On optimal computation of MPLS label binding for multipoint-to-point connections

Most network operators have considered reducing Label Switched Routers (LSR) label spaces (i.e. the number of labels that can be used) as a means of simplifying management of underlaying Virtual Private Networks (VPNs) and, hence, reducing operational expenditure (OPEX). This letter discusses the problem of reducing the label spaces in Multiprotocol Label Switched (MPLS) networks using label merging - better known as MultiPoint-to-Point (MP2P) connections. Because of its origins in IP, MP2P connections have been considered to have tree- shapes with Label Switched Paths (LSP) as branches. Due to this fact, previous works by many authors affirm that the problem of minimizing the label space using MP2P in MPLS - the Merging Problem - cannot be solved optimally with a polynomial algorithm (NP-complete), since it involves a hard- decision problem. However, in this letter, the Merging Problem is analyzed, from the perspective of MPLS, and it is deduced that tree-shapes in MP2P connections are irrelevant. By overriding this tree-shape consideration, it is possible to perform label merging in polynomial time. Based on how MPLS signaling works, this letter proposes an algorithm to compute the minimum number of labels using label merging: the Full Label Merging algorithm. As conclusion, we reclassify the Merging Problem as Polynomial-solvable, instead of NP-complete. In addition, simulation experiments confirm that without the tree-branch selection problem, more labels can be reduced

Superheavy nuclei in relativistic effective Lagrangian model

Isotopic and isotonic chains of superheavy nuclei are analyzed to search for spherical double shell closures beyond Z=82 and N=126 within the new effective field theory model of Furnstahl, Serot, and Tang for the relativistic nuclear many-body problem. We take into account several indicators to identify the occurrence of possible shell closures, such as two-nucleon separation energies, two-nucleon shell gaps, average pairing gaps, and the shell correction energy. The effective Lagrangian model predicts N=172 and Z=120 and N=258 and Z=120 as spherical doubly magic superheavy nuclei, whereas N=184 and Z=114 show some magic character depending on the parameter set. The magicity of a particular neutron (proton) number in the analyzed mass region is found to depend on the number of protons (neutrons) present in the nucleus.

Entropy of a correlated system of nucleons

Realistic nucleon-nucleon interactions induce correlations to the nuclear many-body system, which lead to a fragmentation of the single-particle strength over a wide range of energies and momenta. We address the question of how this fragmentation affects the thermodynamical properties of nuclear matter. In particular, we show that the entropy can be computed with the help of a spectral function, which can be evaluated in terms of the self-energy obtained in the self-consistent Green's function approach. Results for the density and temperature dependences of the entropy per particle for symmetric nuclear matter are presented and compared to the results of lowest order finite-temperature Brueckner-Hartree-Fock calculations. The effects of correlations on the calculated entropy are small, if the appropriate quasiparticle approximation is used. The results demonstrate the thermodynamical consistency of the self-consistent T-matrix approximation for the evaluation of the Green's functions.

Decay of unstable states in the presence of colored noise and random initial conditions. I. Theory of nonlinear relaxation times

The general theory of nonlinear relaxation times is developed for the case of Gaussian colored noise. General expressions are obtained and applied to the study of the characteristic decay time of unstable states in different situations, including white and colored noise, with emphasis on the distributed initial conditions. Universal effects of the coupling between colored noise and random initial conditions are predicted.

Phenomenological approach to nonlinear Langevin equations

In this paper we address the problem of consistently constructing Langevin equations to describe fluctuations in nonlinear systems. Detailed balance severely restricts the choice of the random force, but we prove that this property, together with the macroscopic knowledge of the system, is not enough to determine all the properties of the random force. If the cause of the fluctuations is weakly coupled to the fluctuating variable, then the statistical properties of the random force can be completely specified. For variables odd under time reversal, microscopic reversibility and weak coupling impose symmetry relations on the variable-dependent Onsager coefficients. We then analyze the fluctuations in two cases: Brownian motion in position space and an asymmetric diode, for which the analysis based in the master equation approach is known. We find that, to the order of validity of the Langevin equation proposed here, the phenomenological theory is in agreement with the results predicted by more microscopic models

Reconstruction of the join time-delay Doppler-scale reflectivity density in the wide-band regime. A frame theory based approach

The inverse scattering problem concerning the determination of the joint time-delayDoppler-scale reflectivity density characterizing continuous target environments is addressed by recourse to the generalized frame theory. A reconstruction formula,involving the echoes of a frame of outgoing signals and its corresponding reciprocalframe, is developed. A ‘‘realistic’’ situation with respect to the transmission ofa finite number of signals is further considered. In such a case, our reconstruction formula is shown to yield the orthogonal projection of the reflectivity density onto a subspace generated by the transmitted signals.

Friedman's Excess energy and the McMillan-Mayer theory of solutions:Thermodynamics

In his version of the theory of multicomponent systems, Friedman used the analogy which exists between the virial expansion for the osmotic pressure obtained from the McMillan-Mayer (MM) theory of solutions in the grand canonical ensemble and the virial expansion for the pressure of a real gas. For the calculation of the thermodynamic properties of the solution, Friedman proposed a definition for the"excess free energy" that is a reminder of the ancient idea for the"osmotic work". However, the precise meaning to be attached to his free energy is, within other reasons, not well defined because in osmotic equilibrium the solution is not a closed system and for a given process the total amount of solvent in the solution varies. In this paper, an analysis based on thermodynamics is presented in order to obtain the exact and precise definition for Friedman"s excess free energy and its use in the comparison with the experimental data.

Inverse Problems for multiple invariant curves

Planar polynomial vector fields which admit invariant algebraic curves, Darboux integrating factors or Darboux first integrals are of special interest. In the present paper we solve the inverse problem for invariant algebraic curves with a given multiplicity and for integrating factors, under generic assumptions regarding the (multiple) invariant algebraic curves involved. In particular we prove, in this generic scenario, that the existence of a Darboux integrating factor implies Darboux integrability. Furthermore we construct examples where the genericity assumption does not hold and indicate that the situation is different for these.

Application for fault location in electrical power distribution systems

Fault location has been studied deeply for transmission lines due to its importance in power systems. Nowadays the problem of fault location on distribution systems is receiving special attention mainly because of the power quality regulations. In this context, this paper presents an application software developed in Matlabtrade that automatically calculates the location of a fault in a distribution power system, starting from voltages and currents measured at the line terminal and the model of the distribution power system data. The application is based on a N-ary tree structure, which is suitable to be used in this application due to the highly branched and the non- homogeneity nature of the distribution systems, and has been developed for single-phase, two-phase, two-phase-to-ground, and three-phase faults. The implemented application is tested by using fault data in a real electrical distribution power system

Counterpoise-corrected geometries and harmonic frequencies of N-body clusters: application to (HF)n (n=3,4)

A study was conducted on the methods of basis set superposition error (BSSE)-free geometry optimization and frequency calculations in clusters larger than a dimer. In particular, three different counterpoise schemes were critically examined. It was shown that the counterpoise-corrected supermolecule energy can be easily obtained in all the cases by using the many-body partitioning of energy

Fronts from complex two-dimensional dispersal kernels: theory and application to Reid's paradox

Bimodal dispersal probability distributions with characteristic distances differing by several orders of magnitude have been derived and favorably compared to observations by Nathan [Nature (London) 418, 409 (2002)]. For such bimodal kernels, we show that two-dimensional molecular dynamics computer simulations are unable to yield accurate front speeds. Analytically, the usual continuous-space random walks (CSRWs) are applied to two dimensions. We also introduce discrete-space random walks and use them to check the CSRW results (because of the inefficiency of the numerical simulations). The physical results reported are shown to predict front speeds high enough to possibly explain Reid's paradox of rapid tree migration. We also show that, for a time-ordered evolution equation, fronts are always slower in two dimensions than in one dimension and that this difference is important both for unimodal and for bimodal kernels

Priors about observables in vector autoregressions

Standard practice in Bayesian VARs is to formulate priors on the autoregressive parameters, but economists and policy makers actually have priors about the behavior of observable variables. We show how this kind of prior can be used in a VAR under strict probability theory principles. We state the inverse problem to be solved and we propose a numerical algorithm that works well in practical situations with a very large number of parameters. We prove various convergence theorems for the algorithm. As an application, we first show that the results in Christiano et al. (1999) are very sensitive to the introduction of various priors that are widely used. These priors turn out to be associated with undesirable priors on observables. But an empirical prior on observables helps clarify the relevance of these estimates: we find much higher persistence of output responses to monetary policy shocks than the one reported in Christiano et al. (1999) and a significantly larger total effect.

Bargaining on networks: An experiment

While markets are often decentralized, in many other cases agents in one role can only negotiate with a proper subset of the agents in the complementary role. There may be proximity issues or restricted communication flows. For example, information may be transmitted only through word-of-mouth, as is often the case for job openings, business opportunities, and confidential transactions. Bargaining can be considered to occur over a network that summarizes the structure of linkages among people. We conduct an alternating-offer bargaining experiment using separate simple networks, which are then joined during the session by an additional link. The results diverge sharply depending on how this connection is made. Payoffs can be systematically affected even for agents who are not connected by the new link. We use a graph-theoretic analysis to show that any two-sided network can be decomposed into simple networks of three types, so that our result can be generalized to more complex bargaining environments. Participants appear to grasp the essential characteristics of the networks and we observe a rather consistently high level of bargaining efficiency.

On the complexity of rationalizing behavior

We study the complexity of rationalizing choice behavior. We do so by analyzing two polar cases, and a number of intermediate ones. In our most structured case, that is where choice behavior is defined in universal choice domains and satisfies the "weak axiom of revealed preference," finding the complete preorder rationalizing choice behavior is a simple matter. In the polar case, where no restriction whatsoever is imposed, either on choice behavior or on choice domain, finding the complete preordersthat rationalize behavior turns out to be intractable. We show that the task of finding the rationalizing complete preorders is equivalent to a graph problem. This allows the search for existing algorithms in the graph theory literature, for the rationalization of choice.