Importance sampling for stochastic reaction-diffusion equations in the moderate deviation regime

We develop a provably efficient importance sampling scheme that estimates exit probabilities of solutions to small-noise stochastic reaction-diffusion equations from scaled neighborhoods of a stable equilibrium. The moderate deviation scaling allows for a local approximation of the nonlinear dynamics by their linearized version. In addition, we identify a finite-dimensional subspace where exits take place with high probability. Using stochastic control and variational methods we show that our scheme performs well both in the zero noise limit and pre-asymptotically. Simulation studies for stochastically perturbed bistable dynamics illustrate the theoretical results.Comment: Version to appear in Stochastics and Partial Differential Equations: Analysis and Computations. 46 page

Moderate deviations for systems of slow-fast stochastic reaction-diffusion equations

The goal of this paper is to study the Moderate Deviation Principle (MDP) for a system of stochastic reaction-diffusion equations with a time-scale separation in slow and fast components and small noise in the slow component. Based on weak convergence methods in infinite dimensions and related stochastic control arguments, we obtain an exact form for the moderate deviations rate function in different regimes as the small noise and time-scale separation parameters vanish. Many issues that come up due to the infinite dimensionality of the problem are completely absent in their finite-dimensional counterpart. In comparison to corresponding Large Deviation Principles, the moderate deviation scaling necessitates a more delicate approach to establishing tightness and properly identifying the limiting behavior of the underlying controlled problem. The latter involves regularity properties of a solution of an associated elliptic Kolmogorov equation on Hilbert space along with a finite-dimensional approximation argument.First author draf

The Revisiting Problem in Simultaneous Localization and Mapping: A Survey on Visual Loop Closure Detection

Where am I? This is one of the most critical questions that any intelligent system should answer to decide whether it navigates to a previously visited area. This problem has long been acknowledged for its challenging nature in simultaneous localization and mapping (SLAM), wherein the robot needs to correctly associate the incoming sensory data to the database allowing consistent map generation. The significant advances in computer vision achieved over the last 20 years, the increased computational power, and the growing demand for long-term exploration contributed to efficiently performing such a complex task with inexpensive perception sensors. In this article, visual loop closure detection, which formulates a solution based solely on appearance input data, is surveyed. We start by briefly introducing place recognition and SLAM concepts in robotics. Then, we describe a loop closure detection system's structure, covering an extensive collection of topics, including the feature extraction, the environment representation, the decision-making step, and the evaluation process. We conclude by discussing open and new research challenges, particularly concerning the robustness in dynamic environments, the computational complexity, and scalability in long-term operations. The article aims to serve as a tutorial and a position paper for newcomers to visual loop closure detection.Comment: 25 pages, 15 figure

Moderate deviations for systems of slow-fast stochastic reaction-diffusion equations

The goal of this paper is to study the Moderate Deviation Principle (MDP) for a system of stochastic reaction-diffusion equations with a time-scale separation in slow and fast components and small noise in the slow component. Based on weak convergence methods in infinite dimensions and related stochastic control arguments, we obtain an exact form for the moderate deviations rate function in different regimes as the small noise and time-scale separation parameters vanish. Many issues that come up due to the infinite dimensionality of the problem are completely absent in their finite-dimensional counterpart. In comparison to corresponding Large Deviation Principles, the moderate deviation scaling necessitates a more delicate approach to establishing tightness and properly identifying the limiting behavior of the underlying controlled problem. The latter involves regularity properties of a solution of an associated elliptic Kolmogorov equation on Hilbert space along with a finite-dimensional approximation argument

Continuous Emotion Recognition for Long-Term Behavior Modeling through Recurrent Neural Networks

One’s internal state is mainly communicated through nonverbal cues, such as facial expressions, gestures and tone of voice, which in turn shape the corresponding emotional state. Hence, emotions can be effectively used, in the long term, to form an opinion of an individual’s overall personality. The latter can be capitalized on in many human–robot interaction (HRI) scenarios, such as in the case of an assisted-living robotic platform, where a human’s mood may entail the adaptation of a robot’s actions. To that end, we introduce a novel approach that gradually maps and learns the personality of a human, by conceiving and tracking the individual’s emotional variations throughout their interaction. The proposed system extracts the facial landmarks of the subject, which are used to train a suitably designed deep recurrent neural network architecture. The above architecture is responsible for estimating the two continuous coefficients of emotion, i.e., arousal and valence, following the broadly known Russell’s model. Finally, a user-friendly dashboard is created, presenting both the momentary and the long-term fluctuations of a subject’s emotional state. Therefore, we propose a handy tool for HRI scenarios, where robot’s activity adaptation is needed for enhanced interaction performance and safety

Continuous Emotion Recognition for Long-Term Behavior Modeling through Recurrent Neural Networks

One’s internal state is mainly communicated through nonverbal cues, such as facial expressions, gestures and tone of voice, which in turn shape the corresponding emotional state. Hence, emotions can be effectively used, in the long term, to form an opinion of an individual’s overall personality. The latter can be capitalized on in many human–robot interaction (HRI) scenarios, such as in the case of an assisted-living robotic platform, where a human’s mood may entail the adaptation of a robot’s actions. To that end, we introduce a novel approach that gradually maps and learns the personality of a human, by conceiving and tracking the individual’s emotional variations throughout their interaction. The proposed system extracts the facial landmarks of the subject, which are used to train a suitably designed deep recurrent neural network architecture. The above architecture is responsible for estimating the two continuous coefficients of emotion, i.e., arousal and valence, following the broadly known Russell’s model. Finally, a user-friendly dashboard is created, presenting both the momentary and the long-term fluctuations of a subject’s emotional state. Therefore, we propose a handy tool for HRI scenarios, where robot’s activity adaptation is needed for enhanced interaction performance and safety

Workhorse Free Functional Muscle Transfer Techniques for Smile Reanimation in Children with Congenital Facial Palsy: Case Report and Systematic Review of the Literature.

BACKGROUND Pediatric facial palsy represents a rare multifactorial entity. Facial reanimation restores smiling, thus boosting self-confidence and social integration of the affected children. The purpose of this paper is to present a systematic review of microsurgical workhorse free functional muscle transfer procedures with emphasis on the long-term functional, aesthetic, and psychosocial outcomes. MATERIALS AND METHODS We performed a literature search of the PubMed database from 1995 to 2019 using the following search strategy: "facial paralysis"[Title/Abstract] OR "facial palsy"[Title]. We used as limits: full text, English language, age younger than 18 years, and humans. Two independent reviewers performed the online screening process using Covidence. Forty articles met the inclusion criteria. The protocol was aligned with the PRISMA statement (Preferred Reporting Items for Systematic Reviews and Meta-Analyses) and was registered at the International Prospective Register of Systematic Reviews (PROSPERO, CRD42019150112) of the National Institute for Health Research. RESULTS Free functional muscle transfer procedures include mainly segmental gracilis, latissimus dorsi, and pectoralis minor muscle transfer. Facial reanimation procedures with the use of the cross-face nerve graft (CFNG) or masseteric nerve result in almost symmetric smiles. The transplanted muscle grows harmoniously along with the craniofacial skeleton. Muscle function and aesthetic outcomes improve over time. All children presented improved self-esteem, oral commissure opening, facial animation, and speech. CONCLUSIONS A two-stage CFNG plus an FFMT may restore a spontaneous emotive smile in pediatric facial palsy patients. Superior results of children FFMT compared to adults FFMT are probably attributed to greater brain plasticity