Fractal Weyl law for Linux Kernel Architecture

We study the properties of spectrum and eigenstates of the Google matrix of a directed network formed by the procedure calls in the Linux Kernel. Our results obtained for various versions of the Linux Kernel show that the spectrum is characterized by the fractal Weyl law established recently for systems of quantum chaotic scattering and the Perron-Frobenius operators of dynamical maps. The fractal Weyl exponent is found to be $\nu \approx 0.63$ that corresponds to the fractal dimension of the network $d \approx 1.2$. The eigenmodes of the Google matrix of Linux Kernel are localized on certain principal nodes. We argue that the fractal Weyl law should be generic for directed networks with the fractal dimension $d<2$.Comment: RevTex 6 pages, 7 figs, linked to arXiv:1003.5455[cs.SE]. Research at http://www.quantware.ups-tlse.fr/, Improved version, changed forma

Decoherence induced by a chaotic environment: A quantum walker with a complex coin

We study the differences between the process of decoherence induced by chaotic and regular environments. For this we analyze a family of simple models wich contain both regular and chaotic environments. In all cases the system of interest is a "quantum walker", i.e. a quantum particle that can move on a lattice with a finite number of sites. The walker interacts with an environment wich has a D dimensional Hilbert space. The results we obtain suggest that regular and chaotic environments are not distinguishable from each other in a (short) timescale t*, wich scales with the dimensionality of the environment as t*~log(D). Howeber, chaotic environments continue to be effective over exponentially longer timescales while regular environments tend to reach saturation much sooner. We present both numerical and analytical results supporting this conclusion. The family of chaotic evolutions we consider includes the so-called quantum multi-baker-map as a particular case.Comment: 7 pages, 8 figure

Ulam method for the Chirikov standard map

We introduce a generalized Ulam method and apply it to symplectic dynamical maps with a divided phase space. Our extensive numerical studies based on the Arnoldi method show that the Ulam approximant of the Perron-Frobenius operator on a chaotic component converges to a continuous limit. Typically, in this regime the spectrum of relaxation modes is characterized by a power law decay for small relaxation rates. Our numerical data show that the exponent of this decay is approximately equal to the exponent of Poincar\'e recurrences in such systems. The eigenmodes show links with trajectories sticking around stability islands.Comment: 13 pages, 13 figures, high resolution figures available at: http://www.quantware.ups-tlse.fr/QWLIB/ulammethod/ minor corrections in text and fig. 12 and revised discussio

Using the Hadamard and related transforms for simplifying the spectrum of the quantum baker's map

We rationalize the somewhat surprising efficacy of the Hadamard transform in simplifying the eigenstates of the quantum baker's map, a paradigmatic model of quantum chaos. This allows us to construct closely related, but new, transforms that do significantly better, thus nearly solving for many states of the quantum baker's map. These new transforms, which combine the standard Fourier and Hadamard transforms in an interesting manner, are constructed from eigenvectors of the shift permutation operator that are also simultaneous eigenvectors of bit-flip (parity) and possess bit-reversal (time-reversal) symmetry.Comment: Version to appear in J. Phys. A. Added discussions; modified title; corrected minor error

Efficacy and safety of ixekizumab through 52 weeks in two phase 3, randomised, controlled clinical trials in patients with active radiographic axial spondyloarthritis (COAST-V and COAST-W).

OBJECTIVES: To investigate the efficacy and safety of ixekizumab for up to 52 weeks in two phase 3 studies of patients with active radiographic axial spondyloarthritis (r-axSpA) who were biological disease-modifying antirheumatic drug (bDMARD)-naive (COAST-V) or tumour necrosis factor inhibitor (TNFi)-experienced (COAST-W). METHODS: Adults with active r-axSpA were randomised 1:1:1:1 (n=341) to 80 mg ixekizumab every 2 (IXE Q2W) or 4 weeks (IXE Q4W), placebo (PBO) or 40 mg adalimumab Q2W (ADA) in COAST-V and 1:1:1 (n=316) to IXE Q2W, IXE Q4W or PBO in COAST-W. At week 16, patients receiving ixekizumab continued their assigned treatment; patients receiving PBO or ADA were rerandomised 1:1 to IXE Q2W or IXE Q4W (PBO/IXE, ADA/IXE) through week 52. RESULTS: In COAST-V, Assessment of SpondyloArthritis international Society 40 (ASAS40) responses rates (intent-to-treat population, non-responder imputation) at weeks 16 and 52 were 48% and 53% (IXE Q4W); 52% and 51% (IXE Q2W); 36% and 51% (ADA/IXE); 19% and 47% (PBO/IXE). Corresponding ASAS40 response rates in COAST-W were 25% and 34% (IXE Q4W); 31% and 31% (IXE Q2W); 14% and 39% (PBO/IXE). Both ixekizumab regimens sustained improvements in disease activity, physical function, objective markers of inflammation, QoL, health status and overall function up to 52 weeks. Safety through 52 weeks of ixekizumab was consistent with safety through 16 weeks. CONCLUSION: The significant efficacy demonstrated with ixekizumab at week 16 was sustained for up to 52 weeks in bDMARD-naive and TNFi-experienced patients. bDMARD-naive patients initially treated with ADA demonstrated further numerical improvements after switching to ixekizumab. Safety findings were consistent with the known safety profile of ixekizumab. TRIAL REGISTRATION NUMBER: NCT02696785/NCT02696798

Hypersensitivity and chaos signatures in the quantum baker's maps

Classical chaotic systems are distinguished by their sensitive dependence on initial conditions. The absence of this property in quantum systems has lead to a number of proposals for perturbation-based characterizations of quantum chaos, including linear growth of entropy, exponential decay of fidelity, and hypersensitivity to perturbation. All of these accurately predict chaos in the classical limit, but it is not clear that they behave the same far from the classical realm. We investigate the dynamics of a family of quantizations of the baker's map, which range from a highly entangling unitary transformation to an essentially trivial shift map. Linear entropy growth and fidelity decay are exhibited by this entire family of maps, but hypersensitivity distinguishes between the simple dynamics of the trivial shift map and the more complicated dynamics of the other quantizations. This conclusion is supported by an analytical argument for short times and numerical evidence at later times.Comment: 32 pages, 6 figure

Relativistic graphene ratchet on semidisk Galton board

Using extensive Monte Carlo simulations we study numerically and analytically a photogalvanic effect, or ratchet, of directed electron transport induced by a microwave radiation on a semidisk Galton board of antidots in graphene. A comparison between usual two-dimensional electron gas (2DEG) and electrons in graphene shows that ratchet currents are comparable at very low temperatures. However, a large mean free path in graphene should allow to have a strong ratchet transport at room temperatures. Also in graphene the ratchet transport emerges even for unpolarized radiation. These properties open promising possibilities for room temperature graphene based sensitive photogalvanic detectors of microwave and terahertz radiation.Comment: 4 pages, 4 figures. Research done at Quantware http://www.quantware.ups-tlse.fr/. More detailed analysis is give

An inflammation-targeting hydrogel for local drug delivery in inflammatory bowel disease

There is a clinical need for new, more effective treatments for chronic and debilitating inflammatory bowel disease (IBD), including Crohn’s disease and ulcerative colitis. Targeting drugs selectively to the inflamed intestine may improve therapeutic outcomes and minimize systemic toxicity. We report the development of an inflammation-targeting hydrogel (IT-hydrogel) that acts as a drug delivery system to the inflamed colon. Hydrogel microfibers were generated from ascorbyl palmitate, an amphiphile that is generally recognized as safe (GRAS) by the U.S. Food and Drug Administration. IT-hydrogel microfibers loaded with the anti-inflammatory corticosteroid dexamethasone (Dex) were stable, released drug only upon enzymatic digestion, and demonstrated preferential adhesion to inflamed epithelial surfaces in vitro and in two mouse colitis models in vivo. Dex-loaded IT-hydrogel enemas, but not free Dex enemas, administered every other day to mice with colitis resulted in a significant reduction in inflammation and were associated with lower Dex peak serum concentrations and, thus, less systemic drug exposure. Ex vivo analysis of colon tissue samples from patients with ulcerative colitis demonstrated that IT-hydrogel microfibers adhered preferentially to mucosa from inflamed lesions compared with histologically normal sites. The IT-hydrogel drug delivery platform represents a promising approach for targeted enema-based therapies in patients with colonic IBD

Distribution of resonances in the quantum open baker map

We study relevant features of the spectrum of the quantum open baker map. The opening consists of a cut along the momentum $p$ direction of the 2-torus phase space, modelling an open chaotic cavity. We study briefly the classical forward trapped set and analyze the corresponding quantum nonunitary evolution operator. The distribution of eigenvalues depends strongly on the location of the escape region with respect to the central discontinuity of this map. This introduces new ingredients to the association among the classical escape and quantum decay rates. Finally, we could verify that the validity of the fractal Weyl law holds in all cases.Comment: 6 pages, 7 figures, accepted for publication in Phys. Rev.