347 research outputs found
Improved Bounds on the Phase Transition for the Hard-Core Model in 2-Dimensions
For the hard-core lattice gas model defined on independent sets weighted by
an activity , we study the critical activity
for the uniqueness/non-uniqueness threshold on the 2-dimensional integer
lattice . The conjectured value of the critical activity is
approximately . Until recently, the best lower bound followed from
algorithmic results of Weitz (2006). Weitz presented an FPTAS for approximating
the partition function for graphs of constant maximum degree when
where is the
infinite, regular tree of degree . His result established a certain
decay of correlations property called strong spatial mixing (SSM) on
by proving that SSM holds on its self-avoiding walk tree
where and is an ordering on the neighbors of vertex . As
a consequence he obtained that . Restrepo et al. (2011) improved Weitz's approach for
the particular case of and obtained that
. In this paper, we establish an upper bound for
this approach, by showing that, for all , SSM does not hold on
when . We also present a
refinement of the approach of Restrepo et al. which improves the lower bound to
.Comment: 19 pages, 1 figure. Polished proofs and examples compared to earlier
versio
Solertia: (vol: 1 issue: 1)
Contents:
Challenging Victorian Heteropatriarchy: Reclaiming Muted Voices in Sarah Waters’s Tipping the Velvet and Fingersmith
In what ways can concrete resources support the learning and progress of children in maths, who are lower ability
or have SEN?
In what ways have primary school teachers used technology differently to support children’s learning during remote education and how might this inform their future practice?
McMindfulness or elixir to life’s ills: What are the implications of practicing mindfulness in a secular
context?
Describe how atheism is under threat from postmodernism
Decolonising the secondary drama curriculum: an investigation into the effects and barriers of diversifying the play texts used in the classroom of a predominantly white school. What are the first steps for drama teachers in beginning this process of change
Driving the resonant quantum kicked rotor via extended initial conditions
We study the resonances of the quantum kicked rotor subjected to an extended
initial distribution. For the primary resonances we obtain the dispersion
relation for the map of this system. We find an analytical dependence of the
statistical moments on the shape of the initial distribution. For the secondary
resonances we obtain numerically a similar dependence. This allows us to devise
an extended initial condition which produces an average angular momentum
pointing in a preset direction which increases with time with a preset ratio.Comment: 6 pages, 5 figures, send to EPJ
Breakdown of correspondence in chaotic systems: Ehrenfest versus localization times
Breakdown of quantum-classical correspondence is studied on an experimentally
realizable example of one-dimensional periodically driven system. Two relevant
time scales are identified in this system: the short Ehrenfest time t_h and the
typically much longer localization time scale T_L. It is shown that
surprisingly weak modification of the Hamiltonian may eliminate the more
dramatic symptoms of localization without effecting the more subtle but
ubiquitous and rapid loss of correspondence at t_h.Comment: 4 pages, 5 figures, replaced with a version submitted to PR
Chaos in a double driven dissipative nonlinear oscillator
We propose an anharmonic oscillator driven by two periodic forces of
different frequencies as a new time-dependent model for investigating quantum
dissipative chaos. Our analysis is done in the frame of statistical ensemble of
quantum trajectories in quantum state diffusion approach. Quantum dynamical
manifestation of chaotic behavior, including the emergence of chaos, properties
of strange attractors, and quantum entanglement are studied by numerical
simulation of ensemble averaged Wigner function and von Neumann entropy.Comment: 9 pages, 18 figure
The Middle Way: East Asian masters students’ perceptions of critical argumentation in U.K. universities.
The paper explores the learning experiences of East Asian masters students in dealing with Western academic norms of critical thinking in classroom debate and assignment writing. The research takes a cultural approach, and employs grounded theory and case study methodology, the aims being for students to explain their perceptions of their personal learning journeys. The data suggest that the majority of students interviewed rejected full academic acculturation into Western norms of argumentation. They instead opted for a ‘Middle Way’ that synergizes the traditional cultural academic values held by many East Asian students with those elements of Western academic norms that are perceived to be aligned with these. This is a relatively new area of research which represents a challenge for British lecturers and students
Multiple Bifurcations in atom optics
We report the observation of multiple bifurcations in a nonlinear Hamiltionian system: laser-cooled atoms in a standing wave with single-frequency intensity modulation. We provide clear evidence of the occurrence of bifurcations by analyzing the atomic momentum distributions
Experimental study of the quantum driven pendulum and its classical analogue in atoms optics
We present experimental results for the dynamics of cold atoms in a far detuned amplitude-modulated optical standing wave. Phase-space resonances constitute distinct peaks in the atomic momentum distribution containing up to 65% of all atoms resulting from a mixed quantum chaotic phase space. We characterize the atomic behavior in classical and quantum regimes and we present the applicable quantum and classical theory, which we have developed and refined. We show experimental proof that the size and the position of the resonances in phase space can be controlled by varying several parameters, such as the modulation frequency, the scaled well depth, the modulation amplitude, and the scaled Planck's constant of the system. We have found a surprising stability against amplitude noise. We present methods to accurately control the momentum of an ensemble of atoms using these phase-space resonances which could be used for efficient phase-space state preparation
Enabling global clinical collaborations on identifiable patient data: The Minerva Initiative
The clinical utility of computational phenotyping for both genetic and rare diseases is increasingly appreciated; however, its true potential is yet to be fully realized. Alongside the growing clinical and research availability of sequencing technologies, precise deep and scalable phenotyping is required to serve unmet need in genetic and rare diseases. To improve the lives of individuals affected with rare diseases through deep phenotyping, global big data interrogation is necessary to aid our understanding of disease biology, assist diagnosis, and develop targeted treatment strategies. This includes the application of cutting-edge machine learning methods to image data. As with most digital tools employed in health care, there are ethical and data governance challenges associated with using identifiable personal image data. There are also risks with failing to deliver on the patient benefits of these new technologies, the biggest of which is posed by data siloing. The Minerva Initiative has been designed to enable the public good of deep phenotyping while mitigating these ethical risks. Its open structure, enabling collaboration and data sharing between individuals, clinicians, researchers and private enterprise, is key for delivering precision public health
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