Proper actions, fixed-point algebras and naturality in nonabelian duality

"Vegeu el resum a l'incici del document del fitxer adjunt."

Symmetries and fixed point stability of stochastic differential equations modeling self-organized criticality

A stochastic nonlinear partial differential equation is constructed for two different models exhibiting self-organized criticality: the Bak-Tang-Wiesenfeld (BTW) sandpile model [Phys. Rev. Lett. 59, 381 (1987); Phys. Rev. A 38, 364 (1988)] and the Zhang model [Phys. Rev. Lett. 63, 470 (1989)]. The dynamic renormalization group (DRG) enables one to compute the critical exponents. However, the nontrivial stable fixed point of the DRG transformation is unreachable for the original parameters of the models. We introduce an alternative regularization of the step function involved in the threshold condition, which breaks the symmetry of the BTW model. Although the symmetry properties of the two models are different, it is shown that they both belong to the same universality class. In this case the DRG procedure leads to a symmetric behavior for both models, restoring the broken symmetry, and makes accessible the nontrivial fixed point. This technique could also be applied to other problems with threshold dynamics.

Large-system analysis of a CDMA dynamic channel under a Markovian input process

We study the minimum mean square error (MMSE) and the multiuser efficiency η of large dynamic multiple access communication systems in which optimal multiuser detection is performed at the receiver as the number and the identities of active users is allowed to change at each transmission time. The system dynamics are ruled by a Markov model describing the evolution of the channel occupancy and a large-system analysis is performed when the number of observations grow large. Starting on the equivalent scalar channel and the fixed-point equation tying multiuser efficiency and MMSE, we extend it to the case of a dynamic channel, and derive lower and upper bounds for the MMSE (and, thus, for η as well) holding true in the limit of large signal–to–noise ratios and increasingly large observation time T.

Global periodicity conditions for maps and recurrences via Normal Forms

We face the problem of characterizing the periodic cases in parametric families of (real or complex) rational diffeomorphisms having a fixed point. Our approach relies on the Normal Form Theory, to obtain necessary conditions for the existence of a formal linearization of the map, and on the introduction of a suitable rational parametrization of the parameters of the family. Using these tools we can find a finite set of values p for which the map can be p-periodic, reducing the problem of finding the parameters for which the periodic cases appear to simple computations. We apply our results to several two and three dimensional classes of polynomial or rational maps. In particular we find the global periodic cases for several Lyness type recurrences

A general theory of rank testing

This paper develops an approach to rank testing that nests all existing rank tests andsimplifies their asymptotics. The approach is based on the fact that implicit in every ranktest there are estimators of the null spaces of the matrix in question. The approach yieldsmany new insights about the behavior of rank testing statistics under the null as well as localand global alternatives in both the standard and the cointegration setting. The approach alsosuggests many new rank tests based on alternative estimates of the null spaces as well as thenew fixed-b theory. A brief Monte Carlo study illustrates the results.

Exponentially small splitting of separatrices in the perturbed McMillan map

The McMillan map is a one-parameter family of integrable symplectic maps of the plane, for which the origin is a hyperbolic fixed point with a homoclinic loop, with small Lyapunov exponent when the parameter is small. We consider a perturbation of the McMillan map for which we show that the loop breaks in two invariant curves which are exponentially close one to the other and which intersect transversely along two primary homoclinic orbits. We compute the asymptotic expansion of several quantities related to the splitting, namely the Lazutkin invariant and the area of the lobe between two consecutive primary homoclinic points. Complex matching techniques are in the core of this work. The coefficients involved in the expansion have a resurgent origin, as shown in [MSS08].

Detecció automàtica de punts facials característics utilitzant Random Ferns i el criteri de la información mútua simplificada

En aquest article comparem el rendiment que presenten dos sistemes de reconeixement de punts característics en imatges: en el primer utilitzem la tècnica Random Ferns bàsica i en el segon (que anomenem Ferns amb Informació Mútua o FIM) apliquem una tècnica d'obtenció de Ferns utilitzant un criteri simplificat de la informació mútua.

Dynamic higher order expectations

In models where privately informed agents interact, agents may need to formhigher order expectations, i.e. expectations of other agents' expectations. This paper develops a tractable framework for solving and analyzing linear dynamic rational expectationsmodels in which privately informed agents form higher order expectations. The frameworkis used to demonstrate that the well-known problem of the infinite regress of expectationsidentified by Townsend (1983) can be approximated to an arbitrary accuracy with a finitedimensional representation under quite general conditions. The paper is constructive andpresents a fixed point algorithm for finding an accurate solution and provides weak conditions that ensure that a fixed point exists. To help intuition, Singleton's (1987) asset pricingmodel with disparately informed traders is used as a vehicle for the paper.

N=1 SQCD-like theories with N_f massive flavors from AdS/CFT and beta functions

We study new supergravity solutions related to large-N c N=1 supersymmetric gauge field theories with a large number N f of massive flavors. We use a recently proposed framework based on configurations with N c color D5 branes and a distribution of N f flavor D5 branes, governed by a function N f S(r). Although the system admits many solutions, under plausible physical assumptions the relevant solution is uniquely determined for each value of x ≡ N f /N c . In the IR region, the solution smoothly approaches the deformed Maldacena-Núñez solution. In the UV region it approaches a linear dilaton solution. For x < 2 the gauge coupling β g function computed holographically is negative definite, in the UV approaching the NSVZ β function with anomalous dimension γ 0 = −1/2 (approaching − 3/(32π 2)(2N c  − N f )g 3)), and with β g  → −∞ in the IR. For x = 2, β g has a UV fixed point at strong coupling, suggesting the existence of an IR fixed point at a lower value of the coupling. We argue that the solutions with x > 2 describe a"Seiberg dual" picture where N f  − 2N c flips sign.

On the Connectivity of the Julia sets of meromorphic functions

We prove that every transcendental meromorphic map $f$ with disconnected Julia set has a weakly repelling fixed point. This implies that the Julia set of Newton's method for finding zeroes of an entire map is connected. Moreover, extending a result of Cowen for holomorphic self-maps of the disc, we show the existence of absorbing domains for holomorphic self-maps of hyperbolic regions, whose iterates tend to a boundary point. In particular, the results imply that periodic Baker domains of Newton's method for entire maps are simply connected, which solves a well-known open question.

Highly eccentric hip-hop solutions of the 2N

We show the existence of families of hip-hop solutions in the equal-mass 2N-body problem which are close to highly eccentric planar elliptic homographic motions of 2N bodies plus small perpendicular non-harmonic oscillations. By introducing a parameter ϵ, the homographic motion and the small amplitude oscillations can be uncoupled into a purely Keplerian homographic motion of fixed period and a vertical oscillation described by a Hill type equation. Small changes in the eccentricity induce large variations in the period of the perpendicular oscillation and give rise, via a Bolzano argument, to resonant periodic solutions of the uncoupled system in a rotating frame. For small ϵ ≠ 0, the topological transversality persists and Brouwer's fixed point theorem shows the existence of this kind of solutions in the full system

Empiricism in ecological economics: a perspective from complex systems theory

Economies are open complex adaptive systems far from thermodynamic equilibrium, and neo-classical environmental economics seems not to be the best way to describe the behaviour of such systems. Standard econometric analysis (i.e. time series) takes a deterministic and predictive approach, which encourages the search for predictive policy to ‘correct’ environmental problems. Rather, it seems that, because of the characteristics of economic systems, an ex-post analysis is more appropriate, which describes the emergence of such systems’ properties, and which sees policy as a social steering mechanism. With this background, some of the recent empirical work published in the field of ecological economics that follows the approach defended here is presented. Finally, the conclusion is reached that a predictive use of econometrics (i.e. time series analysis) in ecological economics should be limited to cases in which uncertainty decreases, which is not the normal situation when analysing the evolution of economic systems. However, that does not mean we should not use empirical analysis. On the contrary, this is to be encouraged, but from a structural and ex-post point of view.

Where Has the Old Debate Gone? Realism, Institutionalism, and IR Theory

This paper resorts to the contribution of the science philosopher Gerald Holton to map some of the IR arguments and debates in an unconventional and more insightful way. From this starting point, it is sustained that the formerly all-pervading neorealism-neoinstitutionalism debate has lost its appeal and is attracting less and less interest among scholars. It does not structure the approach of the theoretically-oriented authors any more; at least, not with the habitual intensity. More specifically, we defend that the neo-neo rapprochement, even if it could have demonstrated that international cooperation is possible and relevant in a Realist world, it has also impoverished theoretical debate by hiding some of the most significant issues that preoccupied classical transnationalists. Hence, some authors appear to be trying to rescue some of these arguments in an analytical and systematic fashion, opening up a theoretical querelle that may be the next one to pay attention to.

In Search of a theory of debt management

A growing literature integrates theories of debt management into models of optimal fiscal policy. One promising theory argues that the composition of government debt should be chosen so that fluctuations in the market value of debt offset changes in expected future deficits. This complete market approach to debt management is valid even when the government only issues non-contingent bonds. A number of authors conclude from this approach that governments should issue long term debt and invest in short term assets. We argue that the conclusions of this approach are too fragile to serve as a basis for policy recommendations. This is because bonds at different maturities have highly correlated returns, causing the determination of the optimal portfolio to be ill-conditioned. To make this point concrete we examine the implications of this approach to debt management in various models, both analytically and using numerical methods calibrated to the US economy. We find the complete market approach recommends asset positions which are huge multiples of GDP. Introducing persistent shocks or capital accumulation only worsens this problem. Increasing the volatility of interest rates through habits partly reduces the size of these simulations we find no presumption that governments should issue long term debt ? policy recommendations can be easily reversed through small perturbations in the specification of shocks or small variations in the maturity of bonds issued. We further extend the literature by removing the assumption that governments every period costlessly repurchase all outstanding debt. This exacerbates the size of the required positions, worsens their volatility and in some cases produces instability in debt holdings. We conclude that it is very difficult to insulate fiscal policy from shocks by using the complete markets approach to debt management. Given the limited variability of the yield curve using maturities is a poor way to substitute for state contingent debt. The result is the positions recommended by this approach conflict with a number of features that we believe are important in making bond markets incomplete e.g allowing for transaction costs, liquidity effects, etc.. Until these features are all fully incorporated we remain in search of a theory of debt management capable of providing robust policy insights.

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