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The established thermodynamic formalism of chaotic dynamics, valid at statistical equilibrium, is here generalized to systems out of equilibrium that have yet to relax to a steady state. A relation between information, escape rate, and the phase-space average of an integrated observable (e.g., Lyapunov exponent, diffusion coefficient) is obtained for finite time. Most notably, the thermodynamic treatment may predict the phase-space profile of any integrated observable for finite time, from the leading and subleading eigenfunctions of the Perron-Frobenius or Koopman transfer operator. Examples of that equivalence are shown, and the theory is tested analytically on the Bernoulli map while numerically on the perturbed cat map, the Hénon map, and the Ikeda map, all paradigms of chaos.

We outline formal and physical similarities between the quantum dynamics of open systems and the mesoscopic description of classical systems affected by weak noise. The main tool of our interest is the dissipative Wigner equation, which, for suitable timescales, becomes analogous to the Fokker-Planck equation describing classical advection and diffusion. This correspondence allows, in principle, to surmise a finite resolution, other than the Planck scale, for the quantized state space of the open system, particularly meaningful when the latter underlies chaotic classical dynamics. We provide representative examples of the quantum-stochastic parallel with noisy Hopf cycles and Van der Pol-type oscillators.

We report the numerical observation of scarring, which is enhancement of probability density around unstable periodic orbits of a chaotic system, in the eigenfunctions of the classical Perron-Frobenius operator of noisy Anosov ("perturbed cat") maps, as well as in the noisy Bunimovich stadium. A parallel is drawn between classical and quantum scars, based on the unitarity or nonunitarity of the respective propagators. For uniformly hyperbolic systems such as the cat map, we provide a mechanistic explanation for the classical phase-space localization detected, based on the distribution of finite-time Lyapunov exponents, and the interplay of noise with deterministic dynamics. Classical scarring can be measured by studying autocorrelation functions and their power spectra.

Background and Objectives: Peach gibberellin-regulated protein (peamaclein) has recently emerged as a relevant food allergen in cypress pollen-hypersensitive patients. Objective: We investigated monosensitization to peamaclein among Italian cypress pollen-allergic patients., Material and Methods: A total of 835 cypress pollen-hypersensitive patients from 28 Italian allergy centers underwent a thorough work-up to determine food-allergic reactions and performed skin prick testing with a commercial peach extract containing peamaclein. IgE to rPru p 3 was measured in peach reactors, and those with negative results were enrolled as potentially monosensitized to peamaclein. IgE reactivity to rPru p 7 was evaluated using immunoblot and an experimental ImmunoCAP with rPru p 7., Results: Skin prick tests were positive to peach in 163 patients (19.5%); however, 127 (77.9%) were excluded because they reacted to Pru p 3. Twenty-four patients (14.7%) corresponding to 2.8% of the entire study population) were considered potentially monosensitized to peamaclein. No geographic preference was observed. Seventeen of the 24 patients (70.8%) had a history of food allergy, mainly to peach (n=15). Additional offending foods included other Rosaceae, citrus fruits, fig, melon, tree nuts, and kiwi. On peach immunoblot, only 3 of 18 putative peamaclein-allergic patients reacted to a band at about 7 kDa; an additional 4 patients reacted at about 50-60 kDa. Ten of 18 patients (56%) had a positive result for Pru p 7 on ImmunoCAP., Conclusion: Allergy and sensitization to peamaclein seem rare in Italy. Most patients react to peach, although other Rosaceae fruits and several citrus fruits may also be offending foods. Peach and cypress pollen probably also share cross-reacting allergens other than peamaclein.

Summary: The current therapy with direct trombin inhibitors (DTI) is indicated for the prevention of stroke in non-valvular atrial fibrillation. Side effects are reported, particularly skin hypersensitivity, for this whole category of drugs as well as for other modern antiplatelet and anticoagulant drugs. For their clinical features, these reactions appear as delayed T-cell mediated drug hypersensitivity, but at present there are no diagnostic methods of investigation. We reported a case of delayed skin reaction to edoxaban and we found the non-irritant concentration for patch test in the whole category of drugs. The patch test resulted positive for edoxaban. A successive challenge with alternative DTIs and/or a switch to warfarin is proposed as alternative therapy.

We present tocilizumab desensitization of a 47-year-old woman affected by rheumatoid arthritis with full body delayed erythematous urticarial reaction. Skin test for tocilizumab gave cutaneous reaction after 6 h at 20 mg/mL. The schedule of desensitization was then adapted for non-immediate reaction. We prepared a desensitization procedure reaching the cumulative dose of 516 mg in 5 weeks. After 6 months, the repetition of skin tests had a negative result, with demonstration of tolerance induction. Today the patient has good control of the disease., (© 2018 S. Karger AG, Basel.)

A deformed dielectric microcavity is used as an experimental platform for the analysis of the statistics of chaotic resonances, in the perspective of testing fractal Weyl laws at optical frequencies. In order to surmount the difficulties that arise from reading strongly overlapping spectra, we exploit the mixed nature of the phase space at hand, and only count the high-Q whispering-gallery modes (WGMs) directly. That enables us to draw statistical information on the more lossy chaotic resonances, coupled to the high-Q regular modes via dynamical tunneling. Three different models [classical, Random-Matrix-Theory (RMT) based, semiclassical] to interpret the experimental data are discussed. On the basis of least-squares analysis, theoretical estimates of Ehrenfest time, and independent measurements, we find that a semiclassically modified RMT-based expression best describes the experiment in all its realizations, particularly when the resonator is coupled to visible light, while RMT alone still works quite well in the infrared. In this work we reexamine and substantially extend the results of a short paper published earlier [L. Wang et al., Phys. Rev. E 93, 040201(R) (2016)2470-004510.1103/PhysRevE.93.040201].

Distributions of eigenmodes are widely concerned in both bounded and open systems. In the realm of chaos, counting resonances can characterize the underlying dynamics (regular vs chaotic), and is often instrumental to identify classical-to-quantum correspondence. Here, we study, both theoretically and experimentally, the statistics of chaotic resonances in an optical microcavity with a mixed phase space of both regular and chaotic dynamics. Information on the number of chaotic modes is extracted by counting regular modes, which couple to the former via dynamical tunneling. The experimental data are in agreement with a known semiclassical prediction for the dependence of the number of chaotic resonances on the number of open channels, while they deviate significantly from a purely random-matrix-theory-based treatment, in general. We ascribe this result to the ballistic decay of the rays, which occurs within Ehrenfest time, and importantly, within the time scale of transient chaos. The present approach may provide a general tool for the statistical analysis of chaotic resonances in open systems.

The finest state-space resolution that can be achieved in a physical dynamical system is limited by the presence of noise. In the weak-noise approximation, the stochastic neighborhoods of deterministic periodic orbits can be computed from distributions stationary under the action of a local Fokker-Planck operator and its adjoint. We derive explicit formulas for widths of these distributions in the case of chaotic dynamics, when the periodic orbits are hyperbolic. The resulting neighborhoods form a basis for functions on the attractor. The global stationary distribution, needed for calculation of long-time expectation values of observables, can be expressed in this basis.

We introduce a single-channel opening in a random Hamiltonian and a quantized chaotic map: localization on the opening occurs as a sensible deviation of the wave-function statistics from the predictions of random matrix theory, even in the semiclassical limit. Increasing the coupling to the open channel in the quantum model, we observe a similar picture to resonance trapping, made of a few fast-decaying states, whose left (right) eigenfunctions are entirely localized on the (preimage of the) opening, and plentiful long-lived states, whose probability density is instead suppressed at the opening. For the latter, we derive and test a linear relation between the wave-function intensities and the decay rates, similar to the Breit-Wigner law. We then analyze the statistics of the eigenfunctions of the corresponding (discretized) classical propagator, finding a similar behavior to the quantum system only in the weak-coupling regime.

A quantized chaotic map exhibiting localization of wave function intensity is opened. We investigate how such patterns as scars in the Husimi distributions are influenced by the losses through a number of numerical experiments. We find the scars to relocate on the stable or unstable manifolds depending on the position of the opening, and provide a classical argument to explain the observations. For asymmetrically introduced openings mode interaction contributes to determine the localization patterns. We finally show examples of similar localization in a simulated dielectric microcavity.

All physical systems are affected by some noise that limits the resolution that can be attained in partitioning their state space. For chaotic, locally hyperbolic flows, this resolution depends on the interplay of the local stretching or contraction and the smearing due to noise. We propose to determine the "finest attainable" partition for a given hyperbolic dynamical system and a given weak additive white noise, by computing the local eigenfunctions of the adjoint Fokker-Planck operator along each periodic point, and using overlaps of their widths as the criterion for an optimal partition. The Fokker-Planck evolution is then represented by a finite transition graph, whose spectral determinant yields time averages of dynamical observables. Numerical tests of such "optimal partition" of a one-dimensional repeller support our hypothesis.