem for grid graphs where . We give
a complete characterisation of solutions whose cardinalities are 2 or 3, and
show that the maximum cardinality of a solution is . We also provide a
characterisation of a class of minimals whose cardinalities range from to
.Comment: 21 pages, 10 figure
The two-child limit & 'choices' over family size: when policy presentation collides with lived experiences
The two-child limit restricts the child element in Universal Credit and Tax Credits to two children in a household (for children born after April 2017). One objective of the two-child limit is to influence the fertility decisions of parents in (or at risk of) poverty; therefore it is especially important to explore and understand its fertility effects. Previous analysis of administrative birth records suggests that the two-child limit had only a very small impact on the fertility of third and subsequent births in England and Wales. In this paper, we contrast the policy assumptions underpinning the two-child limit with everyday realities of fertility decision making. To do this, we draw on qualitative interviews conducted with those directly affected by the policy. This reveals a series of mismatches between policy presentation and lived realities, which help explain the absence of sizeable fertility effects. This also points to the importance of better and more sustained engagement with qualitative evidence in the design and review of policies. It is especially vital to continue to monitor the impact of the two-child limit, given the extent of the harms it can cause, and its status as an internationally unusual and significant policy
Chiral density wave versus pion condensation at finite density
The quark-meson model is often used as an effective low-energy model for QCD
to study the chiral transition at finite temperature , baryon chemical
potential , and isospin chemical potential . The parameters of
the model are determined by matching the meson and quark masses, as well as the
pion decay constant to their physical values using the on-shell and modified
minimal subtraction schemes. In this paper, we study the possibility of
different phases at zero temperature. In particular, we investigate the
competition between an inhomogeneous chiral condensate and a pion condensate.
For the inhomogeneity, we use a chiral-density wave ansatz. For a sigma mass of
MeV, we find that an inhomogeneous chiral condensate exist only for pion
masses below approximately 37 MeV. We also show that due to our parameter
fixing, the onset of pion condensation takes place exactly at
in accordance with exact results.Comment: 14 pages and 11 figs. v2: Minor changes, matches published version in
PR
On-shell parameter fixing in the quark-meson model
The quark-meson model is often used as an effective low-energy model for QCD to study the chiral transition at finite temperature T and baryon chemical potential μB. The parameters in the quark-meson model can be found by expressing them in terms of the sigma mass mσ, the pion mass mπ, the constituent quark mass mq and the pion decay constant fπ. In practice, this matching is done at tree level, which is inconsistent once loop effects of the effective potential are taken into account. We show how to properly perform the matching in the quark-meson model by using the on-shell and the minimal subtraction renormalization schemes relating the physical masses and the pion decay constant to the running mass parameter and couplings. We map out the phase diagram in the μB–T plane and compare our results with other approximations.acceptedVersio
Pion condensation and phase diagram in the Polyakov-loop quark-meson model
We use the Polyakov-loop extended two-flavor quark-meson model as a low-energy effective model for QCD to study the phase diagram in the μI–T planewhere μI is the isospin chemical potential. In particular, we focus on the Bose condensation of charged pions. At T ¼ 0, the onset of pion condensation is at μI ¼ 1 2mπ in accordance with exact results. The phase transition to a Bose-condensed phase is of second order for all values of μI and in the Oð2Þuniversality class. The chiral critical line joins the critical line for pion condensation at a point whose position depends on the Polyakov-loop potential and the sigma mass. For larger values of μI these curves are on top of each other. The deconfinement line enters smoothly the phase with the broken Oð2Þ symmetry. We compare our results with recent lattice simulations and find overall good agreement.publishedVersio
THE EFFECT OF TALO-CRURAL JOINT MANIPULATION ON RANGE OF MOTION AT THE ANKLE JOINT IN SUBJECTS WITH A HISTORY OF ANKLE INJURY
Introduction: There is little research available on the effects of peripheral joint manipulation. Only a few studies have examined the effect of manipulation on ankle range of motion, with conflicting results. This study aimed to determine whether a single high-velocity, low-amplitude (HVLA) thrust manipulation to the talo-crural joint altered ankle range of motion in subjects with a history of lateral ligament sprain
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