A discrete Schrodinger spectral problem and associated evolution equations

A recently proposed discrete version of the Schrodinger spectral problem is considered. The whole hierarchy of differential-difference nonlinear evolution equations associated to this spectral problem is derived. It is shown that a discrete version of the KdV, sine-Gordon and Liouville equations are included and that the so called `inverse' class in the hierarchy is local. The whole class of related Darboux and Backlund transformations is also exhibited.Comment: 14 pages, LaTeX2

Peakons, R-Matrix and Toda-Lattice

The integrability of a family of hamiltonian systems, describing in a particular case the motionof N ``peakons" (special solutions of the so-called Camassa-Holm equation) is established in the framework of the $r$-matrix approach, starting from its Lax representation. In the general case, the $r$-matrix is a dynamical one and has an interesting though complicated structure. However, for a particular choice of the relevant parameters in the hamiltonian (the one corresponding to the pure ``peakons" case), the $r$-matrix becomes essentially constant, and reduces to the one pertaining to the finite (non-periodic) Toda lattice. Intriguing consequences of such property are discussed and an integrable time discretisation is derived.Comment: 12 plain tex page

A Novel Hierarchy of Integrable Lattices

In the framework of the reduction technique for Poisson-Nijenhuis structures, we derive a new hierarchy of integrable lattice, whose continuum limit is the AKNS hierarchy. In contrast with other differential-difference versions of the AKNS system, our hierarchy is endowed with a canonical Poisson structure and, moreover, it admits a vector generalisation. We also solve the associated spectral problem and explicity contruct action-angle variables through the r-matrix approach.Comment: Latex fil

Dynamical R-Matrices for Integrable Maps

The integrability of two symplectic maps, that can be considered as discrete-time analogs of the Garnier and Neumann systems is established in the framework of the $r$-matrix approach, starting from their Lax representation. In contrast with the continuous case, the $r$-matrix for such discrete systems turns out to be of dynamical type; remarkably, the induced Poisson structure appears as a linear combination of compatible ``more elementary" Poisson structures. It is also shown that the Lax matrix naturally leads to define separation variables, whose discrete and continuous dynamics is investigated.Comment: 16 plain tex page

The dark side of network functions virtualization: A perspective on the technological sustainability

The Network Functions Virtualization (NFV) paradigm is undoubtedly a key technological advancement in the Information and Communication Technology (ICT) community, especially for the upcoming 5G network design. While most of its promise is quite straightforward, the implied reduction of the power consumption/carbon footprint is still debatable, and not in line with the energy efficiency perspective forecasted by the ETSI NFV working group (WG). In this paper, we provide an estimate of the possible future requirements of this upcoming technology when deployed according to the virtual Evolved Packet Core (vEPC) use case specified by the ETSI NFV WG. Our estimation is based on real performance levels, certified by independent third-party laboratories, and datasheet values provided by existing commercial products for both the legacy and NFV network architectures, under different deployment scenarios. Obtained results show that a massive deployment of the current NFV technologies in the EPC may lead to a minimum increase of 106 % in the carbon footprint/energy consumption with respect to the Business As Usual (BAU) network solutions. Moreover, these values tend to increase at a very high pace when the most suitable software/hardware combination is not applied, or when packet processing latency is taken into account

Effect of litter size on prepartum metabolic and amino acidic profile in rabbit does.

The use of modern prolific lines of rabbit does in intensive production systems leads to an increase in productivity but also causes a rise in several problems related to the does' health status. Hence, the aim of this study was to investigate the effect of the litter size on the metabolic, inflammatory and plasma amino acid profile in rabbit does. The blood of 30 pregnant does was sampled on the 27th day of pregnancy. The does were retrospectively grouped according to the number of offspring into a high litter size group (HI, does with ≥ 12 kits; n = 16) and a low litter size group (LO, does with ≤ 11 kits; n = 14). Data were subjected to Pearson's correlation analysis. Further, data were analysed in agreement to a completely randomized design in which the main tested effect was litter size. The linear or quadratic trends of litter size on parameters of interests were post hoc compared by using orthogonal contrasts. In addition, compared with the LO group, the HI group had lower levels of glucose (-5%; P < 0.01), zinc (-19%; P < 0.05), albumin (-6%; P < 0.05) and total cholesterol (-13%; P < 0.07), but the total bilirubin level was higher in the HI group (+14%; P < 0.05). Regarding the plasma amino acids, the HI group had lower concentrations of threonine (-15%), glycine (-16%), lysine (-16%) and tryptophan (-26%) and a higher level of glutamic acid (+43%; P < 0.05) compared with the LO group. The exclusively ketogenic amount of amino acids was lower (P < 0.06) in the HI (55.8 mg/100 ml) does compared with the LO does (56.8 mg/100 ml). These results show that a few days before delivery, rabbit does that gave birth to a higher number of offspring had a metabolic profile and an inflammatory status that was less favourable with respect to does who gave birth to a lower number of offspring. Moreover, the plasma amino acid profile points out that there was an enhanced catabolic condition in the rabbit does with a high number of gestated foetuses; it was likely related to the greater energy demand needed to support the pregnancy and an early inflammatory response

A discrete time relativistic Toda lattice

Four integrable symplectic maps approximating two Hamiltonian flows from the relativistic Toda hierarchy are introduced. They are demostrated to belong to the same hierarchy and to examplify the general scheme for symplectic maps on groups equiped with quadratic Poisson brackets. The initial value problem for the difference equations is solved in terms of a factorization problem in a group. Interpolating Hamiltonian flows are found for all the maps.Comment: 32 pages, LaTe

The lattice Schwarzian KdV equation and its symmetries

In this paper we present a set of results on the symmetries of the lattice Schwarzian Korteweg-de Vries (lSKdV) equation. We construct the Lie point symmetries and, using its associated spectral problem, an infinite sequence of generalized symmetries and master symmetries. We finally show that we can use master symmetries of the lSKdV equation to construct non-autonomous non-integrable generalized symmetries.Comment: 11 pages, no figures. Submitted to Jour. Phys. A, Special Issue SIDE VI

Relativistic quantum clocks

The conflict between quantum theory and the theory of relativity is exemplified in their treatment of time. We examine the ways in which their conceptions differ, and describe a semiclassical clock model combining elements of both theories. The results obtained with this clock model in flat spacetime are reviewed, and the problem of generalizing the model to curved spacetime is discussed, before briefly describing an experimental setup which could be used to test of the model. Taking an operationalist view, where time is that which is measured by a clock, we discuss the conclusions that can be drawn from these results, and what clues they contain for a full quantum relativistic theory of time.Comment: 12 pages, 4 figures. Invited contribution for the proceedings for "Workshop on Time in Physics" Zurich 201