The dynamical nature of time

It is usually assumed that the "$t$" parameter in the equations of dynamics can be identified with the indication of the pointer of a clock. Things are not so easy, however. In fact, since the equations of motion can be written in terms of $t$ but also of $t'=f(t)$, $f$ being any well behaved function, each one of those infinite parametric times $t'$ is as good as the Newtonian one to study classical dynamics. Here we show that the relation between the mathematical parametric time $t$ in the equations of dynamics and the physical dynamical time $\sigma$ that is measured with clocks is more complex and subtle than usually assumed. These two times, therefore, must be carefully distinguished since their difference may have significant consequences. Furthermore, we show that not all the dynamical clock-times are necessarily equivalent and that the observational fingerprint of this non-equivalence has the same form as that of the Pioneer anomaly.Comment: 13 pages, no figure

Mixing-induced Spontaneous Supersymmetry Breaking

It is conjectured that flavor mixing furnishes a universal mechanism for the spontaneous breaking of supersymmetry. The conjecture is proved explicitly for the mixing of two Wess--Zumino $\mathcal{N}=1$ supermultiplets and arguments for its general validity are given. The mechanism relies on the fact that, despite mixing treats fermions and bosons symmetrically, both the fermionic and the bosonic zero point energies are shifted by a positive amount and this kind of shift does not respect supersymmetry.Comment: 5 pages, 1 figure, Eq(12) of V1 corrected to Eq(22), explicit off-shell formulation included, one reference adde

Parsimonious Time Series Clustering

We introduce a parsimonious model-based framework for clustering time course data. In these applications the computational burden becomes often an issue due to the number of available observations. The measured time series can also be very noisy and sparse and a suitable model describing them can be hard to define. We propose to model the observed measurements by using P-spline smoothers and to cluster the functional objects as summarized by the optimal spline coefficients. In principle, this idea can be adopted within all the most common clustering frameworks. In this work we discuss applications based on a k-means algorithm. We evaluate the accuracy and the efficiency of our proposal by simulations and by dealing with drosophila melanogaster gene expression data

Sample-to-sample fluctuations of power spectrum of a random motion in a periodic Sinai model

The Sinai model of a tracer diffusing in a quenched Brownian potential is a much studied problem exhibiting a logarithmically slow anomalous diffusion due to the growth of energy barriers with the system size. However, if the potential is random but periodic, the regime of anomalous diffusion crosses over to one of normal diffusion once a tracer has diffused over a few periods of the system. Here we consider a system in which the potential is given by a Brownian Bridge on a finite interval $(0,L)$ and then periodically repeated over the whole real line, and study the power spectrum $S(f)$ of the diffusive process $x(t)$ in such a potential. We show that for most of realizations of $x(t)$ in a given realization of the potential, the low-frequency behavior is $S(f) \sim {\cal A}/f^2$, i.e., the same as for standard Brownian motion, and the amplitude ${\cal A}$ is a disorder-dependent random variable with a finite support. Focusing on the statistical properties of this random variable, we determine the moments of ${\cal A}$ of arbitrary, negative or positive order $k$, and demonstrate that they exhibit a multi-fractal dependence on $k$, and a rather unusual dependence on the temperature and on the periodicity $L$, which are supported by atypical realizations of the periodic disorder. We finally show that the distribution of ${\cal A}$ has a log-normal left tail, and exhibits an essential singularity close to the right edge of the support, which is related to the Lifshitz singularity. Our findings are based both on analytic results and on extensive numerical simulations of the process $x(t)$.Comment: 8 pages, 5 figure

Impact of Lorentz Violation Models on Exoplanets’ Dynamics

Many exoplanets have been detected by the radial velocity method, according to which the motion of a binary system around its center of mass can produce a periodical variation of the Doppler effect of the light emitted by the host star. These variations are influenced by both Newtonian and non-Newtonian perturbations to the dominant inverse-square acceleration; accordingly, exoplanetary systems lend themselves to testing theories of gravity alternative to general relativity. In this paper, we consider the impact of the Standard Model Extension (a model that can be used to test all possible Lorentz violations) on the perturbation of radial velocity and suggest that suitable exoplanets’ configurations and improvements in detection techniques may contribute to obtaining new constraints on the model parameters

RAYGO: Reserve As You GO

The capability to predict the precise resource requirements of a microservice-based application is a very important problem for cloud services. In fact, the allocation of abundant resources guarantees an excellent quality of experience (QoE) for the hosted services, but it can translate into unnecessary costs for the cloud customer due to the reserved (but unused) resources. On the other side, poor resource provisioning may turn out in scarce performance when experiencing an unexpected peak of demand. This paper proposes RAYGO, a novel approach for dynamic resource provisioning to microservices in Kubernetes that (i) reliefs the customers from the definition of appropriate execution boundaries, (ii) ensures the right amount of resources at any time, according to the past and the predicted usage, and (iii) operates at the application level, acknowledging the dependency between multiple correlated microservices

Computing Without Borders: The Way Towards Liquid Computing

Despite the de-facto technological uniformity fostered by the cloud and edge computing paradigms, resource fragmentation across isolated clusters hinders the dynamism in application placement, leading to suboptimal performance and operational complexity. Building upon and extending these paradigms, we propose a novel approach envisioning a transparent continuum of resources and services on top of the underlying fragmented infrastructure, called liquid computing. Fully decentralized, multi-ownership-oriented and intent-driven, it enables an overarching abstraction for improved applications execution, while at the same time opening up for new scenarios, including resource sharing and brokering. Following the above vision, we present liqo, an open-source project that materializes this approach through the creation of dynamic and seamless Kubernetes multi-cluster topologies. Extensive experimental evaluations have shown its effectiveness in different contexts, both in terms of Kubernetes overhead and compared to other open-source alternatives

Fine-root morphological and growth traits in a Turkey-oak stand in relation to seasonal changes in soil moisture in the Southern Apennines, Italy

We investigated the effects of seasonal changes in soil moisture on the morphological and growth traits of fine roots (<2 mm in diameter) in a mature Turkeyoak stand (Quercus cerris L.) in the Southern Apennines of Italy. Root samples (diameter: <0.5, 0.5\u20131.0, 1.0\u20131.5, and 1.5\u20132.0 mm) were collected with the Auger method. Mean annual fine-root mass and length on site was 443 g m!2 (oak fine roots 321 g m!2; other species 122 g m!2) and 3.18 km m!2 (oak fine roots 1.14 km m!2; other species 2.04 km m!2), respectively. Mean specific root length was 8.3 m g!1. All fine-root traits displayed a complex pattern that was significantly related to season. In the four diameter classes, both fineroot biomass and length peaked in summer when soil water content was the lowest and air temperature the highest of the season. Moreover, both fine-root biomass and length were inversely related with soil moisture (p < 0.001). The finest roots (<0.5 mm in diameter) constituted an important fraction of total fine-root length (79 %), but only 21 % of biomass. Only in this root class, consequent to change in mean diameter, specific root length peaked when soil water content was lowest showing an inverse relationship (p < 0.001). Furthermore, fine-root production and turnover decreased with increasing root diameter. These results suggest that changes in root length per unit mass, and pulses in root growth to exploit transient periods of low soil water content may enable trees to increase nutrient and water uptake under seasonal drought conditions