6,431 research outputs found
The Accuracy of Perturbative Master Equations
We consider open quantum systems with dynamics described by master equations
that have perturbative expansions in the system-environment interaction. We
show that, contrary to intuition, full-time solutions of order-2n accuracy
require an order-(2n+2) master equation. We give two examples of such
inaccuracies in the solutions to an order-2n master equation: order-2n
inaccuracies in the steady state of the system and order-2n positivity
violations, and we show how these arise in a specific example for which exact
solutions are available. This result has a wide-ranging impact on the validity
of coupling (or friction) sensitive results derived from second-order
convolutionless, Nakajima-Zwanzig, Redfield, and Born-Markov master equations.Comment: 6 pages, 0 figures; v2 updated references; v3 updated references,
extension to full-time and nonlocal regime
Chromosome 9p deletion in clear cell renal cell carcinoma predicts recurrence and survival following surgery
BACKGROUND: Wider clinical applications of 9p status in clear cell renal cell carcinoma (ccRCC) are limited owing to the lack of validation and consensus for interphase fluorescent in situ hybridisation (I-FISH) scoring technique. The aim of this study was to analytically validate the applicability of I-FISH in assessing 9p deletion in ccRCC and to clinically assess its long-term prognostic impact following surgical excision of ccRCC. METHODS: Tissue microarrays were constructed from 108 renal cell carcinoma (RCC) tumour paraffin blocks. Interphase fluorescent in situ hybridisation analysis was undertaken based on preset criteria by two independent observers to assess interobserver variability. 9p status in ccRCC tumours was determined and correlated to clinicopathological variables, recurrence-free survival and disease-specific survival. RESULTS: There were 80 ccRCCs with valid 9p scoring and a median follow-up of 95 months. Kappa statistic for interobserver variability was 0.71 (good agreement). 9p deletion was detected in 44% of ccRCCs. 9p loss was associated with higher stage, larger tumours, necrosis, microvascular and renal vein invasion, and higher SSIGN (stage, size, grade and necrosis) score. Patients with 9p-deleted ccRCC were at a higher risk of recurrence (P=0.008) and RCC-specific mortality (P=0.001). On multivariate analysis, 9p deletion was an independent predictor of recurrence (hazard ratio 4.323; P=0.021) and RCC-specific mortality (hazard ratio 4.603; P=0.007). The predictive accuracy of SSIGN score improved from 87.7% to 93.1% by integrating 9p status to the model (P=0.001). CONCLUSIONS: Loss of 9p is associated with aggressive ccRCC and worse prognosis in patients following surgery. Our findings independently confirm the findings of previous reports relying on I-FISH to detect 9p (CDKN2A) deletion
Interplay of structure and spin-orbit strength in magnetism of metal-benzene sandwiches: from single molecules to infinite wires
Based on first-principles density functional theory calculations we explore
electronic and magnetic properties of experimentally producible sandwiches and
infinite wires made of repeating benzene molecules and transition-metal atoms
of V, Nb, and Ta. We describe the bonding mechanism in the molecules and in
particular concentrate on the origin of magnetism in these structures. We find
that all the considered systems have sizable magnetic moments and ferromagnetic
spin-ordering, with the single exception of the V3-Bz4 molecule. By including
the spin-orbit coupling into our calculations we determine the easy and hard
axes of the magnetic moment, the strength of the uniaxial magnetic anisotropy
energy (MAE), relevant for the thermal stability of magnetic orientation, and
the change of the electronic structure with respect to the direction of the
magnetic moment, important for spin-transport properties. While for the V-based
compounds the values of the MAE are only of the order of 0.05-0.5 meV per metal
atom, increasing the spin-orbit strength by substituting V with heavier Nb and
Ta allows to achieve an increase in anisotropy values by one to two orders of
magnitude. The rigid stability of magnetism in these compounds together with
the strong ferromagnetic ordering makes them attractive candidates for
spin-polarized transport applications. For a Nb-benzene infinite wire the
occurrence of ballistic anisotropic magnetoresistance is demonstrated.Comment: 23 pages, 8 figure
An overview of Viscosity Solutions of Path-Dependent PDEs
This paper provides an overview of the recently developed notion of viscosity
solutions of path-dependent partial di erential equations. We start by a quick
review of the Crandall- Ishii notion of viscosity solutions, so as to motivate
the relevance of our de nition in the path-dependent case. We focus on the
wellposedness theory of such equations. In partic- ular, we provide a simple
presentation of the current existence and uniqueness arguments in the
semilinear case. We also review the stability property of this notion of
solutions, in- cluding the adaptation of the Barles-Souganidis monotonic scheme
approximation method. Our results rely crucially on the theory of optimal
stopping under nonlinear expectation. In the dominated case, we provide a
self-contained presentation of all required results. The fully nonlinear case
is more involved and is addressed in [12]
Non-Markovian Dynamics and Entanglement of Two-level Atoms in a Common Field
We derive the stochastic equations and consider the non-Markovian dynamics of
a system of multiple two-level atoms in a common quantum field. We make only
the dipole approximation for the atoms and assume weak atom-field interactions.
From these assumptions we use a combination of non-secular open- and
closed-system perturbation theory, and we abstain from any additional
approximation schemes. These more accurate solutions are necessary to explore
several regimes: in particular, near-resonance dynamics and low-temperature
behavior. In detuned atomic systems, small variations in the system energy
levels engender timescales which, in general, cannot be safely ignored, as
would be the case in the rotating-wave approximation (RWA). More problematic
are the second-order solutions, which, as has been recently pointed out, cannot
be accurately calculated using any second-order perturbative master equation,
whether RWA, Born-Markov, Redfield, etc.. This latter problem, which applies to
all perturbative open-system master equations, has a profound effect upon
calculation of entanglement at low temperatures. We find that even at zero
temperature all initial states will undergo finite-time disentanglement
(sometimes termed "sudden death"), in contrast to previous work. We also use
our solution, without invoking RWA, to characterize the necessary conditions
for Dickie subradiance at finite temperature. We find that the subradiant
states fall into two categories at finite temperature: one that is temperature
independent and one that acquires temperature dependence. With the RWA there is
no temperature dependence in any case.Comment: 17 pages, 13 figures, v2 updated references, v3 clarified results and
corrected renormalization, v4 further clarified results and new Fig. 8-1
James J. Kaput (1942â2005) imagineer and futurologist of mathematics education
Jim Kaput lived a full life in mathematics education and we have many reasons to be grateful to him, not only for his vision of the use of technology in mathematics, but also for his fundamental humanity. This paper considers the origins of his âbig ideasâ as he lived through the most amazing innovations in technology that have changed our lives more in a generation than in many centuries before. His vision continues as is exemplified by the collected papers in this tribute to his life and work
Purification and characterization of N-ethylmaleimide-insensitive phosphatidic acid phosphohydrolase (PAP2) from rat liver
Ising-link Quantum Gravity
We define a simplified version of Regge quantum gravity where the link
lengths can take on only two possible values, both always compatible with the
triangle inequalities. This is therefore equivalent to a model of Ising spins
living on the links of a regular lattice with somewhat complicated, yet local
interactions. The measure corresponds to the natural sum over all 2^links
configurations, and numerical simulations can be efficiently implemented by
means of look-up tables. In three dimensions we find a peak in the ``curvature
susceptibility'' which grows with increasing system size. However, the value of
the corresponding critical exponent as well as the behavior of the curvature at
the transition differ from that found by Hamber and Williams for the Regge
theory with continuously varying link lengths.Comment: 11 page
Beyond the Fokker-Planck equation: Pathwise control of noisy bistable systems
We introduce a new method, allowing to describe slowly time-dependent
Langevin equations through the behaviour of individual paths. This approach
yields considerably more information than the computation of the probability
density. The main idea is to show that for sufficiently small noise intensity
and slow time dependence, the vast majority of paths remain in small space-time
sets, typically in the neighbourhood of potential wells. The size of these sets
often has a power-law dependence on the small parameters, with universal
exponents. The overall probability of exceptional paths is exponentially small,
with an exponent also showing power-law behaviour. The results cover time spans
up to the maximal Kramers time of the system. We apply our method to three
phenomena characteristic for bistable systems: stochastic resonance, dynamical
hysteresis and bifurcation delay, where it yields precise bounds on transition
probabilities, and the distribution of hysteresis areas and first-exit times.
We also discuss the effect of coloured noise.Comment: 37 pages, 11 figure
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