Stochastic and Collective Properties of Nonlinear Oscillators

Two systems of nonlinear oscillators are considered: (a) a single periodically driven nonlinear oscillator interacting with a heat bath, which may operate in the regime of bistability or monostability, and (b) a one-dimensional chain of self-sustaining phase oscillators with nearest-neighbor interaction. For a single oscillator we analyze the scaling crossovers in the thermal activation barrier between the two stable states. The rate of metastable decay in nonequilibrium systems is expected to display scaling behavior: the logarithm of the decay rate should scale as a power of the distance to a bifurcation point where the metastable state disappears. We establish the range where different scaling behavior is displayed and show how the crossover between different types of scaling occurs. Using the instanton method, we map numerically the entire parameter range of bistability and find the regions where the scaling exponents are 1 or 3/2, depending on the damping. The exponent 3/2 is found to extend much further from the bifurcation then where it would be expected to hold as a result of an overdamped soft mode. Additionally, we uncover a new scaling behavior with exponent of ≈1.3 that extends beyond the close vicinity of the bifurcation point. We also study the pattern of fluctuational trajectories in the monostable regime. For nonequilibrium systems, fluctuational and relaxational trajectories are not simply related by time-reversibility, as is the case in thermal equilibrium. One of the consequences of this is the onset of singularities in the pattern of fluctuational trajectories, where most probable paths to neighboring states are far away from each other. This also creates nonsmoothness in the probability distribution of the system in its phase space. We discover that the pattern of optimal paths in equilibrium systems is fragile with respect to the driving strength F, and investigate how the singularities occur as the system is driven away from equilibrium. As the strength of the driving F approaches zero, the cusp of the spiral caustic system recedes to larger radius R and the angle of the cusp also decreases. The dependence of R on F displays two scaling laws with crossovers, where the scaling exponents depend on the damping. For the one-dimensional chain of nearest-neighbor coupled phase oscillators, we develop a renormalization group method to investigate synchronization clusters. We apply it numerically to Lorentzian distributions of intrinsic frequencies and couplings and investigate the statistics of the resultant cluster sizes and frequencies. We find that the distributions of sizes of frequency clusters are exponential, with a characteristic length. The dependence of this length upon parameters of these Lorentzian distributions develops an asymptotic power law with an exponent of 0.48 ± 0.02. The findings obtained with the renormalization group are compared with numerical simulations of the equations of motion of the chain, with an excellent agreement in all the aforementioned quantities.</p

Tivozanib versus sorafenib as initial targeted therapy for patients with metastatic renal cell carcinoma: Results from a phase III trial

© 2013 by American Society of Clinical Oncology. Purpose: Tivozanib is a potent and selective tyrosine kinase inhibitor of vascular endothelial growth factor receptor 1 (VEGFR1), -2, and -3. This phase III trial compared tivozanib with sorafenib as initial targeted therapy in patients with metastatic renal cell carcinoma (RCC). Patients and Methods: Patients with metastatic RCC, with a clear cell component, prior nephrectomy, measurable disease, and 0 or 1 prior therapies for metastatic RCC were randomly assigned to tivozanib or sorafenib. Prior VEGF-targeted therapy and mammalian target of rapamycin inhibitor were not permitted. The primary end point was progression-free survival (PFS) by independent review. Results: A total of 517 patients were randomly assigned to tivozanib (n = 260) or sorafenib (n = 257). PFS was longer with tivozanib than with sorafenib in the overall population (median, 11.9 v 9.1 months; hazard ratio [HR], 0.797; 95% CI, 0.639 to 0.993; P = .042). One hundred fifty-six patients (61%) who progressed on sorafenib crossed over to receive tivozanib. The final overall survival (OS) analysis showed a trend toward longer survival on the sorafenib arm than on the tivozanib arm (median, 29.3 v 28.8 months; HR, 1.245; 95% CI, 0.954 to 1.624; P = .105). Adverse events (AEs) more common with tivozanib than with sorafenib were hypertension (44% v 34%) and dysphonia (21% v 5%). AEs more common with sorafenib than with tivozanib were hand-foot skin reaction (54% v 14%) and diarrhea (33% v 23%). Conclusion: Tivozanib demonstrated improved PFS, but not OS, and a differentiated safety profile, compared with sorafenib, as initial targeted therapy for metastatic RCC

Search for Scalar Diphoton Resonances in the Mass Range 65−60065-600 GeV with the ATLAS Detector in pppp Collision Data at s\sqrt{s} = 8 TeVTeV

A search for scalar particles decaying via narrow resonances into two photons in the mass range 65–600 GeV is performed using $20.3\text{}\text{}{\mathrm{fb}}^{-1}$ of $\sqrt{s}=8\text{}\text{}\mathrm{TeV}$ $pp$ collision data collected with the ATLAS detector at the Large Hadron Collider. The recently discovered Higgs boson is treated as a background. No significant evidence for an additional signal is observed. The results are presented as limits at the 95% confidence level on the production cross section of a scalar boson times branching ratio into two photons, in a fiducial volume where the reconstruction efficiency is approximately independent of the event topology. The upper limits set extend over a considerably wider mass range than previous searches

Measurements of the Total and Differential Higgs Boson Production Cross Sections Combining the H??????? and H???ZZ*???4??? Decay Channels at s\sqrt{s}=8??????TeV with the ATLAS Detector

Measurements of the total and differential cross sections of Higgs boson production are performed using 20.3~fb$^{-1}$ of $pp$ collisions produced by the Large Hadron Collider at a center-of-mass energy of $\sqrt{s} = 8$ TeV and recorded by the ATLAS detector. Cross sections are obtained from measured $H \rightarrow \gamma \gamma$ and $H \rightarrow ZZ ^{*}\rightarrow 4\ell$ event yields, which are combined accounting for detector efficiencies, fiducial acceptances and branching fractions. Differential cross sections are reported as a function of Higgs boson transverse momentum, Higgs boson rapidity, number of jets in the event, and transverse momentum of the leading jet. The total production cross section is determined to be $\sigma_{pp \to H} = 33.0 \pm 5.3 \, ({\rm stat}) \pm 1.6 \, ({\rm sys}) \mathrm{pb}$. The measurements are compared to state-of-the-art predictions.Measurements of the total and differential cross sections of Higgs boson production are performed using 20.3  fb-1 of pp collisions produced by the Large Hadron Collider at a center-of-mass energy of s=8  TeV and recorded by the ATLAS detector. Cross sections are obtained from measured H→γγ and H→ZZ*→4ℓ event yields, which are combined accounting for detector efficiencies, fiducial acceptances, and branching fractions. Differential cross sections are reported as a function of Higgs boson transverse momentum, Higgs boson rapidity, number of jets in the event, and transverse momentum of the leading jet. The total production cross section is determined to be σpp→H=33.0±5.3 (stat)±1.6 (syst)  pb. The measurements are compared to state-of-the-art predictions.Measurements of the total and differential cross sections of Higgs boson production are performed using 20.3 fb$^{-1}$ of $pp$ collisions produced by the Large Hadron Collider at a center-of-mass energy of $\sqrt{s} = 8$ TeV and recorded by the ATLAS detector. Cross sections are obtained from measured $H \rightarrow \gamma \gamma$ and $H \rightarrow ZZ ^{*}\rightarrow 4\ell$ event yields, which are combined accounting for detector efficiencies, fiducial acceptances and branching fractions. Differential cross sections are reported as a function of Higgs boson transverse momentum, Higgs boson rapidity, number of jets in the event, and transverse momentum of the leading jet. The total production cross section is determined to be $\sigma_{pp \to H} = 33.0 \pm 5.3 \, ({\rm stat}) \pm 1.6 \, ({\rm sys}) \mathrm{pb}$. The measurements are compared to state-of-the-art predictions

Search for Higgs and ZZ Boson Decays to J/ψγJ/\psi\gamma and Υ(nS)γ\Upsilon(nS)\gamma with the ATLAS Detector

A search for the decays of the Higgs and $Z$ bosons to $J/\psi\gamma$ and $\Upsilon(nS)\gamma$ ($n=1,2,3$) is performed with $pp$ collision data samples corresponding to integrated luminosities of up to $20.3\mathrm{fb}^{-1}$ collected at $\sqrt{s}=8\mathrm{TeV}$ with the ATLAS detector at the CERN Large Hadron Collider. No significant excess of events is observed above expected backgrounds and 95% CL upper limits are placed on the branching fractions. In the $J/\psi\gamma$ final state the limits are $1.5\times10^{-3}$ and $2.6\times10^{-6}$ for the Higgs and $Z$ bosons, respectively, while in the $\Upsilon(1S,2S,3S)\,\gamma$ final states the limits are $(1.3,1.9,1.3)\times10^{-3}$ and $(3.4,6.5,5.4)\times10^{-6}$, respectively