Events & Talks

Perceiving Systems Talk Timo Bolkart 09-06-2016 Dynamic and Groupwise Statistical Analysis of 3D Faces The accurate reconstruction of facial shape is important for applications such as telepresence and gaming. It can be solved efficiently with the help of statistical shape models that constrain the shape of the reconstruction. In this talk, several methods to statistically analyze static and dynamic 3D face data are discussed. When statistically analyzing faces, various challenges arise from noisy, corrupt, or incomplete data. To overcome the limitations imposed by the poor data quality, we leverage redundancy in the data for shape processing. This is done by processing entire motion seq...

Autonomous Motion Talk Christian Ebenbauer 08-06-2016 Extremum Seeking Control: Theory and Applications in Multi-Agent Systems In many control applications it is the goal to operate a dynamical system in an optimal way with respect to a certain performance criterion. In a combustion engine, for example, the goal could be to control the engine such that the emissions are minimized. Due to the complexity of an engine, the desired operating point is unknown or may even change over time so that it cannot be determined a priori. Extremum seeking control is a learning-control methodology to solve such kind of control problems. It is a model-free method that optimizes the steady-state behavior of a dynamical syste... Sebastian Trimpe

Max Planck Lecture Professor Naomi Ehrich Leonard 06-06-2016 On the Nonlinear Dynamics of Collective Decision-Making in Nature and Design The successful deployment of complex, multi-agent systems requires well-designed, agent-level control strategies that accommodate sensing, communication, and computational limitations on individual agents.

Talk Georg Martius 31-05-2016 Self-organization of behavior in autonomous robot development I am studying the question how robots can autonomously develop skills. Considering children, it seems natural that they have their own agenda. They explore their environment in a playful way, without the necessity for somebody to tell them what to do next. With robots the situation is different. There are many methods to let robots learn to do something, but it is always about learning to do a specific task from a supervision signal. Unfortunately, these methods do not scale well to systems with many degrees of freedom, except a good prestructuring is available. The hypothesis is t... Jane Walters

Autonomous Motion IS Colloquium Angela Schoellig 25-04-2016 Safe Learning Control for Mobile Robots In the last decade, there has been a major shift in the perception, use and predicted applications of robots. In contrast to their early industrial counterparts, robots are envisioned to operate in increasingly complex and uncertain environments, alongside humans, and over long periods of time. In my talk, I will argue that machine learning is indispensable in order for this new generation of robots to achieve high performance. Based on various examples (and videos) ranging from aerial-vehicle dancing to ground-vehicle racing, I will demonstrate the effect of robot learning, and hi... Sebastian Trimpe

Perceiving Systems Talk Cordelia Schmid 21-04-2016 Pose-based human action recognition. In this talk we present some recent results on human action recognition in videos. We, first, show how to use human pose for action recognition. To this end we propose a new pose-based convolutional neural network descriptor for action recognition, which aggregates motion and appearance information along tracks of human body parts. Next, we present an approach for spatio-temporal action localization in realistic videos. The approach first detects proposals at the frame-level and then tracks high-scoring proposals in the video. Our tracker relies simultaneously on instance-level and class-le...

Perceiving Systems Talk Gül Varol 12-04-2016 Long-term Temporal Convolutions for Action Recognition Typical human actions such as hand-shaking and drinking last several seconds and exhibit characteristic spatio-temporal structure. Recent methods attempt to capture this structure and learn action representations with convolutional neural networks. Such representations, however, are typically learned at the level of single frames or short video clips and fail to model actions at their full temporal scale. In this work we learn video representations using neural networks with long-term temporal convolutions. We demonstrate that CNN models with increased temporal extents improve the accuracy ...

Perceiving Systems Talk Helge Rhodin 08-04-2016 Ray Tracing for Computer Vision Proper handling of occlusions is a big challenge for model based reconstruction, e.g. for multi-view motion capture a major difficulty is the handling of occluding body parts. We propose a smooth volumetric scene representation, which implicitly converts occlusion into a smooth and differentiable phenomena (ICCV2015). Our ray tracing image formation model helps to express the objective in a single closed-form expression. This is in contrast to existing surface(mesh) representations, where occlusion is a local effect, causes non-differentiability, and is difficult to optimize. We demon...

Perceiving Systems Talk Aamir Ahmad 05-04-2016 Multirobot Cooperative State Estimation - towards Scalability and Active Perception The core focus of my research is on robot perception. Within this broad categorization, I am mainly interested in understanding how teams of robots and sensors can cooperate and/or collaborate to improve the perception of themselves (self-localization) as well as their surroundings (target tracking, mapping, etc.). In this talk I will describe the inter-dependencies of such perception modules and present state-of-the-art methods to perform unified cooperative state estimation. The trade-off between accuracy of estimation and computational speed will be highlighted through a new optimization...

Perceiving Systems Talk Valsamis Ntouskos 04-04-2016 Regularization and Statistical Inverse Problems in Shape and Motion Modeling Modeling and reconstruction of shape and motion are problems of fundamental importance in computer vision. Inverse Problem theory constitutes a powerful mathematical framework for dealing with ill-posed problems as the ones typically arising in shape and motion modeling. In this talk, I will present methods inspired by Inverse Problem theory, for dealing with four different shape and motion modeling problems. In particular, in the context of shape modeling, I will present a method for component-wise modeling of articulated objects and its application in computing 3D models of anim...

Optics and Sensing Laboratory Talk Eric Price 10-03-2016 Computer Vision on UAVs – practical considerations Computer vision on flying robots - or UAVs - brings its own challenges, especially if conducted in real time. On-board processing is limited by tight weight and size constraints for the electronics while off-board processing is challenged by signal delays and connection quality, especially considering the data rates required for high fps high resolution video. Unlike ground based vehicles, precision odometry is unavailable. Positional information is provided by GPS, which can have signal losses and limited precision, especially near terrain. Exact orientation can be even more problematic du... Alina Allakhverdieva

Empirical Inference IS Colloquium Catrin Misselhorn 07-03-2016 How to Implement Moral Capacities in Autonomous Artificial Systems? Theoretical Foundations and a Roadmap for a Geriatric Care Robot The development of increasingly intelligent and autonomous technologies will inevitably lead to these systems having to face morally problematic situations. This is particularly true of artificial systems that are used in geriatric care environments. It will, therefore, be necessary in the long run to develop machines which have the capacity for a certain amount of autonomous moral decision-making. The goal of this talk is to provide the theoretical foundations for artificial morality, i.e., for implementing moral capacities in artificial systems in general and a roadmap for developing an a... Ludovic Righetti Philipp Hennig

Perceiving Systems Talk Lars Mescheder 03-03-2016 From image restoration to image understanding Inverse problems are ubiquitous in image processing and applied science in general. Such problems describe the challenge of computing the parameters that characterize a system from the outcomes. While this might seem easy at first for simple systems, many inverse problems share a property that makes them much more intricate: they are ill-posed. This means that either the problem does not have a unique solution or this solution does not depend continuously on the outcomes of the system. Bayesian statistics provides a framework that allows to treat such problems in a systematic way. The missi...

Empirical Inference Talk Sascha Quantz 01-03-2016 Images of planets orbiting other stars The detection and characterization of planets orbiting other stars than the Sun, i.e., so-called extrasolar planets, is one of the fastest growing and most vibrant research fields in modern astrophysics. In the last 25 years, more than 5400 extrasolar planets and planet candidates were revealed, but the vast majority of these objects was detected with indirect techniques, where the existence of the planet is inferred from periodic changes in the light coming from the central star. No photons from the planets themselves are detected. In this talk, however, I will focus on the direct detectio...

Perceiving Systems Talk Helga Griffiths 24-02-2016 Interaction of Science and Art In general Helga Griffiths is a Multi-Sense-Artist working on the intersection of science and art. She has been working for over 20 years on the integration of various sensory stimuli into her “multi-sense” installations. Typical for her work is to produce a sensory experience to transcend conventional boundaries of perception. Emma-Jayne Holderness

Autonomous Motion Talk Felix Berkenkamp 23-02-2016 Safe Bayesian Optimization: From Safe Parameter Optimization to the Exploration of Unknown Environments Bayesian optimization is a powerful tool that has been successfully used to automatically optimize the parameters of a fixed control policy. It has many desirable properties, such as data-efficiently and being able to handle noisy measurements. However, standard Bayesian optimization does not consider any constraints imposed by the real system, which limits its applications to highly controlled environments. In this talk, I will introduce an extension of this framework, which additionally considers multiple safety constraints during the optimization process. This method enables safe... Sebastian Trimpe

Empirical Inference IS Colloquium Aldo Faisal 25-01-2016 What can we learn if we record the complete perception and action of a person? Our research questions are centred on a basic characteristic of human brains: variability in their behaviour and their underlying meaning for cognitive mechanisms. Such variability is emerging as a key ingredient in understanding biological principles (Faisal, Selen & Wolpert, 2008, Nature Rev Neurosci) and yet lacks adequate quantitative and computational methods for description and analysis. Crucially, we find that biological and behavioural variability contains important information that our brain and our technology can make us of (instead of just averaging it away): Using advanced body... Matthias Hohmann

Empirical Inference IS Colloquium Tim Sullivan 11-01-2016 Probabilistic Numerics for Differential Equations Beginning with a seminal paper of Diaconis (1988), the aim of so-called "probabilistic numerics" is to compute probabilistic solutions to deterministic problems arising in numerical analysis by casting them as statistical inference problems. For example, numerical integration of a deterministic function can be seen as the integration of an unknown/random function, with evaluations of the integrand at the integration nodes proving partial information about the integrand. Advantages offered by this viewpoint include: access to the Bayesian representation of prior and posterior uncertaintie... Philipp Hennig

Autonomous Motion Talk Jun Nakanishi 01-12-2015 Motor Learning and Control from Dynamical Systems Based Approach and Optimal Control Understanding the principles of natural movement generation has been and continues to be one of the most interesting and important open problems in the fields of robotics and neural control of movement. In this talk, I introduce an overview of our previous work on the control of dynamic movements in robotic systems towards the goal of control design principles and understanding of motion generation. Our research has focused in the fields of dynamical systems theory, adaptive and optimal control and statistical learning, and their application to robotics towards achieving dynamically... Ludovic Righetti

Event 30-11-2015 Max Planck ETH Center for Learning Systems Inauguration Learning systems are part of our everyday life, either as software in internet search as well as in image recognition or as physical systems such as robot vacuum cleaners and autonomous vehicles. The Max Planck ETH Center for Learning Systems promotes leading experts as well as junior scientists in the interdisciplinary, pioneering research field of learning systems. It establishes a centre of excellence offering a unique platform for scientific networking and research into novel technologies at the science and technology hub in Baden-Wuerttemberg and Switzerland. Jane Walters Matthias Tröndle Claudia Daefler

Empirical Inference IS Colloquium Gernot Müller-Putz 23-11-2015 Towards Non-Invasive EEG-based Neuroprosthesis Control in Spinal Cord Injury More than half of the persons with spinal cord injuries (SCI) are suffering from impairments of both hands, which results in a tremendous decrease of quality of life and represents a major barrier for inclusion in society. Functional restoration is possible with neuroprostheses (NPs) based on functional electrical stimulation (FES). A Brain-Computer Interface provides a means of control for such neuroprosthetics since users have limited abilities to use traditional assistive devices. This talk presents our early research on BCI-based NP control based on motor imagery, discusses hybrid BCI s... Moritz Grosse-Wentrup

Autonomous Motion Talk Alexander Sprowitz 23-11-2015 Control and design of very dynamic legged robots inspired from biomechanical and neurocontrol studies The current performance gap between legged animals and legged robots is large. Animals can reach high locomotion speed in complex terrain, or run at a low cost of transport. They are able to rapidly sense their environment, process sensor data, learn and plan locomotion strategies, and execute feedforward and feedback controlled locomotion patterns fluently on the fly. Animals use hardware that has, compared to the latest man-made actuators, electronics, and processors, relatively low bandwidth, medium power density, and low speed. The most common approach to legged robot locomotion... Ludovic Righetti

Autonomous Motion IS Colloquium Prof. Pieter Abbeel 13-11-2015 Making Robots Learn Programming robots remains notoriously difficult. Equipping robots with the ability to learn would by-pass the need for what often ends up being time-consuming task specific programming. In this talk I will describe the ideas behind two promising types of robot learning: First I will discuss apprenticeship learning, in which robots learn from human demonstrations, and which has enabled autonomous helicopter aerobatics, knot tying, basic suturing, and cloth manipulation. Then I will discuss deep reinforcement learning, in which robots learn through their own trial and error, and which has ... Stefan Schaal

Workshop 11-11-2015 - 13-11-2015 Learning Control Workshop (Max Planck ETH Center for Learning Systems) We are pleased to announce the First Max Planck ETH Workshop on Learning Control within the Max Planck ETH Center for Learning Systems. The workshop will take place November 11-13 2015 at the Max Planck Institute for Intelligent Systems (MPI-IS) in Tübingen. We cordially invite all researchers from ETH Zürich and MPI-IS interested in the area of Learning Control to participate and actively contribute to this workshop. Sebastian Trimpe Ludovic Righetti Melanie Zeilinger

Talk Prof. David W. Jacobs 10-11-2015 Understanding Plants and Animals I will describe a series of work that aims to automatically understand images of animals and plants. I will begin by describing recent work that uses Bounded Distortion matching to model pose variation in animals. Using a generic 3D model of an animal and multiple images of different individuals in various poses, we construct a model that captures the way in which the animal articulates. This is done by solving for the pose of the template that matches each image while simultaneously solving for the stiffness of each tetrahedron of the model. We minimize an L1 norm on stiffness, produci... Stephan Streuber

Perceiving Systems Talk Prof. David W. Jacobs 10-11-2015 Understanding Plants and Animals I will describe a series of work that aims to automatically understand images of animals and plants. I will begin by describing recent work that uses Bounded Distortion matching to model pose variation in animals. Using a generic 3D model of an animal and multiple images of different individuals in various poses, we construct a model that captures the way in which the animal articulates. This is done by solving for the pose of the template that matches each image while simultaneously solving for the stiffness of each tetrahedron of the model. We minimize an L1 norm on stiffness, produci... Stephan Streuber

Perceiving Systems Talk Olga Diamanti 28-10-2015 Design of Tangent Vector-Set Fields using Polynomials The design of tangent vector fields on discrete surfaces is a basic building block for many geometry processing applications, such as surface remeshing, parameterization and architectural geometric design. Many applications require the design of multiple vector fields (vector sets) coupled in a nontrivial way; for example, sets of more than two vectors are used for meshing of triangular, quadrilateral and hexagonal meshes. In this talk, a new, polynomial-based representation for general unordered vector sets will be presented. Using this representation we can efficiently interpolate user pr... Gerard Pons-Moll

IS Colloquium Jonas Richiardi 19-10-2015 Imaging genomics of functional brain networks Moritz Grosse-Wentrup Michel Besserve

Empirical Inference IS Colloquium Jonas Richiardi 19-10-2015 Imaging genomics of functional brain networks During rest, brain activity is intrinsically synchronized between different brain regions, forming networks of coherent activity. These functional networks (FNs), consisting of multiple regions widely distributed across lobes and hemispheres, appear to be a fundamental theme of neural organization in mammalian brains. Despite hundreds of studies detailing this phenomenon, the genetic and molecular mechanisms supporting these functional networks remain undefined. Previous work has mostly focused on polymorphisms in candidate genes, or used a twin study approach to demonstrate heritability... Moritz Grosse-Wentrup Michel Besserve

Perceiving Systems Talk Max Welling 19-10-2015 Learning to generate The recent amazing success of deep learning has been mainly in discriminative learning, that is, classification and regression. An important factor for this success has been, besides Moore's law, the availability of large labeled datasets. However, it is not clear whether in the future the amount of available labels grows as fast as the amount of unlabeled data, providing one argument to be interested in unsupervised and semi-supervised learning. Besides this there are a number of other reasons why unsupervised learning is still important, such as the fact that data in the life sciences ... Peter Vincent Gehler

IS Colloquium Vladimir Vapnik 12-10-2015 Intelligent Learning Michel Besserve

Autonomous Motion Talk Yasemin Bekiroglu 12-10-2015 Shape and Stability Estimation based on Learning from Visual and Tactile Data Unknown information required to plan grasps such as object shape and pose needs to be extracted from the environment through sensors. However, sensory measurements are noisy and associated with a degree of uncertainty. Furthermore, object parameters relevant to grasp planning may not be accurately estimated, e.g., friction and mass. In real-world settings, these issues can lead to grasp failures with serious consequences. I will talk about learning approaches using real sensory data, e.g., visual and tactile, to assess grasp success (discriminative and generative) that can be used to trigge... Jeannette Bohg

Empirical Inference Talk Gael Varoquaux 09-10-2015 Using machine learning to understand cognition from brain images Moritz Grosse-Wentrup

Talk Robin Evans 29-09-2015 Causal Models and How to Refute Them Directed acyclic graph models (DAG models, also called Bayesian networks) are widely used in the context of causal inference, and they can be manipulated to represent the consequences of intervention in a causal system. However, DAGs cannot fully represent causal models with confounding; other classes of graphs, such as ancestral graphs and ADMGs, have been introduced to deal with this using additional kinds of edge, but we show that these are not sufficiently rich to capture the range of possible models. In fact, no mixed graph over the observed variables is rich enough, regardless of how ... Sabrina Rehbaum

Empirical Inference IS Colloquium Sach Mukherjee 28-09-2015 High-dimensional statistical approaches for personalized medicine Human diseases show considerable heterogeneity at the molecular level. Such heterogeneity is central to personalized medicine efforts that seek to exploit molecular data to better understand disease biology and inform clinical decision making. An emerging notion is that diseases and disease subgroups may differ not only at the level of mean molecular abundance, but also with respect to patterns of molecular interplay. I will discuss our ongoing efforts to develop methods to investigate such heterogeneity, with an emphasis on some high-dimensional aspects. Michel Besserve Jonas Peters

Autonomous Motion Talk Anna Belardinelli 25-09-2015 Action in the eye of the beholder: anticipatory gaze strategies for manual object interaction Our eyes typically anticipate the next action module in a sequence, by targeting the relevant object for the following step. Yet, how the final goal, or the way we intend to achieve it, is reflected in the early visual exploration of each object has been less investigated. In a series of experiments we considered how scan paths on real-world objects would be affected by different factors such as task, object orientation, familiarity, or low-level saliency, hence revealing which components can account for fixation target selection during eye-hand coordination. In each experiment, the fixatio... Jeannette Bohg

Perceiving Systems Talk Lilla LoCurto and Bill Outcalt 21-09-2015 "Artist" Talk Lilla and Bill are two returning artists to Perceiving Systems. Their talk will update us on the exciting projects that they’ve been involved with since their last visit and to present some of their current plans that will unfold during the week (Sept 21st - 25th). They will be joining our department and working with professional dancers in the 4D scanner as part of an art project on mental health. In general, Lilla and Bill have been using 3D captures as an artistic tool to visualize the human body in a contemporary form for some time. They produce marionettes or avatars which can be se... Emma-Jayne Holderness

Talk Utkan Demirci 18-09-2015 Micro- and nano-scale technologies for applications in medicine and biology

Talk Iain D. Couzin 11-09-2015 Collective Sensing and Decision-Making in Animal Groups: From Fish Schools to Primate Societies Jane Walters

Perceiving Systems Talk Irfan Essa 10-09-2015 Data-Driven Methods for Video Analysis and Enhancement In this talk, I will start with describing the pervasiveness of image and video content, and how such content is growing with the ubiquity of cameras. I will use this to motivate the need for better tools for analysis and enhancement of video content. I will start with some of our earlier work on temporal modeling of video, then lead up to some of our current work and describe two main projects. (1) Our approach for a video stabilizer, currently implemented and running on YouTube, and its extensions. (2) A robust and scaleable method for video segmentation. I will describe, in some deta... Naejin Kong

Perceiving Systems Talk Sergi Rocamora 08-09-2015 Bayesian Image-Based Rendering and Application to Stereoscopic Cinema and 3DTV Optics with long focal length have been extensively used for shooting 2D cinema and television, either to virtually get closer to the scene or to produce an aesthetical effect through the deformation of the perspective. However, in 3D cinema or television, the use of long focal length either creates a ``cardboard effect'' or causes visual divergence. To overcome this problem, state-of-the-art methods use disparity mapping techniques, which is a generalization of view interpolation, and generate new stereoscopic pairs from the two image sequences. We propose to use more than two cameras to s...

Perceiving Systems Talk Darren Cosker 02-09-2015 Applying Computer Vision and Graphics Research in Visual Effects and Entertainment The visual effects and entertainment industries are now a fundamental part of the computer graphics and vision landscapes - as well as impacting across society in general. One of the issues in this area is the creation of realistic characters, creating assets for production, and improving work-flow. Advances in computer graphics, vision and rendering have underlined much of the success of these industries, built on top of academic advances. However, there are still many unsolved problems. In this talk I will outline some of the challenges we have faced in crossing over academic research i... Silvia Zuffi

Perceiving Systems Talk Bojan Pepik 01-09-2015 Towards Richer Object Representations for Object Class Detection in Real World Images Current object class detection methods typically target 2D bounding box localization, encouraged by benchmark data sets, such as Pascal VOC. While this seems suitable for the detection of individual objects, higher-level applications, such as autonomous driving and 3D scene understanding, would benefit from more detailed and richer object hypotheses. In this talk I will present our recent work on building more detailed object class detectors, bridging the gap between higher level tasks and state-of-the-art object detectors. I will present a 3D object class detection method that can reliably...

Perceiving Systems Talk Luca del Pero 26-08-2015 Articulated motion discovery using pairs of trajectories Most computer vision systems cannot take advantage of the abundance of Internet videos as training data. This is because current methods typically learn under strong supervision and require expensive manual annotations. (e.g. videos need to be temporally trimmed to cover the duration of a specific action, object bounding boxes, etc.). In this talk, I will present two techniques that can lead to learning the behavior and the structure of articulated object classes (e.g. animals) from videos, with as little human supervision as possible. First, we discover the characteristic motion patterns o... Laura Sevilla

Optics and Sensing Laboratory Talk Felipe Guzman 29-07-2015 Novel optical sensing technologies Coherent light enables optical measurements of exquisite sensitivity, advancing technologies for improved sensing and autonomous systems. From my previous work on gravitational physics, I will present a brief overview on technologies for laser-interferometric gravitational-wave observatories, particularly within the scope of the European mission LISA Pathfinder, to be launched at the end 2015. In addition, I will talk about my current work in novel and highly compact optomechanical systems and photonic crystals, optical micro-resonators with sensitivities below femtometer levels, as ... Senya Polikovsky

Empirical Inference IS Colloquium Kevin T. Kelly 27-07-2015 New Foundations for Ockham’s Razor in Statistical Inductive Inference, with Applications to Causal Discovery from Non-experimental Data In machine learning, the standard explanation of Ockham's razor is to minimize predictive risk. But prediction is interpreted passively---one may not rely on predictions to change the probability distribution used for training. That limitation may be overcome by studying alternatively manipulated systems in randomized experimental trials, but experiments on multivariate systems or on human subjects are often infeasible or immoral. Happily, the past three decades have witnessed the development of a range of statistical techniques for discovering causal relations from non-experimental dat... Michel Besserve Kun Zhang

Symposium 24-07-2015 Günter Petzow Colloquium (interesting speakers and talks - mostly in German) Seit 2002 veranstaltet das Institut am Standort Stuttgart ein wissenschaftliches Kolloquium, das der Kontaktpflege mit den Alumni und Freunden des Instituts dient. Wir bitten um Anmeldung bis 30. Juni 2015, entweder per Post oder unter: www.is.mpg.de/gpk2015

Talk Valentin Volchkov 16-07-2015 (Matter) Waves in disordered media The propagation of waves in inhomogeneous media is a vast subject, spanning many different research communities. The ability of waves to interfere leads to the celebrated phenomenon of Anderson localization. Constructive interference increases the probability of return and therefore it can reduce or even cancel the propagation in a disordered medium. Anderson localization was first predicted for electrons in 'dirty' condensed matter systems, very soon however, it was generalized to all kind of waves and has been studied since with light, microwaves, ultrasound, and ultra cold atoms. Here... Senya Polikovsky

Empirical Inference Conference 13-07-2015 - 24-07-2015 MLSS 2015 - Machine Learning Summer School 2015 in Tübingen MLSS's are a renowned venue for graduate students, researchers, and professionals. They offer an opportunity to learn about fundamental and advanced aspects of machine learning, data analysis and inference, from intellectual leaders of the field. <br> In the summer of 2015 the MLSS will make its fourth appearance in Tübingen. Michael Hirsch Philipp Hennig Bernhard Schölkopf

Symposium 12-07-2015 Symposium on Intelligent Systems in Science and Industry (SISSI) Symposium on Intelligent Systems / Alumni Meeting of MPI-IS: Claudia Daefler Matthias Tröndle

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