Romain David
email: romain.david@erinha.eu@romain_david_13websites

Alison Specht

Margaret O'brien

Lesley Wyborn

Christina Drummond

Rorie Edmunds

Claudia Filippone

Jeaneth Machicao

Nobuko Miyairi

Graham Parton

Debora Pignatari Drucker

Shelley Stall

Niklas Zimmer

Multilingual Data Challenges in Professionalizing Data Stewardship worldwide

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

The use of common FAIR vocabularies, that are both human and machine readable, is a key criterion in the FAIR principles (e.g. Principle I2 of Wilkinson et al 2016 specifies '(meta)data use vocabularies that follow FAIR principles'). Using common FAIR vocabularies will enable data interoperability and the necessary meta-analyses even when data have different origins and are based on multiple vocabularies. The objective of this poster is to offer an overview of the many multi-language challenges for effective Data Stewardship. For instance, some bottlenecks are highly dependent on community approval processes that are linked to data dictionary understandability, and/or related training challenges. Translation challenges are also organisational and sustainability challenges:

Good practices

Care must be taken to ensure that datasets resulting from projects that practice co-creation and co-evolution of knowledge are translated into indigenous languages such that they can be used by the affected communities. Taking these challenges into account, we have to consider human effort and the level of translation, e.g. a low or minimum yet sustainable level, that is legally allowable. How can such minimal objectives be linked with FAIR principle compliance (especially FAIR and community approved vocabularies)? In several communities, translation is voluntary. One of the sustainability challenges is the need for ongoing engagement: how to keep interested groups involved. We need expert translators, as described, to maintain the quality level critical to achieve effective harmonization among languages.

Acknowledgements:

PARSEC is funded by the Belmont Forum through the National Science Foundation (NSF), The São Paulo Research Foundation (FAPESP), the French National Research Agency (ANR), and the Japan Science and Technology Agency (JST). This work is partially funded by the EOSC-Life European program (grant agreement No. 824087).We acknowledge wikipedia for R2D2, C-3PO and Tie fighter pictures.

My name is C-3PO! I am fluent in over six million forms of communication… And you?

Science must be universally shared, in an interdisciplinary way, respecting that all disciplines are creating new concepts. The fact that science is always creating them is the core challenge for translators

The "TERM WARS" at global Scale: a time and space story

Discrepancies between regions and groups (culture, content, workflows, language, semantics, translation, funds…) are numerous whether for individual data users or more universally. We must anticipate issues such as which is the preferred language, polysemy (1 term, multiple meanings), confusion (multiple terms for 1 meaning or 'false friends' between 2 languages), plus existing and evolving nuances (not an exact match between languages and during time). Furthermore, terms are often adopted from another language with different contexts and disciplinary realms (that might decrease interoperability) and impedes translation of all versions at the same time.

Translation occurs at the concept level, not as a simple one to one translation of (consecutive) words.

Over time, research evolves, disciplines are created, split and new terms are necessary to describe new concepts…

  For translators: ○ Scientific skills with at least good command of target languages ○ Validators to check work translated ○ A clear versioning system ○ A translating strategy with prioritization levels For Databases: ○ Data dictionary with ■ disambiguated definitions both linked to and linked by concepts in shared ontologies ■ the date of the definition ■ the context of use (disciplinary -protocol -necessary skills…) ○ A description of the community approval process (that can be adopted for new terms by other communities) Very few, if any, of our present problems such as biodiversity decline, climate change, and viral pandemics stop at national, disciplinary and linguistic boundaries, yet our most vital responses to the shared problems, the information generated to analyze and derive solutions, is still siloed in different languages and locations throughout the world. It is clear that in order for us to effectively respond, we need to collaborate globally and communicate information more effectively. Globalization of research requires interoperability of our observations and experimentation systems. Author affiliations : 1 ERINHA (European Research Infrastructure on Highly Pathogenic Agents) AISBL, FR, ORCID: 0000-0003-4073-7456; 2 The University of Queensland, AU, ORCID: 0000-0002-2623-0854; 3 University of California Santa Barbara, USA, ORCID:0000-0002-1693-8322; 4 Australian National University, AU, ORCID: 0000-0001-5976-4943; 5 Educopia Institute), ORCID: 0000-0001-5794-0413; 6 DataCite; 7 University of São Paulo, ORCID: 0000-0002-1202-0194, 8 Nobuko Miyairi, ORCID: 0000-0002-3229-5662, 9 Center for Environmental Data Analysis, ORCID: 0000-0003-4157-0352, 10 Embrapa Digital Agriculture, ORCID: 0000-0003-4177-1322, 11 American Geophysical Union, ORCID: 0000-0003-2926-8353, 12 University of Cape Town ORCID: 0000-0001-8078-0403 RDA 19th Plenary Meeting, Part Of International Data Week, 20-23 June 2022, Seoul, South Korea


Jeaneth Machicao

Ali Ben Abbes

Leandro Meneguzzi

Pedro Corrêa

Alison Specht

Romain David

Gérard Subsol

Danton Vellenich

Rodolphe Devillers

Shelley Stall

Mene

Danton Ferreira Vellenich

Laure Berti-Equil

Reproducing Deep Learning experiments: common challenges and recommendations for improvement

de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Reproducing Deep Learning experiments: common challenges and recommendations for improvement

Website: https://parsecproject.org/ twitter: @PARSEC_News Reproducibility: why is this important?

One of the challenges in Machine Learning research is to ensure that the presented and published results are sound and reliable. Reproducibility is an important step to promote open and accessible research, thereby allowing the scientific community to quickly integrate new findings and convert ideas to practice.

We already went through the path of darkness:

We proposed a set of recommendations ('fixes') to overcome these reproducibility challenges that a researcher may encounter in order to improve Reproducibility and Replicability (R&R) and reduce the likelihood of wasted effort.

These strategies can be used as "swiss army knife" to move from DL to more general areas as they are organized as (i)

the quality of the dataset (and associated metadata), (ii) the Deep Learning method, (iii) the implementation, and the infrastructure used.

We identified the main challenges and constraints from these papers and presented them accordingly. Finally, with the lessons learned in the previous step, we propose a set of mitigation strategies to overcome the main reproducibility challenges and help researchers achieve their goals.

Conclusion:

The

Mitigation Strategies and FAIR advice

Implementation and Infrastructure ○ Internet flaws. ex. when dealing with APIs ○ Bugs. It is expected that some bugs will be found in the scripts. ○ Versioning. Use the same versions as the original in order to avoid 'deprecated' versions. ○ Source code is available but there are many branches. ○ Programming language. If the source code is in a particular programming language it is good advice to search for another trustable version.

Advice about FAIR principles criteria ○ Some FAIR principles are mandatory in dataset design ○ Some FAIR principles need scientific community agreement and information about dataset quality. ○ Accept uncertainty when achieving FAIR, because a dataset is never perfect.

  Authors: J. Machicao, A. Ben Abbes, L. Meneguzzi, P.L.P. Corrêa, A. Specht, R. David, G. Subsol, D. Vellenich, R. Devillers, S. Stall, N. Mouquet, M. Chaumont, L. Berti-Equille, D. Mouillot Contact: P.L.P. Corrêa

  requirement for reproducibility and replicability of experiments, let alone those in which new techniques such as Deep Learning are employed, is very recent. There are few instances where R & R has been practically tested, and more work is needed to develop best practices and make this a real possibility for the achievement of truly open, defensible science.Regarding FAIR principles, there have been some recent efforts to establish standards for FAIR ML and DL models[START_REF] Pineau | The Machine Learning reproducibility checklist[END_REF][START_REF] Walsh | DOME: Recommendations for machine learning validation in biology[END_REF]. However, our knowledge, this is a first-of-its-kind initiative that presents a problem of reproducibility in remote sensing imagery and Deep Learning problems for real-world tasks. However, there are still some limitations to this work. It tries to be general, but it is an initiative for the DL community. is obtaining similar results as presented in a paper or talk, using the same code and data (when available), is a necessary step to verify the reliability of research findings. Quality of the dataset ○ Validate the dataset used in the study. ○ Use a sample of the dataset. ○ Check parameters of the datasets or code. ○ Check the preprocessing steps. ○ Verify the data construction method. ○ Test different configurations of data split. Deep Learning methodology ○ Look for workflows. ○ Look for model architecture as source code. ○ Look for different setups of experiments.

  Making a Deep Learning (DL) research experiment reproducible requires a lot of work to document, verify, and make the system usable. These challenges are increased by the inherent complexity of DL, such as large number of parameters and hyperparameters, volumes of data (with possibly missing datasets and changes to the data), changes to some of the algorithms, and, as a result, versioning issues to deal with many iterations during training, which can be challenging for Reproducibility & Replicability (R&R) . Due to the stochastic nature of the variables within a DL methodology, such as: I the dataset, (ii) the DL architecture, (iii) the optimization procedure, (iv) the hyperparameters for optimization, and (v) the implementation and infrastructure, all of these are referred to as a source of 'variability' [1]. Flowchart of Poverty Estimation using remote sensing data and DL approaches.

Acknowledgements:

PARSEC is funded by the Belmont Forum through the National Science Foundation (NSF), The São Paulo Research Foundation (FAPESP), the French National Research Agency (ANR). J.M. is grateful for the support from FAPESP (grant 2020/03514-9). RDA 19th Plenary Meeting, Part Of International Data Week, 20-23 June 2022, Seoul, South Korea


Steven James Bartlett

PHILOSOPHY AS NEGATIVE SCIENCE

Keywords: negative science, metalogic of reference, theory of identification, transcendental argumentation, systemic error, propagating error, metalogical projection

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Avoiding errors in philosophy: Kant's notion of "negative science"

ommon to perhaps all philosophers is the wish to avoid making mistakes. In this they are no different from scientists. And yet, unlike science, philosophy has not yet developed an autonomous sub-specialty devoted to methods of error detection and error avoidance. Both mathematics and the sciences have incorporated in their methodologies techniques specifically designed to permit self-monitoring and the avoidance of error.

They have been able to accomplish this in part because mathematicians and scientists adhere to rigorous and universally accepted and enforced standards of proof, but especially because they have developed methods to detect errors in advance: Mathematicians expend considerable efforts in checking proofs for errors before publication, sometimes employing computer assistance; software developers run errorchecking computer code before software is implemented; physicists and chemists identify possible sources of error before running experiments. In such ways, systematic efforts are made in advance to recognize the possible introduction of errors in proofs, calculations, measurements, proposed procedures and designs, etc. It is because of the reliance upon error-checking in advance that aircraft can be designed that have a high likelihood of not crashing and bridges of not collapsing. In physics, for example, error analysis is now an established and essential adjunct to the discipline. Such error analysis may study potential sources of statistical errors, uncertainty that arises as a result of the inherent imprecision of instruments, snowballing effects when errors are propagated, and systemic error that may occur when the very design of a system can be anticipated to lead to unsatisfactory results.

Philosophy, too, has its own widely used means of correcting and avoiding certain kinds of errors. Informal logic is most commonly the principal means that philosophers rely upon; usually this is traditional, classical logic, but some philosophers also apply formalized modern logics. Before reading or publishing a paper, a philosopher will usually try to identify sources of error in the form of self-contradictions, statements whose presuppositions cannot be defended, errors of inference and deduction, etc. For millennia, logic has supplied the main tool of error detection, elimination, and avoidance in philosophy. And in addition to logic, philosophy also makes recourse to general and informal standards of plausible reasoning, moral and prudential reasoning, adequacy of evidence, accuracy of scholarly claims concerning the work of other philosophers, etc. C < 3 > Notwithstanding the central importance of logic as a tool for detecting mistakes, philosophy has yet to develop an autonomous sub-specialty devoted to error analysis and error theory. In parallel with the approaches to error analysis mentioned above, a philosophical theory of error would have as its objective the formulation of a methodology capable of identifying-in advance of actual philosophical argumentationmajor sources of potential conceptual errors so that philosophers may avoid them.

This goal was, in a limited sense, only hinted at, suggestively and in passing, by Kant in one of his letters to Johann Heinrich Lambert (1728-1777), a Swiss-German philosopher, physicist, and mathematician. Lambert was the first to prove that π is irrational, one of the first to seek to develop a calculus of logic, and perhaps the first philosopher to employ the term 'phenomenology'. 1 Lambert described phenomenology as "the doctrine of illusion," the study of which enables us to recognize illusions [Scheine] that seduce us into making erroneous claims about experience. He conceived of phenomenology as a study that makes it possible to avoid the errors resulting from such illusion, and thereby come to recognize what is true. Translated into the terms I use here, phenomenology for Lambert would have as its general purpose the detection and elimination of error arising from sense experience.

Kant thought highly of Lambert and became interested in Lambert's conception of phenomenology. In a letter to Lambert dated September 2, 1770, Kant proposed what he called a 'phaenomologia2 generalis', that is, a general phenomenology that would serve as a propaedeutic discipline which would prevent, in advance, the introduction into metaphysics of errors resulting from the misleading illusions that can beset sense experience. The propaedeutic-preventative purpose of such a general phenomenology led Kant to call it a "negative science." This the way he expressed his suggestion:

The most universal laws of sensibility play a deceptively large role in metaphysics, where, after all, it is merely concepts and principles of pure reason that are at issue. A quite special, though purely negative science, general phenomenology (phaenomologia [sic] generalis), seems to me to be presupposed by metaphysics. In it the principles of sensibility, their validity and their limitations, would be determined, so that these principles could not be confusedly applied to objects of pure reason, as has heretofore almost always happened. For space and time, and the axioms for considering all things under these conditions, are, with respect to empirical knowledge and all objects of sense, very real; they are actually the conditions of all appearances and all empirical judgments. But extremely mistaken conclusions emerge if we apply the basic concepts of sensibility to something that is not at all an object of sense, that is, something thought through a universal or pure concept of the understanding as a thing or substance in general, and so on. (Kant, 1997, pp. 108-109, italics added) As far as I know, Kant was never again to use the expression 'negative science' nor did he attempt to develop an error-preventing negative science. A negative science was to < 4 > remain a never-to-be-developed embryonic idea. As he imagined it, it would have formed a discipline capable of determining "the principles of sensibility, their validity and their limitations ... so that these principles could not be confusedly applied to objects of pure reason." If such a negative science were to be developed as Kant suggested, it would ideally provide philosophy with a propaedeutic, an indispensable preliminary, or what today we might call a safeguard designed to prevent the introduction of error that can originate from potentially illusory sense experience.

Two and a half centuries have passed since then. In the approach to philosophy as a negative science which I shall turn now to discuss, my development of a negative science should not be equated with Kant's notion; I don't seek to develop negative science in order to accomplish Kant's intentions. Nonetheless, the term 'negative science' accords well with the error-eliminative purposes I have in view. Since these purposes are closely allied with certain post-Kantian modern approaches to transcendental argumentation, my use of the term 'negative science' may be thought of as a nod of recognition to a paragraph written in a letter centuries ago.

A systematic approach to negative science

Two classes of tools that can help philosophers avoid error should be distinguished: There are the tools provided by logic, as mentioned earlier. When applied by philosophers, these largely involve appeals to individual logical laws, such as noncontradiction or the law of excluded middle, or to principles of inference or deduction, such as modus ponens, reductio ad absurdum, conditional proof, etc. Let us call these specific tools that help us to detect logical errors which involve particular violations of individual logical laws or principles of inference.

There is another class of methods that is less widely recognized. Earlier in this paper, I mentioned two varieties of error which physics has sought to find rigorous ways to recognize and avoid: systemic error, which can occur when the very design or structure of a system leads to unacceptable erroneous results, and errors of propagation which occur when the effects of errors snowball in a domino-like way, resulting in the spread and escalation of error. These forms of error, which occur on what a general systems theorist would call a systems-wide level, have interested and concerned me for many years. Philosophers commonly make use of a shared familiar vocabulary of concepts, concepts which have received their meaning both as a result of the uses to which past philosophers have put them, and as a result of the accretion of meaning and criticism which often contribute over long spans of time to the evolution of the meanings of those concepts. This vocabulary of concepts upon which we philosophers rely in order to communicate with one another itself comprises a system, a system both of linguistic use and conceptual understanding. We are not accustomed to think that the very system of concepts that have become familiar, conventional, and habitual can itself be a source of error.

In much the same systems-based perspective, the thought of individual philosophers often forms a system-and here I do not solely include philosophers who have engaged in "systems building," but include those philosophers who present us with more limited accounts of aspects of reality or thought, and whose "system" is not wholly expressed within their work, but by implication extends outward beyond their specialized individually expressed views by relying, again, upon portions of the commonly accepted vocabulary of philosophical concepts.

In both of these ways-in terms of the vocabulary of concepts upon which conventional philosophical discourse is based, and in terms of the system formed by an individual philosopher's work-both varieties of error-systemic and propagating-can occur. Systemic errors and errors that are propagated in a systems-based way come about when the very set of concepts in question-whether they comprise the commonly accepted vocabulary of a large group, or the individual set of concepts a philosopher uses-is intrinsically and sometimes fatally prone to error.

Let us pause for a moment to consider a rough example of specific versus systemic and propagating error: Nearly all of us are familiar with typographical errors: If we're using a keyboard, while typing we touch a key inadvertently and then find that what we've typed is a mistake. This is a specific error; we correct it by applying familiar rules of spelling, punctuation, or grammar.

Consider, however, a keyboard which itself is malfunctioning. Even though we type accurately, still typographical errors are the result. Perhaps the circuitry of the keyboard or its computer or printer connection has failed. Whatever the reason, as long as the malfunctioning keyboard continues to be used as it stands, typographical errors will continue to occur. What we have here is a systemic source of error, and as long as the same malfunctioning keyboard continues to be used, errors will be propagated.

As far as I know, the work I have published during the past 50-plus years is the main, and again, to my knowledge, the only philosophical effort to date to develop a systematic "negative science" that is capable of detecting, avoiding, and eliminating conceptual errors of the systemic and propagating kinds.

In what follows in this short paper, I cannot of course provide a full and adequate account of this approach; for this purpose, readers are referred to the References where selected, representative publications are listed. The most comprehensive account will be found in my recently published book, Critique of Impure Reason: Horizons of Possibility and Meaning (Bartlett, 2021). Due to its length of nearly 900 pages, to assist readers I've also published a short Primer on Bartlett's Critique of Impure Reason (Bartlett, 2021a).

My purpose in this paper is to provide readers with an overview so they may have a sense of how philosophy as a negative science may be undertaken, to provide a few suggestive examples of its application, while including a few autobiographical, more personal comments that may help readers acquire an understanding of the in-principle conceptual difficulty of communicating a critique of the very philosophical concepts we commonly rely upon in order to communicate.

Philosophy as negative science by means of a metalogic of reference

One of the most conceptually fundamental levels from which to study the functioning of our concepts is reference: We may wish to understand how our concepts refer or fail to refer, what must be presupposed in order for it to be possible for reference to occur, how < 6 > meaning and reference are interrelated, and how reference can fail on a systemic level, often without our awareness.

Theory of reference has in the main been studied by philosophers of language. However, although the employment of our concepts often is expressed through language, reference very frequently occurs in non-linguistic contexts: Among many examples, there is simple non-verbal ostensive pointing, as well as the forms of reference involved in the multitude of non-linguistic phenomena with which we're all acquainted in everyday life, whether we attend to body language, recognize natural sounds, experience expressions in art, dance, and music, or simply consider the referential nature of much non-verbal thought in the form, for example, of memories, anticipations, worry, fears, etc.; the list is potentially endless.

Rather than approach reference from the now-traditional perspective of language, instead I've sought to develop a general theory of identification. Identification is commonly thought of as individualizing and specific reference, as when a given Social Security number uniquely refers to one and only one person. There also is, however, nonspecific reference, which does not single out specifically and singly an individual object of reference, but may instead only identify an object or set of objects vaguely or within a certain degree of imprecision or probability.

The general theory of identification I've developed itself forms a reflexive system, including itself within its own scope of reference. Logician Frederic Brenton Fitch called such a reflexive theory whose scope of application is all frames of reference, its own included, a theory developed on the level of 'maximum theoretical generality'. 3 As I have formulated it, such a general theory of identification can be characterized as a metalogic. When we establish a superordinate frame of reference that makes it possible to refer to subordinate individual systems of reference or individual theories, the superordinate reference frame is commonly termed a 'metalanguage'. The formal study of the subordinate systems is then routinely called 'metalogic'. 4 With an interest in its formal and to some extent its formalizable structure, I've therefore called the general theory of identification 'metalogic of reference'.

The metalogic of reference has a direct transcendental focus and application: It seeks to describe general principles that govern possible reference to any subordinate system of reference; at the same time, these general principles, which come to be recognized as invariant for all reference frames, themselves also govern possible reference to the metalogic of reference itself. The concern throughout is to identify those preconditions of possible reference without which reference and ultimately also meaning become impossible. Very evidently this is a transcendental project.

It is also evidently a highly abstract undertaking-as one would expect of any theory developed on the level of "maximum theoretical generality." It requires on the part of any reader a mind comfortable with high levels of theoretical abstraction, and it also requires certain other mental, and even psychological, predispositions which I've sought to identify elsewhere. 5 The central concern of such a metalogic of reference is negative in the sense of a negative science alluded to earlier. The foremost concern is to recognize those constraints upon possible reference which, if transgressed, result in the impossibility of both reference and meaning. To show this requires more than a single paper can accommodate. Instead, let us consider a few examples that may give readers a more intuitive understanding of what can be expected from such a metalogical study of reference.

A few epistemological examples

The metalogic of reference as I've developed it begins with an analysis of reference frames: the systems of reference that are relied upon for reference to be possible to whatever sorts of objects we may have in view. Such an analysis is concerned to identify general and invariant principles that govern reference, principles which, if violated, undermine the possibility of reference and meaning. To succeed in such an undertaking, we require a clear and well-defined concept of reference, as well as definitions of meaning, identification, reference frames, objects of reference, etc. For the purpose of the following examples, we will make do with our everyday intuitive notions of these things.

Discovery or invention

Especially in mathematics and in physics an appealing question has frequently been raised, but never satisfactorily answered. This is the question whether the results that mathematicians and physicists reach are "discovered" or "invented." Some mathematicians experience a deeply seated conviction that mathematical truths are discovered-that they are, in some perhaps inarticulable way, "out there," existing independently of the thought processes and analytical abilities of all mathematicians. In much the same way, some physicists express wonder that physical nature is so amenable to mathematical representation, and come to believe that physical laws, once they have been formulated and have repeatedly been confirmed, express underlying structures of the physical universe, structures or principles of order which similarly exist autonomously of all human activity. Physicists who are members of this group tend to think that physical laws are discovered-they are principles that "existed beforehand" and "were always there," ready to be disclosed to physicists once they had acquired the necessary knowledge and instrumentation.

There are mathematicians and physicists who don't agree with this point of view: They believe that mathematical truths and physical laws are results acquired as a function of the analytical activity of mathematicians and physicists, that such truths and laws are conceptual "constructs" and hence are really "inventions" of the human mind in its efforts to understand the nature of mathematical or physical objects and phenomena. Intuitionist mathematicians are members of this group, as are some quantum theorists today. 6 The metalogic of reference steps back from this controversy and asks instead, What conditions would need to be satisfied in order for it to be possible to identify < 8 > mathematical truths or physical laws independently of the reference frames by means of which such truths and laws are formulated and can be ascertained? As I have tried to show,7 a careful analysis to answer this question leads to an answer that can be demonstrated since its very denial undermines its own possibility of reference and meaning. If we were to undertake such a systematic analysis of the referential preconditions involved in the discovery-or-invention question, we should find neither answer-that mathematical truths are discovered or invented, or that physical laws are discovered or invented-can possibly be meaningful since the conditions that would need to be satisfied in order to refer to the framework-independence or framework-dependence of such truths or laws cannot possibly be satisfied.

In brief, the metalogic of reference leads here to the conclusion that the discovery-orinvention question poses an illusory, deceptive question: It is a question that involves what amounts to a conceptual sleight-of-hand that encourages a delusion. That delusion encourages us to search for something which, in principle, is impossible.

The problem of the external world

The problem of the external world, which has attracted the interest and concern of philosophers for millennia, similarly lends itself to a metalogical analysis of the preconditions of reference which this problem, in order possibly to refer and to make the sense it intends, must presuppose.

Idealism and realism with respect to the question whether there exists-or does not exist-an independent external reality may be placed in parallel with the question whether mathematical results and physical laws are discovered or invented.

Although the specific steps of referential analysis are different, a metalogical analysis can be undertaken of the referential preconditions that would need to be satisfied in order for the question of the external world possibly to be answered. Such an analysis leads to a similar result,8 one which cannot be denied without a form of self-referential inconsistency that has not been widely recognized, which I've called 'metalogical projection'. Stated in necessarily abbreviated form here, such an inconsistency precludes the very possibility of reference and meaning: It is a form of self-referential inconsistency that is transcendental, concerning the preconditions of the possibility of reference and meaning.

In connection with the problem of the external world, the result to which the metalogic of reference leads is a recognition that both idealism and realism are philosophical positions which, at their very heart, involve a conceptual sleight-of-hand that encourages a referential delusion of a certain important kind, a variety that encourages a systemic error of the sort pointed to earlier.

The perturbation theory of measurement in quantum theory

There exists a multitude of examples that lend themselves to a metalogical analysis of referential preconditions. In this paper, I've so far outlined two of these: the first expresses an often-asked question by mathematicians and physicists about the ontological < 9 > status of mathematical truths and physical laws, and the second, also an ontological question, is asked by philosophers about the status of the external world. To conclude this short list of examples, let us look briefly at a problem that has come in recent years to concern quantum physicists.

To do this, let us first consider the inhabitants of an imagined world of purely tactile sensation: The inhabitants are, we shall assume, in principle limited to the sense of touch; there is no other possible means for them to sense objects in their world. But despite this limitation, they have developed a primitive stage of quantum physics based wholly upon touch. The only way they can therefore make any measurements is by touch. Some of their quantum theorists have come to believe that whenever any quantum phenomenon is touched, it is changed by virtue of the very activity of touching it. Other tactile quantum theorists disagree: They claim that it is fundamentally misleading to suggest that measurement perturbs what is measured. They point out that to detect a change, touch must be used-since touch is the only way for them to make any observation. But how, in principle, can touch be used to detect that the activity of touching changes what is touched? They claim that simple reflection shows that it cannot possibly do this, in principle.

There is, and long has been, a similar disagreement among the quantum theorists of our own multi-sensory world concerning what is called the 'perturbation theory of measurement'. According to this view, quantum-level measurement inevitably "changes" what is measured. A careful metalogical analysis of the possible referential means of existing quantum theory9 shows that two main referential preconditions would need to be satisfied in order for such a "change"-in principle-to be detected: the "act of observation" must exert some kind of perturbing influence upon what is measured, and such an influence must result in a "change" in the phenomenon measured. These two claims are combined in the notion that there exists a relationship of perturbation between the quantum observer, the measuring instruments employed, and the quantum phenomena measured.

In the history of quantum theory, Niels Bohr stands out among the most epistemologically self-conscious quantum physicists. Repeatedly he reminded his fellow physicists of the need for restraint when they make claims about "perturbing interactions" when quantum-level measurements are made. Here is one such warning he published:

[O]ne sometimes speaks of "disturbance of phenomena by observation" or "creation of physical attributes to atomic objects by measurements." Such phrases, however, are apt to cause confusion, since words like phenomena and observation, just as attributes and measurements, are here used in a way incompatible with common language and practical definition. On the lines of objective description, it is indeed more appropriate to use the word phenomenon to refer only to observations obtained under circumstances whose description includes an account of the whole experimental arrangement. (Bohr, 1958, p. 73) A metalogical analysis of the referential preconditions that would need to be satisfied in order for quantum theorists to claim that quantum measurements perturb the phenomena < 10 > measured shows us, however, that incompatibility with common language and practical definition are not what is at stake as Bohr suggested, but rather referential impossibility. 10 We are able immediately to see that the inhabitants of a world of purely tactile sensation cannot perceive any "change" that their own activity of touching "produces" when a quantum measurement is made: After all, to perceive such a change, they would need to measure (touch) the state of a quantum object before it is touched in order to detect that it has undergone a change as a result of the measurement (touch). But to do this, they would need to touch that object before they touch it, a theoretical impossibility.

Much the same limitative obstacle stands in the way of the perturbation theory of measurement. This is a limitative result of present day quantum theory: As long as quantum theory in its present formulation is accepted, then-in principle-quantum theorists have no possible way to obtain information about any alleged pre-measurement properties of the quantum phenomena studied, properties which are purported to have a pre-existing state that is "changed" as a result of the activity of measurement. This isn't a matter that can, in principle, be resolved through the creation of more sensitive instruments of detection; it is not a matter of an absence of practical means at this time.

Instead, what we encounter is an impossibility in principle. Bohr seems to have been conscious of this impossibility in principle:

[N]o result of an experiment concerning a phenomenon which, in principle, lies outside the range of classical physics can be interpreted as giving information about independent properties of the objects, but is inherently connected with a definite situation in the description of which the measuring instruments interacting with the objects also enter essentially. (Bohr, 1958, p. 26) If this analysis were to be extended in detail, we should find that the referential impossibility involved here applies not simply to the impossibility of referring to premeasurement independent states or properties of quantum phenomena, but to the impossibility of reference to any putative "influence" resulting from whatever measuring instruments are employed. We should find that the notion of "perturbation interaction" runs into an impenetrable wall of theoretical impossibility of separately distinguishing quantum-level phenomena from the system formed by the observer, the observer's measuring apparatus, and the phenomena measured. 11 Elsewhere, I have called such impenetrable walls of theoretical impossibility 'metalogical horizons'.12 They comprise limits beyond which reference becomes not only impossible, but self-undermining on a transcendental level in a way that involves the denial or rejection of the preconditions of possible reference and possible meaning. Unfortunately, there is a deeply rooted human compulsion to transgress beyond such limits.

< 11 >

Delusional reference: The human compulsion to transgress beyond the limits of possibility

Within the human mind there is a powerful, perhaps primordial, desire to go beyond the limits of human knowledge.... Many, many lay persons and professional thinkers invest significant resources in a lifelong attempt to cross the transcendental horizon of the human situation and live in another world or dimension-and to grasp a sense of meaning and security that are not immediately generated by empirical reality alone....

[T]he human mind, apparently, will go to any lengths in order to gratify the need for this particular kind of transcendence. No amount of sophistry, no amount of internal contradiction of methods, and no amount of contradiction of empirical reality seem to function as an effective deterrent. In many cases, the non-recognition of empirical reality and the rejection of formal logic are basic methodological instruments in the pursuit of meaning, transcendence-and escape.

-Roy D. Morrison (1994, p. 352) Delusions and deceptions often require some implicit cooperation on our part in order that we may become victims of them. The systemic conceptual errors with which I have been concerned appear to rely upon such implicit complicity, a complicity that is not forced upon us, but which, when such errors do not merely form part of habits that have become automatic, we often voluntarily, even if not always self-critically, accept.

In the three examples above, relating to the discovery-or-invention, external world, and measurement perturbation controversies, proponents for or against each issue can be observed in their in-person behavior and published writings to be motivated by deeply seated, deeply felt beliefs. These beliefs appear not only to be difficult to engage through direct rational criticism and challenge, but to elicit resistance when those beliefs are questioned. To illustrate this, I briefly describe my own admittedly anecdotal personal experiences that bear this out:

I completed a portion of my graduate work at a leading university in California. I proposed a doctoral dissertation whose objective was to develop a method to detect, eliminate, and when possible to correct malfunctioning philosophical concepts of a sort which today I call 'systemic'. My proposal claimed that such malfunctioning concepts were pervasive in philosophy, and for this reason their detection, elimination, and, when possible, their correction could potentially have far-reaching consequences when considered in relation to the major questions that have occupied philosophy for millennia.

Such a dissertation proposal was admittedly unconventional, innovative, and bold. Unlike most doctoral dissertations in philosophy, it did not seek to study any one particular philosophical problem, philosopher, or group of philosophers, but instead proposed an original work that was an honest and undisguised potential threat to much of established mainstream philosophy.

My department responded by requiring that my dissertation proposal would first have to be evaluated at an oral examination before a committee of all 19 members of the department, including a specialist flown in from another college and supplemented by an < 12 > extra-departmental member from another discipline. Elsewhere I have described this rather unusual experience. 13 It was the first of other experiences which have made clear to me that critiques which bring critical attention to bear on alleged systemic errors within a discipline are, understandably and predictively, likely to encounter resistance.

The department refused to allow me to proceed with such a dissertation proposal and required that I change to a topic for which the department had a member with the requisite background and training. I was, however, determined to develop the subject I had in view. I decided to re-locate my doctoral work to the Université de Paris. Gabriel Marcel had taken a special interest in my proposed project and surprised me by having already arranged in advance with Paul Ricoeur for him to direct my dissertation.

Ricoeur was not threatened by the nature of my proposal and was comfortable with a young aspirant's wish to critique the main concepts in terms of which many traditional problems of philosophy have been formulated. Ricoeur was at ease with frameworks not his own and possessed a sense of humor: In meetings with him in his Nanterre office, he would admit that the results I had reached were incontrovertible, and yet in public lectures that I attended shortly afterwards, he would sometimes fall back into the very errors he had just admitted were undeniable and ought to be avoided. There was humor in this, for I think we both realized that shifting away from an established and habitual vocabulary of concepts is not only difficult, but can only be made haltingly and with the recognition that old concepts can persist with a tenacity of their own (what I now refer to as "propagating error").

In my subsequent university teaching, I've had many other opportunities to witness the deeply seated reluctance and sometimes the recalcitrance of even the brightest students (a) to give up habitual concepts even though they have come to recognize and admit that these are malfunctioning, and (b) to replace them with reformulated, corrected concepts that comply with the requirements of referential consistency. Some students are of course more successful in doing this than others. My interest in the intellectual dispositions and skills that distinguish such students has comprised a separate, more psychologically-focus study. 14 When these dispositions and skills are lacking, systemic errors of the kind that have concerned me flourish and multiply easily. Earlier in this paper I referred to such errors as involving what metaphorically might be called 'conceptual sleights-of-hand' that encourage delusions. Such delusions seduce us to pose and attempt to answer questions in a search for something which, in principle, is impossible. 15 13 This experience, as well as others that similarly illustrate characteristic human responses to intellectual dissent, is described in Bartlett (2017a). 14 See note 5. 15 To avoid misunderstanding, it is important to note that such conceptual delusions are not to be equated with assertions of "transcendence." The term 'transcendence' is broad and has been put to a variety of uses. One common use is exemplified by objects in one's visual field which are often thought to be "transcendent" insofar as the perceiver may believe, for example, that by walking around the perceived object, other sides or aspects of the object are likely to be seen; in this sense, the perceived object is thought to "transcend" what is given in the individual's visual field at any one time. Another use is found in claims that objects of a certain kind extend beyond a given means of apprehending them: For example, an object may be said to transcend visual perception insofar as it can also be experienced as an auditory phenomenon. Still further, objects are often believed to transcend anyone's experience, or to transcend everyone's. -All of these uses of the term 'transcendence' relate to what is believed in fact to be the case.

The conceptual delusions with which I am concerned in this paper, however, relate to limits of possibility. This is essentially a modal focus, concerning concepts or claims that undermine their possible reference and meaning. The variety of conceptual delusion at issue involves an attempt to refer to an alleged object of reference, but in such a < 13 > In his Critique of Pure Reason, Kant expressed his awareness of the human tendency to overstep certain epistemological limits. In talking of "the understanding which is concerned merely with its empirical application," he commented: But if it cannot distinguish whether certain questions lie within its horizon [Horizont] or not, then it will never be sure of its claims and its possessions, but can only count on a variety of shameful rebukes when it oversteps [überschreitet] the boundaries [Grenzen] of its domain (as is inevitable), and goes astray in delusion and deceptions. (A238/B297, italics added) 16 Two years after the publication of the first edition of the Critique, Kant went on to recognize that underlying the phenomenon of overstepping boundaries is a pervasive human compulsion to do this:

[W]ho does not feel himself compelled [fühlt sich nicht notgedrungen], notwithstanding all interdictions against losing himself in transcendent ideas, to seek rest and contentment beyond all the concepts which he can vindicate by experience...? 17 This inner feeling of being "compelled" leads to transgressions beyond the boundaries of possible knowledge, and motivates us, as Kant recognized, to embrace what is delusional and deceptive.

At this point, I again depart from Kant's thought, and will translate into different terms his suggestion that there is a pervasive human propensity, and even a compulsion, to overstep rational limitations. Our interest will be focused in a more specialized way on transgressions of the preconditions of reference of the conceptual frameworks we use.

Delusion-inducing concepts and asking the wrong questions

If many of the philosophical concepts that we've come habitually to use involve or encourage transgressions of preconditions that must be satisfied in order for reference to be possible, then, to be sure, the discipline of philosophy is in rather deep trouble. I take for granted that for many readers, the 'if' that began the previous sentence is a BIG IF! I understand and can sympathize with any reader for whom the antecedent of this conditional may be felt to fall somewhere along a scale running from ridiculous and deserving to be dismissed without further ado, to unsettling and even irritating. If our commonly accepted philosophical conceptual vocabulary is systemically error-producing, manner that undermines the very conditions of possible reference. This is putative reference-reference in appearance only, deceptive and illusory. 16 This is my translation from the second edition. It's unfortunate that both Norman Kemp Smith and J. M. D.

Meiklejohn ignored what I take to be Kant's fundamentally important word choices here: 'Wahn' and 'Blendwerke', which Kemp Smith translates as "opinions that are baseless and misleading," and Meiklejohn translates as "fanciful opinions and blinding illusions." On the contrary, Wahn and Blendwerke mean that delusions and deceptions are involved; "opinions" are not. 17 Kant & Beck (1950/1783, §57, italics added).

< 14 > then by means of what conceptual tools can we know this, and how are we to proceed?! It might seem that we are potentially defeated before we begin.

These are intelligent questions, questions that cannot be answered in this short paper. But yet to communicate to readers an idea of what is at stake and what would be involved in order to offer a solution, below is a partial listing of commonly employed philosophical concepts which, as I've tried to show elsewhere, 18 are precisely of the delusion-inducing, transcendentally self-undermining variety. Following each is a reference in braces to the chapter and section in Bartlett (2021) which provides a detailed metalogical analysis of that concept:

The concept of discovery {19.1-19.2} invention {19.1-19.2} the finitude of knowledge {20.2} the incompleteness of knowledge {20.3} the unlimitedness of our ignorance {20.4} thinking beyond the limits of thought {20.5} expressing the inexpressible {20.6} unknown truths {20.7-20.8} unanswerable questions {20.10} the external world {21 For each of the above concepts, I've sought to demonstrate that the human propensity to transgress beyond the preconditions of possible reference and possible meaning leads to conceptual errors of the systemic kind described in this paper. The very fact that such a large number of these concepts appears on the above list, many of them basic to so much philosophical inquiry, should make evident the possible existence of a form of error about which we should be concerned. That the same variety of error is identifiable in one central philosophical concept after another would lend support to the idea that an error of the systemic kind is likely to be involved.

The widespread compulsion to overstep the boundaries of reference and meaning is subtle, difficult to resist, and hard to eliminate. Nonetheless, for a great many of the above-listed concepts, as I have tried to show in Bartlett (2021) and other works, it is possible-through the application of a unitary systematic method, which itself cannot be rejected on pain of metalogical self-referential inconsistency-to formulate replacement concepts that salvage much of the putative meaning of the original concepts. But in connection with those concepts for which errors of metalogical transgression cannot be corrected, we have no other rational alternative but to renounce them and leave them behind.

The above results, if successful, would make a significant step in providing a philosophical conceptual vocabulary from which a pervasive systemic and propagating variety of error is eliminated in advance, fulfilling a central objective of a philosophical approach undertaken as negative science.

Policing philosophy?

"The work of the philosophical policeman," replied the man in blue, "is at once bolder and more subtle than that of the ordinary detective. The ordinary detective goes to pot-houses to arrest thieves; we go to artistic tea-parties to detect pessimists. The ordinary detective discovers from a ledger or a diary that a crime has been committed. We discover from a < 16 > book of sonnets that a crime will be committed. We have to trace the origin of those dreadful thoughts that drive men on at last to intellectual fanaticism and intellectual crime.... "We deny the snobbish English assumption that the uneducated are the dangerous criminals.... We say that the dangerous criminal is the educated criminal. We say that the most dangerous criminal now is the entirely lawless modern philosopher." -G. K. Chesterton (1908, Chap. IV) Where there is no enforcement there are no laws. Where there are no laws everything is allowed. Where everything is allowed there is nothing certain.

Where nothing is certain all is mere opinion.

-Teltrab Nevets, unpublished thoughts If I haven't said enough already to discomfort or rankle many philosophers, the very notion that philosophy may stand in need of "policing" is likely to achieve this! We philosophers have come to cherish our unbounded intellectual freedom to question, posit, propose, defend, and make cases for whatever issues that concern us-and to feel and to be at liberty to engage in these things without the imposition of stringent, authoritarian standards of validity and admissibility that would constrain our thought and its expression. We generally bow to the principle of non-contradiction (though not always), and when considering other basic laws of logic, we may not always wish to exclude the middle. There are few if any universal strictures of acceptability that by common consent we agree ought to shackle our minds and their expression. The discipline of philosophy has come to believe and to claim that it is relevant and applicable to virtually all areas of human thought and behavior, to nearly everything, and most especially in recent times to claim that philosophy is of value in shedding light on such social, political, and educational issues as racism, feminism, the concerns of proliferating gender identities, the teaching of philosophy for children, philosophy for the workplace, philosophical methods appropriate to the teaching of fact-resistant students, etc.-in short, to just about anything that philosophers have a desire to include within the discipline's embrace.

At the same time that the scope of application of philosophy has expanded outward, during the past several decades we increasingly see the telltale signs of the expression of mere opinion: The phrases "I believe," "I assume," and their kindred occur, in my tally, ever more frequently in the literature. No invariant and commonly agreed upon set of rigorous objective standards of assessment is by consensus enforced-not by selfpolicing nor by discipline-wide enforcement. Such a unifying methodological consensus < 17 > would offer hope in constraining the human propensity to formulate, propound, and everinconclusively argue on behalf of the beliefs a philosopher comes to prefer and favor. If the systemic errors I have worked to bring to light are avoided, some of the principal obstacles that have stood in the way of incremental progress in the discipline might be overcome so that future philosophical work is not saddled by the weight of proliferating error.

As I have suggested, philosophy as a negative science sets as its general task the elimination of conceptual error. When applied to the discipline of philosophy itself, its function-expressed in an overstated but frank fashion-is one of internal disciplinary policing, of identifying forms of conceptual error that occur in the discipline, and then of enforcing rigorous standards of validity and acceptability that avoid such error. In particular, the approach to philosophy as negative science that I've outlined would serve the discipline by identifying and eliminating a widespread but generally unrecognized form of systemic and propagating conceptual error. Should this form of error be recognized and admitted, the responsibility then falls upon us to correct and revise many of the commonly accepted concepts that make up much of the central vocabulary of today's philosophy.

Whether there ought to be boundaries of conceptual acceptability, whether in fact there already exist such boundaries of a systemic kind, but of a sort not as yet commonly recognized, or whether there is any way to enforce such boundaries in order to encourage the development of a discipline so it may become substantially more than an endlessly proliferating and ramifying set of mere opinions, as a number of leading philosophers have complained19 -these are fundamental questions to which philosophy as a negative science seeks to respond and, at least in part, to answer.

Consequences of the human drive to transgress beyond the limits of reference and meaning

The human urge to transgress the boundaries of possible reference and meaning is unfortunately not confined to purely intellectual philosophical discourse. The frameworktranscending drive that disregards and seeks to violate the boundaries of metalogical horizons, attempting to breach limits of what is possible and meaningful, has consequences that extend considerably beyond the highly abstract theoretical domain considered in this paper.

The systemic and propagating nature of the errors we have touched upon is responsible for the pervasiveness and the spread of those errors. The compulsion to engage in what I've called 'metalogical projection' has implications not only for philosophy, but serious consequences of both a psychological and behavioral nature. Among these are those that affect political and religious ideologies, leading people deceptively to posit and situate what they desire in an illusory realm beyond the limits of possible reference and meaning. We see this in our species' urge to reify horizontransgressing delusions of many kinds, all-too-often resulting in pathological patterns of

In Lambert (1764, Vol. 1, p. 4).

This was Kant's misspelling in his letter; he evidently intended 'phaenomenologia generalis'.

[START_REF] Fitch | Self-reference in philosophy[END_REF], see also[START_REF] Fitch | Universal metalanguages for philosophy[END_REF].

SeeBartlett (2021, Chap. 4.8) and also, e.g.,Feys and Fitch (1969, ¶ 90.1).

SeeBartlett (2021, Appendix II. "Epistemological Intelligence"; published earlier in an online version,Bartlett, 2017).

SeeBartlett (2021, Chapters 26, 27).

Bartlett (2021, Chapter 19.1-19.2).

SeeBartlett (2021, Chapter 21).

SeeBartlett (2021, Chapters 27-28).

See the preceding note.

For more detailed analysis, seeBartlett (2021, Chapter 27).

Bartlett (2021).

For commentary and an overview of some of the authors who have made this claim, seeBartlett (2021, Part I: "Why Philosophy Has Made No Progress and How It Can").

< 18 > thought and behavior that are highly destructive, bringing about much human as well as non-human suffering. 20 Due to the systemic and propagating nature of metalogical projection, philosophy undertaken as a negative science may offer error-eliminating benefits not only for the discipline of philosophy itself, but benefits that bring about a better understanding and contribute to the potential resolution of some of humanity's most painful problems.

Readers interested in an examination of the psychological and behavioral consequences of the systemic and propagating errors described in this paper are directed to other publications by the author. 21


Cyprien Tamekue

Dario Prandi

Yacine Chitour

REPRODUCING SENSORY INDUCED HALLUCINATIONS VIA NEURAL FIELDS

Keywords: MacKay effect, visual stimulation, geometric visual hallucinations, neural field equation

Understanding sensory induced cortical patterns in the primary visual cortex V1 is an important challenge both for physiological motivations and for improving our understanding of human perception and visual organisation. In this work we focus on pattern formation in the visual cortex when the cortical activity is driven by a geometric visual hallucinationlike stimulus. In particular, we present a theoretical framework for sensory induced hallucinations which allows one to reproduce novel psychophysical results such as the MacKay effect (Nature, 1957) and the Billock and Tsou experiences (PNAS, 2007).

INTRODUCTION

Spontaneous patterns forming in the primary visual cortex, which are the basis for visual hallucinations and illusions, inform us on the underlying mechanisms of human perception, allowing to refine its modelling and consequent implementation in various image processing or computer vision tasks.

In the pioneering works [START_REF] Ermentrout | A mathematical theory of visual hallucination patterns[END_REF][START_REF] Bressloff | Geometric visual hallucinations, euclidean symmetry and the functional architecture of striate cortex[END_REF], the neural fields (NF) introduced in [START_REF] Wilson | A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue[END_REF] are used to theoretically describe spontaneous pattern formation in absence of external stimulus of geometric patterns in V1 striate cortex (V1 for short). Such patterns are the result of activity spreading over the field and correspond to paroxismic states of intrinsic cortical activity in V1. Taking into account the retinotipic correspondence between V1 and the visual field [START_REF] Tootell | Deoxyglucose analysis of retinotopic organization in primate striate cortex[END_REF][START_REF] Schwartz | Spatial mapping in the primate sensory projection: analytic structure and relevance to perception[END_REF], these patterns are yields the geometric visual hallucinations (or form constants) classified by Klüver [START_REF] Klüver | Mescal and mechanisms of hallucinations chicago[END_REF], e.g., funnels, tunnels, spirals, checkerboards, cobwebs, etc... However, these results lack to provide a description of more complex geometric visual hallucinations as those induced by flickering lights [START_REF] Smythies | The stroboscopic patterns: I. the dark phase[END_REF], or regular patterns with redundant informations [START_REF] Mackay | Moving visual images produced by regular stationary patterns[END_REF] and with visual noise [START_REF] Mackay | Visual effects of non-redundant stimulation[END_REF]. Such complex geometric visual hallucinations result from an external (visual) stimulus that disturbs the intrinsic activity in the field before the paroxismic state of cortical activity in V1 occurs. Fig. 1. The MacKay effect: the presentation of the stimulus to the left induces the superimposed perception of the complementary image on the right. Reproduced from [START_REF] Mackay | Visual effects of non-redundant stimulation[END_REF] In this work we investigate such hallucinations, by explicitly taking into account the external visual stimulus in the NF equations.

The focus of this paper lies mainly in the MacKay effect, described in [START_REF] Mackay | Moving visual images produced by regular stationary patterns[END_REF][START_REF] Mackay | Visual effects of non-redundant stimulation[END_REF] (see Figure 1). The psycophysical experiences presented in these papers show that, e.g., presenting as a visual stimulus a funnel pattern (fan shape) with highly redundant information at the fovea, will induce the emergence in the visual field of a "complementary" tunnel pattern (concentric circles) in the background, superimposed to the stimulus pattern. It is also reported that a tunnel pattern would produce a superimposed funnel pattern in the background as an after-image.

Mathematically, we interpret Mackay effects as a controllability problem of NF equations describing cortical activity in V1, where the control term is the external (visual) stimulus, which corresponds to the V1 representation of the presented hallucination-like pattern. As a first step in the description of such effects, this work focuses on a simple model of V1 ≃ R 2 based on a one-layer Amari-type equation [START_REF] Amari | Dynamics of pattern formation in lateralinhibition type neural fields[END_REF] for the evolution of the cortical activity a : R 2 → R:

∂ t a = -αa + µ ω * f (a) + I . (1)
Here, α, µ > 0 are parameters, * denotes the spatial convolution operation, ω : R 2 → R is an interaction (convolutional) kernel modelling cortical connections in V1, f is a sigmoid non-linearity, and I : R 2 → R is the cortical representation of the presented visual stimulus. In our discussion, the choice of the parameters in (1) is such that, in absence of an external stimulus I, the cortical state converges exponentially fast to the 0 equilibrium. From a neurophysiological point of view, this means that we are considering an unaltered state, where no spontaneous geometric hallucination arises. This prevents us from using bifurcation techniques as those employed in [START_REF] Bressloff | Geometric visual hallucinations, euclidean symmetry and the functional architecture of striate cortex[END_REF], and that allowed the authors of [START_REF] Nicks | Understanding sensory induced hallucinations: From neural fields to amplitude equations[END_REF] to obtain MacKay effects near the critical parameters for a variation of (1) incorporating a feedback effect in the external stimulus.

In this setting we first present a mathematically sound framework allowing us to define the input-output map Ψ, that associates to a time-invariant input stimulus I the stationary solution toward which (1) tends as t → +∞. Then, we prove that highly redundant information in the centre of the funnel pattern is necessary for a MacKay effect to manifest. Namely, if the V1 representation of the visual stimulus is a funnel pattern, then the output obtained via (1) will have the same shape. Following [START_REF] Bressloff | Geometric visual hallucinations, euclidean symmetry and the functional architecture of striate cortex[END_REF] we represent such patterns as contrasting light and dark regions. Finally, we present numerical simulations obtained when the input patterns have highly redundant information in the sense of MacKay [START_REF] Mackay | Moving visual images produced by regular stationary patterns[END_REF], showing that these reproduce the MacKay observations. We also reproduce visual hallucinations in the spirit of those recorded by Billock and Tsou [START_REF] Billock | Neural interactions between flicker-induced self-organized visual hallucinations and physical stimuli[END_REF]. We stress that this is the first instance that these nonlocal phenomena are directly obtained via (1) (see [START_REF] Nicks | Understanding sensory induced hallucinations: From neural fields to amplitude equations[END_REF] for a different take on the question).

RETINO-CORTICAL MAP

One of the striking features of the functional architecture of V1 striate cortex is its retinotopic organisation: (i) Neurons are organised in an orderly fashion called topographic or retinotopic mapping, in the sense that they form a 2D representation of the visual image formed on the retina in such a way that neighbouring regions of the image in the visual field are represented bijectively by neighbouring regions in V1 area; (ii) Sufficiently close to the fovea (the centre of the visual field), the image has a much larger representation in V1 than in the visual field [START_REF] Sereno | Borders of multiple visual areas in humans revealed by functional magnetic resonance imaging[END_REF] so that near the fovea, this map is an enlargement of the identity map; (iii) Far away from the fovea, this map is a log-polar transformation [START_REF] Tootell | Deoxyglucose analysis of retinotopic organization in primate striate cortex[END_REF].

This map is represented analytically as a complex logarithmic [START_REF] Schwartz | Spatial mapping in the primate sensory projection: analytic structure and relevance to perception[END_REF]. After rescaling, it takes the form

re iθ → (x 1 , x 2 ) := (log r, θ) . (2)
Here (r, θ) are retinal polar coordinates and (x 1 , x 2 ) are cortical cartesian cordinates. A circle of radius r and a ray of constant θ in the visual field become a vertical line and a horizontal line in V1 respectively, see Figure 2.

NEURAL FIELDS FOR CORTICAL ACTIVITY IN V1

We assume cortical activity in V1 to be driven by equation [START_REF] Ermentrout | A mathematical theory of visual hallucination patterns[END_REF], where the non-linearity f : R → R is assumed to be a bounded C 2 odd function normalized such that f ′ (0) = max f ′ (t) = 1 and ∥f ∥ ∞ = 1. Following [START_REF] Ermentrout | A mathematical theory of visual hallucination patterns[END_REF], we also assume that the interaction kernel ω is radial (i.e., ω(x) = ω(|x|)), and that its Fourier transform ω reaches its maximum at some non-zero critical wavenumber q c > 0. We call a vector ξ c ∈ R 2 satisfying |ξ c | = q c a critical wavevector. This is the case, e.g., for the so-called Mexican hat distribution (or DoG, difference of Gaussians) but not for a simple Gaussian interaction kernel. It is shown in [START_REF] Bressloff | Geometric visual hallucinations, euclidean symmetry and the functional architecture of striate cortex[END_REF] that under these assumptions there exists a critical value µ c = α/ω(q c ) such that equation (1) with I ≡ 0 is exponentially stable at a ≡ 0 if µ < µ c . The spontaneous cortical patterns are then obtained as the novel marginally stable equilibria appearing as bifurcations for µ = µ c . These marginally stable equilibria are the elements in the kernel of the linear operator

L µc a = -αa + µ ω * a. (3)
In particular, this kernel consists of linear combinations of functions of the form cos(2π⟨ξ j , x⟩) where, ξ j = q c e iθj , θ j ∈ R.

THEORETICAL RESULTS

Let µ 0 := α/∥ω∥ 1 < µ c . As we shall see below, given I ∈ L ∞ (R 2 ), µ 0 is the (natural) largest value of µ up to which we can provide a stationary output to equation (1) in the space L ∞ (R 2 ). From now on, we assume that the excitability rate µ, of V1 satisfies µ < µ 0 . We first have the following.

Proposition 1. Let µ < µ 0 . Then, there exists a map Ψ :

L ∞ (R 2 ) → L ∞ (R 2
) such that for any initial datum a 0 ∈ L ∞ (R 2 ) the solution to (1) with input I ∈ L ∞ (R 2 ) converges exponentially to Ψ(I). Moreover, Ψ is bi-Lipschitz so that

Ψ(I) = I /α + (µ/α)ω * f (Ψ(I)). (4)
Proof. Since the r.h.s. of ( 1) is a Lipschitz map on

L ∞ t (R) × L ∞ x (R 2 ), it is standard to obtain that any initial datum a 0 ∈ L ∞ (R 2 ) admits a unique solution a ∈ C([0, +∞); L ∞ (R 2 )).
The existence of a unique stationary solution (i.e., such that ȧ = 0) to ( 1) is obtained via a Banach fixed point argument. The map Ψ is then defined as the map associating the input I with this stationary solution. The exponential convergence to Ψ(I) for any initial datum a 0 is obtained by the variation of constants formula and Gronwall's Lemma. We now focus on the funnel and tunnel patterns appearing in the MacKay effect. Taking into account the retino-cortical map, these patterns are generated by the cortical stimuli

P T (x) = cos(λx 1 ) P F (x) = cos(λx 2 ), λ > 0. (5)
As a consequence of Remark 4.1, one deduces that Ψ(P T ) (resp. Ψ(P F )) is a function of x 1 only (resp. x 2 only) even and π/λ anti-periodic (one uses here the fact that f is odd).

The following notation is needed: if F is a real valued function, we use F -1 ({0}) to denote the set of zeroes of F . Theorem 1. Under the assumption µ < µ 0 /2, we have P -1 T ({0}) = Ψ(P T ) -1 ({0}) and P -1 F ({0}) = Ψ(P F ) -1 ({0}). Proof. We present an argument only for the first equality since the other one is obtained similarly by using the symmetries of Equation ( 1) and the fact that ω is radial.

Let us set A T = Ψ(P T ), for ease of notations. Then,

A T = P T /α + (µ/α)ω * f (A T ). (6)
In particular

A -1 T ({0}) ⊃ {±π/2λ + 2kπ | k ∈ Z}. To show the converse inclusion, let x * := (x * 1 , x * 2 ) verify- ing A T (x * ) = 0. From (6), it follows cos(λx * 1 ) = -µ R 2 ω(y)f (A T (x * -y))dy. ( 7
)
On the one hand, by exploiting additions formulae for the cosine, one has for a. e., y ∈ R 2 ,

A T (x * -y) = sin(λx * 1 ) sin(λy 1 )/α + (µ/α) R 2 k(y, z)f (A T (x * -z))dz, (8)
where k(x, y) := ω(x -y) -cos(λx 1 )ω(y), satisfies

K := sup x∈R 2 R 2 |k(x, y)|dy = 2∥ω∥ 1 . (9)
Since µ < µ 0 /2, a Banach fixed point argument shows that for every

I ∈ L ∞ (R 2 ) there exists an unique solution b ∈ L ∞ (R 2 ) to b(x) = I(x)/α + (µ/α) R 2 k(x, y)f (b(y))dy. (10)
By [START_REF] Mackay | Moving visual images produced by regular stationary patterns[END_REF], function b(y) := A T (x * -y) is the unique solution of the above equation associated to I(y) = sin(λx * 1 ) sin(λy 1 ). On the other hand, since ω is symmetric and the sigmoid f is an odd function, we have also for a. e., y ∈ R 2 ,

-A T (x * + y) = sin(λx * 1 ) sin(λy 1 )/α + (µ/α) R 2 k(y, z)f (-A T (x * + z))dz,
so that, the function b(y) = -b(-y) is also solution of equation (10) associated to I(y) = sin(λx * 1 ) sin(λy 1 ). By unicity of solution, one then has b(-y) = -b(y) for a. e., y ∈ R 2 . This shows that y → ω(y)f (A T (x * -y)) is an odd function on R 2 , since ω is symmetric and f is an odd function, which implies that the r.h.s. of ( 7) is equal to 0 and thus that x * ∈ P -1 T ({0}).

The above theorem shows that, for our model of cortical activity in V1, one cannot obtain a MacKay effect without perturbing the external input when chosen equal to P F or P T . This does not contradicts the results of [START_REF] Nicks | Understanding sensory induced hallucinations: From neural fields to amplitude equations[END_REF], where effects of MacKay type are derived directly with an input equal to P F or P T but for a different model of cortical activity in V1. Indeed, the actual input injected in their model is not equal P F or P T but equal to aP F and aP T , a being the cortical activity .

We observe that P -1 T ({0}) ⊂ Ψ(P T ) -1 ({0}) is valid for µ < µ 0 . Indeed, numerical simulations suggest that Theorem 1 is valid even for µ 0 /2 ≤ µ < µ 0 . The above remark motivates the following.

Conjecture 1. Let P T be the tunnel pattern defined in [START_REF] Schwartz | Spatial mapping in the primate sensory projection: analytic structure and relevance to perception[END_REF]. Assume that the kernel ω is symmetric and the activation function f is an odd function. Then, under Assumption µ < µ 0 , P T and Ψ(P T ) have the same set of zeroes.

NUMERICAL RESULTS

According to the results of Section 4, for MacKay effects to occur it is necessary to break the E(2)-symmetry of the stimulus pattern, say, P F , via highly redundant information at the fovea. In our implementation we add to the stimulus pattern a localized perturbation εv, where ε > 0 and v is a localized function, viz. v(x) := χ Ω (x), Ω ⊂ R 2 . The numerical implementation is performed in Julia [START_REF] Bezanson | Julia: A fresh approach to numerical computing[END_REF], and is available at www.github.com/dprn/MacKay. The operator Ψ is numerically implemented via an iterative fixed-point method. The cortical data is defined on a square [-L, L] 2 , with L = 10. The interaction kernel is taken to be a DoG with variances σ 1 = 0.1 and σ 2 = 0.5, yielding µ 0 = 0.217 and µ c = 1.26, and the non-linearity is chosen as f (t) = tanh(t). The other parameters are chosen as α = 1, µ = 0.99µ 0 and ε = 0.025. We stress that µ is quite far from the bifurcation point µ c .

We collected some representative results in Figures 3 and4. Here, we visualize the input (left image) and the output (right image) in the retinal representation obtained from the cortical stimuli via the inverse retino-cortical map. Also, following the convention adopted in [START_REF] Ermentrout | A mathematical theory of visual hallucination patterns[END_REF][START_REF] Bressloff | Geometric visual hallucinations, euclidean symmetry and the functional architecture of striate cortex[END_REF] for geometric visual hallucinations, we present binary versions of these images, where black corresponds to negative values and white to positive ones.

We also present Figure 5 and6, where we show that our model can reproduce the psychophysiscal results of Billock and Tsou. We remark that these results are obtained with a different choice of nonlinearity f (t) = (1 + exp(-t + 0.25)) -1 -(1 + exp(0.25)) -1 .

CONCLUSIONS

In this paper we presented a model and theoretical framework for the description of sensory induced hallucinations. We also presented numerical experiences indicating the capability of this approach to reproduce the MacKay effects and psychophysical observations of [START_REF] Billock | Neural interactions between flicker-induced self-organized visual hallucinations and physical stimuli[END_REF]. To our knowledge, this is the most parsimonious model to be able of such reproduction.

The numerical simulations provided in this work indicate also that the anisotropic nature of cortical connections in V1 need not to be integrated in the model in order to reproduce the psychophysical results of [START_REF] Billock | Neural interactions between flicker-induced self-organized visual hallucinations and physical stimuli[END_REF]. This is in contrast with the conjecture advanced by the authors of [START_REF] Billock | Neural interactions between flicker-induced self-organized visual hallucinations and physical stimuli[END_REF].

We highlight that both MacKay effects and psychophysical observations of [START_REF] Billock | Neural interactions between flicker-induced self-organized visual hallucinations and physical stimuli[END_REF] result from input patterns, with global E(2)-symmetry broken. In the former case, the symmetry is broken by localised highly redundant information in the input pattern, whereas, in the latter, the global symmetry is broken by localising the input pattern either in the left or in the right area of the cortex.

Fig. 2 .

 2 Fig.2. Visual illustration of the retino-cortical map. Reproduced from[START_REF] Billock | Neural interactions between flicker-induced self-organized visual hallucinations and physical stimuli[END_REF]

Remark 4 . 1 .

 41 Under assumptions on the kernel ω, the map v → ω * f (v) commutes with E(2), the group of rigid motion of the plane, see, [1, Appendix A]. It follows that a subgroup Γ ⊂ E(2) is a symmetry group of I ∈ L ∞ (R 2 ) if and only if, it is a symmetry group of Ψ(I).

Fig. 3 .

 3 Fig. 3. MacKay effect (right) on a funnel-like pattern (left). Initial input I = P F +εχ Ω , Ω = [-L, 2]×[-L, L]. Compare with Figure 1.

Fig. 4 .

 4 Fig. 4. MacKay effect (right) on a tunnel-like pattern (left). Initial input I = P T + χ Ω , Ω = [-L, L] × [-0.25, 0.25].

Fig. 5 .

 5 Fig. 5. Billock and Tsou visual hallucination, with initial stimulus I = P F χ Ω , Ω = [-L, 5] × [-L, L]. Compare with [12, Fig 3., a].

Fig. 6 .

 6 Fig. 6. Billock and Tsou visual hallucination, with initial stimulus I = P F χ Ω , Ω = [5, L] × [-L, L]. Compare with [12, Fig 3., c].

The first author was supported by a grant from the "Fondation CFM pour la Recherche".


Lucile Rapin
email: lucile.rapin@gipsa-lab.inpg.fr

Hélène Loevenbruck

Marion Dohen

Mircea Polosan

Collecting Traces of Activity in Orofacial Muscles during Auditory Verbal Hallucinations in Schizophrenic Patients

HAL is

Introduction

Background

Auditory verbal hallucinations (AVH) are a common feature of the schizophrenia psychosis, affecting 50% to 80% of the patients [START_REF] Nc Andreasen | Schizophrenia: the characteristic symptoms[END_REF]. They often have a stressful impact on the patient's daily life. AVH are defined as speech perception in the absence of an external auditory stimulus [START_REF] David | Auditory hallucinations: phenomenology, neuropsychology and neuroimaging update[END_REF].

One appealing hypothesis is that the production of inner speech is disturbed in a way that the verbal thoughts of the patient are considered as external voices [START_REF] Frith | The cognitive neuropsychology of schizophrenia[END_REF]. The efference copy, a mechanism responsible for the monitoring of our actions, coming from the frontal cortex, cannot alert the auditory cortex that the verbal thoughts are self-generated, leading to the misattribution of inner speech to an external agent. This hypothesis is supported by neuroimaging studies showing abnormal patterns of activations between the frontal and temporal lobes in schizophrenic patients [START_REF] Mcguire | Increased blood flow in Broca's area during auditory hallucinations in schizophrenia[END_REF][START_REF] Mcguire | Functional anatomy of inner speech and auditory verbal imagery[END_REF].

A second way to establish a relationship between AVH and inner speech is to measure orofacial muscle activity, using electromyography (EMG), either with inserted electrodes or non-invasively with surface electrodes (sEMG). EMG activity has been detected in the speech musculature during verbal mental imagery, silent reading and silent recitation [START_REF] Jacobson | Imagination, recollection, and abstract thinking involving the speech musculature[END_REF][START_REF] Mcguigan | Patterns of covert speech behavior and phonetic coding[END_REF][START_REF] Livesay | Covert speech behavior during a silent language recitation task[END_REF].

The first study supporting a relationship between the occurrence of AVH and subvocal speech was from Gould [START_REF] Gould | Verbal hallucinations and activity of vocal musculature: an electromyographic study[END_REF]. Using an electroencephalograph to explore the activity of the vocal musculature, Gould observed that 83% of the patients experiencing AVH showed an increase in muscle potentials in the lips and chin, whereas 90% of patients not experiencing AVH showed no increase. This result suggests that the AVH are associated with activity of the speech musculature. A similar report was made by McGuigan [START_REF] Mcguigan | Covert oral behavior and auditory hallucinations[END_REF] on one subject. McGuigan observed a significant increase in chin muscle action potential and breathing amplitude immediately prior to reporting an AVH. The increase in chin activity was accompanied by a faint whisper. Inouye and Shimizu [START_REF] Inouye | The electromyographic study of verbal hallucinations[END_REF] also reported increased EMG activity from the speech musculature in nine hallucinating patients. The patients had to hold a switch down until the end of a hallucination. The authors measured a rise in EMG activity in the speech-related muscles (cricothyroid, sternohyoid, orbicularis oris, and depressor anguli oris) in 47.6% of the hallucinations. They also noticed a correlation between the length of verbal hallucinations and the duration of intensification of EMG activity. Bick & Kinsbourne [START_REF] Bick | Auditory hallucinations and subvocal speech in schizophrenic patients[END_REF] asked patients to perform three simple procedures while experiencing AVH. They consisted in opening the mouth wide (experimental condition), closing the eyes and making a fist (control conditions). The findings reveal a reduction of selfreport of hallucinations when the subjects opened the mouth but not when they performed the two control conditions. This indicates that subvocal activity is associated with the experience of AVH.

Meanwhile, Junginger & Rauscher [START_REF] Junginger | Vocal activity in verbal hallucinations[END_REF] recorded vocal and nonvocal EMG activity of 19 hallucinating and 22 nonhallucinating psychiatric patients. The authors failed to find a relationship between increases in vocal EMG and reports of hallucinations.

The studies cited above presented methodological limitations (limited number of subjects, lack of clear correlation between EMG measurements and AVH reports, imprecision in the time-windows observed); nevertheless, they provided some original findings.

Aim

The advent of more adapted techniques such as sensitive surface electromyography, and more robust signal analysis methods has opened up new possibilities of testing subvocalisation during AVH.

The long term aim of our research project is to record orofacial sEMG signals during the occurrence of AVH in schizophrenic patients. This would determine whether sEMG activity during AVH is higher than the baseline rest activity. Such an observation would corroborate the hypothesis that AVH result from a dysfunction of inner speech production. In this paper, we validate a methodological protocol to be applied in aim.

Methods

Subjects

Patients are recruited at the Centre Hospitalier Universitaire of Grenoble (hospital). They are all diagnosed paranoid schizophrenic under the DSM-IV criteria (America Psychiatric Association, 1994) by experienced psychiatrists. Patients presenting language and/or auditory deficits are excluded from the study. All patients are native French speakers and give written consent to participate in the study. All patients are receiving antipsychotic medication and are experiencing frequent hallucinations at the time of the study. Control healthy subjects are also examined.

Material

The experiment takes place at the Centre Hospitalier Universitaire of Grenoble. Data are recorded on a Biopac MP150 surface EMG system, using the Acqknowledge software. Bipolar sEMG recordings are obtained from orofacial speech muscles. Laryngeal data are also obtained by electroglottography (EGG). EGG allows for quantitative measurements of vertical laryngeal movements. The experiment is video monitored using a Canon video camera to track visible facial movements. A microphone is placed 15 cm from the patient's lips to record the patient's speech during the overt reading conditions. sEMG, EGG and audio data are all recorded through the Biopac acquisition system and are thus synchronised.

Procedure

Four conditions are examined. In the overt speech reading and in the whispered speech reading, patients are asked to read sentences at a comfortable delivery. The reading conditions last approximately 10 minutes. The overt speech condition is used to obtain reference sEMG activation level for overt speech in each subject for all the muscles. From pilot tests on one healthy subject, it was expected that muscular activity should be reduced in the whispered speech condition, compared with overt speech, if the subject's whispers were low enough. The whispered speech condition was thus used to check that our sEMG system is sensitive enough for low muscle activation.

In the silent condition, the subjects are asked to remain silent and not to move for 10 seconds.

In the hallucinatory condition, they are asked to remain silent, not to move, and not to refrain from hearing voices. They are asked to signal when they hear a voice by pressing a button 1 . They are told not to establish a verbal interaction with the voice, in order to limit the occurrence of subvocal speech associated with their response to the voice. This condition lasts approximately 15 minutes, depending on the patient's responsiveness and degree of anxiety.

Our expectation is to find higher sEMG activations in overt speech than in whispered speech in all speechrelated muscles. In addition, we expect to observe a sEMG activation continuum, with similar types of activations but with decreasing amplitude, from the overt speech condition to the silent condition (where a quasi-null activation is expected) through the whispered speech condition and the hallucinating state.

The patients take a pre-experiment questionnaire on the frequency, latency, nature and content of their everyday AVH and a post-experiment questionnaire derived from the Hoffman AVH rating scale on the frequency, latency, nature and content of the AVH experienced during the hallucinatory condition.

The experiment is thus shaped: pre-experiment questionnaire, silent condition, overt reading condition, silent condition, whispered reading condition, silent condition, hallucinatory condition, post-experiment questionnaire.

Data Processing

Data are exported from the Acqknowledge software and then resampled using Matlab software. The mean amplitude values over the duration of each sentence in each of the reading conditions and for each hallucinatory fragment are calculated. The hallucinatory periods are detected from the button presses. The results are then compared to the baseline, obtained from the mean amplitude value in the baseline condition, for each patient. Figure 1 shows the sEMG trace for the orbicularis oris inferior (first panel) during overt reading for one patient. The second panel shows that the control EMG trace for the forearm flexor is flat. The third panel displays the button pressing signal and the last panel provides the audio trace.

Protocol Evaluation

In order to design a valid experimental protocol, our original protocol underwent various changes through the eight patients tested so far: P1, P2, … P8.

Baseline determination

The silent condition was originally designed as a control to measure the resting "activation" of the muscles. However throughout the experiments, two patients reported having experienced AVH during this condition. Therefore it could not be used as a control (nonhallucinatory, baseline) condition anymore. Instead we took parts of the hallucinating condition where the patient indicated, by not pressing the button that he/she was not hallucinating. These parts became our baseline condition for the further data analyses.

Corpus determination

The first corpus elaborated contained 20 sentences derived from schizophrenic patients' testimonies as well as our own created sentences.

They were of various lengths. P1, P2 and P3 were recorded using this corpus. We then decided to change to a more phonetically adequate corpus, i.e. the CNET corpus [START_REF] Combescure | 20 listes de 10 phrases phonétiquement équilibrées[END_REF] and we added 9 vowelconsonant-vowel (VCV) sequences where V was /a/, /i/, /y/ and C was /b/, /d/ or /g/. There were then 26 sentences. P4, P5, P6, P7 and P8 used this corpus. The latest change consisted in reducing the number of sentences to 15 so as not to wear the participants out. Apart from the nondominant forearm flexorcontrol muscle, all the muscles examined are involved in speech production, overt, whispered or covert [START_REF] Inouye | The electromyographic study of verbal hallucinations[END_REF]. Throughout the different versions of the protocol, the orbicularis oris superior, the orbicularis oris inferior and the zygomaticus major muscles were always measured. In a first version (P1, P2, P3), we also examined the mentalis. We observed this muscle was not strongly activated, we therefore decided to suppress it from our protocol. In the second version we added the depressor anguli oris and the masseter. As a result, we now examine five orofacial muscles (see Figure 2) and one non-speech muscle.

Muscle set determination

Reaction time determination

In order to estimate the reaction time between hearing a voice sound and pressing a button, we designed an overt listening task where the participants had to press the button once they heard the played voice and keep it pressed until the voice ended. This test allows us to measure each participant's mean reaction time in order to analyze the hallucinatory data more accurately: the mean reaction time is subtracted from the measured time of onset of each hallucination, as detected from the button press. After series of tests on healthy subjects to determine an Orbic. oris inf.

Forearm flexor

Button press

Audio wave average reaction time, P8 was the first patient to take the test.

Preliminary results

The results presented here are not sufficient for group statistical analysis yet.

Only sEMG data for seven subjects (six schizophrenic patients and one control subject) are presented here. Inter-speaker and inter-muscle variability was observed, as expected. The orbicularis oris inferior showed the most activation in all conditions, which could be expected, as it is strongly involved in speech, especially in French [START_REF] Abry | Labialité et Phonétique[END_REF]. As shown in Figure 3, in five patients out of six, sEMG activity for this muscle was lower in the hallucinatory condition than in the overt and whispered speech conditions.

Orbicularis Oris Inferior activation

The overt speech condition was associated with higher sEMG levels than the whispered speech in only three subjects (out of seven). The instructions were probably not clear enough. A comparison with the baseline condition was also carried out. In three patients out of six, mean sEMG activation in the orbicularis oris inferior was very slightly higher in the hallucinatory condition than in the baseline condition.

Perspectives

More analyses are in progress to examine potential speech muscle activity during AVH. Furthermore, we are currently in the process of improving the sEMG signal pre-processing and analysis. New control healthy subjects will be examined with the latest improvements of our protocol.

Figure 1 :

 1 Figure 1: Orbicularis oris inf. and forearm flexor sEMG graphs during overt reading

Figure 2 :

 2 Figure 2: Set of orofacial muscles examined

  Overt Speaking Average value for Whispered Speaking Average value for AVH & Inner Speech Average value for Baseline

Figure 3 :

 3 Figure 3: Mean orbicularis oris inferior activation for each participant and condition.

In a first version, patients were asked to press a button as soon as they heard a voice and to press it again at the end of the hallucinatory fragment (sentence, word or discourse).

Acknowledgements

We sincerely thank Monica Baciu, Gérard Bailly and Pascal Perrier for helpful discussions; Alain Arnal, Christophe Savariaux and Coriandre Vilain for their help in the experimental design; Muriel Brix for her help in locating muscles; Lucie Pennel for her help with the patients; and all the participants to the experiments.