The problem of non-integrability of the circular restricted three-body problem is very classical and important in the theory of dynamical systems. It was partially solved by Poincaré in the nineteenth century: he showed that there exists no real-analytic first integral which depends analytically on the mass ratio of the second body to the total and is functionally independent of the Hamiltonian. When the mass of the second body becomes zero, the restricted three-body problem reduces to the two-body Kepler problem. We prove the non-integrability of the restricted three-body problem both in the planar and spatial cases for any non-zero mass of the second body. Our basic tool of the proofs is a technique developed here for determining whether perturbations of integrable systems which may be non-Hamiltonian are not meromorphically integrable near resonant periodic orbits such that the first integrals and commutative vector fields also depend meromorphically on the perturbation parameter. The technique is based on generalized versions due to Ayoul and Zung of the Morales–Ramis and Morales–Ramis–Simó theories. We emphasize that our results are not just applications of the theories.

Williamson’s theorem states that for any $2n \times 2n$ real positive definite matrix A, there exists a $2n \times 2n$ real symplectic matrix S such that $S^TAS=D \oplus D$, where D is an $n\times n$ diagonal matrix with positive diagonal entries known as the symplectic eigenvalues of A. Let H be any $2n \times 2n$ real symmetric matrix such that the perturbed matrix $A+H$ is also positive definite. In this paper, we show that any symplectic matrix $\tilde {S}$ diagonalizing $A+H$ in Williamson’s theorem is of the form $\tilde {S}=S Q+\mathcal {O}(\|H\|)$, where Q is a $2n \times 2n$ real symplectic as well as orthogonal matrix. Moreover, Q is in symplectic block diagonal form with the block sizes given by twice the multiplicities of the symplectic eigenvalues of A. Consequently, we show that $\tilde {S}$ and S can be chosen so that $\|\tilde {S}-S\|=\mathcal {O}(\|H\|)$. Our results hold even if A has repeated symplectic eigenvalues. This generalizes the stability result of symplectic matrices for non-repeated symplectic eigenvalues given by Idel, Gaona, and Wolf [Linear Algebra Appl., 525:45–58, 2017].

Let $\{X_n\}_{n\in{\mathbb{N}}}$ be an ${\mathbb{X}}$-valued iterated function system (IFS) of Lipschitz maps defined as $X_0 \in {\mathbb{X}}$ and for $n\geq 1$, $X_n\;:\!=\;F(X_{n-1},\vartheta_n)$, where $\{\vartheta_n\}_{n \ge 1}$ are independent and identically distributed random variables with common probability distribution $\mathfrak{p}$, $F(\cdot,\cdot)$ is Lipschitz continuous in the first variable, and $X_0$ is independent of $\{\vartheta_n\}_{n \ge 1}$. Under parametric perturbation of both F and $\mathfrak{p}$, we are interested in the robustness of the V-geometrical ergodicity property of $\{X_n\}_{n\in{\mathbb{N}}}$, of its invariant probability measure, and finally of the probability distribution of $X_n$. Specifically, we propose a pattern of assumptions for studying such robustness properties for an IFS. This pattern is implemented for the autoregressive processes with autoregressive conditional heteroscedastic errors, and for IFS under roundoff error or under thresholding/truncation. Moreover, we provide a general set of assumptions covering the classical Feller-type hypotheses for an IFS to be a V-geometrical ergodic process. An accurate bound for the rate of convergence is also provided.

The dynamics of the fragmentation equation with size diffusion is investigated when the size ranges in $(0,\infty)$ . The associated linear operator involves three terms and can be seen as a nonlocal perturbation of a Schrödinger operator. A Miyadera perturbation argument is used to prove that it is the generator of a positive, analytic semigroup on a weighted $L_1$ -space. Moreover, if the overall fragmentation rate does not vanish at infinity, then there is a unique stationary solution with given mass. Assuming further that the overall fragmentation rate diverges to infinity for large sizes implies the immediate compactness of the semigroup and that it eventually stabilizes at an exponential rate to a one-dimensional projection carrying the information of the mass of the initial value.

Weaning is a critical transition phase in swine production in which piglets must cope with different stressors that may affect their health. During this period, the prophylactic use of antibiotics is still frequent to limit piglet morbidity, which raises both economic and public health concerns such as the appearance of antimicrobial-resistant microbes. With the interest of developing tools for assisting health and management decisions around weaning, it is key to provide robustness indexes that inform on the animals’ capacity to endure the challenges associated with weaning. This work aimed at developing a modelling approach for facilitating the quantification of piglet resilience to weaning. A total of 325 Large White pigs weaned at 28 days of age were monitored and further housed and fed conventionally during the post-weaning period without antibiotic administration. Body weight and diarrhoea scores were recorded before and after weaning, and blood was sampled at weaning and 1 week later for collecting haematological data. A dynamic model was constructed based on the Gompertz–Makeham law to describe live weight trajectories during the first 75 days after weaning, following the rationale that the animal response is partitioned in two time windows (a perturbation and a recovery window). Model calibration was performed for each animal. Our results show that the transition time between the two time windows, as well as the weight trajectories are characteristic for each individual. The model captured the weight dynamics of animals at different degrees of perturbation, with an average coefficient of determination of 0.99, and a concordance correlation coefficient of 0.99. The utility of the model is that it provides biologically meaningful parameters that inform on the amplitude and length of perturbation, and the rate of animal recovery. Our rationale is that the dynamics of weight inform on the capability of the animal to cope with the weaning disturbance. Indeed, there were significant correlations between model parameters and individual diarrhoea scores and haematological traits. Overall, the parameters of our model can be useful for constructing weaning robustness indexes by using exclusively the growth curves. We foresee that this modelling approach will provide a step forward in the quantitative characterisation of robustness.

We highlight a state variable misspecification with one accepted method to implement stochastic volatility (SV) in DSGE models when transforming the nonlinear state-innovation dynamics to its linear representation. Although the technique is more efficient numerically, we show that it is not exact but only serves as an approximation when the magnitude of SV is small. Not accounting for this approximation error may induce substantial spurious volatility in macroeconomic series, which could lead to incorrect inference about the performance of the model. We also show that, by simply lagging and expanding the state vector, one can obtain the correct state-space specification. Finally, we validate our augmented implementation approach against an established alternative through numerical simulation.

We define and study a metric independence notion in a homogeneous metric abstract elementary class with perturbations that is dp-superstable (superstable wrt. the perturbation topology), weakly simple and has complete type spaces and we give a new example of such a class based on B. Zilber’s approximations of Weyl algebras. We introduce a way to measure the dependence of a tuple a from a set B over another set A. We prove basic properties of the notion, e.g., that a is independent of B over A in the usual sense of homogeneous model theory if and only if the measure of dependence is < ε for all ε > 0. In well behaved situations, the measure corresponds to the distance to a free extension. As an example of our measure of dependence we show a connection between the measure and entropy in models from quantum mechanics in which the spectrum of the observable is discrete. As an application, we show that weak simplicity implies a very strong form of simplicity and study the question of when the dependence inside a set of all realisations of some type can be seen to arise from a pregeometry in cases when the type is not regular. In the end of the paper, we demonstrate our notions and results in one more example: a class built from the p-adic integers.

A temporal analysis of the benthic polychaete community and its relationship with environmental variables was conducted by comparing coastal sediment samples collected in three separate sampling events between 1998 and 2013 from the southern end of the Southern California Bight (SCB). Environmental variables indicated a spatio-temporal increase of the sand fraction in sediment composition. Station stratification by depth from shallow to deep, and a reduction of trace metal enrichment (Co, Cr, Cu, Mn, Ni, Pb and Zn) was also found. There was a notable change in polychaete family composition due to high abundances and frequency of Spionidae, Chaetopteridae and Phyllodocidae in 2013, especially close to the Binational wastewater treatment plant discharge. An increase in polychaete abundance, richness and diversity was indicative of a probable relationship with regional weather conditions (El Niño-Southern Oscillation and recent drought events during sampling) along with local anthropogenic discharges of wastewater treatment plants in the area.

Sensitivity analysis plays an important role in finding an optimal design of a structure under uncertainty. Quantifying relative importance of random parameters, which leads to a rank ordering, helps in developing a systematic and efficient way to reach the optimal design. In this work, lift prediction and sensitivity analysis of a potential flow around a submerged body is considered. Such flow is often used in the initial design stage of structures. The flow computation is carried out using a vortex-panel method. A few parameters of the submerged body and flow are considered as random variables. To improve the accuracy in lift prediction in a computationally efficient way, a new semi-intrusive stochastic perturbation method is proposed. Accordingly, a perturbation is applied at the linear system solving level involving the inuence coefficient matrix, as opposed to using perturbation in the lift quantity itself. This proposed method, which is partially analogous to the intrusive or Galerkin projection methods in spectral stochastic finite element methods, is found to be more accurate than using perturbation directly on the lift and faster than a direct simulation. The proposed semi-intrusive stochastic perturbation method is found to yield faster estimates of the Sobol’ indices, which are used for global sensitivity analysis. From global sensitivity analysis, the flow parameters are found to be more important than the parameters of the submerged body.

Our view is that intelligence, as expression of the complexity of the human brain and of its evolutionary path, represents an intriguing example of “system level brain plasticity”: tangible proofs of this assertion lie in the strong links intelligence has with vital brain capacities as information processing (i.e., pure, rough capacity to transfer information in an efficient way), resilience (i.e., the ability to cope with loss of efficiency and/or loss of physical elements in a network) and adaptability (i.e., being able to efficiently rearrange its dynamics in response to environmental demands). Current evidence supporting this view move from theoretical models correlating intelligence and individual response to systematic “lesions” of brain connectivity, as well as from the field of Noninvasive Brain Stimulation (NiBS). Perturbation-based approaches based on techniques as transcranial magnetic stimulation (TMS) and transcranial alternating current stimulation (tACS), are opening new in vivo scenarios which could allow to disclose more causal relationship between intelligence and brain plasticity, overcoming the limitations of brain-behavior correlational evidence

Fall-related accidents are among the most serious concerns in elderly people, amputees and subjects with neurological disorders. The aim of this paper was to investigate the behaviour of healthy subjects wearing a novel light-weight pelvis exoskeleton controlled in zero-torque mode while carrying out unperturbed locomotion and managing unexpected perturbations. Results showed that the proposed exoskeleton was unobtrusive and had a minimum loading effect on the human biomechanics during unperturbed locomotion. Conversely, it affected the movement of the trailing leg while subjects managed unexpected slipping-like perturbations. These findings support further investigations on the potential use of powered exoskeletons to assist locomotion and, possibly prevent incipient falls.

In this paper we consider small essential spectral radius perturbations of operators with topological uniform descent—small essential spectral radius perturbations which cover compact, quasinilpotent and Riesz perturbations.

‘Adapt to endure’ has become a necessity in agriculture, but the means to do so remain largely undefined. The aim of this literature review is to analyse how the herd contributes to a livestock farming system's capacity to adapt to a changing world and evolve when the future is uncertain. We identify six categories of elements linked to the herd, called ‘sources of flexibility’, that are used to manage perturbation. The first three are: using the animal's adaptive capacities, using the diversity of species and breeds and combining the diversity of animal products. The last three are: organising the mobility of animals and livestock farmers, juggling the herd numbers and mastering the balance between productivity and herd survival. These sources of flexibility are described in the literature by studying the different ways in which they are used. For example, the ‘juggle herd numbers’ source is described by volume, categories of animals, type of transfer, such as births, purchases or gifts, and timing of use, especially linked to the timing of the perturbation. Identified studies also compare or rank sources and analyse the connections between them. The flexibility framework (management science) is used for this analysis according to the levels of organisation of a livestock farming system: a strategic level referring to long-term options and to the capacity to modify the system structure, and an operational level referring to adjustment decisions during the productive cycle, the presence or absence of intervention by the livestock farmer, and the time scales involved. We conclude that the decision to use one or another source (in terms of modalities, alternatives, scheduling and combinations) is made according to the production objectives, the structural means, the type/frequency/intensity of perturbations and the context/environment. Consequently, the flexibility of a livestock farming system cannot be assessed in absolute terms. Enhancing flexibility needs management of all elements and scales involved (and not only the herd), and requires diversity to be organised at different scales.