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MindMaps, a tool for mLearning

we propose to achieve this goal.

3Mobile Learning : Smartphones and tablets

We can define it in a very simplistic manner: It is e-learning through mobile computational devices. Another feasible definition, combined with distance education: Mobile learning is learning with a specific device, at any time, any place. The device must be capable of presenting learning content and providing wireless two-way communication between teacher(s) and student(s). Adding Social Networking to the equation, Mobile learning could be understood as a new way of learning using mobile networks and tools,with the aim of expanding digital learning channel to get educational information, resources and services anytime, anywhere.

People do not access to social networks unless they do see a clear advantage (utility principle). As smartphones o er more and more facilities such as accessing the Internet through 3G networks, people is accessing social networks through their smartphones to do useful tasks instead of wasting time doing nothing while waiting the bus, i.e.. So, two aspects, useful for learning, can be combined here: smartphones (or tablets) and the access to social networking. Studies such as the one conducted by Dough Vogel et al in [5] shows that mobile learning is shown to be useful to learn. Digital natives are, therefore, at the center of their own personal learning environment (e.g., smartphones, tablets, iPods, etc.) and in contrast to this, limited attention has been given to the impact on learning of mobile devices and associated applications in education. This is why MindMaps is presented here. Usage of mLearning and social networking is further correlated with performance as exhibited on exams (as our we can tell from our experiences). Particular attention is given to the pattern of mobile learning application use, e.g., for exploration of alternatives. We can enhance learning motivation by emphasizing the importance and applicability of the material and by trying to connect the material to students’ intrinsic motives. They particularly note that learning motivation is likely to be greater if a student feels a particular class is consistent with their interests and with personally satisfying career goals. However, learning motivation is malleable and can change over time. In mobile learning environment, students not only study in the classroom or computer but also in any place thanks to their mobile devices. In this paper, we build a learning model based on a tool to navigate through connected conceptual maps, where items are linked to social networks, to University LMS, and enriched with links to resources. The teacher can create conceptual maps for his courses and connect them to other courses’ maps, can provide meta-information for each concept so the student can go for alternative information in social networks, the student can also get only summarized resources into his mobile to study the course while waiting the bus, i.e. We are using both devices, smartphones as the primary device from the students’ side and tablets pcs (TPC) for lecturers. Studies like the one done in [4] states that using the tablet

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J.A. Alvarez-Bermejo, L.J. Belmonte-Urena, C. Bernal-Bravo

PC as a lecturing device o ers the instructor a new set of tools upon which their teaching can be based as it provides the instructor with an extended set of educational tools. From the perspective of the audience, the TPC allows the instructor to maintain a connection with their students. In [2] it is shown how this learning model based in smartphones and tablet pcs, enable a way of knowledge sharing, with the tool that we present in this paper, we intend to extend these characteristics to certain social networks where learning and intelligence sharing can be boosted.

4MindMaps. Our solution

It has been proven that smartphones and tablets are a new chance for students and teachers to seize a new methodology that seems to be better than many others because of its ubiquitous and how the content is summarized to be distributed to such devices. Also, connectivity in these devices is wisely used to access on-line resources when idle time slots occurs, so time is now better employed than before. The tool we are presenting here is designed to seize the advantages underlined for smartphones and tablets in the learning context, but also to let the students explore and get extra motivation for what they are learning. The application is divided into two sections, one for faculties and the other one for students.

Figure 1: Using MindMaps from smartphones

The student uses his smartphone to download maps, and navigate through each concept, in formal or informal networks. The teacher can also leave PDF documents, videos, etc. associated to each concept to provide further information. The teacher creates his own

MindMaps, a tool for mLearning

maps, and leave them in the institutional LMS (learning management system) used by the students. In Fig. 1 the connection to the course content designed by the teacher is shown. Fig. 2 shows the side of MindMaps for teachers. Each concept can be enriched with extra content or links to other maps or social networks (in this case using the tags that the teacher provides).

Figure 2: Creating Conceptual Maps and Linking them to other maps or content (in LMS or in Social Networks)

(a) Creating the Map: the teacher must provide a title and meta-information used to link the current map with other resources

(b) MindMaps allow you to link items to other maps (in the institutional LMS) or to Social Network content. This map is later saved as an exportable file for smartphones or tablets

In Fig. 3 the map is displayed in the smartphone as shown in Fig. 3(a). When the student interacts with the map, on a certain concept, a context menu appears to let him download the resources provided by the teacher, or by explore social networks for that

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J.A. Alvarez-Bermejo, L.J. Belmonte-Urena, C. Bernal-Bravo

concept, or link to other maps (from the same course or from other courses that are related). The student is always provided with a track of the maps he followed to be always contextualized.

Figure 3: MindMaps are accessed by students anywhere, anytime by simply accessing or downloading the map file form the LMS server. When an item is touched, a context menu(b) appears allowing the navigation proceed to other maps, social networks or content.

5Conclusions

In general, our results provide some support for our research model, see Fig.1, and associated postulates. Empirically, those students who were motivated to use the mobile applications tended to achieve higher levels of performance as indicated on their proof exam. This is independent of whether the motivation was intrinsic or extrinsic noting that fewer than half of the students could download and use the application as a test group. The final exam included a question to gather information about their real comprehensive knowledge (Q10. Please explain which is the relationship between units of this course and give reasons why the units are ordered in such way): those who used MindMaps answered correctly, those who didn’t, provided obvious answers. We can conclude that those who received extra knowledge, that contextualized it and were motivated to do so, gained extra skills from this course that is to be useful for the courses related (and they are aware). From the technical side, we could check that the tablet PC o ers many advantages over the traditional blackboard approach to improve the overall learning experience of the students. It enabled the instructor to engage students more thoroughly through the use of added multimedia content.

MindMaps, a tool for mLearning

Acknowledgements

Our sincere gratitude to Jos´e Luis L´opez L´opez, for his valuable work and advices during the development of MindMaps. Jos´e Luis L´opez L´opez is a student that extended and improved MindMaps for his Bachelor’s degree.

References

[1]Peter Marks, Peter Polak, Scott McCoy, and Dennis Galletta. Sharing knowledge. Commun. ACM, 51(2):60–65, February 2008.

[2]N. Matsuuchi, T. Yamaguchi, H. Shiba, K. Fujiwara, and K. Shimamura. Collaborative learning system providing interactive lesson through tablet pcs on wlan. In Information and Telecommunication Technologies, 2008. APSITT. 7th Asia-Pacific Symposium on, pages 47 –51, april 2008.

[3]Zhengzheng Pan. Trust, influence, and convergence of behavior in social networks.

Mathematical Social Sciences, 60(1):69–78, 2010.

[4]M. Stickel. Impact of lecturing with the tablet pc on students of di erent learning styles. In Frontiers in Education Conference, 2009. FIE ’09. 39th IEEE, pages 1 –6, oct. 2009.

[5]Doug Vogel, David M. Kennedy, Kevin Kuan, Ron Kwok, and Jean Lai. Do mobile device applications a ect learning? In System Sciences, 2007. HICSS 2007. 40th Annual Hawaii International Conference on, page 4, jan. 2007.

[6]Angela Yan Yu, Stella Wen Tian, Douglas Vogel, and Ron Chi-Wai Kwok. Can learning be virtually boosted? an investigation of online social networking impacts. Comput. Educ., 55(4):1494–1503, December 2010.

Proceedings of the 12th International Conference on Computational and Mathematical Methods in Science and Engineering, CMMSE 2012 July, 2-5, 2012.

E ects Of Di usion And Transmembrane Potential

On Current Through Ionic Channels

Daniele Andreucci1, Dario Bellaveglia1, Emilio N.M. Cirillo1 and Silvia

Marconi1

1 Department of Basic and Applied Sciences For Engineering

Section of Mathematics,

Sapienza University of Rome Italy

emails: daniele.andreucci@sbai.uniroma1.it, dario.bellaveglia@sbai.uniroma1.it, emilio.cirillo@uniroma1.it,

silvia.marconi@sbai.uniroma1.it

Abstract

We report on some recent results on the modeling of ion exchange through cell membranes, with special attention to the issue of selection of preferred ionic species in the presence of di erent transmembrane voltages and di erent concentrations in the cytosol.

Key words: ionic channel, potassium channel, gating, selectivity

1Introduction

Biological literature has been dealing with potassium currents across cell membranes for a long time (see, for instance, the reviews [3, 10]). The ubiquitous presence and the importance of ionic channels selecting potassium for transmembrane exchange are by now well established.

In the modeling of the large variety of existing ionic channel types it is generally accepted that they all form selective pores in the cell membrane which are able to switch between an open state and a closed state. The open state is the one, obviously, that allows for permeation of a selected ionic species (potassium in K+–channels).

Such change of state, which is called gating, is stochastical in character. Its relation to selectivity, i.e., the ability of the channel to allow the flux of a particular ionic species, is

Diffusion and current through ionic channels

not yet completely understood. The way in which either one is achieved can be di erent from channel to channel [6].

Some models, see [5, 7, 8, 9] describe to some extent the dynamics of ion permeation through the selectivity filter of the channel. In this kinetic approach the concentration of the ionic species in the cell is modeled as a constant parameter. In [2], following [11], we introduced a model where the channel is lumped to a two state stochastic point system, but the interaction between the dynamics of the ions inside the cell and that of the selectivity filter itself is taken into account. That is to say, the channel is seen as a part of the cell more than as an isolated structure. In that paper both an analytical and Monte Carlo study showed the possibility to achieve gating via selection. A continuos version of the model has been investigated in [1].

Here we deal with a modification of that model, aimed at taking into account the e ect of an external voltage di erence through the cell membrane. For simplicity we confine ourselves to a one-dimensional implementation of the model, where exact calculations can be carried out for the stochastical quantities. Our purpose is to predict the behavior of the current–voltage curves. The model is then defined to mimic the three e ects that seem to be the most relevant in the process: (i) di usion of the ions inside the cell; (ii) dynamics of the selectivity filter; (iii) dynamics of the ions inside the channel.

We compare the current–voltage behaviors predicted by our model with those measured in experiments [4] and find them to be in very good agreement.

Figure 1: Potassium flux at different concentrations. Experimental measures (symbols) and model predictions (curves) at the concentrations of 20, 50, 100, 200, 400, 800 mM (from bottom to top).

D.Andreucci, D.Bellaveglia, E.N.M. Cirillo, S.Marconi

Figure 2: Fluxes of different ionic species. Experimental measures (symbols) and model predictions (curves) at the concentration of 100 mM for the species Rb+ , NH+4 ×, Tl+ , K+ +.

2Results

In Figure 1 we compare the experimentally measured current of K+ ions with the one predicted by our model according to the relation

where fK represents the flux (in number) of K+ ions, and SI is a parameter of the model connected to the di usivity of ions in the cytosol; we omit the explicit definition of fK . In reading the results in Figure 1 one should keep in mind that the di erent parameters appearing in our model have been tuned to fit the curve corresponding to concentration 800 mM there, and that the other curves have been fitted by using only SI in (1) and the probability p that the channel is open. Similar results can be obtained by using only either one of SI , p.

In Figure 2 we report the predictions of the model for currents of other (selected by the channel) ionic species: rubidium Rb+, thallium Tl+, ammonium NH+4 , and again potassium K+, all at the same concentration of 100 mM.

References

[1]D. Andreucci and D. Bellaveglia, Permeability of Interfaces with Alternating Pores in Parabolic Problems, Asymptotic Anal. (in press).

Diffusion and current through ionic channels

[2] D. Andreucci, D. Bellaveglia, E. N. M. Cirillo and S.Marconi, Monte Carlo

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study of gating and selection in potassium channels, PhysReview E 84 (2011) 021920 1–13.

[3]D. Fedida and J. C. Hesketh, Gating of voltage-dependent potassium channels, Prog. Bio. Mol. Biology 75 (2001) 165–199.

[4]M. LeMasurier, L. Heginbotham and C. Miller, KcsA: It’s a Potassium Chan-

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nel, J. GenPhysiol. 118 (2001) 303–313.

[5] S. Maf´e and J. Pellicer, Ion conduction in the KcsA potassium channel analyzed

[10]M. Recanatini, A. Cavalli and M. Masetti, Modeling hERG and its Interactions with Drugs: Recent Advances in Light of Current Potassium Channel Simulations, ChemMedChem 3 (2008) 523–535.

[11]A. M. J. VanDongen, K channel gating by an a nity-switching selectivity filter, PNAS 101 (2004) 3248–3252.

Proceedings of the 12th International Conference on Computational and Mathematical Methods in Science and Engineering, CMMSE 2012 July, 2-5, 2012.

A simple meta-epidemic model

Marika Barengo1, Isabella Iennaco1 and Ezio Venturino1

1 Dipartimento di Matematica “Giuseppe Peano”, Universit`a di Torino, via Carlo Alberto 10, 10123 Torino, Italy

emails: marika1288@libero.it, isabella.iennaco@gmail.com, ezio.venturino@unito.it1

Abstract

In this paper we present and analyse a simple model for disease transmission among two di erent geographical locations. Our goal is to unveil the role of the migration coe cients on the disease evolution and to understand what happens to the system on the whole if some external disturbances modify the system topology or the individuals habits. The analysis discusses these modifications as possible tools for disease eradication.

Key words: epidemics, disease transmission, migrations

MSC 2000: AMS codes 92D30

1Introduction

The role of diseases in shaping populations dynamics is widely recognized. Mathematical epidemiology has progressed in the past century to provide the epidemiologists with instruments apt to forecast the disease evolution and take suitable measures agains their propagation. In fact, it is mainly due to mathematical results that in 1980 the WHO has discontinued worldwide the vaccination against smallpox, thereby declaring this disease, which has a ected humanity for centuries, eradicated.

In this paper we consider a simple system in which two patches are present. One population occupies them both, and can migrate from one to the other one. We investigate the stable states and discuss how they are modified when communications between patches are interrupted and when only some of the individuals are able to migrate.

1This paper was completed and written during a visit of the third author at the Max Planck Institut f¨ur Physik Komplexer Systeme in Dresden, Germany. The author expresses his thanks for the facilities provided.