Equilibrium Principle in Colombian Public Contracting

Public contracting in Colombia is conflicting and inefficient. It frequently leads to damage to State property. The Colombian legal system cannot assure efficient and transparent public contracting. The cause is the institutional environment characterized by high transaction costs. Colombian law worsens the process by recognizing the principle of economic equilibrium in public contracts. This principle increasese contract incompleteness and renders impossible the use of economic incentives to control the opportunism of the economic agents. The authors present the hypothesis that the economic equilibrium principle increases the conflictive nature of public contracting. They test the hypothesis empirically. The first section of the paper presents a summary of the literature on transaction costs economics, as well as the legal literature on the historical origin and the content of the economic equilibrium principle. The second section describes the methodology of the empirical study. The third section shows the empirical evidence of the effects that the economic equilibrium principle exerts over the public contracting. The last section presents the conclusions.

The voters of Colombia are free?

A fundamental principle of democracy is citizenship freedom. We suggest that a fair electoral contest is possible if a relationship between free will, electoral preferences and respect to the public institutions (constitutionalism) (section 1) exists. We focus on three illiberal practices that perturb the voter's decision: political clientelism and political markets (sections 2 to 4), media influence (which feeds on the voter's limited rationality and limited information) (section 5), and the suppression of opposition options (section 6). Later (section 8), we provide a brief balance and, additionally, we show how in Colombia the political system has missed opportunities to expand the voters' freedom. Our interpretation of the electoral process in Colombia is an appeal, supported on theoretical arguments and empirical evidence, to doubt about the voters' freedom. Also we make a call for more etudies.

Modelling, control and supervision for a class of hybrid systems

The aim of this thesis is to narrow the gap between two different control techniques: the continuous control and the discrete event control techniques DES. This gap can be reduced by the study of Hybrid systems, and by interpreting as Hybrid systems the majority of large-scale systems. In particular, when looking deeply into a process, it is often possible to identify interaction between discrete and continuous signals. Hybrid systems are systems that have both continuous, and discrete signals. Continuous signals are generally supposed continuous and differentiable in time, since discrete signals are neither continuous nor differentiable in time due to their abrupt changes in time. Continuous signals often represent the measure of natural physical magnitudes such as temperature, pressure etc. The discrete signals are normally artificial signals, operated by human artefacts as current, voltage, light etc. Typical processes modelled as Hybrid systems are production systems, chemical process, or continuos production when time and continuous measures interacts with the transport, and stock inventory system. Complex systems as manufacturing lines are hybrid in a global sense. They can be decomposed into several subsystems, and their links. Another motivation for the study of Hybrid systems is the tools developed by other research domains. These tools benefit from the use of temporal logic for the analysis of several properties of Hybrid systems model, and use it to design systems and controllers, which satisfies physical or imposed restrictions. This thesis is focused in particular types of systems with discrete and continuous signals in interaction. That can be modelled hard non-linealities, such as hysteresis, jumps in the state, limit cycles, etc. and their possible non-deterministic future behaviour expressed by an interpretable model description. The Hybrid systems treated in this work are systems with several discrete states, always less than thirty states (it can arrive to NP hard problem), and continuous dynamics evolving with expression: with Ki ¡ Rn constant vectors or matrices for X components vector. In several states the continuous evolution can be several of them Ki = 0. In this formulation, the mathematics can express Time invariant linear system. By the use of this expression for a local part, the combination of several local linear models is possible to represent non-linear systems. And with the interaction with discrete events of the system the model can compose non-linear Hybrid systems. Especially multistage processes with high continuous dynamics are well represented by the proposed methodology. Sate vectors with more than two components, as third order models or higher is well approximated by the proposed approximation. Flexible belt transmission, chemical reactions with initial start-up and mobile robots with important friction are several physical systems, which profits from the benefits of proposed methodology (accuracy). The motivation of this thesis is to obtain a solution that can control and drive the Hybrid systems from the origin or starting point to the goal. How to obtain this solution, and which is the best solution in terms of one cost function subject to the physical restrictions and control actions is analysed. Hybrid systems that have several possible states, different ways to drive the system to the goal and different continuous control signals are problems that motivate this research. The requirements of the system on which we work is: a model that can represent the behaviour of the non-linear systems, and that possibilities the prediction of possible future behaviour for the model, in order to apply an supervisor which decides the optimal and secure action to drive the system toward the goal. Specific problems can be determined by the use of this kind of hybrid models are: - The unity of order. - Control the system along a reachable path. - Control the system in a safe path. - Optimise the cost function. - Modularity of control The proposed model solves the specified problems in the switching models problem, the initial condition calculus and the unity of the order models. Continuous and discrete phenomena are represented in Linear hybrid models, defined with defined eighth-tuple parameters to model different types of hybrid phenomena. Applying a transformation over the state vector : for LTI system we obtain from a two-dimensional SS a single parameter, alpha, which still maintains the dynamical information. Combining this parameter with the system output, a complete description of the system is obtained in a form of a graph in polar representation. Using Tagaki-Sugeno type III is a fuzzy model which include linear time invariant LTI models for each local model, the fuzzyfication of different LTI local model gives as a result a non-linear time invariant model. In our case the output and the alpha measure govern the membership function. Hybrid systems control is a huge task, the processes need to be guided from the Starting point to the desired End point, passing a through of different specific states and points in the trajectory. The system can be structured in different levels of abstraction and the control in three layers for the Hybrid systems from planning the process to produce the actions, these are the planning, the process and control layer. In this case the algorithms will be applied to robotics ¡V a domain where improvements are well accepted ¡V it is expected to find a simple repetitive processes for which the extra effort in complexity can be compensated by some cost reductions. It may be also interesting to implement some control optimisation to processes such as fuel injection, DC-DC converters etc. In order to apply the RW theory of discrete event systems on a Hybrid system, we must abstract the continuous signals and to project the events generated for these signals, to obtain new sets of observable and controllable events. Ramadge & Wonham¡¦s theory along with the TCT software give a Controllable Sublanguage of the legal language generated for a Discrete Event System (DES). Continuous abstraction transforms predicates over continuous variables into controllable or uncontrollable events, and modifies the set of uncontrollable, controllable observable and unobservable events. Continuous signals produce into the system virtual events, when this crosses the bound limits. If this event is deterministic, they can be projected. It is necessary to determine the controllability of this event, in order to assign this to the corresponding set, , controllable, uncontrollable, observable and unobservable set of events. Find optimal trajectories in order to minimise some cost function is the goal of the modelling procedure. Mathematical model for the system allows the user to apply mathematical techniques over this expression. These possibilities are, to minimise a specific cost function, to obtain optimal controllers and to approximate a specific trajectory. The combination of the Dynamic Programming with Bellman Principle of optimality, give us the procedure to solve the minimum time trajectory for Hybrid systems. The problem is greater when there exists interaction between adjacent states. In Hybrid systems the problem is to determine the partial set points to be applied at the local models. Optimal controller can be implemented in each local model in order to assure the minimisation of the local costs. The solution of this problem needs to give us the trajectory to follow the system. Trajectory marked by a set of set points to force the system to passing over them. Several ways are possible to drive the system from the Starting point Xi to the End point Xf. Different ways are interesting in: dynamic sense, minimum states, approximation at set points, etc. These ways need to be safe and viable and RchW. And only one of them must to be applied, normally the best, which minimises the proposed cost function. A Reachable Way, this means the controllable way and safe, will be evaluated in order to obtain which one minimises the cost function. Contribution of this work is a complete framework to work with the majority Hybrid systems, the procedures to model, control and supervise are defined and explained and its use is demonstrated. Also explained is the procedure to model the systems to be analysed for automatic verification. Great improvements were obtained by using this methodology in comparison to using other piecewise linear approximations. It is demonstrated in particular cases this methodology can provide best approximation. The most important contribution of this work, is the Alpha approximation for non-linear systems with high dynamics While this kind of process is not typical, but in this case the Alpha approximation is the best linear approximation to use, and give a compact representation.

What kind of European Banking Union? Bruegel Policy Contribution [2012/12?]June 25, 2012

This paper discusses the creation of a European Banking Union. First, we discuss questions of design. We highlight seven fundamental choices that decision makers will need to make: Which EU countries should participate in the banking union? To which categories of banks should it apply? Which institution should be tasked with supervision? Which one should deal with resolution? How centralised should the deposit insurance system be? What kind of fiscal backing would be required? What governance framework and political institutions would be needed? In terms of geographical scope, we see the coverage of the banking union of the euro area as necessary and of additional countries as desirable, even though this would entail important additional economic difficulties. The system should ideally cover all banks within the countries included, in order to prevent major competitive and distributional distortions. Supervisory authority should be granted either to both the ECB and a new agency, or to a new agency alone. National supervisors, acting under the authority of the European supervisor, would be tasked with the supervision of smaller banks in accordance with the subsidiarity principle. A European resolution authority should be established, with the possibility of drawing on ESM resources. A fully centralized deposit insurance system would eventually be desirable, but a system of partial reinsurance may also be envisaged at least in a first phase. A banking union would require at least implicit European fiscal backing, with significant political authority and legitimacy. Thus, banking union cannot be considered entirely separately from fiscal union and political union. The most difficult challenge of creating a European banking union lies with the short-term steps towards its eventual implementation. Many banks in the euro area, and especially in the crisis countries, are currently under stress and the move towards banking union almost certainly has significant distributional implications. Yet it is precisely because banks are under such stress that early and concrete action is needed. An overarching principle for such action is to minimize the cost to the tax payers. The first step should be to create a European supervisor that will anchor the development of the future banking union. In parallel, a capability to quickly assess the true capital position of the system’s most important banks should be created, for which we suggest establishing a temporary European Banking Sector Task Force working together with the European supervisor and other authorities. Ideally, problems identified by this process should be resolved by national authorities; in case fiscal capacities would prove insufficient, the European level would take over in the country concerned with some national financial participation, or in an even less likely adverse scenario, in all participating countries at once. This approach would require the passing of emergency legislation in the concerned countries that would give the Task Force the required access to information and, if necessary, further intervention rights. Thus, the principle of fiscal responsibility of respective member states for legacy costs would be preserved to the maximum extent possible, and at the same time, market participants and the public would be reassured that adequate tools are in place to address any eventuality.

The acoustic signature of fluid flow in complex porous media

Effective medium approximations for the frequency-dependent and complex-valued effective stiffness tensors of cracked/ porous rocks with multiple solid constituents are developed on the basis of the T-matrix approach (based on integral equation methods for quasi-static composites), the elastic - viscoelastic correspondence principle, and a unified treatment of the local and global flow mechanisms, which is consistent with the principle of fluid mass conservation. The main advantage of using the T-matrix approach, rather than the first-order approach of Eshelby or the second-order approach of Hudson, is that it produces physically plausible results even when the volume concentrations of inclusions or cavities are no longer small. The new formulae, which operates with an arbitrary homogeneous (anisotropic) reference medium and contains terms of all order in the volume concentrations of solid particles and communicating cavities, take explicitly account of inclusion shape and spatial distribution independently. We show analytically that an expansion of the T-matrix formulae to first order in the volume concentration of cavities (in agreement with the dilute estimate of Eshelby) has the correct dependence on the properties of the saturating fluid, in the sense that it is consistent with the Brown-Korringa relation, when the frequency is sufficiently low. We present numerical results for the (anisotropic) effective viscoelastic properties of a cracked permeable medium with finite storage porosity, indicating that the complete T-matrix formulae (including the higher-order terms) are generally consistent with the Brown-Korringa relation, at least if we assume the spatial distribution of cavities to be the same for all cavity pairs. We have found an efficient way to treat statistical correlations in the shapes and orientations of the communicating cavities, and also obtained a reasonable match between theoretical predictions (based on a dual porosity model for quartz-clay mixtures, involving relatively flat clay-related pores and more rounded quartz-related pores) and laboratory results for the ultrasonic velocity and attenuation spectra of a suite of typical reservoir rocks. (C) 2003 Elsevier B.V. All rights reserved.

Innovative implementation of iLearn e-Portfolio for Personal Development Planning

iLearn is a Web 2.0 tool developed in Blackboard to help students with Personal Development Planning (PDP). This paper describes a case study on how the innovative use of mobile digital technology in iLearn e-Portfolio for developing reflective portfolios for PDP benefits the students. The e-Portfolio tool benefits students as it enables them to create and share portfolios, record achievements and reflections that support future job applications and promotion. Students find it beneficial because they can make use of iLearn e-Portfolio to keep academic records and achievements, activities and interests, work experience, reflective practice, employer information and some other useful resources, and also to tailor their CV and covering letters including evidence to support their CV, transferable skills and selling points. Useful information for preparing for an interview, reflecting after an event and any thoughts and evaluation can be kept in iLearn e-Portfolio. Keeping assessment and feedback records in iLearn e-Portfolio enables students to know their progress, to identify any gaps they need to fill to develop their study practices and areas for development. The key points from the feedback on the assignments and assessments are beneficial for future improvement. The reflections on the assignments and how students make use of the advice are particularly useful to improve their overall performance. In terms of pedagogical benefits, the “Individual Learner Profile” records and reviews evidence in verbal communication, basic and higher academic skills, time management, numeracy skill and IT skills, students become increasingly aware of their own strengths and any weaker areas that may require development. The e-Portfolio also provides opportunity for students to reflect on the experience and skills they have gained whilst participating in activities outside their studies. As the iLearn e-Portfolio is a reflective practice tool, it is consistent with the principle of Schon's reflective practitioner to reframe problems and to explore the consequences of actions. From the students’ feedback, for those who engage regularly in iLearn, they are better able to set agendas for their Personal Tutorial meetings and provide their Personal Tutor with a unique record of their achievements, skills and attributes which help them writing effective references for them. They make the most of their student experience in general. They also enhance their transferable skills and employability overall. The iLearn e-Portfolio prepares for the workplace and life beyond University including continuing professional development. Students are aware of their transferable skills, evidence of the skills and skill level, including award or accreditation, and their personal reflection on their transferable skills. It is beneficial for students to be aware of their transferable skills, to produce evidence of the skills and skills level such as award and accreditation, and to record their personal reflection on their transferable skills. Finally, the innovative use of mobile digital technology in iLearn e-Portfolio for developing reflective portfolios for PDP will improve their employability.

Innovative use of e-portfolio for personal development

iLearn is a quasi-Web 2.0 tool developed in Blackboard to help users with Personal Development Planning (PDP). This paper describes a case study on how the innovative use of mobile digital technology in iLearn e-Portfolio for developing reflective portfolios for PDP benefits the users, who are training to be professionals in construction management and surveying, The e-Portfolio tool benefits users as it enables them to create and share portfolios, record achievements and reflections that support future job applications and promotion. Users find it beneficial because they can make use of iLearn e-Portfolio to keep academic records and achievements, activities and interests, work experience, reflective practice, employer information and some other useful resources, and also to tailor their CV and covering letters including evidence to support their CV, transferable skills and selling points. Useful information for preparing for an interview, reflecting after an event and any thoughts and evaluation can be kept in iLearn e-Portfolio. Keeping assessment and feedback records in iLearn e-Portfolio enables learners to know their progress, to identify any gaps they need to fill to develop their study practices and areas for development. The key points from the feedback on the assignments and assessments are beneficial for future improvement. The reflections on the tasks and how they make use of the advice are particularly useful to improve their overall performance. In terms of pedagogical benefits, the “Individual Learner Profile” records and reviews evidence in verbal communication, basic and higher academic skills, time management, numeracy skill and IT skills, learners become increasingly aware of their own strengths and any weaker areas that may require development. The e-Portfolio also provides opportunity for them to reflect on the experience and skills they have gained whilst participating in activities outside their studies. As the iLearn e-Portfolio is a reflective practice tool, it is consistent with the principle of Schon's reflective practitioner to reframe problems and to explore the consequences of actions. From the users’ feedback, for those who engage regularly in iLearn, they are better able to set agendas for their supervision meetings and provide their supervisor with a unique record of their achievements, skills and attributes which help them writing effective references for them. They make the most of their learning experience in general. They also enhance their transferable skills and employability overall. The iLearn e-Portfolio prepares them for the workplace including continuing professional development. Users are aware of their transferable skills, evidence of the skills and skill level, including award or accreditation, and their personal reflection on their transferable skills. It is beneficial for them to be aware of their transferable skills, to produce evidence of the skills and skills level such as award and accreditation, and to record their personal reflection on their transferable skills. Finally, the innovative use of mobile digital technology in iLearn e-Portfolio for developing reflective portfolios for PDP will improve their employability.

Micellar catalysis for partial oxidation of toluene to benzoic acid in supercritical CO2: effects of fluorinated surfactants

One of the key hindrances on development of solid catalysts containing cobalt species for partial oxidation of organic molecules at mild conditions in conventional liquid phase is the severe metal leaching. The leached soluble Co species with a higher degree of freedom always out-performs those of solid supported Co species in oxidation catalysis. However, the homogeneous Co species concomitantly introduces separation problems. We have recently reponed for the first time, a new oxidation catalyst system for the oxidation of organic molecules in supercritical CO2 using the principle of micellar catalysis. [CF3(CF2)(8)COO](2)Co.xH(2)O (the fluorinated anionic moiety forms aqueous reverse micelles carrying water-soluble Co2+ cations in scCO(2)) was previously shown to be extremely active for the oxidation of toluene in the presence of sodium bromide in water-CO2 mixture, giving 98% conversion and 99% selectivity to benzoic acid at 120 degreesC. In this study, we show that the effects of varying the type of surfactant counterions and the length of the surfactant chains on catalysis. It is found that the use of [CF3(CF2)(8)COO](2)Mg.yH(2)O/Co(II) acetate is as effective as the [CF3(CF2)(8)COO](2)Co.xH(2)O and the fluorinated chain length used has a subtle effect on the catalytic rate measured. It is also demonstrated that this new type of micellar catalyst in scCO(2) can be easily separated via CO2 depressurisation and be reused without noticeable deactivation. (C) 2003 Elsevier B.V. All rights reserved.

Integrable Hamiltonian systems defined on the Lie groups SO(3) and SU(2): an application to the attitude control of a spacecraft

This paper considers left-invariant control systems defined on the Lie groups SU(2) and SO(3). Such systems have a number of applications in both classical and quantum control problems. The purpose of this paper is two-fold. Firstly, the optimal control problem for a system varying on these Lie Groups, with cost that is quadratic in control is lifted to their Hamiltonian vector fields through the Maximum principle of optimal control and explicitly solved. Secondly, the control systems are integrated down to the level of the group to give the solutions for the optimal paths corresponding to the optimal controls. In addition it is shown here that integrating these equations on the Lie algebra su(2) gives simpler solutions than when these are integrated on the Lie algebra so(3).

Singularities of optimal control problems on some 6-D lie groups

This paper considers the motion planning problem for oriented vehicles travelling at unit speed in a 3-D space. A Lie group formulation arises naturally and the vehicles are modeled as kinematic control systems with drift defined on the orthonormal frame bundles of particular Riemannian manifolds, specifically, the 3-D space forms Euclidean space E-3, the sphere S-3, and the hyperboloid H'. The corresponding frame bundles are equal to the Euclidean group of motions SE(3), the rotation group SO(4), and the Lorentz group SO (1, 3). The maximum principle of optimal control shifts the emphasis for these systems to the associated Hamiltonian formalism. For an integrable case, the extremal curves are explicitly expressed in terms of elliptic functions. In this paper, a study at the singularities of the extremal curves are given, which correspond to critical points of these elliptic functions. The extremal curves are characterized as the intersections of invariant surfaces and are illustrated graphically at the singular points. It. is then shown that the projections, of the extremals onto the base space, called elastica, at these singular points, are curves of constant curvature and torsion, which in turn implies that the oriented vehicles trace helices.

Whose land was it anyway? The Crichel Down Rules and the sale of public land

The guiding principle of compulsory purchase of interests in land in England and Wales is that of fairness, best stated in the words of Lord Justice Scott in Horn v Sunderland Corporation when he said that the owner has “the right to be put, so far as money can do it, in the same position as if his land had not been taken from him”. In many instances, land acquired by compulsion subsequently becomes surplus to the requirements of the acquiring authority. This may be because the intended development scheme was scrapped, or substantially modified, or that after the passage of time the use of the land for which the purchase took place is no longer required. More controversially it may be that for ‘operational reasons’ the acquiring authority knowingly purchased more land than was required for the scheme. Under these circumstances, the Crichel Down Rules (‘the Rules’) require government departments and other statutory bodies to offer back to the former owners or their successors, any land previously so acquired by, or under the threat of, compulsory purchase.

On-farm management of rice genetic diversity: understanding farmers' knowledge on rice ecosystems and varietal development

The paper highlights the methodological development of identifying and characterizing rice (Oryza sativa L.) ecosystems and the varietal deployment process through participatory approaches. Farmers have intricate knowledge of their rice ecosystems. Evidence from Begnas (mid-hill) and Kachorwa (plain) sites in Nepal suggests that farmers distinguish ecosystems for rice primarily on the basis of moisture and fertility of soils. Farmers also differentiate the number, relative size and specific characteristics of each ecosystem within a given geographic area. They allocate individual varieties to each ecosystem, based on the principle of ‘best fit’ between ecosystem characteristics and varietal traits, indicating that competition between varieties mainly occurs within the ecosystems. Land use and ecosystems determine rice genetic diversity, with marginal land having fewer options for varieties than more productive areas. Modern varieties are mostly confined to productive land, whereas landraces are adapted to marginal ecosystems. Researchers need to understand the ecosystems and varietal distribution within ecosystems better in order to plan and execute programmes on agrobiodiversity conservation on-farm, diversity deployment, repatriation of landraces and monitoring varietal diversity. Simple and practical ways to elicit information on rice ecosystems and associated varieties through farmers’ group discussion at village level are suggested.

British pharmacy professionals’ beliefs and participation in continuing professional development: a review of the literature.

Objectives Continuing professional development (CPD) has potential to be useful in pharmacy revalidation but past uptake and attitudes to CPD in Great Britain (GB) need to be mapped. This review examines published literature to chart the participation and beliefs of pharmacy professionals towards CPD in GB in a decade that had seen a formal transition from continuing education to CPD. Methods A comprehensive review of the published literature was conducted to identify studies of the uptake of, or attitudes towards, CPD cross different sectors of pharmacy in GB from 2000 to 2010. Key findings Twenty-two studies were included and analysed, including 13 research papers, six conference papers, two news items reporting survey outcomes and one commissioned study. Eight barriers to CPD were identified as: time, financial costs and resource issues, understanding of CPD, facilitation and support for CPD, motivation and interest in CPD, attitudes towards compulsory CPD, system constraints, and technical problems. Pharmacy professionals on the whole agreed with the principle of engaging with CPD but there was little evidence to suggest widespread and wholehearted acceptance and uptake of CPD, essential for revalidation. Conclusions If CPD is to succeed, people's beliefs and attitudes must be addressed by recognising and modifying perceived barriers through a combination of regulatory, professional, work-related and personal channels. A number of recommendations are made. Direct experience of effective CPD in the absence of perceived barriers could impact on personal development, career development and patient benefit thus strengthening personal beliefs in the value of CPD in an iterative manner.

British pharmacy professionals' beliefs and participation in continuing professional development: a review of the literature

Objectives:  Continuing professional development (CPD) has potential to be useful in pharmacy revalidation but past uptake and attitudes to CPD in Great Britain (GB) need to be mapped. This review examines published literature to chart the participation and beliefs of pharmacy professionals towards CPD in GB in a decade that had seen a formal transition from continuing education to CPD. Methods:  A comprehensive review of the published literature was conducted to identify studies of the uptake of, or attitudes towards, CPD cross different sectors of pharmacy in GB from 2000 to 2010. Key findings:  Twenty-two studies were included and analysed, including 13 research papers, six conference papers, two news items reporting survey outcomes and one commissioned study. Eight barriers to CPD were identified as: time, financial costs and resource issues, understanding of CPD, facilitation and support for CPD, motivation and interest in CPD, attitudes towards compulsory CPD, system constraints, and technical problems. Pharmacy professionals on the whole agreed with the principle of engaging with CPD but there was little evidence to suggest widespread and wholehearted acceptance and uptake of CPD, essential for revalidation. Conclusions:  If CPD is to succeed, people's beliefs and attitudes must be addressed by recognising and modifying perceived barriers through a combination of regulatory, professional, work-related and personal channels. A number of recommendations are made. Direct experience of effective CPD in the absence of perceived barriers could impact on personal development, career development and patient benefit thus strengthening personal beliefs in the value of CPD in an iterative manner.

Evidence of dispersion relations for the nonlinear response of the Lorenz 63 system

Along the lines of the nonlinear response theory developed by Ruelle, in a previous paper we have proved under rather general conditions that Kramers-Kronig dispersion relations and sum rules apply for a class of susceptibilities describing at any order of perturbation the response of Axiom A non equilibrium steady state systems to weak monochromatic forcings. We present here the first evidence of the validity of these integral relations for the linear and the second harmonic response for the perturbed Lorenz 63 system, by showing that numerical simulations agree up to high degree of accuracy with the theoretical predictions. Some new theoretical results, showing how to derive asymptotic behaviors and how to obtain recursively harmonic generation susceptibilities for general observables, are also presented. Our findings confirm the conceptual validity of the nonlinear response theory, suggest that the theory can be extended for more general non equilibrium steady state systems, and shed new light on the applicability of very general tools, based only upon the principle of causality, for diagnosing the behavior of perturbed chaotic systems and reconstructing their output signals, in situations where the fluctuation-dissipation relation is not of great help.