Quantum localized modes in capacitively coupled Josephson junctions

We consider the quantum dynamics of excitations in a system of two capacitively coupled Josephson junctions. Quantum breather states are found in the middle of the energy spectrum of the confined nonescaping states of the system. They are characterized by a strong excitation of one junction. These states perform slow tunneling motion from one junction to the other, while keeping their coherent nature. The tunneling time sensitively depends on the initial excitation energy. By using an external bias as a control parameter, the tunneling time can be varied with respect to the escape time and the experimentally limited coherence time. Thus one can control the flow of quantum excitations between the two junctions.Comment: 5 pages, 3 figures. Improved version, title was slightly changed. Accepted in Europhysics Letters (http://www.iop.org/EJ/journal/EPL

Explosive synchronization with partial degree-frequency correlation

Networks of Kuramoto oscillators with a positive correlation between the oscillators frequencies and the degree of the their corresponding vertices exhibits the so-called explosive synchronization behavior, which is now under intensive investigation. Here, we study and report explosive synchronization in a situation that has not yet been considered, namely when only a part, typically small, of the vertices is subjected to a degree frequency correlation. Our results show that in order to have explosive synchronization, it suffices to have degree-frequency correlations only for the hubs, the vertices with the highest degrees. Moreover, we show that a partial degree-frequency correlation does not only promotes but also allows explosive synchronization to happen in networks for which a full degree-frequency correlation would not allow it. We perform exhaustive numerical experiments for synthetic networks and also for the undirected and unweighted version of the neural network of the worm Caenorhabditis elegans. The latter is an explicit example where partial degree-frequency correlation leads to explosive synchronization with hysteresis, in contrast with the fully correlated case, for which no explosive synchronization is observed.Comment: 10 pages, 6 figures, final version to appear in PR

Optimal synchronization of Kuramoto oscillators: a dimensional reduction approach

A recently proposed dimensional reduction approach for studying synchronization in the Kuramoto model is employed to build optimal network topologies to favor or to suppress synchronization. The approach is based in the introduction of a collective coordinate for the time evolution of the phase locked oscillators, in the spirit of the Ott-Antonsen ansatz. We show that the optimal synchronization of a Kuramoto network demands the maximization of the quadratic function $\omega^T L \omega$, where $\omega$ stands for the vector of the natural frequencies of the oscillators, and $L$ for the network Laplacian matrix. Many recently obtained numerical results can be re-obtained analytically and in a simpler way from our maximization condition. A computationally efficient {hill climb} rewiring algorithm is proposed to generate networks with optimal synchronization properties. Our approach can be easily adapted to the case of the Kuramoto models with both attractive and repulsive interactions, and again many recent numerical results can be rederived in a simpler and clearer analytical manner.Comment: 6 pages, 6 figures, final version to appear in PR

Quantum breathers in capacitively coupled Josephson junctions: Correlations, number conservation, and entanglement

We consider the classical and quantum dynamics of excitations in a system of two capacitively coupled Josephson junctions. In the classical case the equations of motion admit discrete breather solutions, which are time periodic and localized predominantly on one of the junctions. In the quantum case breather states are found in the central part of the energy spectrum of the confined nonescaping states of the system. We perform a systematic analysis of their tunneling frequency, site correlations, fluctuations of the number of quanta, and entanglement. Quantum breather states show strong site correlation of quanta and are characterized by a strong excitation of quanta on one junction which perform slow coherent tunneling motion from one junction to the other. They suppress fluctuations of the total number of excited quanta. Quantum breather states are the least entangled states among the group of eigenstates in the same range of the energy spectrum. We describe how quantum breather excitations could be experimentally observed by employing the already developed techniques for quantum information processing using Josephson junctions.Comment: 10 pages, 9 figures. Improved version with further discussions. Accepted in Physical Review

Discontinuous Almost Automorphic Functions and Almost Automorphic Solutions of Differential Equations with Piecewise Constant Argument

In this article we introduce a class of discontinuous almost automorphic functions which appears naturally in the study of almost automorphic solutions of differential equations with piecewise constant argument. Their fundamental properties are used to prove the almost automorphicity of bounded solutions of a system of differential equations with piecewise constant argument. Due to the strong discrete character of these equations, the existence of a unique discrete almost automorphic solution of a non-autonomous almost automorphic difference system is obtained, for which conditions of exponential dichotomy and discrete Bi-almost automorphicity are fundamental

Modelling a layer for real-time management of interactions in web based distance learning

In the last few years, the University of Aveiro, Portugal, has been offering several distance learning courses over the Web, using e-learning platforms. Experience showed that different editions of a same course, using the same contents and structure, and having similar target learners, had different success rates. What would be the reason for that? A hypothesis was considered: The level of success could be directly related with the remote follow-up of the learners’ participation in the courses; the best results usually occur when the follow-up is closer. The existing e-learning platforms offer and the standardization works being developed by organizations and consortiums like IMS (IMS Global Learning Consortium, Inc), ADL SCORM (Advanced Distributed Learning Sherable Content Object Reference Model), IEEE LTSC LOM (Institute of Electrical and Electronic Engineers Learning Technologies Standard Committee Learning Object Metadata), ARIADNE (ARIADNE Foundation for the European Knowledge Pool), AICC CMI (Aviation Industry CBT Committee Computer Managed Instruction), etc, don’t cover the course monitorization concerns mentioned. Those projects were focused on aspects like contents and its delivery in the context of the execution of the courses’ activities. This is even true in the SCORM project that doesn’t include any reference to the management of the e-learning processes. Recently, in the context of the IMS Global Consortium, a new project designated IMS LD (Learning Design) is under development, providing a framework for the description of learning units under a three level model. In the most recently defined level, the C level, some functionalities related to notifications were proposed, expressing similar concerns to the ones that triggered our research. However, the extent at which IMS LD takes the functionalities is, from our point of view, not complete. This article describes a proposal of a reference model and functionalities towards a specification of a layer for real-time management of user interactions on LMSs, and its possible integration with the ADL SCORM standard proposal. The paper includes a discussion of the management metadata model for the LMS sub-system and how the integration of the management module under SCORM may be achieved

Enhancing web supported learning in higher education by adding a management layer to LMSs

There are many situations in the e-Learning experiences that can compromise the success of the courses. Many times simple reasons are great enough to motivate people to abandon them. For example, if someone does not execute a programmed activity inside the defined window of time, it can compromise the rest of the course to that person. In such situations it would be important that the teacher knew about the situation in useful time, to be able to take any corrective action. Another example could be presented, involving the professor and the learners. Let us assume that an activity A2 is programmed to be executed by the learners and that it depends on the previous knowledge of the result of the evaluation of a work submitted by the learners to the teacher (activity A1). If the teacher doesn’t inform the learners about their classification in useful time, that can compromise the execution of the activity A2. It seems to be necessary to use mechanisms of automatic management, in real time, of the envolvement of each participant in a distance learning course using LMS (Learning Management System). Such a functionality allows the detection of deviations to the scheduled activities planned for each actor. If it is the case, the referred mechanism can initiate the process of sending notifications to the relevant entities, enabling the correction of these deviations. Several organizations and consortiuns, involving the industry, governmental institutions and universities, are developing projects of standardization. It seemed important to us to see how the referred aspects were covered by those projects, and to perceive how it could be possible to articulate our work with the ones that are available from these organizations and consortiuns. This article describes the work that the authors are developing towards the specification of a layer for real-time management of user interactions with LMSs, during the operationalization of a course, and also includes a management meta-data model, related to that management layer