562 research outputs found
The Computational Complexity of the Game of Set and its Theoretical Applications
The game of SET is a popular card game in which the objective is to form Sets
using cards from a special deck. In this paper we study single- and multi-round
variations of this game from the computational complexity point of view and
establish interesting connections with other classical computational problems.
Specifically, we first show that a natural generalization of the problem of
finding a single Set, parameterized by the size of the sought Set is W-hard;
our reduction applies also to a natural parameterization of Perfect
Multi-Dimensional Matching, a result which may be of independent interest.
Second, we observe that a version of the game where one seeks to find the
largest possible number of disjoint Sets from a given set of cards is a special
case of 3-Set Packing; we establish that this restriction remains NP-complete.
Similarly, the version where one seeks to find the smallest number of disjoint
Sets that overlap all possible Sets is shown to be NP-complete, through a close
connection to the Independent Edge Dominating Set problem. Finally, we study a
2-player version of the game, for which we show a close connection to Arc
Kayles, as well as fixed-parameter tractability when parameterized by the
number of rounds played
Euclidean wormholes with Phantom field and Phantom field accompanied by perfect fluid
We study the classical Euclidean wormhole solutions for the gravitational
systems with minimally coupled pure Phantom field and minimally coupled Phantom
field accompanied by perfect fluid. It is shown that such solutions do exist
and then the general forms of the Phantom field potential are obtained for
which there are classical Euclidean wormhole solutions.Comment: 15 pages, major revision with perfect flui
Surface vacuum energy and stresses for a brane in de Sitter spacetime
Vacuum expectation values of the surface energy-momentum tensor is
investigated for a massless scalar field obeying mixed boundary condition on a
brane in de Sitter bulk. To generate the corresponding vacuum surface densities
we use the conformal relation between de Sitter and Rindler spacetimes.Comment: 8 pages, no figure, an appendix added, version to appear in PL
Tree-Level Stability Without Spacetime Fermions: Novel Examples in String Theory
Is perturbative stability intimately tied with the existence of spacetime
fermions in string theory in more than two dimensions? Type 0'B string theory
in ten-dimensional flat space is a rare example of a non-tachyonic,
non-supersymmetric string theory with a purely bosonic closed string spectrum.
However, all known type 0' constructions exhibit massless NSNS tadpoles
signaling the fact that we are not expanding around a true vacuum of the
theory. In this note, we are searching for perturbatively stable examples of
type 0' string theory without massless tadpoles in backgrounds with a spatially
varying dilaton. We present two examples with this property in non-critical
string theories that exhibit four- and six-dimensional Poincare invariance. We
discuss the D-branes that can be embedded in this context and the type of gauge
theories that can be constructed in this manner. We also comment on the
embedding of these non-critical models in critical string theories and their
holographic (Little String Theory) interpretation and propose a general
conjecture for the role of asymptotic supersymmetry in perturbative string
theory.Comment: harvmac, 29 pages; v2 minor changes, version to appear in JHE
Symmetric Points in the Landscape as Cosmological Attractors
In the landscape, if there is to be any prospect of scientific prediction, it
is crucial that there be states which are distinguished in some way. The
obvious candidates are states which exhibit symmetries. Here we focus on states
which exhibit discrete symmetries. Such states are rare, but one can speculate
that they are cosmological attractors. We investigate the problem in model
landscapes and cosmologies which capture some of the features of candidate flux
landscapes. In non-supersymmetric theories we find no evidence that such states
might be cosmologically favored. In supersymmetric theories, simple arguments
suggest that states which exhibit symmetries might be. Our considerations
lead us to raise questions about some popular models of eternal inflation.Comment: 27 pages, latex, minor typo correcte
Denosumab for the prevention of skeletal complications in metastatic castration-resistant prostate cancer: comparison of skeletal-related events and symptomatic skeletal events
Abstract
Background
In a phase III trial in patients with castration-resistant prostate cancer (CRPC) and bone metastases, denosumab was superior to zoledronic acid in reducing skeletal-related events (SREs; radiation to bone, pathologic fracture, surgery to bone, or spinal cord compression). This study reassessed the efficacy of denosumab using symptomatic skeletal events (SSEs) as a prespecified exploratory end point.
Patients and methods
Patients with CRPC, no previous bisphosphonate exposure, and radiographic evidence of bone metastasis were randomized to subcutaneous denosumab 120 mg plus i.v. placebo every 4 weeks (Q4W), or i.v. zoledronic acid 4 mg plus subcutaneous placebo Q4W during the blinded treatment phase. SSEs were defined as radiation to bone, symptomatic pathologic fracture, surgery to bone, or symptomatic spinal cord compression. The relationship between SSE or SRE and time to moderate/severe pain was assessed using the Brief Pain Inventory Short Form.
Results
Treatment with denosumab significantly reduced the risk of developing first SSE [HR, 0.78; 95% confidence interval (CI) 0.66–0.93; P = 0.005] and first and subsequent SSEs (rate ratio, 0.78; 95% CI 0.65–0.92; P = 0.004) compared with zoledronic acid. The treatment differences in the number of patients with SSEs or SREs were similar (n = 48 and n = 45, respectively). Among patients with no/mild pain at baseline, both SSEs and SREs were associated with moderate/severe pain development (P < 0.0001). Fewer patients had skeletal complications, particularly fractures, when defined as SSE versus SRE.
Conclusion
In patients with CRPC and bone metastases, denosumab reduced the risk of skeletal complications versus zoledronic acid regardless of whether the end point was defined as SSE or SRE
QED and String Theory
We analyze the D9-D9bar system in type IIB string theory using Dp-brane
probes. It is shown that the world-volume theory of the probe Dp-brane contains
two-dimensional and four-dimensional QED in the cases with p=1 and p=3,
respectively, and some applications of the realization of these well-studied
quantum field theories are discussed. In particular, the two-dimensional QED
(the Schwinger model) is known to be a solvable theory and we can apply the
powerful field theoretical techniques, such as bosonization, to study the
D-brane dynamics. The tachyon field created by the D9-D9bar strings appears as
the fermion mass term in the Schwinger model and the tachyon condensation is
analyzed by using the bosonized description. In the T-dualized picture, we
obtain the potential between a D0-brane and a D8-D8bar pair using the Schwinger
model and we observe that it consists of the energy carried by fundamental
strings created by the Hanany-Witten effect and the vacuum energy due to a
cylinder diagram. The D0-brane is treated quantum mechanically as a particle
trapped in the potential, which turns out to be a system of a harmonic
oscillator.
As another application, we obtain a matrix theory description of QED using
Taylor's T-duality prescription, which is actually applicable to a wide variety
of field theories including the realistic QCD. We show that the lattice gauge
theory is naturally obtained by regularizing the matrix size to be finite.Comment: 33 pages, Latex, 4 figures, a reference adde
Beyond locutionary denotations: exploring trust between practitioners and policy
This study reports the findings of a research on the trust relationship between practitioners in the Skills for Life (SfL) area and the policy that informs their practice. The exploration of this relationship was premised on an extended notion of trust relationship which draws from the Speech Act theory of Austin (1962; Searle 1969; Kissine 2008), leading to the claim that the existence of different layers of imports in textual analysis makes it possible for a trust relationship to exist between the human/physical and the non human/non physical. The study found that the majority of practitioners in the SfL field trust policy to deliver its inherent policy only to a limited extent. Amongst others, the study identified the impact of the perlocutionary import of policy text on practitioners as a viable reason for this limited level of trust. Such perlocutionary imports, it also found, have adverse impact on practitioners who are considered to have drawn from previous experience to mediate the import of contemporary policies
D-brane anti-D-brane effective action and brane interaction in open string channel
We construct the effective action of a -brane-anti--brane system by
making use of the non-abelian extension of tachyonic DBI action. We succeed the
construction by restricting the Chan-Paton factors of two non-BPS -branes
in the action to the Chan-Paton factors of a system. For the
special case that both branes are coincident, the action reduces to the one
proposed by A. Sen. \\The effective potential indicates that
when branes separation is larger than the string length scale, there are two
minima in the tachyon direction. As branes move toward each other under the
gravitational force, the tachyon tunneling from false to true vacuum may make a
bubble formation followed by a classical evolution of the bubble. On the other
hand, when branes separation is smaller than the string length scale, the
potential shows one maximum and one minimum. In this case, a homogeneous
tachyon rolling in real time makes an attractive potential for the branes
distance. This classical force is speculated to be the effective force between
the two branes.Comment: Latex, 14 pages, 1 figure, the version appears in JHE
Non-perturbative equivalences among large N gauge theories with adjoint and bifundamental matter fields
We prove an equivalence, in the large N limit, between certain U(N) gauge
theories containing adjoint representation matter fields and their orbifold
projections. Lattice regularization is used to provide a non-perturbative
definition of these theories; our proof applies in the strong coupling, large
mass phase of the theories. Equivalence is demonstrated by constructing and
comparing the loop equations for a parent theory and its orbifold projections.
Loop equations for both expectation values of single-trace observables, and for
connected correlators of such observables, are considered; hence the
demonstrated non-perturbative equivalence applies to the large N limits of both
string tensions and particle spectra.Comment: 40 pages, JHEP styl
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