Optimization viewpoint on Kalman smoothing, with applications to robust and sparse estimation

In this paper, we present the optimization formulation of the Kalman filtering and smoothing problems, and use this perspective to develop a variety of extensions and applications. We first formulate classic Kalman smoothing as a least squares problem, highlight special structure, and show that the classic filtering and smoothing algorithms are equivalent to a particular algorithm for solving this problem. Once this equivalence is established, we present extensions of Kalman smoothing to systems with nonlinear process and measurement models, systems with linear and nonlinear inequality constraints, systems with outliers in the measurements or sudden changes in the state, and systems where the sparsity of the state sequence must be accounted for. All extensions preserve the computational efficiency of the classic algorithms, and most of the extensions are illustrated with numerical examples, which are part of an open source Kalman smoothing Matlab/Octave package.Comment: 46 pages, 11 figure

Descent algorithm for nonsmooth stochastic multiobjective optimization

International audienceAn algorithm for solving the expectation formulation of stochastic nonsmooth multiobjective optimization problems is proposed. The proposed method is an extension of the classical stochastic gradient algorithm to multi-objective optimization using the properties of a common descent vector defined 10 in the deterministic context. The mean square and the almost sure convergence of the algorithm are proven. The algorithm efficiency is illustrated and assessed on an academic example

Design of a flight control architecture using a non-convex bundle method

We design a feedback control architecture for longitudinal flight of an aircraft. The multi-level architecture includes the flight control loop to govern the short term dynamics of the aircraft, and the autopilot to control the long term modes. Using H1 performance and robustness criteria, the problem is cast as a non-convex and non-smooth optimization program. We present a non-convex bundle method, prove its convergence, and show that it is apt to solve the longitudinal flight control problem

From error bounds to the complexity of first-order descent methods for convex functions

This paper shows that error bounds can be used as effective tools for deriving complexity results for first-order descent methods in convex minimization. In a first stage, this objective led us to revisit the interplay between error bounds and the Kurdyka-\L ojasiewicz (KL) inequality. One can show the equivalence between the two concepts for convex functions having a moderately flat profile near the set of minimizers (as those of functions with H\"olderian growth). A counterexample shows that the equivalence is no longer true for extremely flat functions. This fact reveals the relevance of an approach based on KL inequality. In a second stage, we show how KL inequalities can in turn be employed to compute new complexity bounds for a wealth of descent methods for convex problems. Our approach is completely original and makes use of a one-dimensional worst-case proximal sequence in the spirit of the famous majorant method of Kantorovich. Our result applies to a very simple abstract scheme that covers a wide class of descent methods. As a byproduct of our study, we also provide new results for the globalization of KL inequalities in the convex framework. Our main results inaugurate a simple methodology: derive an error bound, compute the desingularizing function whenever possible, identify essential constants in the descent method and finally compute the complexity using the one-dimensional worst case proximal sequence. Our method is illustrated through projection methods for feasibility problems, and through the famous iterative shrinkage thresholding algorithm (ISTA), for which we show that the complexity bound is of the form $O(q^{k})$ where the constituents of the bound only depend on error bound constants obtained for an arbitrary least squares objective with $\ell^1$ regularization

Role of the mesoamygdaloid dopamine projection in emotional learning

Amygdala dopamine is crucially involved in the acquisition of Pavlovian associations, as measured via conditioned approach to the location of the unconditioned stimulus (US). However, learning begins before skeletomotor output, so this study assessed whether amygdala dopamine is also involved in earlier 'emotional' learning. A variant of the conditioned reinforcement (CR) procedure was validated where training was restricted to curtail the development of selective conditioned approach to the US location, and effects of amygdala dopamine manipulations before training or later CR testing assessed. Experiment 1a presented a light paired (CS+ group) or unpaired (CS- group) with a US. There were 1, 2 or 10 sessions, 4 trials per session. Then, the US was removed, and two novel levers presented. One lever (CR+) presented the light, and lever pressing was recorded. Experiment 1b also included a tone stimulus. Experiment 2 applied intra-amygdala R(+) 7-OH-DPAT (10 nmol/1.0 A mu l/side) before two training sessions (Experiment 2a) or a CR session (Experiment 2b). For Experiments 1a and 1b, the CS+ group preferred the CR+ lever across all sessions. Conditioned alcove approach during 1 or 2 training sessions or associated CR tests was low and nonspecific. In Experiment 2a, R(+) 7-OH-DPAT before training greatly diminished lever pressing during a subsequent CR test, preferentially on the CR+ lever. For Experiment 2b, R(+) 7-OH-DPAT infusions before the CR test also reduced lever pressing. Manipulations of amygdala dopamine impact the earliest stage of learning in which emotional reactions may be most prevalent

Heroes and villains of world history across cultures

© 2015 Hanke et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are creditedEmergent properties of global political culture were examined using data from the World History Survey (WHS) involving 6,902 university students in 37 countries evaluating 40 figures from world history. Multidimensional scaling and factor analysis techniques found only limited forms of universality in evaluations across Western, Catholic/Orthodox, Muslim, and Asian country clusters. The highest consensus across cultures involved scientific innovators, with Einstein having the most positive evaluation overall. Peaceful humanitarians like Mother Theresa and Gandhi followed. There was much less cross-cultural consistency in the evaluation of negative figures, led by Hitler, Osama bin Laden, and Saddam Hussein. After more traditional empirical methods (e.g., factor analysis) failed to identify meaningful cross-cultural patterns, Latent Profile Analysis (LPA) was used to identify four global representational profiles: Secular and Religious Idealists were overwhelmingly prevalent in Christian countries, and Political Realists were common in Muslim and Asian countries. We discuss possible consequences and interpretations of these different representational profiles.This research was supported by grant RG016-P-10 from the Chiang Ching-Kuo Foundation for International Scholarly Exchange (http://www.cckf.org.tw/). Religion Culture Entropy China Democracy Economic histor

Co-ordinated Gene Expression in the Liver and Spleen during Schistosoma japonicum Infection Regulates Cell Migration

Determining the molecular events induced in the spleen during schistosome infection is an essential step in better understanding the immunopathogenesis of schistosomiasis and the mechanisms by which schistosomes modulate the host immune response. The present study defines the transcriptional and cellular events occurring in the murine spleen during the progression of Schistosoma japonicum infection. Additionally, we compared and contrasted these results with those we have previously reported for the liver. Microarray analysis combined with flow cytometry and histochemistry demonstrated that transcriptional changes occurring in the spleen were closely related to changes in cellular composition. Additionally, the presence of alternatively activated macrophages, as indicated by up-regulation of Chi3l3 and Chi3l4 and expansion of F4/80+ macrophages, together with enhanced expression of the immunoregulatory genes ANXA1 and CAMP suggests the spleen may be an important site for the control of S. japonicum-induced immune responses. The most striking difference between the transcriptional profiles of the infected liver and spleen was the contrasting expression of chemokines and cell adhesion molecules. Lymphocyte chemokines, including the homeostatic chemokines CXCL13, CCL19 and CCL21, were significantly down-regulated in the spleen but up-regulated in the liver. Eosinophil (CCL11, CCL24), neutrophil (CXCL1) and monocyte (CXCL14, CCL12) chemokines and the cell adhesion molecules VCAM1, NCAM1, PECAM1 were up-regulated in the liver but unchanged in the spleen. Chemokines up-regulated in both organs were expressed at significantly higher levels in the liver. Co-ordinated expression of these genes probably contributes to the development of a chemotactic signalling gradient that promotes recruitment of effector cells to the liver, thereby facilitating the development of hepatic granulomas and fibrosis. Together these data provide, for the first time, a comprehensive overview of the molecular events occurring in the spleen during schistosomiasis and will substantially further our understanding of the local and systemic mechanisms driving the immunopathogenesis of this disease

Similarities and Differences of the Soleus and Gastrocnemius H-reflexes during Varied Body Postures, Foot Positions, and Muscle Function: Multifactor Designs for Repeated Measures

<p>Abstract</p> <p>Background</p> <p>Although the soleus (Sol), medial gastrocnemius (MG), and lateral gastrocnemius (LG) muscles differ in function, composition, and innervations, it is a common practice is to investigate them as single H-reflex recording. The purpose of this study was to compare H-reflex recordings between these three sections of the triceps surae muscle group of healthy participants while lying and standing during three different ankle positions.</p> <p>Methods</p> <p>The Sol, MG and LG muscles' H-reflexes were recorded from ten participants during prone lying and standing with the ankle in neutral, maximum dorsiflexion, and maximum plantarflexion positions. Four traces were averaged for each combination of conditions. Three-way ANOVAs (posture X ankle position X muscle) with planned comparisons were used for statistical comparisons.</p> <p>Results</p> <p>Although the H-reflex in the three muscle sections differed in latency and amplitude, its dependency on posture and ankle position was similar. The H-reflex amplitudes and maximum H-reflex to M-response (H/M) ratios were significantly 1) lower during standing compared to lying with the ankle in neutral, 2) greater during standing with the ankle in plantarflexion compared to neutral, and 3) less with the ankle in dorsiflexion compared to neutral during lying and standing for all muscles (<it>p </it>≤ .05).</p> <p>Conclusion</p> <p>Varying demands are required for muscles activated during distinctly different postures and ankle movement tasks.</p

Supramolecular heterostructures formed by sequential epitaxial deposition of two-dimensional hydrogen-bonded arrays

Two-dimensional (2D) supramolecular arrays provide a route to the spatial control of the chemical functionality of a surface, but their deposition is in almost all cases limited to a monolayer termination. Here we investigated the sequential deposition of one 2D array on another to form a supramolecular heterostructure and realize the growth—normal to the underlying substrate—of distinct ordered layers, each of which is stabilized by in-plane hydrogen bonding. For heterostructures formed by depositing terephthalic acid or trimesic acid on cyanuric acid/melamine, we have determined, using atomic force microscopy under ambient conditions, a clear epitaxial arrangement despite the intrinsically distinct symmetries and/or lattice constants of each layer. Structures calculated using classical molecular dynamics are in excellent agreement with the orientation, registry and dimensions of the epitaxial layers. Calculations confirm that van der Waals interactions provide the dominant contribution to the adsorption energy and registry of the layers