Publications

2024

• Subverting or preserving the institution: Competing IT firm and foundation discourses about open source
  
  • Muselli Laure
  • O'Neil Mathieu
  • Pailler Fred
  • Zacchiroli Stefano
  New Media and Society, SAGE Publications, 2024. The data economy depends on digital infrastructure produced in self-managed projects and communities. To understand how information technology (IT) firms communicate to a volunteer workforce, we examine IT firm and foundation employee discourses about open source. We posit that organizations employ rhetorical strategies to advocate for or resist changing the meaning of this institution. Our analysis of discourses collected at three open source professional conferences in 2019 is complemented by computational methods, which generate semantic clusters from presentation summaries. In terms of defining digital infrastructure, business models, and the firm-community relationship, we find a clear division between the discourses of large firm and consortia foundation employees, on one hand, and small firm and non-profit foundation employees, on the other. These divisions reflect these entities’ roles in the data economy and levels of concern about predatory “Big Tech” practices, which transform common goods to be shared into proprietary assets to be sold. (10.1177/14614448231222249)
  DOI : 10.1177/14614448231222249
• Comment les biais cognitifs affectent la prise de décision assistée par l'IA explicable
  
  • Belloum Rafik
  • Bertrand Astrid
  • Eagan James R.
  • Maxwell Winston
  , 2024. This paper summarizes a literature review on cognitive biases influencing XAI-assisted decision-making. It goes beyond mere identification of cognitive biases in XAI, providing a heuristic map, guiding the future development of XAI systems that are more attuned to human cognitive processes. This map contributes to the evolution of the XAI field by emphasizing alignment with how individuals comprehend and use explanations provided by AI systems.
• An Information Theoretic Condition for Perfect Reconstruction
  
  • Delsol Idris
  • Rioul Olivier
  • Béguinot Julien
  • Rabiet Victor
  • Souloumiac Antoine
  Entropy, MDPI, 2024, 26 (1), pp.86. A new information theoretic condition is presented for reconstructing a discrete random variable X based on the knowledge of a set of discrete functions of X. The reconstruction condition is derived from Shannon’s 1953 lattice theory with two entropic metrics of Shannon and Rajski. Because such a theoretical material is relatively unknown and appears quite dispersed in different references, we first provide a synthetic description (with complete proofs) of its concepts, such as total, common, and complementary information. The definitions and properties of the two entropic metrics are also fully detailed and shown to be compatible with the lattice structure. A new geometric interpretation of such a lattice structure is then investigated, which leads to a necessary (and sometimes sufficient) condition for reconstructing the discrete random variable X given a set {X1,…,Xn} of elements in the lattice generated by X. Intuitively, the components X1,…,Xn of the original source of information X should not be globally “too far away” from X in the entropic distance in order that X is reconstructable. In other words, these components should not overall have too low of a dependence on X; otherwise, reconstruction is impossible. These geometric considerations constitute a starting point for a possible novel “perfect reconstruction theory”, which needs to be further investigated and improved along these lines. Finally, this condition is illustrated in five specific examples of perfect reconstruction problems: the reconstruction of a symmetric random variable from the knowledge of its sign and absolute value, the reconstruction of a word from a set of linear combinations, the reconstruction of an integer from its prime signature (fundamental theorem of arithmetic) and from its remainders modulo a set of coprime integers (Chinese remainder theorem), and the reconstruction of the sorting permutation of a list from a minimal set of pairwise comparisons. (10.3390/e26010086)
  DOI : 10.3390/e26010086
• Bidding efficiently in Simultaneous Ascending Auctions using Monte Carlo Tree Search
  
  • Pacaud Alexandre
  , 2024. Since its introduction in 1994 in the United States, the Simultaneous Ascending Auction (SAA) has become the privileged mechanism for spectrum auctions. As sometimes billions of euros are at stake in an SAA, and a mobile operator’s business plan highly depends on the auction outcome, establishing an efficient bidding strategy is crucial. Despite the importance of this problem, there is a lack of research dedicated to developing an efficient bidding strategy for the SAA. The intrinsic complexity of the SAA makes its analysis very challenging for auction theory and exact game resolution methods. Additionally, the mechanism introduces strategical issues such as the exposure problem, adding an extra layer of complexity to its study.This thesis proposes the use of Monte Carlo Tree Search (MCTS) to compute an efficient bidding strategy for the SAA. The six chapters of the thesis are structured as follows. The first chapter introduces spectrum auction mechanisms, highlighting their pros and cons. The second chapter details the bidding problem in the SAA, along with relevant related research.The third chapter provides a summary of adversarial search methods, with a specific focus on MCTS. Chapters four to six are dedicated to developing an efficient MCTS bidding strategy for the SAA. The fourth chapter considers a turn-based deterministic model of the SAA with perfect and complete information. Numerical experiments are only undertaken on small instances.The fifth chapter considers a n-player simultaneous move model of SAA with incomplete information. Extensive numerical experiments are undertaken on instances of realistic size. The sixth chapter extends the preceding game to incomplete information to introduce uncertainties. For each model, an algorithm that significantly outperforms state-of-the-art bidding strategies is proposed, notably by better tackling the exposure problem. Moreover, a final price prediction method is developed throughout the chapters, upon which each MCTS algorithm relies.
• TD2: Source and detection in quantum communications
  
  • Fabre N
  , 2024.
• Teleportation of polarized single photon states
  
  • Fabre N.
  , 2024.
• Le théorème d’échantillonnage... de Shannon ?
  
  • Rioul Olivier
  , 2024. Le théorème d'échantillonnage, souvent appelé théorème de Shannon, constitue une des bases du domaine du traitement de l'information. Mais Shannon lui-même ne s'en attribue pas le mérite et effectivement, on le retrouve sous une forme ou une autre dans de nombreux travaux antérieurs. Cet article nous permet de remonter le temps aux sources de ce théorème, aussi bien chez les ingénieurs que les mathématiciens.
• Exploiting temporal information to detect conversational groups in videos and predict the next speaker
  
  • Tosato Lucrezia
  • Fortier Victor
  • Bloch Isabelle
  • Pelachaud Catherine
  Pattern Recognition Letters, Elsevier, 2024, 177, pp.164-168. Studies in human-human interaction have introduced the concept of F-formation to describe the spatial arrangement of participants during social interactions. This paper has two objectives. It aims at detecting F-formations in video sequences and at predicting the next speaker in a group conversation. The proposed approach exploits time information and multimodal signals of humans in video sequences. In particular, we rely on measuring the engagement level of people as a feature of group belonging. Our approach makes use of a recursive neural network, the Long Short Term Memory (LSTM), to predict who will take the speaker's turn in a conversation group. Experiments on the MatchNMingle dataset led to 85% true positives in group detection and 98% accuracy in predicting the next speaker. (10.1016/j.patrec.2023.10.002)
  DOI : 10.1016/j.patrec.2023.10.002
• Ausgewählte Themen des Malliavin-Kalküls
  
  • Decreusefond Laurent
  , 2024. Dieses Buch ist keine Forschungsmonographie zum Malliavin-Kalkül mit neuesten Ergebnissen und besonders anspruchsvollen Beweisen. Es enthält nicht alle Ergebnisse, die für die behandelten grundlegenden Themen bekannt sind. Das Ziel ist vielmehr, eine möglichst große Vielfalt an Beweistechniken zu bieten. Zum Beispiel haben wir uns nicht auf den Beweis der Konzentrationsungleichung für Funktionale der Brownschen Bewegung konzentriert, da er sich eng an das analoge Ergebnis für Poisson-Funktionale anlehnt. Dieses Buch ist aus den Graduiertenkursen entstanden, die ich in den letzten Jahren an den Universitäten Paris-Sorbonne und Paris-Saclay gehalten habe. Es soll so zugänglich wie möglich für Studierende sein, die über Kenntnisse der Itô-Kalkulation und einige Grundlagen der Funktionalanalysis verfügen. Die Übersetzung wurde mit Hilfe von künstlicher Intelligenz durchgeführt. Eine anschließende menschliche Überarbeitung erfolgte vor allem in Bezug auf den Inhalt.
• On the importance of wind predictions in wake steering optimization
  
  • Kadoche Elie
  • Bianchi Pascal
  • Carton Florence
  • Ciblat Philippe
  • Ernst Damien
  Wind Energy Science, Göttingen Copernicus Publications, 2024, pp.1-27. Abstract. Wake steering is a technique that optimises the energy production of a wind farm by employing yaw control to misalign upstream turbines with the incoming wind direction. This work highlights the important dependence between wind direction variations and wake steering optimization. The problem is formalized over time as the succession of independent and steady-state yaw control problems. Then, this work proposes a reformulation of each steady-state problem by augmenting the objective function by a new heuristic based on a wind prediction. The heuristic acts as a penalization for the optimization, encouraging solutions that will guarantee future energy production. Finally, a synthetic sensibility analysis of the wind direction variations and wake steering optimization is conducted. Because of the rotational constraints of the turbines, as the magnitude of the wind direction fluctuations increases, the importance of considering wind prediction in a steady-state optimization is empirically demonstrated. The heuristic proposed in this work greatly improves the performance of controllers and compared to a model predictive control (MPC) approach, it does not increase complexity. (10.5194/wes-2023-172)
  DOI : 10.5194/wes-2023-172
• Source-Guided Similarity Preservation for Online Person Re-Identification
  
  • Rami Hamza
  • Giraldo Jhony H.
  • Winckler Nicolas
  • Lathuilière Stéphane
  , 2024, pp.1700-1709. Online Unsupervised Domain Adaptation (OUDA) for person Re-Identification (Re-ID) is the task of continuously adapting a model trained on a well-annotated source-domain dataset to a target domain observed as a data stream. In OUDA, person Re-ID models face two main challenges: catastrophic forgetting and domain shift. In this work, we propose a new Source-guided Similarity Preservation (S2P) framework to alleviate these two problems. Our framework is based on the extraction of a support set composed of source images that maximizes the similarity with the target data. This support set is used to identify feature similarities that must be preserved during the learning process. S2P can incorporate multiple existing UDA methods to mitigate catastrophic forgetting. Our experiments show that S2P outperforms previous state-of-the-art methods on multiple real-to-real and synthetic-to-real challenging OUDA benchmarks. (10.1109/WACV57701.2024.00173)
  DOI : 10.1109/WACV57701.2024.00173
• Mini but Mighty: Finetuning ViTs with Mini Adapters
  
  • Marouf Imad Eddine
  • Tartaglione Enzo
  • Lathuilière Stéphane
  , 2024, pp.1721-1730. Vision Transformers (ViTs) have become one of the dominant architectures in computer vision, and pre-trained ViT models are commonly adapted to new tasks via fine-tuning. Recent works proposed several parameter-efficient transfer learning methods, such as adapters, to avoid the prohibitive training and storage cost of finetuning. In this work, we observe that adapters perform poorly when the dimension of adapters is small, and we propose MiMi, a training framework that addresses this issue. We start with large adapters which can reach high performance, and iteratively reduce their size. To enable automatic estimation of the hidden dimension of every adapter, we also introduce a new scoring function, specifically designed for adapters, that compares the neuron importance across layers. Our method outperforms existing methods in finding the best trade-off between accuracy and trained parameters across the three dataset benchmarks DomainNet, VTAB, and Multi-task, for a total of 29 datasets. (10.1109/WACV57701.2024.00175)
  DOI : 10.1109/WACV57701.2024.00175
• On Ranking-based Tests of Independence
  
  • Limnios Myrto
  • Clémençon Stéphan
  , 2024. In this paper we develop a novel nonparametric framework to test the independence of two random variables $\mathbf{X}$ and $\mathbf{Y}$ with unknown respective marginals $H(dx)$ and $G(dy)$ and joint distribution $F(dx dy)$, based on {\it Receiver Operating Characteristic} (ROC) analysis and bipartite ranking. The rationale behind our approach relies on the fact that, the independence hypothesis $\mathcal{H}_0$ is necessarily false as soon as the optimal scoring function related to the pair of distributions $(H\otimes G,\; F)$, obtained from a bipartite ranking algorithm, has a ROC curve that deviates from the main diagonal of the unit square. We consider a wide class of rank statistics encompassing many ways of deviating from the diagonal in the ROC space to build tests of independence. Beyond its great flexibility, this new method has theoretical properties that far surpass those of its competitors. Nonasymptotic bounds for the two types of testing errors are established. From an empirical perspective, the novel procedure we promote in this paper exhibits a remarkable ability to detect small departures, of various types, from the null assumption $\mathcal{H}_0$, even in high dimension, as supported by the numerical experiments presented here.
• A Gaussian Process Based Approach for Validation of Multi-Variable Measurement Systems: Application to SAR Measurement Systems
  
  • Bujard Cédric
  • Neufeld Esra
  • Douglas Mark
  • Wiart Joe
  • Kuster Niels
  IEEE Access, IEEE, 2024, 12, pp.60404-60424. Resource-efficient and robust validation of systems designed to measure a multi-dimensional parameter space is an unsolved problem as it would require millions of test permutations for comprehensive validation coverage. In the paper, an efficient and comprehensive validation approach based on a Gaussian Process (GP) model of the test system has been developed that can operate system-agnostically, avoids calibration to a fixed set of known validation benchmarks, and supports large configuration spaces. The approach consists of three steps that can be performed independently by different parties: 1) GP model creation, 2) model confirmation, and 3) targeted search for critical cases. It has been applied to two systems that measure specific absorption rate (SAR) for compliance testing of wireless devices and apply different SAR measurement methods: a probe-scanning system (per IEC/IEEE 62209–1528), and a static sensor-array system (per IEC 62209–3). The results demonstrate that the approach is practical, feasible, suitable for proving effective equivalence, and can be applied to any measurement method and implementation. The presented method is sufficiently general to be of value not only for SAR system validation, but also in a wide variety of applications that require critical, independent, and efficient validation. (10.1109/ACCESS.2024.3393778)
  DOI : 10.1109/ACCESS.2024.3393778
• MALLIAVIN STRUCTURE FOR CONDITIONALLY INDEPENDENT RANDOM VARIABLES
  
  • Decreusefond Laurent
  • Vuong Christophe
  , 2024. On any denumerable product of probability spaces, we extend the discrete Malliavin structure for conditionally independent random variables. As a consequence, we obtain the chaos decomposition for functionals of conditionally independent random variables. We also show how to derive some concentration results in that framework. The Malliavin-Stein method yields Berry-Esseen bounds for U-Statistics of such random variables. It leads to quantitative statements of conditional limit theorems: Lyapunov's central limit theorem, De Jong's limit theorem for multilinear forms. The latter is related to the fourth moment phenomenon. The final application consists of obtaining the rates of normal approximation for subhypergraph counts in random exchangeable hypergraphs including the Erdös-Rényi hypergraph model. The estimator of subhypergraph counts is an example of homogeneous sums for which we derive a new decomposition that extends the Hoeffding decomposition.
• Check-Bit Region Exploration in Two-Dimensional Error Correction Codes
  
  • Freitas David
  • Mota David
  • Coelho David
  • Fontinele Humberto
  • Coelho Alexandre
  • Silveira Jarbas
  • Naviner Lirida
  • Mota João
  • Marcon César
  IEEE Access, IEEE, 2024, 12, pp.131830-131841. The diversity of nanosatellite applications is increasingly attracting the scientific community’s attention. The main component of these satellites is the OnBoard Computer (OBC), which is responsible for all control and processing. Also, OBC encompasses memory elements highly susceptible to failure; due to spatial radiation, errors in these memories can cause severe damage. As integrated circuit technology advances, cluster errors are more and more frequent. Error Correction Code (ECC) is one of the most used techniques for mitigating errors, and two-dimensional ECCs are used to reach higher error correction power. The paper aims to assess the number of checkbit regions to include for code enhancement. Our analysis investigates the impact of incorporating up to three checkbit regions. The results are analyzed through adjacent and exhaustive error injection tests and compared to other ECCs. Besides, reliability, redundancy, and hardware implementation costs are investigated, and an evaluation metric is proposed to choose the best ECC. Experiments with random error patterns show that the proposal with three crossed check-bit regions achieves a correction of 100% for up to four bitflips and greater than 90% for up to seven bitflips. Additionally, considering adjacent error patterns, the proposal achieves a correction greater than 97.4% with up to five bitflips. (10.1109/ACCESS.2024.3456582)
  DOI : 10.1109/ACCESS.2024.3456582
• Coarse Ricci curvature of quantum channels
  
  • Gao Li
  • Rouzé Cambyse
  Journal of Functional Analysis, Elsevier, 2024, 286 (8), pp.110336. Following Ollivier's work [60], we introduce the coarse Ricci curvature of a quantum channel as the contraction coefficient of non-commutative metrics on the state space. These metrics are defined as a non-commutative transportation cost in the spirit of [41], [40], which gives a unified approach to different quantum Wasserstein distances in the literature. We prove that the coarse Ricci curvature lower bound and its dual gradient estimate, under suitable assumptions, imply the Poincaré inequality (spectral gap) as well as transportation cost inequalities. Using intertwining relations, we obtain positive coarse Ricci curvature bounds of Gibbs samplers, Bosonic beam-splitters as well as Pauli channels on n-qubits. (10.1016/j.jfa.2024.110336)
  DOI : 10.1016/j.jfa.2024.110336
• New dominating, locating-dominating or identifying codes in the q-ary Lee Hypercube
  
  • Hudry Olivier
  WSEAS Transactions on Mathematics, World Scientific and Engineering Academy and Society (WSEAS), 2024. Let $q$ be an integer and $F_q$ the set $\{0, 1, \ldots , q-1\}$ and let $F_q^n$ be the $q$-ary hypercube of dimension $n$, i.e. the set of vectors whose the $n$ components belong to $F_q$. For $x=(x_1, \ldots ,x_n) \in F_q^n$ and ${y=(y_1, \ldots , y_n) \in F_q^n}$, the {\it Lee distance} between $x$ and $y$ is equal to ${\sum _{i=1}^{n}\min(|x_i-y_i|,q-|x_i-y_i|)}$. Let $C\subseteq F_q^n$; $C$ is called a {\it code}. Given an integer radius $r\geqslant 1$, we consider three types of codes with respect to the Lee distance: an $r$-{\it dominating code} $C$ (also called an $r$-{\it covering code}) is such that any element $x\in F_q^n$ is within distance $r$ from at least one codeword $c\in C$ (then $c$ $r$-{\it dominates}~$x$); an $r$-{\it locating-dominating code} $C$ is (i)~$r$-dominating and (ii)~such that any two elements $x$ and $y$ belonging to $F_q^n \setminus C$ are $r$-dominated by distinct sets of codewords; an $r$-{\it identifying code} $C$ is (i)~$r$-dominating and (ii)~such that any two elements $x$ and $y$ belonging to $F_q^n$ are $r$-dominated by distinct sets of codewords. We look for minimum such codes. We improve the cardinalities of $r$-dominating codes, $r$-locating-dominating codes or $r$-identifying codes of $F_q^n$ for some values of the alphabet size $q\in \{4,5,6\}$, of the dimension $n$ up to~$7$, and the radius $r$ up to~$5$.
• On Iiro Honkala’s contributions to identifying codes
  
  • Hudry Olivier
  • Junnila Ville
  • Lobstein Antoine
  Fundamenta Informaticae, Polskie Towarzystwo Matematyczne, 2024, 191 (3-4), pp.165-196. A set C of vertices in a graph G = (V, E) is an identifying code if it is dominating and any two vertices of V are dominated by distinct sets of codewords. This paper presents a survey of Iiro Honkala's contributions to the study of identifying codes with respect to several aspects: complexity of computing an identifying code, combinatorics in binary Hamming spaces, infinite grids, relationships between identifying codes and usual parameters in graphs, structural properties of graphs admitting identifying codes, and number of optimal identifying codes. (10.3233/FI-242178)
  DOI : 10.3233/FI-242178
• Analyse combinatoire
  
  • Hudry Olivier
  • Charon Irène
  , 2024.
• Diffusive limits of Lipschitz functionals of Poisson measures
  
  • Besançon Eustache
  • Coutin Laure
  • Decreusefond Laurent
  • Moyal Pascal
  The Annals of Applied Probability, Institute of Mathematical Statistics (IMS), 2024, 34 (1A), pp.555-584. Continuous Time Markov Chains, Hawkes processes and many other interesting processes can be described as solution of stochastic differential equations driven by Poisson measures. Previous works, using the Stein's method, give the convergence rate of a sequence of renormalized Poisson measures towards the Brownian motion in several distances, constructed on the model of the Kantorovitch-Rubinstein (or Wasserstein-1) distance. We show that many operations (like time change, convolution) on continuous functions are Lipschitz continuous to extend these quantified convergences to diffuse limits of Markov processes and long-time behavior of Hawkes processes. (10.1214/23-AAP1972)
  DOI : 10.1214/23-AAP1972
• Machine Learning-Driven Low-Complexity Optical Power Optimization for Point-to-Point Links
  
  • Andrenacci Isaia
  • Lonardi Matteo
  • Ramantanis Petros
  • Awwad Élie
  • Irurozki Ekhiñe
  • Clémençon Stephan
  • Serena Paolo
  • Lasagni Chiara
  • Bigo Sébastien
  • Layec Patricia
  , 2024, pp.W2A.19. We propose a strategy to dynamically adjust transmitted power solely based on the analysis of performance fluctuations due to polarization-dependent loss. We show that our method converges faster to optimum compared to a standard approach. (10.1364/OFC.2024.W2A.19)
  DOI : 10.1364/OFC.2024.W2A.19
• HI-AUDIO ONLINE PLATFORM: OPPORTUNITIES AND CHALLENGES OF COLLECTING VARIED MUSIC DATA ON THE WEB
  
  • Gil Panal José Manuel
  • David Aurélien
  • Richard Gael
  , 2024. <div><p>We present in this paper the extended online HI-AUDIO platform which relies on a distributed and iterative music recording paradigm to asynchronously record musicians localised at different remote individual sites. The major goal of this platform is to become a key enabling tool for building a large, varied, multi-genre, multi-track, multiinstrument music dataset, to be ultimately publicly distributed for MIR research purposes. We describe in this paper the main characteristics of the web platform and discuss some of the major challenges for collecting music data on the web. The platform will be demonstrated on site with local and distant access and illustrate its merits for recording collaborative compositions.</p></div>
• Learning quantum many-body systems from a few copies
  
  • Rouzé Cambyse
  • Stilck França Daniel
  Quantum, Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften, 2024, 8, pp.1319. Estimating physical properties of quantum states from measurements is one of the most fundamental tasks in quantum science. In this work, we identify conditions on states under which it is possible to infer the expectation values of all quasi-local observables of a state from a number of copies that scales polylogarithmically with the system's size and polynomially on the locality of the target observables. We show that this constitutes a provable exponential improvement in the number of copies over state-of-the-art tomography protocols. We achieve our results by combining the maximum entropy method with tools from the emerging fields of classical shadows and quantum optimal transport. The latter allows us to fine-tune the error made in estimating the expectation value of an observable in terms of how local it is and how well we approximate the expectation value of a fixed set of few-body observables. We conjecture that our condition holds for all states exhibiting some form of decay of correlations and establish it for several subsets thereof. These include widely studied classes of states such as one-dimensional thermal and high-temperature Gibbs states of local commuting Hamiltonians on arbitrary hypergraphs or outputs of shallow circuits. Moreover, we show improvements of the maximum entropy method beyond the sample complexity that are of independent interest. These include identifying regimes in which it is possible to perform the postprocessing efficiently as well as novel bounds on the condition number of covariance matrices of many-body states. (10.22331/q-2024-04-30-1319)
  DOI : 10.22331/q-2024-04-30-1319
• The European approach to regulating AI through technical standards
  
  • Gornet Mélanie
  • Maxwell Winston
  Internet Policy Review, Alexander von Humboldt Institute for Internet and Society, 2024, 13 (3), pp.1-27. In December 2023, the European institutions reached a political agreement on the AI Act, a new regulation on artificial intelligence. The AI Act will require providers of high-risk AI systems to test their products against harmonised standards (hENs) before affixing a European Conformity (CE) mark to allow AI products to circulate freely on the European market. The CE mark and hENs are long-established European regulatory tools to deal with product safety and already apply to a wide range of products. To date, however, they have never been used to attest to compliance with fundamental rights, something the AI Act aims to achieve. In this article, we examine the role of hENs and CE marking in the AI Act, and how these product safety regulatory techniques have been expanded to cover protection of fundamental rights. We analyse the 5 March 2024 CJEU decision and the respective opinion of the Advocate General in the Public.Resource.Org case which raises questions on democratic processes in standardisation organisations. We show that unlike compliance with product safety norms, compliance with fundamental rights cannot be certified through use of technical standards because violations of rights are too context-specific and require a judicial determination. However, technical standards have an important role to play in encouraging best practices in AI governance. (10.14763/2024.3.1784)
  DOI : 10.14763/2024.3.1784