Pierre Lévy
email: plevy@tue.nl

AND EMOTION RESEARCH 2020 ARTEFACTUAL EMPTINESS ON APPROPRIATION IN KANSEI DESIGN

Keywords: appropriation, emptiness, design, everyday, kansei 1

Appropriation is the phenomenon by which an artefact is adapted for a specific use, distinct from the original design intention. By essence, it cannot be planned by design. However, it is a major aspect in the experience one may have in interaction with an artefact, as it leads to the feelings of ownership and to the effective situatedness of the artefact. It is therefore significantly contributing to designing for sustainability and for the everyday. This paper intends to address how design can consider the possibility of appropriation. Taking a kansei design approach, inspired from the nishidian philosophy on perception, we introduce the notion of artefactual emptiness as a space provided by design and left to the user to adapt the artefact for its integration in the habitability of the world. This space is made accessible and inviting by involving irregularities, suggested by Yanagi Soetsu as a means towards beauty, and implemented in design through micro-considerations and micro-frictions. Artefactual emptiness leads to beauty in experience, expected from a kansei perspective and made possible by kansei design. This work on appropriation through kansei design also leads to question the attention appropriation should have in other domains of kansei research, especially kansei evaluation. It calls for finding ways in kansei research to evaluate over time the kansei effect of appropriation on experience.

INTRODUCTION

Considering the current global issues our societies face (United Nations, 2015), and especially the ones related to sustainability, design is ought to extend its considerations on the relation between the user and the artefact to the evolution of this relation. The question raised by sustainability is not only the perception and the appreciation of an artefact "at the first sight", but more importantly the appreciation over time.

If the impression at the first sight has been for a long time a complex challenge at the core of kansei research, because of its contextual, cultural, and temporal nature, the appreciation over time is equally complex and possibly more challenging. The way an artefact enters the daily life of a person is based on a process of appropriation that remains a clear challenge for design as this process results in a difference between the design intention and the way the artefact is actually used.

In this paper, we intend to open up this challenge by addressing it from a kansei design perspective. After specifying briefly our approach in kansei design, we will address the challenge posed by the phenomenon of appropriation to design. Reframing it from a kansei design perspective, we will inquire the notion of artefactual emptiness as a concept to address appropriation, in a way that the designer may provide a space that invites the possibility of beautiful appropriation through irregularity. We will then conclude by reconsidering the challenge of appropriation in kansei design, and in kansei research at large.

KANSEI DESIGN

Despite numerous attempts to explain kansei (e.g., [START_REF] Harada | On the definition of Kansei[END_REF][START_REF] Lee | ON KANSEI AND KANSEI DESIGN A DESCRIPTION OF JAPANESE DESIGN APPROACH[END_REF][START_REF] Lévy | Towards a definition of Kansei[END_REF][START_REF] Lokman | Design & Emotion: The Kansei Engineering Methodology[END_REF][START_REF] Nagamachi | Kansei Engineering and Kansei Evaluation[END_REF][START_REF] Schütte | Engineering Emotional Values in Product Design-Kansei Engineering in Development[END_REF]), this notion is not yet described by a commonly recognised and stable way. Although being aware of the disputable nature of the following description, we propose here to provide such description that we consider contributing to the question of what kansei is, as well as fitting to the way kansei is considered in this paper and in the related research.

As one of the most important concepts in the nishidian philosophy on perception, actingintuition [START_REF] Nishida | [END_REF] implies a mutual influence between the world and the subject of which it is a part. As [START_REF] Wilkinson | Nishida and Western philosophy[END_REF] suggests: "We must experience the world in order to act on it. Just as he [Nishida] insists that the practical reason is deeper than the theoretical reason, he also insists that our natural state of being in the world is not contemplative but active, an aspect of the constant mutual interaction between being and the world." This mutual and constant interaction between the being and the world is of course essential, as well as also ineluctable.

This perspective can be clarified with an example. The recent development of action or simulation video games has considerably improved the potential level of the player's engagement in the game, notably thanks to so-called immersive technologies (e.g., virtual reality), and to theories on engagement (e.g., flow theory [START_REF] Csikszentmihalyi | Finding flow: The psychology of engagement with everyday life[END_REF]). The level of engagement is such that the psycho-physiological reactions of the players show a strong tension on the part of the engaged player. However, there is still a major difference between, for example, a fighting game on a virtual battlefield and a "real" fight on an actual battlefield. The earlier can be completely interrupted at any time, not the latter; the risk of dying is virtual in the earlier (and one often has several lives, after that we can start again!), not in the latter. In other words, the combat video game, as immersive and real as it may seem, allows for an experience that can be suspended. The experience of a real fight is ineluctable: no switch can be used to remove oneself from the experience at any time, no matter how terrifying it may be. And this ineluctability is not without consequences on the experience itself. The experience of the ineluctability of an experience, that is a form of meta-experience, significantly influences the affective aspects of the experience. We kansei the affective dimension of this meta-experience. Thus, kansei denotes the affective relationship to the world as experienced, reinforced by its ineluctability.

Following on this perspective, taking its roots in the Japanese philosophy elaborated by School of Kyoto, and therefore related to phenomenology, kansei design focuses on the active relation to the world as described by the notion of action-intuition, and addresses how kansei is influenced by and influences the design of artefacts. This aspect demands to clarify two types of kansei design that can be found in the literature. The first type focuses on the production of artefacts and proposes design methods and models to optimize design processes (e.g., [START_REF] Bouchard | Modélisation et computation des processus cognitifs et informationnels en conception amont: Une investigation chez les designers et les concepteurs[END_REF]). We call this type indirect kansei design as it is based on indirect psychological theories [START_REF] Lévy | Impact of Perception Theories on Kansei Design[END_REF]. The second type focuses on the relation between humans and artefacts, and on the in-between space (e.g., [START_REF] Duel | The Chatter Door, designing for in-between spaces[END_REF]). We call this type direct kansei design, as it is based on direct psychological theories [START_REF] Lévy | Impact of Perception Theories on Kansei Design[END_REF]. This research fully subscribes to direct kansei design, which will be designated as "kansei design" in the rest of this paper.

Kansei design draws on Japanese philosophy and culture to explore and to understand the affective relationship to the world and its ineluctability. It aims to provide a practical perspective for designing, towards the creation of artefacts that aims to the emergence of beauty in interaction with these artefacts and in the resulting experience. This perspective is meant to be coherent and holistic at sensory, perceptual, experiential and contextual levels, and essentially rich in terms of the kansei descriptors determined during the creative process [START_REF] Lévy | Le temps de l'expérience, enchanter le quotidien par le design[END_REF].

Consequently, the research related to kansei design is a practical research, i.e., contributes to the practice of design, inspired by Japanese philosophy and culture insofar as these allow us to grasp the aesthetics in interaction of the being-in-the-world.

APPROPRIATION AND DESIGN

Appropriation

The notion of appropriation can be first defined as the action to adapt an artefact to a specific activity. The term adaptation suggests that such action is not as to the designer's intention (i.e., an artefact used as intended by the design is not the result of an appropriation). People adopt artefacts based on their potential utility and performance in the situation of the interaction, often away from the designers' intention and projection of the situation of use. This concerns tangible designs (e.g., a piece of folded paper used to stabilize a wobbly table, a knife used as a screwdriver) as well as digital technologies (e.g., sending notes to one's self by email). [START_REF] Dix | Designing for appropriation[END_REF] proposes three major aspects to consider for appropriation:

• Situatedness -Interacting with an artefact, either tangible or digital, takes place in an environment. Therefore, comprehending the interaction and the appropriation cannot be done ignoring the qualities of the environment.

• Dynamics -Expectations, environments, values, ways of doing change over time and over space, and so does appropriation. Therefore, design should focus on the dynamics of change, rather than on the stability of a situation snapshot.

• Ownership -Appropriation leads to the emergence of ownership, translated possibly as a feeling of control or mastery, or a feeling of doing "my own way". This leads also to a greater feeling of engagement in the interaction and in the related activities. [START_REF] Carroll | Identity, Power And Fragmentation in Cyberspace: Technology Appropriation by Young People[END_REF] propose as well a technology appropriation model, distinguishing the technology-as-designed (as envisaged by its design and then produced), the technology-in-use (as actually used by the user(s)), and the appropriation process, as being the emergent process of change leading to a satisfactory (in case of appropriation) or dissatisfactory (in case of disappropriation) use. In this model, technology (and the related innovation) is therefore transformed by the process of appropriation, from technology-as-designed to technology-in-use, considered as two distinct concepts.

Opening for appropriation in design

Although this approach is valuable to analyse and to make sense of the notion of appropriation, it also indicates that the ambition to establish a practical understanding of how technology-in-use can be handled by design is a lost battle. The process of appropriation is indeed playing here a role of distanciation between technology-as-designed and technology-in-use, and therefore blurs any possibility of accurately considering technology-in-use while designing. Consequently, this paper intends to focus on the practice of design and to suggest a way to consider the possibility of appropriation through design.

For design, by offering action possibilities wider than the core design intentions, artefacts can be used in many ways, which make appropriation possible. The phenomenon of appropriation should not be considered as a design failure, but rather as an opportunity delivered through design. Appropriation takes place when the artefact is getting distant from the design intention and closer to the user's sensemaking of it in a situated way. In other words, the process of appropriation enables the integration of the artefact in the habitability of the world [START_REF] Findeli | Research Through Design and Transdisciplinarity: A Tentative Contribution to the Methodology of Design Research[END_REF] from the eyes of the user, and contributes to the process of domestication and quotidianisation [START_REF] Bégout | La découverte du quotidien[END_REF][START_REF] Lévy | Designing for the everyday through thusness and irregularity[END_REF]. The notion of quotidianisation is described as "a process of material organization of the uncertain world in a frequented environment, the work of overcoming the original misery of our condition by creating familiar forms of life" (Bégout, 2010, p. 313). It is a way the new and the unfamiliar integrate the familiar and the already domesticated. Its outcome is the constituents of the everyday life, making things usual and liveable with peace of mind. However, it has been shown that the everyday is a challenging topic in design: "The difficulty in approaching the everyday in design lies first and foremost in the fact of its familiarity, in its apparent obviousness, and therefore in its difficult questioning and analysis. Design needs to find in the everyday something to explore, to question, and to shape." [START_REF] Lévy | Designing for the everyday through thusness and irregularity[END_REF]. Providing means for design to consider appropriation in its own processes is therefore a key to improve the consideration of the everyday in and through design.

ARTEFACTUAL EMPTINESS

The case of muji

Such perspective on the everyday has been the focus of Mujirushi Ryohin (also known as muji), that designs and retails a large variety of products, from pens to houses, as well as clothes and food, while still keeping a coherent visual identity. [START_REF] Kusunoki | Opinion[END_REF] describe them as "simple, ordinary, and empty", which actually relate to the first three terms proposed by Hara as the concepts that have shaped muji over time (2015): nature, house, emptiness, water, and earth. Simplicity is both functional and aesthetic, and can be related to the notion of nature (shizen in Japanese -自然) which denotes the primary, possibly exclusive, expression of what is essential in the artefact and in its use. Ordinary indicates that the products are usual and useful for everyday life. They are therefore part of a wider environment considered as a field of possibilities. It also goes back to the idea that muji's products are not signed, but rather are a base, a vehicle giving the user the possibility to develop his own lifestyle with these products. The notion of house (ie -家) thus invites the notion of habitability by these artefacts and the users in a shared space, and structured by a lifestyle. Finally, the notion of emptiness (kara -空) describes the idea that the artefact is such as to give the user a space of possibilities to develop his own way of interacting with it. The artefact provides possibilities and does not impose itself.

These three notions, describing the design project of muji, especially the notion of emptiness, seem to align with the project of quotidianisation of artefacts, and therefore with the attention design may have both for the everyday and for appropriation. Emptiness denotes the idea that the artefact is such that it gives the user a space of opportunity to develop his or her own way of interacting with it. The artefact opens up possibilities and does not impose itself. It is in the interaction with its emptiness, i.e. thanks to the artefactual emptiness that quotidianisation can take shape [START_REF] Lévy | Le temps de l'expérience, enchanter le quotidien par le design[END_REF].

Emptiness as a space for appropriation

We argue that the notion of emptiness is relevant to address how we can consider the possibility of appropriation through design. First, the emptiness provides a space that enables the user to adapt the artefact through interacting with it. Second, considering further the notion of emptiness in Japanese philosophy, especially in relation with the work of the School of Kyoto on the notion of śūnyatā (This term has been translated in Japanese by either kū (空) or mu (無), themselves translated by emptiness or nothingness. While discussing the distinction between these notions is beyond the scope of this paper, we use here the term emptiness, more adequate to address what design considered as a space), this notion suggests that everything comes to exist in an interdependent premise (engi -縁 起 ), which implies that no phenomenon can be independent and is only by its relation to other phenomena. Emptiness invites to consider first and foremost relationships between things, rather than to the things themselves. These relations are social, artefactual, temporal, etc.

Emptiness for the everyday

We have proposed a way design can involve the possibility of appropriation in its practice. Including emptiness in the artefact enables for such appropriation. However, if the actual aim is to open up the practice of design for appropriation, then we should also question the possibility of embracing appropriation through design. The difference between considering and embracing appropriation is significant. In the earlier, design would simply make appropriation possible, with no clear value for it. If we do value appropriation, then embracing it requires to invite for it through design.

On this topic, [START_REF] Dix | Designing for appropriation[END_REF] notes the oxymoronic nature of this intention: "plan for the unexpected". Designing for something that diverges from the intention of the design, implies that it should remain unexpected and therefore implanifiable. An attention on a similar oxymoron is found on the notion of irregularity [START_REF] Lévy | Designing for the everyday through thusness and irregularity[END_REF][START_REF] Lévy | 3D-modeling and 3D-printing Explorations on Japanese Tea Ceremony Utensils[END_REF], inspired from the work of Yanagi Sōetsu's critic on (im)perfection [START_REF] Yanagi | The Unknown Craftsman: A Japanese Insight into Beauty[END_REF]. According to him, perfection is synonym to final and static. It prevents openness and freedom, which he associates to beauty. However, freedom should not be the obliged of beauty, as it would then be an illusionary freedom. This way, Yanagi overcomes the dualism between perfection and imperfection, proposing the notion of irregularity, "by default of a better word", to address such beauty when something remains unexplained, which cannot be planned. Such beauty can be found for example in the textile design work of Minagawa (Minä [START_REF] Perhonen | Minä perhonen 2 embroidery[END_REF], both in the expression and in the gesture domains. The irregularity created by Minagawa is done through a specific use of the embroidery machine. The designer conceived patterns that demand the machine to reach and possibly go beyond its mechanical limits (such as stitching numerous times at the same place, so that the needle cannot go straight through the textile anymore and has to bend to pursue its course). At these limits, provoked by design, the machine creates unpredictable irregularities, source of beauty in the sense of Yanagi, and well perceivable in the outcoming artefacts (embroidery patterns).

The value of such beauty is that it finds its essence in the irregularity, which leads to the unexpected, and invites for exploration in a space that can be arranged. In other words,

irregularity invites the user to arrange and appreciate the artefactual emptiness. Designing with irregularity supports such ambition [START_REF] Lévy | Designing for the everyday through thusness and irregularity[END_REF].

CONSEQUENCES FOR KANSEI DESIGN AND KANSEI RESEARCH

In this paper, we proposed a way to look at and to address through kansei design the phenomenon of appropriation. The artefactual emptiness and the irregularity allow us to consider and to conceive the technology-in-use no longer as something distant from the technology-asdesigned, but as a constituent of the technology-in-use. The duality between technology-in-use and the technology-as-designed is then overcome. However, there is still a need to qualify this artefactual emptiness, i.e., to topologize this space in order to guide the designer in the creation of possible spaces. The notions of micro-considerations, micro-friction and (es)sential details [START_REF] Lévy | Designing for the everyday through thusness and irregularity[END_REF] provide hints for such endeavor.

Finally, focusing on appropriation in kansei studies leads as well to discuss the relevancy of considering appropriation in the broader context of kansei research, especially in kansei evaluation. Is appropriation relevant in kansei evaluation? If so, how does this field resist to the integration of appropriation into design processes, whether these processes belong to kansei engineering, kansei science, or kansei design? Paying attention to such phenomenon may readdressed fundamentals in these fields of kansei research. Determining a method to measure over time the kansei effect of appropriation can be a way to study kansei aspects of the everyday life through kansei science and kansei engineering.


Benjamin Lambert

Florence Forbes

Senan Doyle

Alan Tucholka

Michel Dojat

Fast Uncertainty Quantification for Deep Learning-based MR Brain Segmentation

Quantifying the uncertainty attached to Deep Learning models predictions can help their interpretation, and thus their acceptance in critical fields. Yet, current standard approaches rely on multi-steps approaches, increasing the inference time and memory cost. In clinical routine, the automated prediction has to integrate into the clinical consultation timeframe, raising the need for faster and more efficient uncertainty quantification methods. In this work, we propose a novel model, named as BEHT, and evaluate it on an automated segmentation task of White-Matter Hyperintensities from T2-weighted FLAIR MRI sequences of Multiple-Sclerosis (MS) patients. We demonstrate that this approach outputs predictive uncertainty much faster than the state-of-the-art Monte Carlo Dropout approach, with a similar -and even slightly better -accuracy. Interestingly, our approach distinguishes 2 distinct sources of uncertainties, namely aleatoric and epistemic uncertainties.

Introduction

The ever-growing usage of Deep Learning (DL) models in the industry, as well as their potential impact on human lives, is raising concerns regarding the opacity of their predictions. Thus, many studies have been focusing on producing explainable DL models to facilitate their interpretation by end-users [START_REF] Arrieta | Explainable artificial intelligence (XAI): concepts, taxonomies, opportunities and challenges toward responsible AI[END_REF]. Among the large variety of explanations that can be provided along with a given prediction, Uncertainty Quantification (UQ) techniques stand out as one of the most popular amongst clinicians [START_REF] Tonekaboni | What clinicians want: Contextualizing explainable machine learning for clinical end use[END_REF]. UQ methods complement a prediction with an uncertainty score, providing the user with additional information regarding the model confidence in its own prediction.

Predictive uncertainty, i.e. the uncertainty attached to the output of a DL model for a given query input, is traditionally decomposed in 2 parts: (i) aleatoric and (ii) epistemic uncertainties [START_REF] Gal | Uncertainty in deep learning[END_REF]. Aleatoric uncertainty (i) relates to random effects impacting the prediction, such as the presence of noise or artifacts in the input data. This part is irreducible, meaning that introducing extra data will not diminish it. Aleatoric uncertainty can be further split in two categories : homoscedastic uncertainty, which is constant for each input, and heteroscedastic that depends on the input. On the other hand, epistemic uncertainty (ii) is linked to the choice of the model parameters. It represents the lack of knowledge of the model and can be reduced given additional and complementary data.

Various methods have been proposed in the literature to quantify uncertainty attached to DL predictions [START_REF] Abdar | A review of uncertainty quantification in deep learning: Techniques, applications and challenges[END_REF]. Popular approaches rely on a multi-step process, either based on the computation of multiple predictions from the same stochastic model [START_REF] Blundell | Weight uncertainty in neural network[END_REF][START_REF] Gal | Dropout as a bayesian approximation: Representing model uncertainty in deep learning[END_REF], or alternatively based on the aggregation of predictions from multiple models [START_REF] Lakshminarayanan | Simple and scalable predictive uncertainty estimation using deep ensembles[END_REF]. This results in a prolonged inference process, representing a significant obstacle for the full acceptance of these solutions in the clinical field, where time is a critical variable.

In this work, we propose a new DL model that quantifies both aleatoric and epistemic uncertainties attached to DL prediction, with a single forward pass. We illustrate our framework on an automatic segmentation task to detect White-Matter Hyperintensities (WMH) from T2weighted FLAIR MRI sequences of Multiple-Sclerosis (MS) patients, and compare it with the Monte Carlo Dropout (MC-Dropout) state-of-the-art approach.

2 Related Work

Aleatoric and Epistemic Uncertainty

Distinguishing between aleatoric and epistemic uncertainties is challenging, as both sources are usually mixed up in the final estimated uncertainty [START_REF] Hüllermeier | Aleatoric and epistemic uncertainty in machine learning: An introduction to concepts and methods[END_REF]). Yet, this distinction is particularly important in the medical domain. For example, a radiologist could react differently in response to a high predictive uncertainty if informed that it is caused by a lack of knowledge of the model about the observed pathology (epistemic uncertainty), or by the presence of an artifact or noise in the MRI input data (aleatoric uncertainty) [START_REF] Senge | Reliable classification: Learning classifiers that distinguish aleatoric and epistemic uncertainty[END_REF].

Previous work has attempted to make such a distinction. [START_REF] Kendall | What uncertainties do we need in bayesian deep learning for computer vision[END_REF] implemented a Monte Carlo Dropout network with 2 outputs: one for the predictive mean ŷ and one for the predictive variance σ2 . Such a model is trained with Dropout, which is kept on at inference. As a result, multiple forward passes through the Neural Network (NN) yield to different predictions, as the Dropout mask is stochastically sampled at each pass. Additionally, they used a special loss to learn the variance σ2 during training and interpret it as the aleatoric uncertainty. At inference, T Monte Carlo Dropout samples were computed for each input query x, resulting in a set {ŷ t , σ2 t } T t=1 . The final voxel-wise predictive uncertainty P U (x), combining an epistemic and an aleatoric part, was obtained with :

P U (x) = 1 T T t=1 ŷ2 t - 1 T T t=1 ŷt 2 epistemic + 1 T T t=1 σ2 t aleatoric (1)
Similarly, [START_REF] Kwon | Uncertainty quantification using bayesian neural networks in classification : Application to biomedical image segmentation[END_REF] used a MC-Dropout model to quantify the two types of uncertainty. They proposed 2 distinct estimators to evaluate epistemic and aleatoric uncertainties based solely on the output predicted probabilities {p t } T t=1 , obtained after applying the Softmax function to a set of Monte Carlo Dropout samples. For a given input x, the predictive uncertainty is obtained as :

P U (x) = 1 T T t=1 (p t -p t ) ⊗2 epistemic + 1 T T t=1 diag(p t ) -p⊗2 t aleatoric (2)
where

p t = T t=1 pt /T and v ⊗2 = vv T .
Depeweg et al. ( 2018) implemented a Bayesian NN by placing distributions over the model weights w. At inference, they approximated the predictive distribution p(y|x, D) associated with the training dataset D by sampling the weight distribution using a Monte Carlo approach. The authors further computed the total predictive uncertainty as the entropy of the predictive distribution H[p(y|x)]. This term includes both the epistemic and aleatoric sources. By fixing a set of weights, the epistemic term disappears, meaning that the expectation over the entropies can be used as an estimator of the aleatoric uncertainty. Finally, both sources can be obtained as follows:

H[y|x] -E w|D H[p|y, x) aleatoric = I(y, w) epistemic (3)

Efficient Uncertainty Quantification Methods

Methods presented in the previous section -such as MC-Dropout or Bayesian NNrequire sampling at inference, highly extending the inference time. In a similar way, Deep Ensemble [START_REF] Lakshminarayanan | Simple and scalable predictive uncertainty estimation using deep ensembles[END_REF], another popular approach for UQ based on the inference of multiple models, drastically increases the computational and memory cost during both training and testing. In clinical routine, e.g for MS follow-up, the DL-based assistance is useful only when the automatic analysis is fast enough to be integrated into the clinical consultation. This motivates the need for efficient and fast UQ methods. In the following, we review several techniques that tend toward this goal. Each of these methods, when applied to a 3D image segmentation task, provide one measure of uncertainty per voxel. [START_REF] Wen | Batchensemble: an alternative approach to efficient ensemble and lifelong learning[END_REF] proposed an efficient alternative to Deep Ensemble called BatchEnsemble, which highly reduces its memory cost. The method proposes to train an ensemble of NN within a single architecture. To achieve this result, the weights of the NN are expressed as the Hadamard product of a shared weight among all ensemble members (called as slow weights) and member-specific rank-one matrices (called as fast weights). This special formulation results in different weight configurations for each member, hence modeling the possible variance of the weights, and thus the epistemic uncertainty. For an ensemble of 4 models, BatchEnsemble reduces test time and memory by up to 3 times, compared to Deep Ensemble.

Similarly, an effective approach to quantify heteroscedastic aleatoric uncertainty was proposed in [START_REF] Mckinley | Uncertainty-driven refinement of tumor-core segmentation using 3d-to-2d networks with Fast Uncertainty Quantification for Deep Learning-based MR Brain Segmentation label uncertainty[END_REF]. As in [START_REF] Kendall | What uncertainties do we need in bayesian deep learning for computer vision[END_REF], the model output is divided in two parts: the prediction and the uncertainty. Authors proposed a Labelflip loss, which is used to learn the uncertainty associated with input images without labels. This forces the model to learn the Labelflip probability, i.e. the probability the predicted label and the ground truth label differ. This method thus outputs the prediction and the associated aleatoric uncertainty in a single forward step.

Alternative works have directly used the output predicted probabilities as a measure of uncertainty, with no further computation. This very simple and efficient approach was successfully applied to detect misclassified and out-of-distribution images [START_REF] Hendrycks | A baseline for detecting misclassified and out-ofdistribution examples in neural networks[END_REF], as well as adversarial examples [START_REF] Zhang | des approches multi-étapes, ce qui augmente le temps d'inférence ainsi que les coûts en mémoire. En routine clinique, l'utilisation d'outils prédictifs nécessite une intégration dans le temps de la consultation clinique, ce qui motive le développement de nouvelles méthodes rapides et efficaces pour quantifier l'incertitude des modèles Deep Learning[END_REF].

These methods, although being more efficient regarding inference time or memory cost, yet fail at distinguishing between aleatoric and epistemic uncertainties. In the next section, we propose a new method addressing this challenge, that we call BEHT for BatchEnsemble Heteroscedastic Tiramisu.

Methods

In this section, we introduce a novel approach to quantify both epistemic and aleatoric uncertainties in an fast and efficient manner. This is achieved by combining a BatchEnsemble approach with a Heteroscedastic model, starting from a baseline Tiramisu 2.5D architecture. We named this compound model as the BatchEnsemble Heteroscedastic Tiramisu, or BEHT.

Dataset

We illustrate our proposed approach on a supervised segmentation task. We use a proprietary brain dataset composed of 238 T2-weighted FLAIR MRI sequences of MS patients, with ground truth segmentations of WMH. The dataset is split into 187 scans for training and 51 for testing. The images are rigidly registered to a template and resampled to a 1mm isotropic resolution of 160 × 192 × 160 to focus on brain tissue. Intensities are normalized to zero mean and unit variance.

Baseline 2.5D Architecture

We start with a standard Tiramisu Convolutional Neural Network (CNN) for image segmentation, originally proposed for 2D images semantic segmentation [START_REF] Jégou | The one hundred layers tiramisu: Fully convolutional densenets for semantic segmentation[END_REF]. Processing 3D biomedical image is challenging, as the input data has a high dimensionality and requires large memory capabilities. To circumvent this limitation, we implement an intermediate 2.5D version of the Tiramisu network. In this setting, the segmentation model focuses on one slice, with several upper and lower slices provided to the model. More precisely, 3D images of shape H × W × D are processed sequentially. At each step, C consecutive 2D slices are extracted from the volume and stacked as distinct image channels, resulting in a C ×H ×W input. We use C = 5 in our experiments. Our Tiramisu 2.5D networks is composed of the same construction blocks than the original 2D Tiramisu, with a succession of Dense Blocks (DB), Transition Down (TD) and Transition Up (TU) layers (see [START_REF] Jégou | The one hundred layers tiramisu: Fully convolutional densenets for semantic segmentation[END_REF] for implementation details). This baseline model is made of a total of 51 convolutional layers and 950k parameters. The model produces for each voxel a unique probability of being in the lesion class. Probabilities are obtained by applying the Sigmoid function to the predicted logits. Details of the proposed architecture are presented in Table 1.

The Tiramisu 2.5D network and following models are implemented using the Pytorch DL library [START_REF] Paszke | Pytorch: An imperative style, high-performance deep learning library[END_REF]. Training is performed using the ADAM optimizer ( [START_REF] Kingma | Adam: A method for stochastic optimization[END_REF] until convergence, with a learning rate of 5e -4 . We use a batch-size of 48, and train on a single NVIDIA T4 GPU.

Modeling Epistemic Uncertainty with BatchEnsemble

Building on the baseline architecture, we model epistemic uncertainty using the BatchEnsemble framework presented in [START_REF] Wen | Batchensemble: an alternative approach to efficient ensemble and lifelong learning[END_REF]. We obtain a BatchEnsemble of N = 6 members from a single Tiramisu 2.5D by replacing each convolutional weights by :

W i = W • F i (4)
where W is a common weight matrix shared by each ensemble member (slow weight) and F i is a rank-one matrix specific to each of the i-th ensemble members (fast weight). Learning of these weights is parallelized within a single GPU device using a mini-batch approach. We divide the batch of length b = 48 in N = 6 sub-batches of length M = 8, such as b = N × M . Each member's weight W i receives a single sub-batch during training, allowing to train the BatchEnsemble with an optimal vectorized approach. At inference, the input is repeated i times, so that each member processes it in parallel. Lastly, we take the mean of the prediction as the final output. These steps are illustrated in Figure 1 Writing {p n } N n=1 the set of lesion probabilities obtained with each member of the BatchEnsemble for a given input image x, the epistemic uncertainty Ep(x) is obtained by computing the variance of this set :

Ep(x) = 1 N N n=1 p 2 n - 1 N N n=1 p n 2 (

Modeling Aleatoric Uncertainty with the Labelflip loss

We transform our model into a heteroscedastic one by following the steps of [START_REF] Mckinley | Uncertainty-driven refinement of tumor-core segmentation using 3d-to-2d networks with Fast Uncertainty Quantification for Deep Learning-based MR Brain Segmentation label uncertainty[END_REF]. In addition to the lesion probability for each voxel, the NN also predicts its attached uncertainty q in a single forward pass. To learn the uncertainty part during training, the Labelflip loss is employed. Writing x the binary ground truth label, w = (1-x) * q+x * (1-q), and z the disagreement indicator between the predicted class and the ground truth, the labelflip loss is defined as :

Focal KL (w∥p) + BCE(q, z) (6)
with Focal KL (w∥p) = (p -w) 2 (wlog(w) -wlog(p))

This function forces the model to output a high uncertainty in areas where the segmentation is not confident. The use of a Kullback-Leibler divergence term guarantees that uncertain voxels remain close to the decision boundary. We used the Dice loss in conjonction of the Labelflip loss to train the model.

Reminding that BEHT outputs a distinct prediction per member of the BatchEnsemble, we obtained a set of {q n } N n=1 uncertainties for each input image. The final aleatoric uncertainty is formulated as the mean of this ensemble :

Al(x) = 1 N N n=1
q n (8)

Predictive Uncertainty Quantification using the BEHT approach

The overall predictive uncertainty is obtained by summing the aleatoric and epistemic contributions. Yet, both quantities have distinct numeric ranges due to the different methods employed to compute them, which makes normalization step necessary. To do so, we first compute epistemic and aleatoric uncertainty maps for each test image, and extract the minimum and maximum voxel uncertainties across the test dataset. We then normalize each map in the range [0, 1] by subtracting by the minimum and dividing by the range. The final predictive uncertainty P U (x) for a given query image x is finally obtained with :

P U (x) = 1 2 [Ep [0,1] (x) + Al [0,1] (x)] (9)
4 Experiments

We evaluated our proposed model with respect to 3 aspects: the quality of uncertainty estimates, the performance of the segmentation, and the inference time. To compare these results with state-of-the-art method, we also implemented a MC-Dropout Tiramisu 2.5D. Starting from the baseline model, a dropout rate of 20% is applied in the Dense-Blocks and Transition-Down layers, as proposed in [START_REF] Jégou | The one hundred layers tiramisu: Fully convolutional densenets for semantic segmentation[END_REF]. The model is trained with a combination of the Dice and the Binary Cross-entropy losses. At inference, epistemic and aleatoric uncertainties are obtained using Equation 2 with T = 20 Monte Carlo samples. For each method, we compute segmentation masks and uncertainty maps. Representative examples of the obtained predictions are presented in Figure 2.

Evaluating Uncertainty Estimates

To evaluate the performance of the different uncertainty maps -epistemic, aleatoric, and predictive -generated by the 2 competing approaches, we implement a stratification approach. The desired uncertainty quantification highlights unconfident predictions, which are more likely to be incorrect. Thus, we expect uncertainty to be higher for incorrect predictions (IP) than for correct predictions (CP). By filtering predictions based on their certainty, we should remove more IP than CP.

To evaluate this property, we progressively filter out predicted voxels based on their certainty and monitor the variation of CP and IP. More precisely, at each step, we remove the X% most uncertain predicted voxels, where X is a threshold varying in the set [0, 100]. As a result, we obtain of couple (CP, IP ) for each threshold X, used to draw a Stratification Curve. As the evaluated methods have varying segmentation performances, the CP and IP counts are different. Thus, we normalize the CP and IP counts in the range [0, 1] so that the segmentation performance does not impact the evaluation of the uncertainty estimates. A CP of 1 corresponds to the maximum number of CP, obtained when no filtering is applied. A CP of 0.5 indicates that 50% of the CP are filtered out. To obtain a single quantitative score, we use the Area Under the Stratification Curve (AUSC).

Segmentation Performance

The desired UQ method should provide useful uncertainty estimates, while also preserving a satisfying segmentation performance. To evaluate this property, we assess the segmentation performance using Dice scores, a measure of overlap between the predicted segmentation and the ground truth. Segmentation quality improves as the Dice score increases.

  FIG. 1 -Illustration of the training and inference stages in a BatchEnsemble model. In this example, a batch of 16 samples is distributed to 4 members during training. At inference, a batch of 4 is duplicated and distributed to each member weight.

FIG. 2 -

 2 FIG.2-Representative examples of the segmentation masks and uncertainty maps obtained using each method.

FIG. 3 -

 3 FIG. 3 -Evaluation of incertainty estimates. A, B: Variation of Correct (CP) and Incorrect (IP) Predictions counts, respectively, with respect to the uncertainty threshold; C: Corresponding Stratification Curve and associated AUSC scores. Ep: Epistemic uncertainty; Al: Aleatoric uncertainty; PU: Predictive Uncertainty.

  Kingma and Architecture details of the baseline Tiramisu 2.5D model used in the experiments. Conv=Convolution 2D, DB=Dense Blocks, TD=Transition Down, TU=Transition UP

	Architecture Details
	Input
	3x3 Conv + DB block (1 layer)
	DB block (3 layers) + TD
	DB block (5 layers) + TD
	DB block (7 layers) + TD
	TD + DB block (10 layers) + TU
	TU + DB block (7 layers)
	TU + DB block (5 layers)
	TU + DB block (3 layers)
	DB block (1 layer) + 1x1 Convolution
	Sigmoid
	TAB. 1 -

BEHT

MC-Dropout Dice 0.785 ± 0.076 0.777 ± 0.083 TAB. 2 -Segmentation performance. For each method, we provide the mean Dice and the standard deviation. Top performing method is highlighted in green.

Inference time

Lastly, for smooth integration in clinical practice, the method should be as fast as possible. We compute the Mean Inference Time (MIT), representing the total duration in seconds of the computations steps for a single 3D volume. This represents the iterative segmentation of the volume using the 2.5D model, as well as the uncertainty quantification. The fastest method is the one that minimises the MIT.

BEHT

MC-Dropout MIT 5.434 ± 0.062 16.535 ± 0.485 TAB. 3 -Inference time performance. For each method, we provide the MIT and the associated standard deviation. Top performing method is highlighted in green.

Results and Discussion

Overall, BEHT outperforms the MC-Dropout approach on all 3 metrics. Regarding the UQ task, Figure 3 reveals that the AUSC score of the predictive uncertainty obtained with BEHT is slighty better than for MC-Dropout : 0.839 versus 0.834. Furthermore, the proposed approach also achieve the best segmentation quality as shown in Table 2. Finally, the most impressive improvement comes from the inference time, as the BEHT approach is 3-times faster than the MC-Dropout one, as presented in Table 3. In summary, our new BEHT method reachesand even slightly overpasses -the UQ and segmentation performance of the state-of-the-art MC-Dropout approach, while drastically reducing the inference time.

Interestingly, for both approaches, combining the aleatoric and epistemic uncertainties results in improving the quality of the uncertainty estimates, demonstrated by the improvement of the AUSC score (see Figure 3). This suggests that taking into account both uncertainty sources is important and can actually provide more robust uncertainty estimates. Finally, our model provide robust uncertainty estimates without sacrificing segmentation performance, reaching a Dice score of 0.785 on the test dataset.

Future Directions

The proposed 2.5D approach is efficient regarding memory consumption, yet the 3D volume is processed sequentially, which prolonged the inference process and also limits the segmentation quality. Our future work will consist in the implementation of a fully 3D model which could reduce the inference time.


domain: phys chim

text:
E V Ermakova

A G Bessmertnykh-Lemeune

M Meyer

L V Ermakova

A Y Tsivadze

V V Arslanov

Supramolecular Assembly of Planar Systems from Modular Molecules with a Given Hydrophilic-Lipophilic Balance: Film Sensors with an Anthraquinone Signal Group

This work presents an original approach to obtaining highly sensitive ultrathin film sensors that allows molecular design of surface-active modular molecules by completing a signal anthraquinone block with hydrophobic radicals and polar receptor groups, with their number and size provided in accordance with the sensor type. An important advantage of the suggested approach is that it not only allows the functioning of sensors in the aqueous medium, but also their manufacturing (supramolecular assembly). The key regularity of ligands of the suggested series is selectivity with respect to mercury and copper cations. Application of amphipilic ligands in film liquid (Langmuir monolayers) and solid-state (Langmuir-Blodgett films) sensors allowed developing optical sensors for mercury and copper cations with the detection limit, as dependent on the sensor type, varying from several to hundredths of ppm.

INTRODUCTION

In recent years, one of the most important problems of chemical science, which encompasses various spheres of human life, including health protection, is development of diagnostic systems [START_REF] Li | Biosensor Nanomaterials[END_REF][START_REF] Gumpu | [END_REF][3]. These systems must provide the monitoring of harmful and dangerous ions and molecules both in the environment and in the human body. Among them, cations of such toxic metals as mercury, lead, cadmium, and copper that are powerful metabolic poisons for plants, animals, and human beings, are particularly dangerous. Herewith, mercury cations are considered as the most harmful inorganic substances [4,5]. In the last hundred years, the amount of mercury in the upper 100 m of the World Ocean has doubled. The content of mercury in fish and in human hair in different countries of the world regularly exceeds the safe level [6]. Inorganic compounds of mercury are most widespread; they are extracted with solid particles or organic compounds. Hg(II) ions are bound both by organic and inorganic ligands and can be methylated.

Such wide spreading of mercury in different objects in the ecosphere requires developing various detection methods, including high-sensitivity and high-precision ones. Therefore, development of efficient ligands for the binding of Hg 2+ simultaneously solving two problems: analytical (determination of Hg 2+ in aqueous media) and ecological (purification of aqueous solutions from this type of contamination [7][8][9][10]).

Copper is one of the important microelements that enter the human body. High copper concentrations stimulate generation of active oxygen forms, which results in oxidative damage to proteins and nucleic acids. However, this drawback of copper causes inactivation of the key antioxidant enzymes and results in disruption of energy processes in living systems [11,12].

The content of copper in natural sources is relative low, but its concentration in water increases significantly due to corrosion of water-supply pipes. In this regard, the efforts of a significant part of the scientific community are aimed at development of systems of high-selectivity sensitive detection of mercury or copper cations, and other toxic metals in water that can irreparably damage the environment and human health. This work presents a number of ligands (Scheme 1) containing the signal anthraquinone group, as well as hydrophilic and hydrophobic modules, and their number and size adjusted for development of stable and efficient thin film sensors for selective detection of mercury and copper cations in aqueous solutions. Molecular design was carried out according to two directions providing for an increase in lipophilicity of ligands for their application in ultrathin films: monolayers and Langmuir-Blodgett films. In the first case, the length of the hydrocarbon part of the molecule was lengthened by replacing two -OC12H25 radicals (ligand C12) by -OC18H37 (ligand C18); in the second case, the polar part of the molecule was decreased by Protection of Metals and Physical Chemistry of Surfaces 2018, 54, 6-18 -DOI: 10.1134/S2070205118010057 4 eliminating one hydrophilic receptor moiety while preserving the two hydrocarbon -OC12H25 chains (ligand N12) (Scheme 1). One note that, when we developed this series of ligands, we attempted to preserve the architecture of classical amphipilic molecules that provided a high level of molecular organization at interfaces. Scheme 1. Chemical formulas of anthraquinone ligands with different lipophilicity, the corresponding schematic images and HLB values calculated according to the Griffin method [13].

EXPERIMENTAL

Synthesis of ligands was carried out according to the methods described in [14]; the physicochemical characteristics of the obtained compounds correspond to those published earlier [15]. Chloroform (analytical grade) (Merck) was distilled over CaH2. Hexahydrates of copper(II) and mercury(II) perchlorates (98%, Aldrich) were used without any additional purification. Ligand solutions (0.1 mM) were prepared by sample dissolution in chloroform.

The subphase used was deionized water (18 MΩ cm, Vodolei, NPP Khimelektronika) or aqueous solutions of perchlorates. Gilson Distriman microsamplers were used for application of monolayer-forming solutions. Compression isotherms of monolayers were obtained using 1000-2 KSV Minitrough setup (Finland) equipped by a Teflon Langmuir trough, polyacetal hydrophilic barriers, a Wilhelmy plate (platinum plate) for determination of the surface pressure of the monolayer, and a device for automated transfer of monolayers to solid substrates.

Transfer of monolayers to solid substrates was carried out using the Langmuir-Blodgett method with constant surface pressure. Electronic-absorption spectra of monolayers on the aqueous subphase surface in the wavelength range of 200-800 nm were registered using a fiber-optic AvaSpec-2048 FT-SPU spectrophotometer (Netherlands). A reflectometric UV/VIS tester with the fiber diameter of Protection of Metals and Physical Chemistry of Surfaces 2018, 54, 6-18 -DOI: 10.1134/S2070205118010057 5 400 m joined together with a six-fiber irradiating cable was positioned normally to the studied surface at the distance of 3 mm from the monolayer. Electronic-absorption spectra of films supported on the surface of quartz substrate were recorded using a SHIMADZU-2450 spectrometer (Japan) in the wavelength range of 200-900 nm.

RESULTS AND DISCUSSION

Monolayers of Amphipilic С12, С18, and N12 Ligands on the Surface of Deionized Water

Using amphipilic ligands in sensors with sensitive elements in the form of ultrathin films on the liquid (water) surface has a triple goal: (1) determination of complexing properties of ligands in labile organized systems with the uniform orientation of functional groups (2D transition systems between the solution and solid substrate), (2) preorganization and assembly of chromoionophores in monolayers at the air/water interface for their further transfer to solid substrates using the Langmuir-Blodgett method, and (3) development of liquid sensors for the purposes of nano(micro)fluidics. Obviously, these directions imply analysis of the processes of cation binding by ligand monolayers from the subphase. The proximity of isotherms and high values of the limiting surface area of all three related compounds indicates a certain conservatism in the development of molecules with rather different structures. The observed high limiting areas per single molecule for condensed states of the monolayer indicate that the anthraquinone fragment is located in parallel to the subphase surface (according to the model, its area is 100 Å 2 [16]) and that at high surface pressures bulk polar groups can occupy areas commensurable with the aromatic fragment. Obviously, the polarity (hydrophilicity) values of ether oxygens and oxygen of the carbonyl group are enough to "lay down" the anthraquinone fragment onto the surface into the "face-on" position already in the course of monolayer formation. Usually, when monolayers are compressed, f lat aromatic fragments are displaced from the interface surface and their planes in the condensed state are arranged normally to the subphase surface, i.e., they assume an "edge-on" orientation owing to the energy gain owing to the - stacking interactions. Here, low values of the monolayer area are registered. They correspond to this very orientation of aromatic moieties of the molecules [17][18][19][20][21].

Nevertheless, the observed slight difference in the shape and position of compression isotherms allows correlating molecular construction of the ligand and its organization in the monolayer on the surface. Firstly, one must point out that transition from С12 to С18 leads to a shift of the isotherm towards lower areas and an increase of the collapse pressure; here, the shape of isotherms is preserved. Secondly, transition from ligand С12 to N12, for which a single branched polar group remains instead of two, results in a steeper rise of the curve at lower surface areas in the condensed state.

Taking into consideration that both the signal group and polar groups of the C12 and C18 ligands immersed into the subphase manifest close organization on the water surface, the above shift in the isotherm of С18 into the condensed region can be due only to an increase in the length of the hydrocarbon radical turned toward the air phase. Therefore, despite the complexity of parts of modular molecules attached to the "tails," the difference in the length of the latter produces a similar effect on the behavior of monolayers, as in the case of fatty acids with the corresponding chain size (e.g., lauric and stearic acids). However, as seen in Fig. 1a, in the presence of polar modules with an area significantly exceeding the area of the cross section of the hydrocarbon radical, the effect of the difference in the chain length is much lesser than in the case of fatty acid monolayers. The С18 isotherm is only slightly shifted toward lower areas as compared to the С12 isotherm, which is explained by an increase in the contribution of interchain interactions at an increase in the "tail" length. The scheme (Fig. 1b) shows fragments of С12 and С18 monolayers explaining the higher degree of monolayer condensation of the ligand with a long chain. Obviously, in this case, the bulky polar groups prevent full implementation of the contribution of interchain interactions (as in the case of fatty acid monolayers), not allowing hydrocarbon chains to approach each other to the required distance even at high monolayer compression degrees.

Thus, the ligands of the suggested series, owing to the architecture of classical amphipilic molecules, form stable monolayers at the air/water interface. Here, comparison of the shape and position of compression isotherms of the three ligands point to the fact that rigidity of their monolayers is determined by the anthraquinone fragment preserving the horizontal position on the surface of water in the course of the whole compression process; an increase in the length of the hydrocarbon radical in the molecule enhances condensation of the monolayer, just as does elimination of one polar group from the molecule, which provides a closer contact between the planar signal groups in the "face-on" orientation.

Monolayers of Amphipilic Ligands С12, С18, and N12 on the Surface of Aqueous Solutions Containing Mercury and Copper Cations

Langmuir monolayers offer a unique possibility to study complexation in an aqueous medium of ligands that are insoluble in water (or form very dilute solutions). In the case of the sensors considered in this work, this allows determining the performance and selectivity of the binding of inorganic analytes. Such interactions play the key role in obtaining hybrid metal-complex monolayers for the further formation of Surface-Anchored metal-organic frameworks (SURMOFs) [22,23].

Figure 2a demonstrates the effect of mercury cations in the subphase (1 mM) on the compression isotherms of the С12, С18, and N12 monolayers. Interaction with mercury cations causes a shift in all isotherms toward lower areas. Obviously, these interactions limit the freedom of movement of polar groups, which imparts higher compactness to the thus-formed sublayer.

Thus, addition of mercury cations causes condensation of monolayers same as in the case of fatty acids [24]. However, shrinkage of fatty acid monolayers originated from a compensation of negative charges of carboxylate headgroups in the presence of positively charged metal ions.

On the other hand, the authors observed strong expansion of monolayers due to electrostatic repulsion of positively charged complexes in the studies of the binding of transition metal cations by monolayers of dicetylcyclene [25,26] or tert-butylthiacalixarene [27,28]. The studied ligands do not bear any negative charges, as opposed to acids, and, in the case of the binding of cations, the behavior of their monolayers should bring to mind the behavior of dicetylcyclene monolayers, i.e., expansion of the monolayer. The observed shrinkage indicates a different mechanism. Obviously, the bulkiness of polar nodes decreases considerably in the case of the binding of the cations and mobility of "brushes" is limited. Here, this effect must be enhanced at an increase in the cation concentration in the subphase. Figure 2b shows as an example compression isotherms for the C12 ligand monolayer on the surface of the aqueous subphase containing different concentrations of Hg(ClO4)2. One can see that isotherms are consistently shifted toward smaller areas and the compression modulus increases at an increase in the concentration of Hg 2+ cations in the subphase. Such a behavior of monolayers in the course of the binding of cations is also characteristic for the two other ligands.

The scheme presented in Fig. 2c explains the effect of the concentration of mercury cations in the subphase on the change in the monolayer structure and, accordingly, on the position and shape of compression isotherms. Before interaction with the cations, polar groups of "brushes" are in chaotic motion, occupy a large volume, and prevent the drawing together of lipophilic groups on the surface near the air phase. The binding of cations deprives the "brushes" of mobility and results in monolayer shrinkage. At an increase in the concentration of mercury cations in the subphase, an ever-higher number of modes is involved in this process and the monolayer shrinkage is greater. An important difference between the receptors located directly on the water surface (dicetylcyclene, tret-butylthiacalixarene) and immersed into the aqueous subphase (the ligands considered here) consists in a more effective compensation of the complex charge by counterions in the latter case. This effect also contributes to the monolayer shrinkage.

Thus, compression isotherms of monolayers of all ligands change regularly when mercury cations are introduced into the subphase. However, as we showed in [19,20], the change in the compression isotherms of monolayers after addition of metal cations into the subphase provides no unambiguous answer as to the presence of complexation in the system. The shift in the -Аcurves as a result of addition of cations may be related to film reorganization due to physical adsorption of charged particles, changed of double electric layer characteristics, etc. Besides, it is possible that the isotherms do not change their position as a result of compensation of effects caused by complexation. At the same time, spectral shifts for the systems with complexation are always pronounced. In this connection, information on complexation was obtained using in situ fiber-optic reflectance-absorption spectroscopy of monolayers. The presented data are obtained under the conditions when interaction of the Hg 2+ cations with the ligand monolayer occurs in the subphase already containing these cations (Fig. 3b). The binding of mercury cations by the С12 ligand is registered directly after the solution spreads over the surface and the solvent evaporates (15 min): the absorption maximum of the monolayer on the pure water surface (max = 560 nm) shifts hypsochromically by 25 nm and the band intensity increases in the course of the monolayer compression, while its position is preserved.

Therefore, no aggregation occurs in the monolayer even at high surface concentrations even when complexes are formed.

We changed the experiment so as to determine the kinetics of the binding of mercury cations by the С12 monolayer. First, a monolayer was formed on the pure water subphase; then, it was compressed to  = 12.5 mN/m; and, after this, mercury cations were added by replacement of the subphase and their concentration was adjusted to 1 mM. As seen in Fig. 4a, monolayer compression on the pure water surface from  = 0 to  = 12.5 mN/m, just as in the previous experiments, results in growth of the absorption intensity without any shift in the bands. After the cations are added into the subphase, the characteristic band corresponding to the pure ligand instantaneously shifts hypsochromically by ∼25 nm, which indicates formation of the complex.

When this monolayer is compressed, absorption intensity increases and a slight bathochromic band shift related to establishment of the equilibrium in the system is observed. The change in the surface pressure in the range of 10-15 mN/m at the mercury cation concentration in the subphase of 0.1 mM (the second method) produces practically no effect on the rate of the complexation reaction. At another tenfold decrease in the concentration (0.01 mM), the binding rate for  = 10 mN/m decreases by almost six times (Fig. 4b). Therefore, complexation in the С12 monolayer for mercury ion concentrations C > 0.1 mM occurs at high rates, which indicates high availability of functional groups (receptor modules) in sensors of this type. Let us also point out that the binding of cations in the sublayer of polar groups resulting in an increase in polarity of this part of the monolayer causes no reconstruction of the monolayer structure. In [20], in the studies of the monolayer of the macrocyclic pentaaminoanthraquinone we observed a change in the orientation of an anthraquinone fragment from the planar one (face-on) to the vertical one (edge-on) that is caused by immersion of the macrocyclic receptor fragment into the aqueous subphase as a result of protonation of its amino groups. Obviously, this effect is not implemented in this case and the anthraquinone group preserves its orientation on the surface, which prevents aggregation of the aromatic module.

Protection of Metals and Physical Chemistry of Surfaces 2018, 54, 6-18 -DOI: 10.1134/S2070205118010057 12 When compression isotherms of the С12 and С18 monolayer on the surface of pure water (Fig. 1a) were compared, it was shown that the ligand with a longer chain provides a more condensed monolayer: Alim = 140 Å 2 for С18 and Alim = 200 Å 2 for С12. Therefore, despite the fact that the large size and branched structure of polar groups similar for both ligands and also the horizontal orientation of the antraquinone group are responsible for the large monolayer areas, the hydrocarbon radical affects the monolayer organization: the longer hydrocarbon "tail" of С18 enhances the monolayer condensation. The same tendency is also preserved for monolayers on surface of the aqueous mercury salt solution and the differences in the limiting areas of monolayers of the two ligands decrease: 110 Å 2 for С18 and 140 Å 2 for С12 at [Hg 2+ ] = 1 mM. Spectroscopic studies of the binding of mercury cations by monolayers of the C18 ligand showed that, just as for the C12 monolayer, interaction between mercury cations and the monolayer of its long-chain counterpart causes a hypsochromic shift of the main ligand band at  = 25 nm (Fig. 5). Thus, monolayers of the С12 and С18 ligands differing only in the length of the hydrocarbon radical bind mercury cations from the subphase with similar efficiency. In the case of monolayers of the N12 ligand, addition of mercury and copper cations into the subphase results in a shift of isotherms into the region of small areas for  < 15 mN/m. In the Protection of Metals and Physical Chemistry of Surfaces 2018, 54, 6-18 -DOI: 10.1134/S2070205118010057 13 range of high surface pressures, the isotherms do not differ much and the isotherms for cationcontaining subphases manifest higher destruction pressures and rigidity (Fig. 6).

Nevertheless, one should emphasize that, in the case of mercury cations, the shrinkage, rigidity, and monolayer-destruction pressure are higher than in the case of copper cations. These data indicate that a more compact monolayer is formed in the first case and that, if these changes are due to complexation, then its mechanisms differ for the two systems. At least, one must state that, in accordance with the coordination numbers of these cations, a larger number of functional groups participates in formation of the coordination sphere of Hg 2+ than in the case of Cu 2+ .

Complexation was studied using electronic absorption spectra of N12 monolayers on the corresponding subphases. Figure 7a shows the effect of copper cations in the subphase on the electronic-absorption spectra of the N12 monolayer in the case of the second method of addition of cations. One can see that addition of copper cations under the formed monolayer leads to the bathochromic band shift by 52 nm. The absorption spectra of the monolayer on the surface of the aqueous subphase containing mercury cations is shifted in the opposite direction, i.e., hypsochromically, by 34 nm (Fig. 7b). First of all, one must note that the value of the hypsochromic shift of the main band for the N12 monolayer as a result of complexation (max) with mercury cations corresponds to the value of this shift for the С12 and С18 ligands. This reflects the similarity both in the complexation mechanism and in the structure of the forming complexes for the three ligands. In the case of the binding of copper cations by the N12 monolayer, max is shifted bathochromically and to a much greater value than in the case of Hg 2+ , which indicates implementation of a different type of interactions with participation of other functional receptor groups. We suggest that the binding of copper and mercury cations by the molecules of N12 and С12 (С18) occurs in accordance with the reactions shown in Scheme 2. Unfortunately, it appears impossible to confirm the structure of the complexes, as no crystals of these compounds can be grown. Nevertheless, one can state that the binding of copper cations is accompanied by deprotonation of aromatic amino groups conjugated with the signal fragment and amide groups of the polar ligand nodes undergo deprotonation in the course of coordination in the case of mercury cations.

Selectivity and Regeneration of Sensor Monolayers from the С12, С18 and N12

Chromoionophores

We showed earlier that the compression isotherms of the three ligands, though they yield information on organization of molecules in the film, but change negligibly and consistently when the cations are bound. This does not allow using the characteristics of compression isotherms for determination of selectivity of the liquid sensor with respect to metal cations.

The selectivity of sensors was determined using the method of fiber optic spectroscopy by successive addition to the subphase of the Cu 2+ , Pb 2+ , Cd 2+ , Ca 2+ , and Hg 2+ cations. As is seen in fig. 8, the presence of cations of metals from different groups of the periodic system (with the exception of Hg 2+ ) in a C12-ligandbased sensor produces practically no shift in the electronic-absorption spectra of monolayer absorption. A slight hypsochromic shift (3 nm) caused a change in the ionic composition of the monolayer due to physical adsorption of cations.

When Hg 2+ cations are added to the mixture, the spectrum shifts hypsochromically by 20 nm. Selectivity of the binding of Hg 2+ cations by the monolayer of the long-chain C18 ligand was determined in the same way as for the C12 monolayer, by successive addition into the subphase of the Cu 2+ , Pb 2+ , Ca 2+ , Cd 2+ , and Hg 2+ cations. These studies led to a similar result: the binding of mercury cations occurs with the same high performance.

Interesting results were obtained by studying a competitive binding of Hg 2+ and Cu 2+ cations by the N12 monolayer (Fig. 9). No band shift was observed after monolayer compression to 10 mN/m and addition of lead, calcium, and cadmium cations (Fig. 9a,2). Introduction of copper (Fig. 9a,3) and mercury (Fig. 9b,4) causes a shift in the spectrum of the pure ligand monolayer, accordingly, into the red and blue ranges. Moreover, in the case when Hg 2+ cations are added after Cu 2+ cations, the spectrum shifted into the red region as a result of complexation of the ligand with Cu(II) undergoes a hypsochromic shift. In the case of the reverse sequence of addition of these cations, the spectrum that has shifted hypsochromically after addition of Hg 2+ , does not change its position after addition of Cu cations. Therefore, Hg 2+ cations can substitute Cu 2+ cations in the complex, but not vice versa. This result indicates that the complex of the ligand with mercury cations possesses a higher binding constant than does the ligand-Cu 2+ complex. We showed above in analysis of compression isotherms that the behavior of monolayers at high compression degrees is determined by anthraquinone fragments in the "face-on" orientation and that implementation of such a structure requires compression of branched polar nodes ("brushes"). Obviously, under these conditions, steric limitations can appear that hinder formation of the coordination sphere characteristic for ligand and cation complexes both in the solution and in the monolayer at low surface pressure values. The effect of this factor was studied using electronic-absorption spectra of monolayers. After monolayer compression to  = 10, 15, and 20 mN/m, cations were introduced into the subphase. It was found that they were binding in the case of the cation concentration not exceeding 1 mM occurred practically instantaneously at all surface pressure values. Kinetic studies showed that the complexation time increases significantly at a decrease in the cation concentration; here, the surface pressure produces practically no effect on the reaction rate.

The importance of results obtained in this section consists not only in the fact that they represent the first detailed studies of complexation in monolayers for the hierarchical series of chromoionophores and different cations. The suggested study protocol allows one to obtain reliable information as to implementation of the complexation process in Langmuir monolayers, which demonstrates the correctness of the above consideration on the necessity of supplementing thermodynamic data (compression isotherm) with data of fiber-optic spectroscopy. Although we have earlier pointed out this rather obvious conclusion [19,20], in this work, owing to spectral regularities of the behavior of the N12 ligand monolayers in the case of the binding of mercury and copper cation, the obtained result appears not only useful, but also rather elegant.

Langmuir-Blodgett Films (LB films) of Chromoionophores C12, C18, and N12

The Langmuir-Blodgett method is one of the most perfect tools capable of collecting functional multilayer structure of monolayers with a given molecular organization and composition on solid substrates. It is used to solve many modern problems of nanotechnology and supramolecular chemistry, such as substrate-induced patterning [29,30], lateral LB films patterning using the approaches of soft-gel lithography [31], immobilization of active molecules in mesh matrices [32], development of miniature chemical sensors [33][34][35], and development of optical and electronic nanodevices [36][37][38].

Certain originality is possessed by recent works on the development of sensors (test strips) based on LB films for visual determination of Cd2+ cations [39,40]. Owing to high extinction of the ligands, already a 16-dye monolayer with the protective polymer layer provides sufficient sensitivity for determination of cadmium cation with the unaided eye. Nevertheless, the problem of obtaining high-quality LB films from nodular molecules remains rather acute. The ease of formation of multilayer highly ordered LB films from classical amphipilic molecules does not also guarantee obtaining a similar structure for amphipilic molecules of complex structure. This in full measure also concerns the ligands studied in this work.

Variation in wide limits of various parameters responsible for obtaining films of the С12 ligand did not lead to development of stable organized multilayer systems (Table 1). The main fault of the obtained LB films is their partial washing away when they are conditioned in water or aqueous solutions of metal salts.

One must note that, despite the higher stability of monolayers on the water surface, the above regularities of their organization determined by the ligand structure did not allow obtaining multilayer films on solid substrates with the required level of organization. Monolayer transfer coefficient () varied in wide limits and in the case of the substrates movement above the  value were higher than in the case of its immersion into the subphase. The LB films quality could be improved when not pure-ligand monolayers were transferred, but those of its complex with mercury cations, which caused enhancement of the compactness and a decrease in the mobility of polar nodes. Ultimately, the transfer coefficient of monolayers of the complex increased by at least 50%. The further operation regarding dissociation of complexes carried out by the conditioning of LB films in an acidic solution (НСl) provided recovery of the ligand efficiency. However, this procedure resulted in the washing away of a considerable amount of film from the substrate surface.

Transition from С12 to more lipophilic ligands С18 allowed significantly enhancing the stability of LB films with respect to washing. The method of spectrophotometry allowed establishing that, in the case of the С12 ligand, up to 50% of LB films is washed away from the quartz surface after 20 s of conditioning in water, while only 20% and 24% of C18 and N12 LB films is washed away in this time.

Enhanced stability of multilayer LB films of С18 produces a positive effect also on the operation of the solid-state film sensor based on this ligand. As seen in Fig. 11, the rate of the washing away of the film formed by the С18 ligand is much lower than that in the case of a short-chain counterpart. The detection limit of copper cations by LB films based on the С12 and С18 ligands is 10 -7 M, which is for 100 times higher than the detection limit of mercury cations by monolayers of ligands on the air/water interface (10 -5 M). Therefore, using ligands with elevated lipophilicity allowed enhancing stability and sensitivity of LB films.

CONCLUSIONS

This work presents an original approach to obtaining highly sensitive ultrathin film sensors relies on molecular design of surface-active modular molecules from a signal anthraquinone block, hydrophobic radicals, and polar receptor groups, the number and size of which being configured in accordance with the sensor type. This approach was employed to develop a series of chromophoric receptor molecules of different lipophilicity (HLB) that are used to obtain sensitive and selective planar elements for optical sensors.

Complexing properties of amphiphilic ligands of a new family in the Langmuir monolayer have been studied in detail. The mechanism of interaction between cations and the sublayer of receptor groups has been suggested on the basis of compression isotherms and the data of fiberoptic spectroscopy. Selectivity of ligands with respect to mercury and copper cations has been shown.

Sensor characteristics of multilayer Langmuir-Blodgett films on the quartz surface have been studied; it is shown that their sensitivity with respect to metal cations is two orders of magnitude higher than for the liquid counterparts. An increase in lipophilicity of the ligands allowed enhancing the stability of operation of sensors in aqueous media.

Thus, new amphipilic anthraquinone derivatives have been used to developed highperformance selective liquid and solid-state film sensors for determination of mercury and copper cations in aqueous solutions.

Figure

  Figure 1a shows compression isotherms of monolayers of three ligands С12, С18, and N12 on the surface of water (pH 5.5). The analysis of compression isotherms of these polyfunctional molecules is expedient to carry out taking into account the influence of each of the three modules: (1) Hydrophobic (hydrocarbon chains), (2) Signal (planar anthraquinone fragment, more hydrophobic than hydrophilic), and (3). Polar (one or two hydrophilic chains of branched [(acetylamino)methyl]diethoxyphosphoryl groups.

Fig. 1 .

 1 Fig. 1. (a) Compression isotherms of monolayers of three ligands С12, С18, and N12 deposited on а water surface. (b) Scheme explaining lower surface areas occupied by the monolayer of

Figure

  Figure3ademonstrates the effect of the compression degree (a surface density) of the monolayer on a pure water surface on the intensity and position of the electronic spectrum of the ligand. One can see that, when the density of the C12 ligand monolayer increases in the course of its compression, only the intensity of the absorption band increases and the position of max = 560 nm remains unchanged. Let us note that max coincides with the position of this band in the spectrum of the С12 solution in water. First, this indicates the absence of aggregation of С12 in the monolayer even at high surface concentrations and, secondly, to the correctness of the suggested organization of ligand monolayers (Figs.1b, 2c), according to which signal groups of ligand molecules in both systems are in close contact with the aqueous phase. The same is indicated by the large value of the monolayer area in the condensed region, which is almost three times higher than the calculated area for the edge-on anthraquinone fragment (or two hydrocarbon chains) and is by 30-40% greater than the face-on positioned anthraquinone part of the molecule.

Fig. 2 .

 2 Fig. 2. (a) Compression isotherms of monolayers of three ligands, C12, C18, and N12, deposited on а 1 mM Hg(ClO4)2 aqueous solution. (b) Compression isotherms of monolayers of the С12 ligand deposited on a Hg(ClO4)2 aqueous solution of different concentration. (c)

Fig. 3 .

 3 Fig. 3. Effect of the surface pressure on the in situ electronic-absorption spectra of the С12 ligand monolayer deposited on (a) а water surface and (b) on а 1 mM Hg(ClO4)2 aqueous solution. Surface pressure of monolayer (a): (1) 5, (2) 10, (3) 20, (4) 25, (5) 30 mN/m. Surface

Fig. 4 .

 4 Fig. 4. In situ electronic-absorption spectra of the C12 ligand monolayer (a) (1, 2) deposited on a water surface, (3-8) after addition of the Hg(ClO4)2 salt (1 mM) into the subphase. Surface pressure of monolayer (a): (1) 5, (2) 12.5, (3) 12.5, (4) 15, (5) 20, (6) 35, (7) 50, (8) 42 mN/m. (b) Shift of the electronic-absorption spectra of the C12 ligand monolayer at an increase in the monolayer conditioning time on the surface of 0.01 mM Hg(ClO4)2 solution from 5 to 20 min,  = 10 mN/m.

Fig. 5 .

 5 Fig. 5. In situ electronic-absorption spectra of a monolayer of the C18 ligand (1, 2) deposited on a water surface and (3-5) on the surface of the aqueous 1 mM solution of the Hg(ClO4)2 salt. Surface pressure of the monolayer: (1) 5, (2) 12.5, (3) 12.5, (4) 20, (5) 30 mN/m.

Fig. 6 .

 6 Fig. 6. Compression isotherms of N12 monolayers deposited on a pure water surface (N12) and on a 1 mM aqueous solution of Cu(ClO4)2 and Hg(ClO4)2.

Fig. 7 .Scheme 2 .

 72 Fig. 7. In situ electronic-absorption spectra of a monolayer of the N12 ligand (1, 2) deposited on a water surface and on the surface of the water subphase containing (a) 1 mM Cu(ClO4)2 solution or (b) 1 mM Hg(ClO4)2 solution. Surface pressure of monolayer (a): (1) 5, (2) 10, (3) 10, (4) 25, (5) 40 mN/m. Surface pressure of monolayer (b): (1) 5, (2) 10, (3) 10, (4) 15, (5) 30 mN/m.

Fig. 8 .

 8 Fig. 8. In situ electronic-absorption spectra of a monolayer of the С12 ligand (1) deposited on the surface of pure water before and after sequential addition of transition metal cations, [M 2+ ] = 1 mM: (2) Cu 2+ + Pb 2+ + Cd 2+ + Ca 2+ ; (3) Cu 2+ + Pb 2+ + Cd 2+ + Ca 2+ + Hg 2+ at the constant surface pressure value of 10 mN/m.

Fig. 9 .

 9 Fig. 9. In situ electronic-absorption spectra of a monolayer of the N12 ligand (1) deposited on the surface of pure water before and after sequential addition of transition metal cations, [M 2+ ] = 1 mM: (a) (2) Pb 2+ + Cd 2+ + Ca 2+ , (3) Pb 2+ + Cd 2+ + Ca 2+ + Cu 2+ , (4) Pb 2+ + Cd 2+ + Ca 2+ + Cu 2+ + Hg 2+ ; (b) (2) Pb 2+ + Cd 2+ + Ca 2+ , (3) Pb 2+ + Cd 2+ + Ca 2+ + Hg 2+ , (4) Pb 2+ + Cd 2+ + Ca 2+ + Hg 2+ + Cu 2+ at the constant surface pressure value of 10 mN/m.

Fig. 10 .

 10 Fig. 10. Regeneration of the N12-Hg complex in the monolayer deposited on a water surface: (1) N12 monolayer on the surface of water, (2) in the presence of mercury cations (1 mM) in the subphase, (3) dissociation of the complex after acidification with HCl (0.1 М, pН 2), (4) neutralization of the subphase by NaOH (0.1 М, pН 5.5) resulting in reduction of the complex.

20 Fig. 11 .

 2011 Fig. 11. Electronic-absorption spectra of multilayer LB films on the surface of quartz. (a) С12 (18 layers) and (b) С18 (10 layers). (1) LB films of ligands; LB films of ligands conditioned in 0.1 mM in aqueous Hg(ClО4)2 solution for (2) 10 and (3) 20 s. Transfer pressure: 20 mN/m.

ACKNOWLEDGMENTS

This work was supported by the Russian Foundation for Basic Research (projects n° 16-29-05272 and 17-53-16018) and Program I.8 P of the Presidium of the Russian Academy of Sciences.