Financial LPPL Bubbles with Mean-Reverting Noise in the Frequency Domain

The log-periodic power law (LPPL) is a model of asset prices during endogenous bubbles. A major open issue is to verify the presence of LPPL in price sequences and to estimate the LPPL parameters. Estimation is complicated by the fact that daily LPPL returns are typically orders of magnitude smaller than measured price returns, suggesting that noise obscures the underlying LPPL dynamics. However, if noise is mean-reverting, it would quickly cancel out over subsequent measurements. In this paper, we attempt to reject mean-reverting noise from price sequences by exploiting frequency-domain properties of LPPL and of mean reversion. First, we calculate the spectrum of mean-reverting \ou noise and devise estimators for the noise's parameters. Then, we derive the LPPL spectrum by breaking it down into its two main characteristics of power law and of log-periodicity. We compare price spectra with noise spectra during historical bubbles. In general, noise was strong also at low frequencies and, even if LPPL underlied price dynamics, LPPL would be obscured by noise

The ghosts of forgotten things: A study on size after forgetting

Forgetting is removing variables from a logical formula while preserving the constraints on the other variables. In spite of being a form of reduction, it does not always decrease the size of the formula and may sometimes increase it. This article discusses the implications of such an increase and analyzes the computational properties of the phenomenon. Given a propositional Horn formula, a set of variables and a maximum allowed size, deciding whether forgetting the variables from the formula can be expressed in that size is $D^p$-hard in $\Sigma^p_2$. The same problem for unrestricted propositional formulae is $D^p_2$-hard in $\Sigma^p_3$. The hardness results employ superredundancy: a superirredundant clause is in all formulae of minimal size equivalent to a given one. This concept may be useful outside forgetting

Redundancy in Logic III: Non-Mononotonic Reasoning

Results about the redundancy of circumscriptive and default theories are presented. In particular, the complexity of establishing whether a given theory is redundant is establihsed.Comment: minor correction

Balancing Security and Democracy: The Politics of Biometric Identification in the European Union

What are the relations between security policies and democratic debate, oversight and rights? And what is the role of expertise in shaping such policies and informing the democratic process? The inquiry that follows tries to answer such questions in the context of the European Union and taking the case of biometric identification, an area where security considerations and the possible impacts on fundamental rights and rule of law are at stake, and where expertise is crucial. Some hypotheses are explored through the case study: that 'securitisation' and 'democratisation' are in tension but some hybrid strategies can emerge, that the plurality of 'authoritative actors' influences policy frames and outcomes, and that knowledge is a key asset in defining these authoritative actors. A counter-intuitive conclusion is presented, namely that biometrics-which seems prima facie an excellent candidate for technocratic decision making, sheltered from democratic debate and accountability-is characterised by intense debate by a plurality of actors. Such pluralism is limited to those actors who have the resources-including knowledge-that allow for inclusion in policy making at EU level, but is nevertheless significant in shaping policy. Tragic events were pivotal in pushing for action on grounds of security, but the chosen instruments were in store and specific actors were capable of proposing them as a solution to security problems; in particular, the strong role of executives is a key factor in the vigorous pursuit of biometric identification. However this is not the whole story, and limited pluralism-including plurality of expertise-explains specific features of the development of biometrics in the EU, namely the central role of the metaphor of 'balancing' security and democracy, and the 'competitive cooperation' between new and more consolidated policy areas. The EU is facing another difficult challenge in the attempt of establishing itself as a new security actor and as a supranational democratic polity: important choices are involved to assure that citizens' security is pursued on the basis of rule of law, respect of fundamental rights and democratic accountability.democracy; pluralism; security/internal

The size of BDDs and other data structures in temporal logics model checking

Temporal Logic Model Checking is a verification method in which we describe a system, the model, and then we verify whether important properties, expressed in a temporal logic formula, hold in the system. Many Model Checking tools employ BDDs or some other data structure to represent sets of states. It has been empirically observed that the BDDs used in these algorithms may grow exponentially as the model and formula increase in size. We formally prove that no kind of data structure of polynomial size can represent the set of valid initial states for all models and all formulae. This result holds for all data structures where a state can be checked in polynomial time. Therefore, it holds not only for all types of BDDs regardless of variable ordering, but also for more powerful data structures, such as RBCs, MTBDDs, ADDs and SDDs. Thus, the size explosion of BDDs is not a limit of these specific data representation structures, but is unavoidable: every formalism used in the same way would lead to an exponential size blow up

A nonlinear macroelement formulation for the seismic analysis of masonry buildings

A macroelement is presented for the nonlinear dynamic analysis of masonry structures under seismic actions. The macroelement, developed in the framework of the equivalent frame model, has a force-based formulation and accounts for flexural and shear failure mechanisms, by means of two flexural hinges at the ends and a shear link, respectively. The flexural hinges are formulated according to the Bouc-Wen model to describe the progressive development of cracks and the hysteresis loops under load reversals. The shear link, in addition to the aforementioned effects, accounts for the strength/stiffness decay and is formulated adopting the Bouc-Wen-Baber-Noori model. Numerical comparisons with experimental tests on masonry piers are presented, showing the suitability of the presented macroelement

Dynamic one-sided out-of-plane behavior of unreinforced-masonry wall restrained by elasto-plastic tie-rods

Past earthquakes have shown the high vulnerability of existing masonry buildings, particularly to out-of-plane local collapse mechanisms. Such mechanisms can be prevented if façades are restrained by tie rods improving the connections to perpendiculars walls. Whereas in the past only static models have been proposed, herein the nonlinear equation of motion of a monolithic wall restrained by a tie rod is presented. The façade, resting on a foundation and adjacent to transverse walls, rotates only around one base pivot and has one degree of freedom. Its thickness is explicitly accounted for and the tie rod is modeled as a linear elastic—perfectly plastic spring, with limited displacement capacity. The model is used to investigate the response to variations of wall geometry (height/thickness ratio, thickness), tie rod features (vertical position, length, prestress level), and material characteristics (elastic modulus, ultimate elongation, yield strength) typical of historical iron. The most relevant parameter is the steel strength, whereas other characteristics play minor roles allowing to recommend reduced values for pre-tensioning forces. The force-based procedure customary in Italy for tie design is reasonably safe and involves protection also against collapse, although probably not enough as desirable