Paul Doyle

Brian Keegan

Damian Gordon

Anna Becevel

Paul J Gibson
email: paul.gibson@telecom-sudparis.eu

Zhiying Jiang
email: jiangzy@mail.buct.edu.cn

Dympna O'sullivan

The World Is Our Classroom: Developing a Model for International Virtual Internships -The Global Innovations Project

Keywords:

In the aftermath of COVID-19, remote working has become the norm, and graduates now need an even wider range of skills, which traditional classrooms and internships do not always provide. Working in multiple time zones, within global multi-cultural teams, and only ever meeting colleagues through online technology are just some of the challenges, which require a new type of global graduate. Transversal skills including leadership, collaboration, innovation, digital, green, organization and communication skills are critical. The disruption from COVID-19 also presents unprecedented opportunities to develop more inclusive approaches to internships and international experiences, to level the playing field for students with special needs, from underrepresented groups or with caring commitments. In this position paper, we present a new Global Innovation internship model that has the aim of allowing students to complete technology internships and projects by working together virtually on real world challenges, guided by experienced industry and academic mentors. The model is being developed as part of an Erasmus+ funded project, and the partnership includes seven Higher Education Institutions from six different countries around the world. This position paper describes the design and development of a pilot programme of the Global Innovations internship model.

INTRODUCTION

An internship is a work experience offered by an organization for a limited period of time. Internships are pedagogically founded upon experiential learning, where the learner actively creates "knowledge through direct experience that is meaningful to the student with guided reflection and analysis" [START_REF] Kolb | Experiential Learning: Experience as the Source of Learning and Development[END_REF]. They provide opportunities through which students experience their chosen professions before formally entering them. Internships have become commonplace in higher education and are often an embedded part of computing programmes. Internships usually take the form of supervised introductory career opportunities provided in partnership between academic institutions and professional organizations. Internships provide significant benefits for employers, academic institutions and students. Graduate recruiters use internships as a means of developing future talent pipelines, bringing innovation and new ideas into their organizations as well as giving students a real sense of what is involved in working in a particular company or sector of industry. Academic institutions can use internships to forge collaborative relationships with industry, to gain an insight into contemporary industry practices with knock-on positive impacts on teaching. Students who return from internships are often better prepared to take on larger pieces of work such as dissertations. From a student perspective, they afford the opportunity to engage in the practical application of theories learned in the classroom, to reinforce technical competencies and allow for development of other skills including communication, teamwork, time management and interpersonal skills. Internships are proven differentiators with students who have completed them having a significant advantage on graduation [START_REF] Aasir | Understanding the Role of Internship as an Activity Based Learning: A Case Study[END_REF][START_REF] Eyler | The power of experiential education[END_REF][START_REF] Silva | The million-dollar question: can internships boost employment?[END_REF].

The COVID-19 pandemic precipitated a shift to remote working and remote learning worldwide. Unfortunately, many internship opportunities were cancelled or had changes made to the internship scope. In many computing programmes, students completed online or virtual internships. Virtual internships predate the pandemic. One of the first reported virtual internships in the literature is by [START_REF] Cheney | Constructivist learning environments: Students' perceptions of a technology skills virtual internship[END_REF][START_REF] Cheney | Constructivist learning environments: Students' perceptions of a technology skills virtual internship[END_REF], where students undertook a virtual internship that facilitated the development of technology skills. Others have worked to incorporate virtual internships into MOOC programmes [START_REF] Pillutla | Towards Massively Open Online Virtual Internships in Computing Education[END_REF]. Advantages of virtual internships are increased access to a more diverse and geographically wider talent pool from an employer point of view. From a student perspective, a virtual internship can build the skills necessary for remote work, for example digital literacy and digital professionalism, telecommunication, self-discipline, and independence. Recent findings have also shown that students on virtual internships had more access to senior staff within organizations -traditionally, only those interns at head office locations had the opportunity to engage with the most senior leaders. However, in travelling less, senior leaders could commit to the sessions such as inductions, virtual coffees, and networking sessions [START_REF] Woo | Internships before and during COVID-19: experiences and perceptions of undergraduate interns and supervisors[END_REF], Collings, 2021).

In this position paper, we describe the design and development of a new model of virtual internships. The Global Innovations (GI) internship model aims to allow students to complete computing internships by working together virtually in international teams on real world challenges guided by experienced industry mentors and academic mentors. The model is being developed as part of an Erasmus+ project and the partnership includes seven higher education institutions from six different countries (Ireland, France, Sweden, Slovenia, China, South Korea), industry professionals and remote learning experts.

The model aims to address the challenges posed to the traditional internship model during COVID-19, to develop a shared understanding beyond national borders and to design innovative curricula to create graduates that are not only capable of adapting to hybrid and online workplaces and situations, but that were specifically trained to work within it. The ultimate aim of the research will produce an open and comprehensive toolkit for the implementation of remote and hybrid internships including a set of guidelines, training materials and reusable artefacts (e.g. resources to support recruitment, onboarding, professional development, and checklists for industry and academic mentors).

In the next section, we provide context on the importance of internship programmes, the pedagogical approaches that underpin them and discuss the emergence of virtual internships. In Section 3 we outline the GI internship model and describe the design and development of a pilot implementation of the programme. We conclude in Section 4 with a description of insights, recommendations, and challenges in delivering such a programme.

BACKGROUND

Internships are based around the concept of 'experiential learning', an engaged learning process whereby students "learn by doing" and by reflecting on the experience [START_REF] Kolb | Experiential Learning: Experience as the Source of Learning and Development[END_REF]. The pedagogy of learning through experience originated in the 19th century [START_REF] Champagne | Service learning: Its origin, evolution, and connection to health education[END_REF][START_REF] Furco | Institutionalizing servicelearning in higher education: Issues and strategies for chief academic officers[END_REF]). In [START_REF] Kolb | Experiential learning theory: Previous research and new directions[END_REF], Kolb, et al provided an explanation of the Experiential Learning Theory (ELT) -"ELT emphasises the central role that experience plays in the learning process, an emphasis that distinguishes ELT from other learning theories. The term "experiential" is used therefore to differentiate ELT both from cognitive learning theories, which tend to emphasise cognition over affect, and behavioural learning theories that deny any role for subjective experience in the learning process".

The introduction of experiential learning as a pedagogy challenged previous academic theories. It challenged the "cognitive style" of "teaching through lecturing" that was and still is prevalent in academic classrooms [START_REF] Furco | Service learning: The essence of the pedagogy[END_REF]. It also challenged the "onedirectional" method of teaching and learning and raised questions about the role of academic institutions in student's learning process while on internship. The literature reveals several important considerations in the development of any internship programme: Firstly, the work environment is often substantially different from what the students are taught or what they experience in the classroom [START_REF] Trede | Investigating what constitutes an effective workplace learning environment: A scoping review of the role physical and material elements play in student learning[END_REF]. Second, academic institutions must prepare the students for the internship work environment [START_REF] D'abate | Making the Most of an Internship: An Empirical Study of Internship Satisfaction[END_REF]. Third, although there is no direct transfer of knowledge from the teacher to the students in most internship courses, the academic institution should take an active role in the learning process, for example through a mentoring process. Internship programs should coordinate with the industry internship sites to manage this mentoring process and thus facilitate the learning process [START_REF] Trede | Investigating what constitutes an effective workplace learning environment: A scoping review of the role physical and material elements play in student learning[END_REF]. Finally, experiential learning should complement and enhance learning that takes place in the classroom [START_REF] Morris | Experiential learning -a systematic review and revision of Kolb's model[END_REF].

As a result of the COVID-19 pandemic, working remotely is now mainstream and has also given rise to an increase in remote internships [START_REF] Jeske | Mentoring and skill development in e-Internships[END_REF]. Before the pandemic, growth in online education, advancements in remote-work technologies, diversity of the workforce, and the need for flexibility in location and time were key drivers of remote internships [START_REF] Jeske | Virtual internships: Learning opportunities and recommendations[END_REF][START_REF] Khushwant | Virtual Internships -A New Reality[END_REF]. Virtual internships resemble traditional internships in most aspects, except that communication takes place via messaging services or interactive software communication. The literature identifies much work on successful virtual internship programmes [START_REF] Woo | Internships before and during COVID-19: experiences and perceptions of undergraduate interns and supervisors[END_REF][START_REF] D'abate | Making the Most of an Internship: An Empirical Study of Internship Satisfaction[END_REF][START_REF] Khushwant | Virtual Internships -A New Reality[END_REF], but also outlines a number of common challenges associated with virtual internships. A key challenge is the authenticity of the experience in simulating professional workplaces. The use of mentorship to provide the guidance necessary for interns to make meaningful connections between professional knowledge elements is vital to overcome this challenge. Furthermore, mentors need to be available to engage with virtual interns on a regular basis to foster engagement and prevent drop-out in an online environment. Other skills such as interpersonal communication, cultural understanding of how to relate to individuals from different cultures, time and performance management needed to organise meetings across time zones are critical in the online environment and interns need guidance on these aspects [START_REF] Jeske | Global in small steps: einternships in small and medium-sized organizations[END_REF]. Careful preparation and planning are also required to enable virtual interns to manage their work effectively (and possibly entirely independently). In the absence of everyday interactions, the materials, instructions, and task descriptions need to be well prepared [START_REF] Jeske | Effort and rewards effects: Appreciation and self-rated performance in einternships[END_REF]. The provision of opportunities for interns to work collaboratively on projects in an online environment is a key requirement for preparing students for online or hybrid workplaces post-graduation and should be provided by industry partners [START_REF] Gill | Graduate employability skills through online internships and projects during the COVID-19 Pandemic: An Australian example[END_REF].

Our work on developing the GI internship model aims to tackle these challenges. In the next section we provide an overview of the GI internship model and describe our approach and the design and development of a pilot implementation of the model.

APPROACH

The GI internship model is focused on simulation of an industry-based internship experience for students in computing and other technology-based disciplines. The GI internship is run within existing validated academic internship modules at each partner institution to ensure a valid learning environment for students is achieved, and to ensure an assessment model consistent with traditional internships is performed. It borrows essential traits from both academic project-based modules, and industry-based internships. The GI internship is also designed to buffer students from the recent fluctuations of the industry-based internship environment that were evident in the first two years of the recent COVID-19 pandemic where technology-based companies have been forced to undergo rapid transformations in their work structures and cultures. These transformations include the requirement for establishing a remote working culture, reliance on video conferencing for meetings, an increase in use of non-verbal digital based collaboration, and increased emphasis on chat applications and other social media platforms for social interaction. As a by-product of these transformations, some of the key advantages of the industry-based internship model are potentially under threat, such as the establishing of professional rolemodels within the work environment, the creation of social contacts and the development of work based social norms. Our research in developing the GI internship model has the following aims:

1. To design a virtual internship which simulates a collaborative environment where students work on an industry project, but with additional academic support to help create graduates that are capable of adapting to hybrid and online workplaces and situation. 2. To construct an inclusive, multicultural, international, and entrepreneurial experience for students through our collaboration with European and Asian universities.

3. To upskill academic and industry mentors to ensure the successful implementation of the virtual internship program. 4. To produce an open toolkit for the implementation of remote and hybrid internships including a set of guidelines, training materials and reusable artefacts.

GI Project Phases

The GI internship model will be developed as part of an Erasmus+ project over a two-year period. The project has four distinct but overlapping phases as shown in Figure 1. The initial phase is the pilot phase which will be run for 6 months to obtain real-world data of a simulated virtual internship including an understanding of required upskilling for industry and academic stakeholders, while the second phase focuses on evaluation of the pilot against the project aims. The third phase will take the combined learning of the pilot, prior experience of each of the partner universities running similar modules, and a review of the literature to ensure a pedagogically sound module is created. The final phase focuses on the implementation of the model across multiple universities in order to develop a shared understanding of virtual and hybrid internships beyond national borders and to ensue that the model can be successfully operationalised.

The Pilot in Context

The GI pilot provides an early opportunity within the project to evaluate how the project aims may be best achieved. In the creation of a virtual internship, a start-up company model was the most feasible type of business environment which could be best simulated. While a typical SME will have established and existing employees within a company to help mentor and act as role models for interns, start-ups are often formed with minimal hierarchy and with limited support structure, procedures and access to senior resources. The core ethos of the project is that it must operate as a new start-up company with a specific technology-based project to focus on. All aspects of the start-up will be run like a business under the direction of the managing director (MD) who will be appointed from industry but who will have limited contact hours with the students. The MD will be recruited based on their experience in business development within small start-up companies and will be the primary point of contact for the students on internship. The MD will also oversee an academic staff member appointed as a consulting chief technical officer (CTO), and a staff officer from an Industry Engagement Office who will act as a business development manager (BDO). These three roles will be the core of the start-up company. Students will be recruited from standard internship programmes. The BDO will secure access to support services for the team, including access to industry consultants in the areas of project management, marketing, business development, human resources, and staff training. The MD, with the support of the CTO and BDO, will control the use of all services and resources.

The GI internship team will simulate the work environment of a new company which has limited resources, but with the added benefit of academic scaffolding. This scaffolding will be in the form of academic mentors who act as experts in the project domain and the creation of a structured internship plan for the students to follow which will focus on developmental workshops and professional training to help students develop the core skills required to achieve the learning outcomes of an internship. Using a start-up model, a company culture is created where the team takes more direct responsibility and ownership for the work they are undertaking. This culture is developed by establishing a client for the project who has a specific requirement in mind, and who will meet with the team to provide input and feedback regarding the progress being made. The concept of academic grading is removed from the project deliverable as the output should be client facing. Grading within the internship is performed in the same way as other internships and is performed separately using our internship support structure and reflective assessment methodology.

The GI team is treated like any other company involved in an academic internship programme. The scaffolding approach ensures that the students work within a diverse team environment, which is multicultural, international and multidisciplinary. This is achieved through our recruitment process which requires students to interview for the position from multiple schools, and multiple international partners, and via a process, where students are split into two groups, which will rotate between working online and onsite at a campus incubation location.

The Pilot Design Methodology Context

The start-up company will include several key roles designed to establish a company environment and to ensure that there are sufficient support structures to facilitate the student learning environment. The MD, appointed from industry, will have between 6-9 contact hours with the team each, and will perform the basic management duties for the internship groups, structuring the work activities of the team. The CTO will be appointed from the academic staff to act as a discipline technology expert to provide high-level guidance and input as the teams explore technology solutions. The DBO role is run by our Industry engagement officer who will work with companies that support start-up companies and facilitate the team by providing access to workshops, training and services designed to support an entrepreneurial business in its early stage of development. A structure will also be developed for the internship to ensure that the learning outcomes of the internship module are achieved.

With the basic structure of the start-up company defined in Figure 2, the following process was followed to develop and assess the pilot programme.

Recruitment

The business focus of the company will be on a technology-based project sourced from a nongovernmental organization (NGO), Charity or organization focused on supporting the United Nations Sustainable Development Goals (SDG's). For the pilot, the client will be a research group with a focus on applied and socially responsible technology within the university who proposed a project on smart energy conservation. For future projects, an Expression of Interest (EOI) will be issued, seeking input from the wider community. Once a project brief is finalized, the company engages with the internship process of the university to interview and select students to work within the Gl team as per standard internship recruitment procedure. Students will be interviewed with a view to the roles within the team they will occupy. The interview process will assess the students in terms of software design and development skills, analytic skills, knowledge of business process, communication and leadership skills.

Team Development

An essential element in the creation of an internship environment is the securing of resources from industry and the business development agencies to provide industry engagement opportunities for the newly formed team. These services include accessing national agencies support programmes such as Enterprise Ireland and the academic incubation centres within the university, which are specifically designed to support and advise small start-up companies. Additional resources are provided in the form of specified and limited hours of consultancy from our university industry partners. The MD of the start-up will work to ensure that these limited industry resources are used effectively to support the students and provide access to experts in the field of human resources, software development, software testing, project management and business development. Additional academic sources from within the university will be used to provide targeted workshops to help develop both transversal skills such as design thinking, problem solving, teambuilding, and goal setting, in additional to more general technical skills such as understanding ethics within technology, data privacy, followed by more targeted technology seminars directly relevant to the project being developed.

Assessment

The pilot will be assessed to determine how well it met the project aims and objectives and to understand how it might be developed for deployment across the European and Asian project partners. Different forms of assessment will be used to help determine the strengths and weaknesses of the pilot, allowing for the assessment to be considered from different perspectives. A specific strength of the pilot model is that the assessment of the students will be done in parallel with and using the same assessment approach by the internship academic coordinator. This provides an independent and external analysis of how the students performed with respect to achieving the learning outcomes compared to standard internships. A second and equally independent assessment of the pilot will be performed by one of our European

The World Is Our Classroom: Developing a Model for International Virtual Internships -The Global Innovations Project university partners who are not involved in the development or running of the pilot. This assessment will probe into the cost of the internship model, the structure of the company and how it performed, and review methods of improving the overall experience of the internships itself.

CONCLUSIONS

The merits of internships are well known and proven differentiators which offer significant advantages to students who undertake them. This position paper presents a model for the implementation of a virtual internship which not only replicates a complete work environment but provides additional academic scaffolding support structures to help create graduates that can adapt to hybrid and online workplaces and situations.

The GI internship model strives to create a collaborative internship environment based on industry best practice, models of experiential learning but with greater academic support. The model identifies and addresses the challenges associated with virtual internships such as the authenticity of the experience and access to industry role-models and experts. The environment promotes interculturalism by design and fosters an entrepreneurial experience. A start-up company is seen as favourable for the model due to its minimal hierarchy and limited support structure. The start-up company include several key roles designed to establish a company environment and to ensure that there are sufficient support structures to facilitate the student learning environment. This provides a uniform experience and facilitates student access to experts and core staff.

The model is seamlessly integrated within an existing validated academic internship modules . The approach will buffer students from recent fluctuations in industry-based internship environments caused by COVID-19 and a move towards remote and hybrid workplaces, offering safeguards over the environment and the student experience. The model offers unique support mechanisms via academic expertise which provides scaffolding not seen in traditional internships. This support is implemented by means of targeted workshops and training to develop core skills. Training is not assessed but instead used to develop a culture of engagement and problem solving for the client. Reflective assessment is used to determine the success of the students' performance and learning experience. Students work in groups and utilise a blended work environment including both online and onsite activities.

The ongoing pilot will be assessed to determine how well it met its aims and objectives and to understand how it might be developed in the future to run across multiple universities in Europe and Asia. This will involve detailed interviews with the participating students, industry and academic stakeholders. A particular focus will be on the upskilling requirements of academic and industry stakeholders to determine specific training needs. A second and independent assessment of the pilot will be performed by a European university partner not involved in the development or running of the pilot. This assessment will probe more into the cost of the internship model for academic and industry organizations, an analysis the internship company performed, and review methods of improving the overall experience of the internships itself. The research will produce an open and comprehensive toolkit for the implementation of remote and hybrid internships including a set of guidelines, training materials and reusable artefacts (e.g. resources to support recruitment, onboarding, professional development and assessment).

Figure 1 :

 1 Figure 1: Global Innovations project phases.

Figure 2 :

 2 Figure 2: Global Innovations internship pilot company structure.

The World Is Our Classroom: Developing a Model for International Virtual Internships -The Global Innovations Project

ACKNOWLEDGEMENTS

The Global Innovation Teams project (Agreement number: 2021-1-IE02-Ka220-HED-000023212) is co-funded by the Erasmus+ Programme of the European Union. The European Commission's support for the production of this publication does not constitute an endorsement of the contents, which reflect the views only of the authors, and the Commission cannot be held responsible for any use which may be made of the information contained therein.


Alain De Cheveigné

Simple and efficient auditory-nerve spike generation

HAL is

Introduction

The ear serves to transduce acoustic vibrations in the air to neural patterns and deliver them to the brain, ultimately yielding a sound-evoked percept or behavior. Sound vibrations are transmitted via the outer and middle ear to the inner ear, where they undergo active amplification and filtering, the outcome of which determines the probability of release of quanta of neurotransmitter at the synapse between inner hair cell and auditory nerve fiber, thus determining the probability of occurrence of a spike within that fiber. Information available to the brain about sound is carried collectively by ~30000 fibers (~10 fibers contact each of ~3000 inner hair cells), each carrying a spike train of up to ~300 spikes/s average rate.

The spike-generation process has been described as an inhomogenous Poisson process with a time-varying rate that follows the deflection (and/or velocity) of the basilar membrane at the position of the hair cell, further modified by refractory effects that depress firing probability immediately after each spike. This widely used approximation is reviewed by Delgutte (1996), some of its limits are discussed by [START_REF] Heil | Spike timing in auditory-nerve fibers during spontaneous activity and phase locking[END_REF].

Auditory models (or model suites) have been developed to approximate auditory transduction [START_REF] Osses | A comparative study of eight human auditory models of monaural processing[END_REF]. They serve two purposes: to embody knowledge accrued about the peripheral auditory system (and test it), and to generate patterns of auditorynerve discharge for simulation of downstream processes within the brainstem. A typical auditory model might combine a linear acoustic filtering module to represent the outer and middle ear, a non-linear filter-bank module to represent cochlear filtering, an inner hair-cell module to represent transduction from vibration to intracellular potential, and a spike generation module that generates an array of spike trains.

Simpler configurations may be used for specific tasks, for example by omitting the initial filtering, or reducing the number of channels, or replacing non-linear by linear filters. While a complete, physiologically-realistic model is a worthy goal, a simpler model is often sufficient, or even preferable because more constrained (fewer parameters) and computationally less expensive. In particular, the final spike-generation phase is often omitted.

Nonetheless, generating actual spike trains (as opposed to a time-varying probability) may be useful to assess the impact of refractory effects (not fully captured by the driving probability), or to drive models that rely on processing the spikes themselves. These include coincidence-based models for example for pitch or binaural unmasking, as well as a wider class of spike-or event-based models of perception or information processing (e.g. [START_REF] Liu | Event-Driven Sensing for Efficient Perception: Vision and Audition Algorithms[END_REF]. Spike generation enables a model to simulate the effects of deafferentation [START_REF] Kujawa | Adding insult to injury: cochlear nerve degeneration after "temporary" noise-induced hearing loss[END_REF], putatively a major component of hearing loss, for example in terms of stochastic under-sampling [START_REF] Lopez-Poveda | Why do I hear but not understand? Stochastic undersampling as a model of degraded neural encoding of speech[END_REF].

Two obstacles to spike generation are computational cost and storage cost, both linked to the common time-sampled simulation approach (e.g. one sample every 10s). According to the inhomogenous Poisson model with refractory effects, spike probability at each time is determined by the product of a time-varying driving function, and a recovery function dependent on time since the latest spike. This can be simulated by drawing a random number at each time step and comparing it with that probability. Downsides are (a) the large number of random numbers required if the sampling rate is high, (b) the space required to store the (very sparse) time series of values (1 for a spike, 0 otherwise) and (c) the limited time resolution of each spike, dependent on the sampling rate.

Two approaches are available to more efficiently simulate an inhomogenous Poisson process. Both rely on the fact that intervals between events of a homogenous Poisson process are distributed exponentially. The two approaches are time transformation (e.g. [START_REF] Jackson | The Spontaneous-Rate Histogram of the Auditory Nerve Can Be Explained by Only Two or Three Spontaneous Rates and Long-Range Dependence[END_REF] and thinning (e.g. [START_REF] Lewis | Simulation of nonhomogeneous Poisson processes by thinning[END_REF]. With time transformation, the duration of each randomly-drawn inter-event interval is scaled by a factor that depends on the instantaneous probability at (presumably) the first event of that interval. With thinning, the maximum value of the time-varying rate is used to simulate a homogenous Poisson process, and the resulting event train is then thinned probabilistically depending on the instantaneous rate at each event of this train.

The time-transformation approach might seem preferable because it requires a single random draw per final spike, whereas thinning is more wasteful. However, time transformation is subject to a subtle issue: the underlying time-varying rate is sparsely sampled by the event train, all the more so as the rate is low. For example, if an event occurs at a dip in the time-varying rate, the next sampling point will be distant in time, possibly missing an intervening section of high rate. Thinning does not have this problem (at least, not to the same degree), and is the approach used here.

The toolbox

The toolbox, implemented in Matlab, contains a small set of routines to create and analyze spike trains. A spike train is represented as an array of floating-point numbers, each number representing time relative to a time reference locked to the beginning of the train.

Spike trains are generated according to the thinning method. The input time series (instantaneous rate aka driving function) is scanned for its maximum value, this value parametrizes a homogenous Poisson process that produces a train of inter-spike intervals at that maximum rate. These are cumulatively summed (assuming a first spike at time 0) to obtain a train of spike times. This spike train is then thinned probabilistically depending on the value of the nominal instantaneous rate at the time of each spike, to simulate the timevarying Poisson process. Finally, the spike train is again thinned probabilistically according to a recovery function. Initial spike generation and thinning are vectorized and thus fast, but the final thinning requires a loop.

The toolbox includes a few additional routines to modify the spike train (jitter, cancellation filter, c.f. de Cheveigné 2021, 2023), and for routine statistics such as first-order and allorder inter-spike interval histograms, peri-stimulus time (PST) histograms, and crosscoincidence histograms).

The toolbox is mainly intended as an add-on to existing auditory model toolboxes (e.g. [START_REF] Osses | A comparative study of eight human auditory models of monaural processing[END_REF]).

The toolbox is archived at https://zenodo.org/badge/latestdoi/635354073.

Results

Spike generation

Figure 1 illustrates the generation process. A homogenous Poisson process with a rate equal to the peak rate of the driving function (top) produces a train of spikes (black dots), that is thinned, first on the basis of the instantaneous values of the driving function (blue), and next on the basis of the recovery function (red).

Constant driving function

In the absence of stimulation, most auditory nerve fibers have a spontaneous activity that can be characterized by a driving function that is constant (at least approximately, c.f. [START_REF] Heil | Spike timing in auditory-nerve fibers during spontaneous activity and phase locking[END_REF]. Stationary stimulation at a high frequency, beyond the phase-locking limit (approximately 5 kHz) also entails a constant driving function. Figure 2 shows interval statistics for constant drive, in the absence (black) or presence (blue and red) of refractory effects. The driving rate was 400/s, the effective rate (after thinning) was ~290/s and ~260/s for the stepwise (blue) and piecewise linear recovery time (red) respectively.

Fig. 2. Interval statistics for spike trains resulting from a constant driving function, in the absence (black) and presence (blue and red) of refractory effects. Left: first-order interval histogram, right: all-order interval histogram, binwidth is 0.05 ms. For the blue curve ("dead time"), the recovery function was a step function equal to 0 below 0.8 ms and 1 beyond. For the red curve, the recovery function was piecewise linear (0 below 0.8 ms, 0.5 at 1 ms, 0.9 at 2 ms, and 1 at 5 ms and beyond). Statistics were gathered over a duration of 600 s.

Halfwave-rectified driving function

Figure 3 (left) shows the peristimulus (PST) histogram for a spike train elicited by a halfwave rectified sinusoidal (100 Hz) driving function in the absence (black) or presence (red) of refractory effects (peak rate 500 spikes/s, average spiking rates 160 and 110 spikes/s respectively). The center and right panels show first-order and all order ISI histograms, respectively. Refractory effects (red) reduce the number of spikes and deplete the zeroorder mode of the interval histograms. There is also a slight distortion of the shape of the PSTH, explored in more detail in the next paragraph.

Side-effects of refractoriness

In the absence of refractory effects (pure non-homogenous Poisson process), the empirical firing rate would faithfully follow the driving function (apart from stochastic variability). The presence of refractory effects induces some distortions that are worth recognizing, so as to avoid attributing them to upstream phenomena (e.g. adaptation).

Figure 4 shows three examples of such effects. The left panel shows a peri-stimulus time histogram (PSTH) in response to 5000 repetitions of a pulse of constant driving rate, either 1000 spikes/s (black) or 5000 spikes/s (red) (effective rates 410 and 730 spikes/s respectively). A small onset overshoot is visible at the lower rate, at the higher rate it takes the form of a ringing pattern with a period close to the absolute refractory period (~1 ms).

The center panel show the all-order ISIH for the same two spike trains, again showing evidence of periodicity at the higher rate. The right-hand panel shows a period histogram in response to a half-wave rectified 200 Hz sinusoidal driving function. The peak driving rate was either 1000 spikes/s (black) or 5000 spikes/s (red) (effective rates 180 and 360 spikes/s respectively). At the lower rate (black) the histogram is a slightly distorted version of the driving function (as in Fig. 3 left), at the higher rate the peak splits into two.

In such conditions, one might be tempted to infer properties of the driving function (reflecting the stimulus, the filter, adaptation processes, etc.) (Lopez-Poveda 2005) that are instead an artifactual side effect of refractoriness. These effects are prominent mostly for high peak driving rates.

Jitter

Adding jitter to spike times is a convenient way to model loss of synchrony at higher frequencies. Loss of synchrony is usually attributed to low-pass filtering effects due to inner hair-cell capacitance [START_REF] Russell | Low-frequency characteristics of intracellularly recorded receptor potentials in guinea-pig cochlear hair cells[END_REF], but its effects are quite well captured by adding a Gaussian jitter to each spike time (Fig. 5) (compare with e.g. [START_REF] Versteegh | Response Characteristics in the Apex of the Gerbil Cochlea Studied Through Auditory Nerve Recordings[END_REF]. Adding Gaussian jitter is thus an expedient way to reproduce phase-locking roll-off at higher frequencies, at least for the purpose of driving downstream processing models.

Cancellation

The cancellation filter involves gating one spike train based on another spike train. Specifically, any input spike that coincides with a gating spike (within a window) is removed.

It can be seen as a form of thinning by which spikes are removed to change the temporal structure of the spike train. If the gating spike train is the same as the input but with some delay (or advance), the filter performs harmonic cancellation (de Cheveigné 1993(de Cheveigné , 2021(de Cheveigné , 2023)).

Figure 6 illustrates this process applied to a spike train generated from the half-wave rectified sum of two sinusoids, 80 Hz and 100 Hz respectively. The top plot shows an allorder ISI histogram calculated from the raw spike train. The middle and bottom plots show the result of applying a cancellation filter with delay equal to 10 ms and 12.5 ms respectively (inverses of the two frequencies). The first filter appears to effectively suppress correlates of 100 Hz, and the second those of 80 Hz. Of course, the same effect could be obtained by filtering before spike generation (for example cochlear filtering), but it is interesting to see a similar result from processing in the neural domain.

The peak firing rate here was 1000 spikes/s, a 1 ms step recovery function was applied, and 10 spike trains were generated and merged (compound rate 1940 spikes/s). The cancellation filter kernel was boxcar-shaped with a width of 1 ms.

Computation and storage

Computation time is data-and parameter-dependent, but to give an idea, simulation of a full set of 30000 fibers takes roughly ten times real time on a 2.4 GHz 8-core MacBook Pro. At 100 spikes/s average output rate, the resulting spike trains require 24 Mbytes storage (double precision) as opposed to 375 Mbytes if the spike trains were stored as a one-bit time series with 100 kHz sampling rate, or more for an integer or float time series.

The toolbox

The Matlab toolbox is available at XXX. Most routines follow the same conventions: calling the routine without output arguments produces a plot reflecting the outcome (in some hopefully helpful fashion), calling it without input arguments runs a short piece of example code, hopefully useful to understand the effects of the routine and how to deploy it.

Summary

This paper documents simple and efficient methods of spike generation and processing for the purpose of modeling peripheral transduction and downstream neural mechanisms. The methods are not new, but they are not often deployed in the context of auditory model simulations, where they can be useful given the high rate and large volumes of neural patterns produced by the roughly 30 000 fibers of the human auditory nerve. Some auditory modeling suites already offer spike train output; a benefit of the present may be to add that capability to those that do not.

The main benefits are fast generation (relative to the uniform time-series approach that a decision to fire or not at each time step), reduced space requirements (relative to a sparse time series of pulses), and precise time resolution (limited by floating-point resolution, rather than sampling rate). Spike times can easily be converted to a time series of pulses, for example for the purpose of autocorrelation or cross-correlation, although the toolbox offers time-based alternatives for those operations.

Time-stamped event-based representations offer theoretical advantages, related to the potentially large amount of information carried by each spike (limited only by the precision of its representation, Maass 2001), and are the focus of intense interest for computational, sensory and cognitive applications [START_REF] Maass | To Spike or Not to Spike: That Is the Question[END_REF][START_REF] Liu | Event-Driven Sensing for Efficient Perception: Vision and Audition Algorithms[END_REF].

Thinning is the key to fast generation of arbitrarily-timed events from a Poisson process with time-varying rate and/or refractory effects. Thinning was also used by the cancellation filter to selectively modify the stimulus-driven temporal structure of the spike train (e.g. suppress a periodic masker). As another example, a Poisson-distributed spike train can be transformed by thinning into a Poisson + gamma mixture distribution, which better models spontaneous auditory-nerve interval distributions (Heil et al 2007). Thinning is quite versatile.

Time-transformation [START_REF] Jackson | The Spontaneous-Rate Histogram of the Auditory Nerve Can Be Explained by Only Two or Three Spontaneous Rates and Long-Range Dependence[END_REF], in principle yet more efficient than thinning, faces the problem that a momentarily low value of the rate will cause the next spike to be distant in time, potentially missing an intervening increase of the rate function that should normally have resulted in spiking. With thinning, the driving function is sampled "uniformly" (albeit stochastically) at the highest rate. There remains the problem that, after thinning, low-amplitude portions of the driving function are more sparsely sampled than high, but this is inherent in stochastic sampling and unrelated to the simulation method.

Refractory effects may modify the relation between the driving function and the empirically-observed spiking rate, particularly at high instantaneous rates. This modification may affect statistics derived from experimental measurements (Fig. 4), and possibly also properties of downstream neural processing. Phenomena such as fast initial adaptation, ringing, or peak splitting are unlikely to result from refractoriness in general, but it is worth keeping that factor in mind when investigating them. Merging multiple spike trains (as captured by shuffled autocorrelation statistics, Joris 2003, or as might result from convergence of afferents from multiple fibers on the same neuron), attenuates some, but not all, effects of refractoriness (not shown).

In summary, this short paper suggests approaches for phenomenological modeling of the spike generation process, for the purpose of better understanding the properties of this spike-based code, to allow simulation of downstream processes that use this code, and possibly also to gain additional insight into the sound-to-spike transduction process itself.

Fig. 1 .

 1 Fig. 1. Top: driving function (half-wave rectified 100 Hz sinusoid). Bottom: spike train produced by a homogenous Poisson process of rate 2000 spikes/second (black), the same after thinning according to the driving function (blue), and after additional thinning according to the recovery function (red).

Fig. 3 .

 3 Fig.3. Peri-stimulus time and interval statistics for spike resulting from a half-wave rectified sinusoidal driving function (100 Hz) of peak rate 500 spikes/s, in the absence (black) and presence (red) of refractory effects. The same piecewise-linear recovery function was used as in Fig.2. Statistics were gathered over a duration of 600 s.

Fig. 4 .

 4 Fig.4. Side-effects of refractoriness. Left: peristimulus time histogram at the onset of a short pulse of constant rate repeated 5000 times, The nominal driving rate was 1000 spikes/s (black) or 5000 spikes/s (red) (effective rates were 410 and 730 spikes/s respectively).

Fig. 5 .

 5 Fig.5. Effect of adding Gaussian jitter to spike times on vector strength, for a half-wave rectified sinusoidal driving function (1000 spikes/s peak rate), for several values of standard deviation. A value of ~50s mimicks quite well the synchrony roll-off observed in auditory-nerve recordings in the cat. The subtle increase in vector strength circa ~400 Hz is a side-effect of refractoriness.

Fig. 6 .

 6 Fig.6. Neural cancellation filter. Top: all-order inter-spike interval histogram for a driving function consisting of the half-wave rectified sum of 80 Hz and 100 Hz sinusoids. Middle and bottom: same, after filtering the spike train with a cancellation filter of delay parameter 10 ms or 12.5 ms (inverses of 80 Hz and 100 Hz).


Spooky tenebrism and gloomy chiaroscuro: how light shapes the landscape to crystallise a Gothic atmosphere in Frankenstein and Dracula Eline de Mathuisieulx Gothic fictional narratives are fraught with intricate references to light, from the pale saffron moonshine to flickering candle flames, not forgetting lurid dawns and sunsets red as blood. The "agent that stimulates sight"1 can be construed as the very essence of Gothic landscapes; it contributes to creating an eerie aesthetic, a dreary environment charged with tension by allowing the reader to catch a glimpse of malevolent monsters, merciless malefactors barbaric murderers or dangerous vampires hiding in every nook and cranny of haunted castles, shadowy graveyards or dark mountainous caves. Yet, light may embellish these harrowing surroundings. As Freud states in his article "The Uncanny" 2 , aesthetic is generally associated with beauty and attractiveness, and triggers positive connotations, but on the other hand, it may emphasise creeping horrors and unpleasantness, what arouses dread and repulsion in the reader's mind.

We shall focus on the use of luminosity as a means to generate an emblematic Gothic atmosphere in Frankenstein and Dracula. Paradoxically, its appearance is meant to increase the overwhelming presence of darkness, while the revealing rays of the moon become ominous harbingers of death.

Spooky tenebrism: how lamps paradoxically highlight prevailing darkness

Luminescence is part and parcel of the Gothic chronotope 3 , as it contributes to creating a bleak setting. In Frankenstein and Dracula, light is seldom bright and warm, it is rather feeble and cold to make the surrounding shadows even greater. In this way, it acts as a foil to Stygian darkness and paradoxically does not correspond to its traditional reassuring function. In her article "Gothic Light:

Vision and Visibility in the Victorian Novel", Stern reminds us that an indistinct environment remains "a trope for danger" where threatening characters can lurk and loom. 4 Villains fade into and emerge from relative obscurity, and the latter especially crystallises our deepest fears when it is associated to macabre sceneries: Within the Gothic genre, a seemingly inexhaustible series of graveyards, catacombs, burial vaults and hidden passageways find their attendant lighting effects in the lightning storm, the dying fire, the flickering candle, and, conversely, the sudden flare within a supposedly vacant space. 5

In the beginning of Dracula, most of the main characters believe that young Lucy Westenra has died of an unknown and incurable illness. Professor Van Helsing tries to convince his friend Dr.

Seward that she has actually turned into an "Un-dead" 6 by the Count. They both wait outside her vault in the dead of night to investigate. As soon as a "distant clock strike[s] twelve", the corpse awakens. 7 It was then very dark, and the scattered lamps made the darkness greater when we were once outside their individual radius. Dr. Seward records in his diary that a tenebrous night has fallen, and that the potentially reassuring glow emanating from the street lamps cannot dissipate the obscureness. On the contrary, it renders sinister shadows thicker and more menacing. It becomes a new enemy that allows the vampire to creep out of her crypt under cover of darkness, allowing her to treacherously attack the two men by surprise.

The sophisticated combination of complete darkness and subdued lamplights shapes Gothic landscapes, while the lucent moon is another overwhelming element heightened through personification.

Gloomy chiaroscuro: the ambivalence of sinister moonlight

In most Gothic novels, the fulgent moon is an omnipresent source of light which very frequently turns into a character through the process of personification. The celestial body usually emerges as a benevolent ally for the protagonists when it casts its soothing gleam. Moonbeams are a symbol for safety and even enable the empowerment of heroes. This reassuring presence lets them see, defeat or break away from, their enemies. This is notably the case for Victor Frankenstein, who avoids the creature in the mountains, and for Jonathan Harker who escapes the clutches of Dracula's nefarious siblings. Nonetheless, this valuable radiation is never to be taken for granted, as inconstancy and variation are considered to be characteristics of the moon. Shakespeare reminds us of this conception in Romeo and Juliet: O, swear not by the moon, th' inconstant moon, That monthly changes in her circled orb, Lest that thy love prove likewise variable." 9 Moonlight is ephemeral, as it changes night after night, and may be obscured from one minute to the next. Whenever a force endangers defenceless characters, scudding clouds will infallibly overshadow the natural satellite and plunge the setting into darkness. The vulnerable protagonists fall prey to the villains lurking in the shadows. Unfortunately, the personified moon is unable to help as it cannot voluntarily influence the plot. This feeling of powerlessness brings Gothic novels closer to Greek tragedies, in which the heroes are condemned to follow their fate, whatever they do to avoid it. [START_REF] Aristotle | Poetics" in Dukore, Dramatic Theory and Criticism: Greeks to Grotowski[END_REF] A parallel can thus be drawn between the moon and the reader who are forced to suffer the agony of suspense in silence.

Far from always being depicted as a static, empathic entity, the heavenly body sometimes turns into an unwanted trespasser, for it enters rooms uninvited, penetrates through windows and invades the characters' personal space. At the same time, this unsolicited guest usually makes horrible scenes visible and sheds light upon tragic developments. We can mention for instance Mina Harker when Dracula forces her to drink his own blood: "The moonlight was so bright that through the thick yellow blind the room was light enough to see". 11 Once she has tasted the vampire's sanguine fluid, the young woman is cursed and gradually metamorphoses into a creature of the night, just like him. Likewise, the moon shines upon the corpse of Elizabeth Lavenza, Frankenstein's bride, whom the creature strangled her on her hymeneal bed: "The windows of the room had before been darkened, and I felt a kind of panic on seeing the pale yellow light of the moon illuminate the chamber". [START_REF] Shelley | or the Modern Prometheus[END_REF] The moon becomes a fateful messenger delivering the sombre news that occurred during the night.

To finish with, the moon violently gives away the results of the man's hubristic experiment.

In the following passage, Frankenstein finally succeeds in giving life to his giant. Yet, when the enthusiastic young man meets the monster's eyes, he is so panic-stricken that he falls down into a swoon. When he wakes up, he contemplates his creation and immediately regrets his demiurgic action:

I started from my sleep with horror; a cold dew covered my forehead, my teeth chattered, and every limb became convulsed; when, by the dim and yellow light of the moon, as it forced its way through the window shutters, I beheld the wretch-the miserable monster whom I had created. 13 Thus, light can be seen as an ambivalent entity, a thing of beauty in contrast to the most loathsome Gothic stereotypes, or a treacherous evildoer that either supports darkness or makes plain the most atrocious peripeteias. In the end, light may always be preferable, as J. R. R. Tolkien writes in The Fellowship of the Ring: "May it be a light to you in dark places, when all other lights go out." 14 +/-1160 words 13 Shelley, 36. https://langues.unistra.fr/search-dev/membres/doctorants/eline-de-mathuisieulx/ Publications -Témoignage de doctorante dans "Le Carnet de recherches de la SAES", 2019.

-"La triple menace eschatologique dans The Lord of the Rings de Tolkien", Caliban n°63 : Dynamiques de l'effondrement dans le fantastique, la fantasy et la SF, 2020.

Communications

-"La paradoxalité des marges : une étude intermédiale des adaptations visuelles du roman The Lord of the Rings de J. R. R. Tolkien" Université de Metz, October 2020.

-"Concerning pipeweed and the addiction to the spectacular", "Mapping addiction: deviant bodies and marginal spaces", Unistra, early 2021.

  14 J. R. R. Tolkien, The Fellowship of the Ring, 491. Biography Eline de Mathuisieulx is ATER at the University of Strasbourg and is a member of SEARCH UR 2325. In October 2019 she started a PhD supervised by Professor Hélène Ibata entitled "The Lord of the Rings by J. R. R. Tolkien, from illustrations to cinema adaptation, Alan Lee, John Howe and Peter Jackson, a quest intertwining the sublime and the spectacular". Her master's thesis is entitled: "The translation of light in 19 th century Gothic novels: Frankenstein, or the Modern Prometheus (1831) by Mary Shelly and Dracula (1897) by Bram Stoker".

  Mikhail Bakhtin, trans. Caryl Emerson and Michael Holquist, "Forms of time and of the chronotope in the novel", in The Dialogic Imagination (Austin: Univ.

	Texas Press, 1981), 431.
	4 Rebecca F. Stern, "Gothic Light: Vision and Visibility in the Victorian Novel" (South Central Review, 1994),
	28.
	5 Stern, 27.

8 3 6 Bram Stoker, Nina Auerbach, and David J. Skal. Dracula: authoritative text, contexts, reviews and reactions, dramatic and film variations, criticism (1st ed. A Norton critical edition. New York: W.W. Norton, 1997), 180. 7 Stoker, 177. 8 Stoker, 175.

Oxforddictionaries.com, accessed August

27, 2020, s.v. "light". 2 Sigmund Freud, "The Uncanny"(Penguin Books, 2003) 2.