Publications

2022

• Repeated Augmented Rehearsal : A simple but strong baseline for online continual learning
  
  • Zhang Yaqian
  • Pfahringer Bernhard
  • Frank Eibe
  • Bifet Albert
  • Lim Nick Jin Sean
  • Jia Yunzhe
  , 2022. Online continual learning (OCL) aims to train neural networks incrementally from a non-stationary data stream with a single pass through data. Rehearsal-based methods attempt to approximate the observed input distributions over time with a small memory and revisit them later to avoid forgetting. Despite their strong empirical performance, rehearsal methods still suffer from a poor approximation of past data’s loss landscape with memory samples. This paper revisits the rehearsal dynamics in online settings. We provide theoretical insights on the inherent memory overfitting risk from the viewpoint of biased and dynamic empirical risk minimization, and examine the merits and limits of repeated rehearsal.Inspired by our analysis, a simple and intuitive baseline, repeated augmented rehearsal (RAR), is designed to address the underfitting-overfitting dilemma of online rehearsal. Surprisingly, across four rather different OCL benchmarks,this simple baseline outperforms vanilla rehearsal by 9\%-17\% and also significantly improves the state-of-the-art rehearsal-based methods MIR, ASER, and SCR. We also demonstrate that RAR successfully achieves an accurate approximation of the loss landscape of past data and high-loss ridge aversion in its learning trajectory. Extensive ablation studies are conducted to study the interplay between repeated and augmented rehearsal, and reinforcement learning (RL) is applied to dynamically adjust the hyperparameters of RAR to balance the stability-plasticity trade-off online.
• A proof system for dialogical anaphora resolution
  
  • Catta Davide
  • Moot Richard
  • Retoré Christian
  • Stevens-Guille Symon Jory
  , 2022. We present a proof-theoretic account of anaphora resolution, namely a sequent calculus corresponding to dialogical games where two players argue to find the reference of some anaphor.
• Give Me a Hand: How to Use Model Checking for Multi-Agent Systems to Help Runtime Verification and Vice Versa
  
  • Ferrando Angelo
  • Malvone Vadim
  , 2022.
• Linear TreeShap
  
  • Yu Peng
  • Xu Chao
  • Bifet Albert
  • Read Jesse
  , 2023. Decision trees are well-known due to their ease of interpretability. To improve accuracy, we need to grow deep trees or ensembles of trees. These are hard to interpret, offsetting their original benefits. Shapley values have recently become a popular way to explain the predictions of tree-based machine learning models. It provides a linear weighting to features independent of the tree structure. The rise in popularity is mainly due to TreeShap, which solves a general exponential complexity problem in polynomial time. Following extensive adoption in the industry, more efficient algorithms are required. This paper presents a more efficient and straightforward algorithm: Linear TreeShap. Like TreeShap, Linear TreeShap is exact and requires the same amount of memory.
• A Conditional Randomization Test for Sparse Logistic Regression in High-Dimension
  
  • Nguyen Binh T.
  • Thirion Bertrand
  • Arlot Sylvain
  , 2022, 35. Identifying the relevant variables for a classification model with correct confidence levels is a central but difficult task in high-dimension. Despite the core role of sparse logistic regression in statistics and machine learning, it still lacks a good solution for accurate inference in the regime where the number of features p is as large as or larger than the number of samples n. Here we tackle this problem by improving the Conditional Randomization Test (CRT). The original CRT algorithm shows promise as a way to output p-values while making few assumptions on the distribution of the test statistics. As it comes with a prohibitive computational cost even in mildly high-dimensional problems, faster solutions based on distillation have been proposed. Yet, they rely on unrealistic hypotheses and result in low-power solutions. To improve this, we propose CRT-logit, an algorithm that combines a variable-distillation step and a decorrelation step that takes into account the geometry of $\ell_1$-penalized logistic regression problem. We provide a theoretical analysis of this procedure, and demonstrate its effectiveness on simulations, along with experiments on large-scale brain-imaging and genomics datasets.
• Benchopt: Reproducible, efficient and collaborative optimization benchmarks
  
  • Moreau Thomas
  • Massias Mathurin
  • Gramfort Alexandre
  • Ablin Pierre
  • Bannier Pierre-Antoine
  • Charlier Benjamin
  • Dagréou Mathieu
  • Dupré La Tour Tom
  • Durif Ghislain
  • Dantas Cassio F.
  • Klopfenstein Quentin
  • Larsson Johan
  • Lai En
  • Lefort Tanguy
  • Malézieux Benoit
  • Moufad Badr
  • Nguyen Binh T
  • Rakotomamonjy Alain
  • Ramzi Zaccharie
  • Salmon Joseph
  • Vaiter Samuel
  , 2022. Numerical validation is at the core of machine learning research as it allows to assess the actual impact of new methods, and to confirm the agreement between theory and practice. Yet, the rapid development of the field poses several challenges: researchers are confronted with a profusion of methods to compare, limited transparency and consensus on best practices, as well as tedious re-implementation work. As a result, validation is often very partial, which can lead to wrong conclusions that slow down the progress of research. We propose Benchopt, a collaborative framework to automate, reproduce and publish optimization benchmarks in machine learning across programming languages and hardware architectures. Benchopt simplifies benchmarking for the community by providing an off-the-shelf tool for running, sharing and extending experiments. To demonstrate its broad usability, we showcase benchmarks on three standard learning tasks: ℓ 2-regularized logistic regression, Lasso, and ResNet18 training for image classification. These benchmarks highlight key practical findings that give a more nuanced view of the state-of-the-art for these problems, showing that for practical evaluation, the devil is in the details. We hope that Benchopt will foster collaborative work in the community hence improving the reproducibility of research findings.
• New architecture and function to improve autonomy, dynamicity, and intelligence of future network management
  
  • Saadon Guy
  , 2022. 5G and IoT networks face an explosion in demand, and therefore become more complex and difficult to manage. Automation is limited and human intervention generates errors. On the standardization side, orchestration, SDN controllers, and network virtualization introduce partial dynamicity. On the research side, user centric services require agility and intelligence. However, the orchestration is monolithic. The dynamicity and autonomy relating to “on-demand” are not guaranteed. Thus, after 20 years of experience in the telecom industry, our contributions attempt to meet these new challenges. Our first architectural and organizational proposal introduces a new layer to design and manage virtual services. Our orchestration is distributed over 5 layers to guarantee autonomy and performance. Our second proposal, functional, supported by a simulation, addresses the dynamicity of “ondemand” services. Our last proposal supported by a numerical analysis, is a decision-making function, based on the high-level SLA in order to improve the ratio of allowable services. Faced with these needs of autonomy, dynamicity, and intelligence of the new ecosystem, our research aims at the holy grail of "zero-touch".
• Towards network automation : planning and monitoring
  
  • Foroughi Parisa
  , 2022. Network management is undergoing drastic changes due to the high expectations of the infrastructure to support new services. The diverse requirements of these services, call for the integration of new enabler technologies that complicate the network monitoring and planning process. Therefore, to alleviate the burden and increase the monitoring and planning accuracy, more automated solutions on the element/device level are required. In this thesis, we propose a semi-automated framework called AI-driven telemetry (ADT) for collecting, processing, and assessing the state of routers using streaming telemetry data. ADT consists of 4 building blocks: collector, detector, explainer, and exporter. We concentrate on the detection block in ADT and propose a multi-variate online change detection technique called DESTIN. Our study on the explainer block of ADT is limited to exploring the potential of the input data and showcasing the possibility of the automated event description. Then, we tackle the problem of planning and dimensioning in radio access networks equipped with distributed edge servers. We propose a model that satisfies the service requirements and makes use of novel enabler technologies, i.e. network slicing and virtualization techniques. We showcase the advantages of using our holistic model to automate RAN planning by utilizing simulated annealing and greedy methods.
• Information Removal at the bottleneck in Deep Neural Networks
  
  • Tartaglione Enzo
  , 2022. Deep learning models are nowadays broadly deployed to solve an incredibly large variety of tasks. Commonly, leveraging over the availability of "big data", deep neural networks are trained as black-boxes, minimizing an objective function at its output. This however does not allow control over the propagation of some specific features through the model, like gender or race, for solving some an uncorrelated task. This raises issues either in the privacy domain (considering the propagation of unwanted information) and of bias (considering that these features are potentially used to solve the given task). In this work we propose IRENE, a method to achieve information removal at the bottleneck of deep neural networks, which explicitly minimizes the estimated mutual information between the features to be kept ``private'' and the target. Experiments on a synthetic dataset and on CelebA validate the effectiveness of the proposed approach, and open the road towards the development of approaches guaranteeing information removal in deep neural networks.
• A Survey on Semi-supervised Learning for Delayed Partially Labelled Data Streams
  
  • Gomes Heitor Murilo
  • Grzenda Maciej
  • Mello Rodrigo Fernandes De
  • Read Jesse
  • Nguyen Minh-Huong Le
  • Bifet Albert
  ACM Computing Surveys, Association for Computing Machinery, 2022, 55 (4), pp.Article No.: 75, Pages 1 - 42. Unlabelled data appear in many domains and are particularly relevant to streaming applications, where even though data is abundant, labelled data is rare. To address the learning problems associated with such data, one can ignore the unlabelled data and focus only on the labelled data (supervised learning); use the labelled data and attempt to leverage the unlabelled data (semi-supervised learning); or assume some labels will be available on request (active learning). The first approach is the simplest, yet the amount of labelled data available will limit the predictive performance. The second relies on finding and exploiting the underlying characteristics of the data distribution. The third depends on an external agent to provide the required labels in a timely fashion. This survey pays special attention to methods that leverage unlabelled data in a semi-supervised setting. We also discuss the delayed labelling issue, which impacts both fully supervised and semi-supervised methods. We propose a unified problem setting, discuss the learning guarantees and existing methods, and explain the differences between related problem settings. Finally, we review the current benchmarking practices and propose adaptations to enhance them. (10.1145/3523055)
  DOI : 10.1145/3523055
• Anatomically constrained CT image translation for heterogeneous blood vessel segmentation
  
  • La Barbera Giammarco
  • Boussaid Haithem
  • Maso Francesco
  • Sarnacki Sabine
  • Rouet Laurence
  • Gori Pietro
  • Bloch Isabelle
  , 2022. Anatomical structures such as blood vessels in contrast-enhanced CT (ceCT) images can be challenging to segment due to the variability in contrast medium diffusion. The combined use of ceCT and contrast-free (CT) CT images can improve the segmentation performances, but at the cost of a double radiation exposure. To limit the radiation dose, generative models could be used to synthesize one modality, instead of acquiring it. The CycleGAN approach has recently attracted particular attention because it alleviates the need for paired data that are difficult to obtain. Despite the great performances demonstrated in the literature, limitations still remain when dealing with 3D volumes generated slice by slice from unpaired datasets with different fields of view. We present an extension of CycleGAN to generate high fidelity images, with good structural consistency, in this context. We leverage anatomical constraints and automatic region of interest selection by adapting the Self-Supervised Body Regressor. These constraints enforce anatomical consistency and allow feeding anatomically-paired input images to the algorithm. Results show qualitative and quantitative improvements, compared to stateof-the-art methods, on the translation task between ceCT and CT images (and vice versa).
• Universal aggregation of permutations
  
  • Irurozki Ekhine
  • Clémençon Stéphan
  , 2022. The estimation of the median and mean is a central problem in statistics. When it comes to permutation data the median estimation problem is called aggregation problem. The problem is challenging both computationally and statistically, since provable algorithms are known only for a hand-full of cases. In this paper, we consider the permutation aggregation problem in a general probabilistic setting. This algorithm is given a data-set drawn form a distribution P and a choose for a distance function d and outputs the provably good estimator for the median of P in polynomial time. For the first time, one algorithm can be shown to work for different generating distributions.
• Toward finding best linear codes for side-channel protections (extended version)
  
  • Cheng Wei
  • Liu Yi
  • Guilley Sylvain
  • Rioul Olivier
  Journal of Cryptographic Engineering, Springer, 2022. Side-channel attacks aim at extracting secret keys from cryptographic devices. Randomly masking the implementation is a provable way to protect the secrets against this threat. Recently, various masking schemes have converged to the “code-based masking” philosophy. In code-based masking, different codes allow for different levels of side-channel security. In practice, for a given leakage function, it is important to select the code which enables the best resistance, i.e., which forces the attacker to capture and analyze the largest number of side-channel traces. This paper is a first attempt to address the constructive selection of the optimal codes in the context of side-channel countermeasures, in particular for code-based masking when the device leaks information in the Hamming weight leakage model. We show that the problem is related to the weight enumeration of the extended dual of the masking code. We first present mathematical tools to study those weight enumeration polynomials, and then provide an efficient method to search for good codes, based on a lexicographic sorting of the weight enumeration polynomial from the lowest to highest degrees. (10.1007/s13389-022-00305-x)
  DOI : 10.1007/s13389-022-00305-x
• Free-space laser communications with quantum cascade devices in the thermal-infrared atmospheric window
  
  • Grillot Frederic
  • Didier Pierre
  • Dely Hamza
  • Bonazzi Thomas
  • Spitz Olivier
  • Awwad Elie
  • Rodriguez Etienne
  • Vasanelli Angela
  • Sirtori Carlo
  , 2022, pp.1-2. (10.1109/IPC53466.2022.9975702)
  DOI : 10.1109/IPC53466.2022.9975702
• Intensity noise and nonlinear properties of a hybrid plasmonic distributed feedback laser
  
  • Cui Di
  • Chen J.
  • Huang Heming
  • Ding Shihao
  • Costantini D.
  • Colombelli R.
  • Bousseskou A.
  • Grillot Frédéric
  , 2022, pp.1-2. Intensity and nonlinear properties of a hybrid plasmonic distributed feedback laser is reported. Interestingly, it is found that this laser exhibits a larger oscillation regime under optical feedback along with a sharper intensity noise response. (10.1109/IPC53466.2022.9975539)
  DOI : 10.1109/IPC53466.2022.9975539
• SpecDefender: Transient Execution Attack Defender using Performance Counters
  
  • Choudhari Amit
  • Guilley Sylvain
  • Karray Khaled
  , 2022. Side-channel attacks based on speculative execution have gained enough traction for researchers. This has resulted in the development of more creative variants of Spectre and its defences. However, many of these defence strategies end up making speculative execution or branch prediction ineffective. While these techniques protect the system, they cut down performance by more than 50%. Hence, these solutions cannot be deployed. In this paper, we present a framework that not only protects against different variants of Spectre but also maintains the performance. We prototyped this framework using a novel tool SpecDefender. It leverages Hardware Performance Counter (HPC) registers to dynamically detect active Spectre attacks and performs dynamic instrumentation to defend against them. This makes the tool widely applicable without any need for static analysis. Overall, the tool brings back the balance between performance and security. The tool was evaluated based on its accuracy and precision to detect an attack in different scenarios. It exhibit ¿90% precision when five out of ten processes were simultaneously attacked. The response time for the tool to detect is 2 sec. Furthermore, the throughput of the process under attack was comparable to normal execution in presence of SpecDefender.
• An Information-theoretic approach to integrated sensing and communication
  
  • Ahmadipour Mehrasa
  , 2022. Next-generation wireless networks are expected to support sensing techniques. Important examples are intelligent transport systems, where vehicles continuously sense environmental changes and exchange information with vehicles or central servers. There are some naive solutions to do both tasks which propose to share the resources between the two. But, the high spectrum and hardware costs of these approaches encourage to integrate the sensing and communication (ISAC) tasks via a single waveform and a single hardware platform. This thesis focuses on information-theoretic ISAC. We review the first information-theoretic model for ISAC in [1] where a statedependent memoryless channel (SDMC) with generalized feedback signals observed at the transmitter (Tx). Our first contribution is to characterize the fundamental tradeoff between communication rates and sensing distortion of statedependent single-Tx two-Rx broadcast channels (BC) that are physically degraded. We also provide inner and outer bounds on the achievable rate-distortion tradeoffs for general BCs. The single-Txs’ optimal sensing strategy is a simple symbol-by-symbol estimator and the optimality of this estimator stems from the fact that the generalized feedback channels and the state-sequence both are memoryless. This is not necessarily the case in setups with more than one Tx. Specifically, for the MAC, we propose collaborative sensing where each Tx first compresses the obtained outputs and inputs to extract state information, then transmits the compression index using a pure channel code to the other Tx. Also, we describe two collaborative ISAC schemes for D2D, based on source-channel separation/Han’s two-way channel scheme and based on joint source-channel coding (JSCC). In both the MAC and the D2D scenario, our ISAC schemes are strictly concave in the rate-distortion pairs and thus also improve over classical time- or resource-sharing strategies.
• A Survey on Spatio-temporal Data Analytics Systems
  
  • Alam Md. Mahbub
  • Torgo Luís
  • Bifet Albert
  ACM Computing Surveys, Association for Computing Machinery, 2022, 54 (10s), pp.219:1--219:38. Due to the surge of spatio-temporal data volume, the popularity of location-based services and applications, and the importance of extracted knowledge from spatio-temporal data to solve a wide range of real-world problems, a plethora of research and development work has been done in the area of spatial and spatio-temporal data analytics in the past decade. The main goal of existing works was to develop algorithms and technologies to capture, store, manage, analyze, and visualize spatial or spatio-temporal data. The researchers have contributed either by adding spatio-temporal support with existing systems, by developing a new system from scratch, or by implementing algorithms for processing spatio-temporal data. The existing ecosystem of spatial and spatio-temporal data analytics systems can be categorized into three groups, (1) spatial databases (SQL and NoSQL), (2) big spatial data processing infrastructures, and (3) programming languages and GIS software. Since existing surveys mostly investigated infrastructures for processing big spatial data, this survey has explored the whole ecosystem of spatial and spatio-temporal analytics. This survey also portrays the importance and future of spatial and spatio-temporal data analytics. (10.1145/3507904)
  DOI : 10.1145/3507904
• Which arithmetic operations can be performed in constant time in the RAM model with addition?
  
  • Grandjean Étienne
  • Jachiet Louis
  , 2022.
• Analysis and control of online interactions through neural natural language processing
  
  • Laugier Léo
  , 2022. Natural Language Processing is motivated by applications where computers should gain a semantic and syntactic understanding of human language. Recently, the field has been impacted by a paradigm shift. Deep learning architectures coupled with self-supervised training have become the core of state-of-the-art models used in Natural Language Understanding and Natural Language Generation. Sometimes considered as foundation models, these systems pave the way for novel use cases. Driven by an academic-industrial partnership between the Institut Polytechnique de Paris and Google Ai Research, the present research has focused on investigating how pretrained neural Natural Language Processing models could be leveraged to improve online interactions.This thesis first explored how self-supervised style transfer could be applied to the toxic-to-civil rephrasing of offensive comments found in online conversations. In the context of toxic content moderation online, we proposed to fine-tune a pretrained text-to-text model (T5) with a denoising and cyclic auto-encoder loss. The system, called CAE-T5, was trained on the largest toxicity detection dataset to date (Civil Comments) and generates sentences that are more fluent and better at preserving the initial content compared to earlier text style transfer systems, according to several scoring systems and human evaluation. Plus the approach showed it could be generalized to additional style transfer tasks, such as sentiment transfer.Then, a subsequent work investigated the human labeling and automatic detection of toxic spans in online conversations. Contrary to toxicity detection datasets and models which classify whole posts as toxic or not, toxic spans detection aims at highlighting toxic spans, that is to say the spans that make a text toxic, when detecting such spans is possible. We released a new labeled dataset to train and evaluate systems, which led to a shared task at the 15th International Workshop on Semantic Evaluation. Systems proposed to address the task include strongly supervised models trained using annotations at the span level as well as weakly supervised approaches, known as rationale extraction, using classifiers trained on potentially larger external datasets of posts manually annotated as toxic or not, without toxic span annotations. Furthermore, the ToxicSpans dataset and systems proved useful to analyze the performances of humans and automatic systems on toxic-to-civil rephrasing.Finally, we developed a recommender system based on online reviews of items, taking part in the topic of explaining users' tastes considered by the predicted recommendations. The method uses textual semantic similarity models to represent a user's preferences as a graph of textual snippets, where the edges are defined by semantic similarity. This textual, memory-based approach to rating prediction holds out the possibility of improved explanations for recommendations. The method is evaluated quantitatively, highlighting that leveraging text in this way can outperform both memory-based and model-based collaborative filtering baselines.
• A Nearly Tight Proof of Duc et al.’s Conjectured Security Bound for Masked Implementations
  
  • Masure Loïc
  • Rioul Olivier
  • Standaert François-Xavier
  , 2023, 13820, pp.69-81. We prove a bound that approaches Duc et al.'s conjecture from Eurocrypt 2015 for the side-channel security of masked imple- mentations. Let Y be a sensitive intermediate variable of a cryptographic primitive taking its values in a set Y. If Y is protected by masking (a.k.a. secret sharing) at order d (i.e., with d + 1 shares), then the complexity of any non-adaptive side-channel analysis measured by the number of queries to the target implementation required to guess the secret key with sucient condence is lower bounded by a quantity inversely proportional to the product of mutual informations between each share of Y and their respective leakage. Our new bound is nearly tight in the sense that each factor in the product has an exponent of −1 as conjectured, and its multiplicative constant is O(log |Y| · |Y|−1 · C−d), where C ≤ 2 log(2) ≈ 1.38. It drastically improves upon previous proven bounds, where the exponent was −1/2, and the multiplicative constant was O|Y|−d. As a consequence for side-channel security evaluators, it is possible to provably and eciently infer the security level of a masked implementation by simply analyzing each individual share, under the necessary condition that the leakage of these shares are independent. (10.1007/978-3-031-25319-5_4)
  DOI : 10.1007/978-3-031-25319-5_4
• Reasoning about Moving Target Defense in Attack Modeling Formalisms
  
  • Ballot Gabriel
  • Malvone Vadim
  • Leneutre Jean
  • Borde Etienne
  , 2022, pp.55-65. Since 2009, Moving Target Defense (MTD) has become a new paradigm of defensive mechanism that frequently changes the state of the target system to confuse the attacker. This frequent change is costly and leads to a trade-off between misleading the attacker and disrupting the quality of service. Optimizing the MTD activation frequency is necessary to develop this defense mechanism when facing realistic, multi-step attack scenarios. Attack modeling formalisms based on DAG are prominently used to specify these scenarios. Our contribution is a new DAG-based formalism for MTDs and its translation into a Price Timed Markov Decision Process to find the best activation frequencies against the attacker's time/cost optimal strategies. For the first time, MTD activation frequencies are analyzed in a state-of-the-art DAG-based representation. Moreover, this is the first paper that considers the specificity of MTDs in the automatic analysis of attack modeling formalisms. Finally, we present some experimental results using Uppaal Stratego to demonstrate its applicability and relevance. (10.1145/3560828.3564009)
  DOI : 10.1145/3560828.3564009
• The Net Automaton of a Rational Expression
  
  • Lombardy Sylvain
  • Sakarovitch Jacques
  , 2022, 13568, pp.376-392. In this paper, we present a new construction of a finite automaton associated with a rational (or regular) expression. It is very similar to the one of the so-called Thompson automaton, but it overcomes the failure of the extension of that construction to the case of weighted rational expressions. At the same time, it preserves all (or almost all) of the properties of the Thompson automaton. This construction has two supplementary outcomes. The first one is the reinterpretation in terms of automata of a data structure introduced by Champarnaud, Laugerotte, Ouardi, and Ziadi for the efficient computation of the position (or Glushkov) automaton of a rational expression, and which consists in a duplicated syntactic tree of the expression decorated with some additional links. The second one supposes that this construction devised for the case of weighted expressions is brought back to the domain of Boolean expressions. It allows then to describe, in terms of automata, the construction of the Star Normal Form of an expression that was defined by Brüggemann-Klein, and also with the purpose of an efficient computation of the position automaton. (10.1007/978-3-031-20624-5_23)
  DOI : 10.1007/978-3-031-20624-5_23
• Training Computational Models of Group Processes without Groundtruth: the Self- vs External Assessment's Dilemma
  
  • Maman Lucien
  • Volpe Gualtiero
  • Varni Giovanna
  , 2022.
• Optical Feedback Dynamics in Dual-state Quantum Dot Lasers
  
  • Jin Zhiyong
  • Zhao Shiyuan
  • Huang Heming
  • Grillot Frédéric
  • Xu Xiaochuan
  • Yao Yong
  • Duan Jianan
  , 2022, pp.1548-1550. In this paper, the dynamics of dual-state quantum dot (QD) lasers under external optical feedback are investigated by solving the three-level rate equations in the time domain. The results show that the high excited-to-ground-state (ES-GS) energy separation in QD lasers leads to a high ES-GS threshold ratio hence strengthening the feedback resistance. These findings shed new light on the fabrication of feedback-resistant dual-state QD lasers for isolator-free photonic integrated circuits. (10.1109/ACP55869.2022.10088534)
  DOI : 10.1109/ACP55869.2022.10088534