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Let Ω be a Polish space with Borel σ -field F and countably generated sub σ -field G ⊂ F. Denote by L (F) the set of all bounded F -upper semianalytic functions from Ω to the reals and by L (G) the subset of G -upper semianalytic functions. Let E (⋅ | G) : L (F) → L (G) be a sublinear increasing functional which leaves L (G) invariant. It is shown that there exists a G -analytic set-valued mapping P G from Ω to the set of probabilities which are concentrated on atoms of G with compact convex values such that E (X | G) (ω) = sup P ∈ P G (ω) E P [ X ] if and only if E (⋅ | G) is pointwise continuous from below and continuous from above on the continuous functions. Further, given another sublinear increasing functional E (⋅) : L (F) → R which leaves the constants invariant, the tower property E (⋅) = E (E (⋅ | G)) is characterized via a pasting property of the representing sets of probabilities, and the importance of analytic functions is explained. Finally, it is characterized when a nonlinear version of Fubini's theorem holds true and when the product of a set of probabilities and a set of kernels is compact. [ABSTRACT FROM AUTHOR]

Data-driven soft sensors are crucial for predicting key quality variables in the process industry. In most processes, the dynamic characteristics are obvious, and the relationship between the primary and secondary variables is strongly nonlinear. Moreover, the worst thing is that labeled samples are usually scarce due to certain technical difficulties or measurement costs. To deal with these issues, this paper first proposes a semi-supervised manifold regularization model based on dual representation (SsMRM-DR). Then, a semi-supervised local manifold regularization model based on dual representation (SsLMRM-DR) is further proposed from the viewpoint of local manifold regularization. In the SsLMRM-DR, a space–time weighted similarity calculation method is designed to reduce the influence of measurement noise on similarity calculation. At the same time, a local manifold regularization method is developed to use unlabeled samples more efficiently and to improve the prediction accuracy and computational efficiency of the SsLMRM-DR. A numerical example and a real industrial process are used to evaluate the performance of the proposed schemes. The results show that SsLMRM-DR is effective and it has a good application prospect of soft sensors in the industry. • Temporal regularization methods cannot utilize unlabeled samples efficiently. • Space–time weighted similarity is for space correlations/time series of varaibles. • Local manifold regularization uses unlabeled samples for computational efficiency. • Strong nonlinear and dynamic problems and sample scarcity are solved concurrently. • A semi-supervised local manifold regularization model is proposed. [ABSTRACT FROM AUTHOR]

• To guarantee high fire detection rate, a L0 norm constraint is introduced into the model. • To speed training and reduce error warning rate, L1 norm PreVM and its nonlinear version is also provided. • Theoretically, we prove the existence of dual representation for the general Lp (p>=1) norm regularization problems and the kernelization of L1 norm problem with implicit feature map. • Compared to the state-of-the-art, our proposed PreVMs are superior in fire detection rate, error warning rate, and real-time fire detection. Machine learning-based fire detection/recognition is very popular in forest-monitoring systems. However, without considering the prior knowledge, e.g., equal attention on both classes of the fire and non-fire samples, fire miss-detected phenomena frequently appeared in the current methods. In this work, considering model's interpretability and the limited data for model-training, we propose a novel pixel-precision method, termed as PreVM (Preferred Vector Machine). To guarantee high fire detection rate under precise control, a new L 0 norm constraint is introduced to the fire class. Computationally, instead of the traditional L 1 re-weighted techniques in L 0 norm approximation, this L 0 constraint can be converted into linear inequality and incorporated into the process of parameter selection. To further speed up model-training and reduce error warning rate, we also present a kernel-based L 1 norm PreVM (L 1 -PreVM). Theoretically, we firstly prove the existence of dual representation for the general L p (p ≥ 1) norm regularization problems in RKHS (Reproducing Kernel Hilbert Space). Then, we provide a mathematical evidence for L 1 norm kernelization to conquer the case when feature samples do not appear in pairs. The work also includes an extensive experimentation on the real forest fire images and videos. Compared with the-state-of-art methods, the results show that our PreVM is capable of simultaneously achieving higher fire detection rates and lower error warning rates, and L 1 -PreVM is also superior in real-time detection. [ABSTRACT FROM AUTHOR]

Highlights: [•] Explored 18-month-old infants’ flexibility in categorization across different object representations. [•] Infants completed superordinate and basic-level categorization tasks with 3D replicas, 2D cut out photographs, or 2D images on photo cubes. [•] Categorization processes differ for 3D and 2D stimuli. [•] Discovery of object properties over time while manipulating objects may facilitate categorization at some levels. [•] The findings are discussed in the context of infants’ representation abilities and the integration of perception and action. [Copyright &y& Elsevier]

Abstract: In the Brownian case, the links between dynamic risk measures and BSDEs have been widely studied. In this paper, we consider the case with jumps. We first study the properties of BSDEs driven by a Brownian motion and a Poisson random measure. In particular, we provide a comparison theorem under quite weak assumptions, extending that of Royer [21]. We then give some properties of dynamic risk measures induced by BSDEs with jumps. We provide a representation property of such dynamic risk measures in the convex case as well as some results on a robust optimization problem in the case of model ambiguity. [Copyright &y& Elsevier]

Abstract: One important design decision for the development of autonomously navigating mobile robots is the choice of the representation of the environment. This includes the question of which type of features should be used, or whether a dense representation such as occupancy grid maps is more appropriate. In this paper, we present an approach which performs SLAM using multiple representations of the environment simultaneously. It uses reinforcement to learn when to switch to an alternative representation method depending on the current observation. This allows the robot to update its pose and map estimate based on the representation that models the surrounding of the robot in the best way. The approach has been implemented on a real robot and evaluated in scenarios, in which a robot has to navigate in- and outdoors and therefore switches between a landmark-based representation and a dense grid map. In practical experiments, we demonstrate that our approach allows a robot to robustly map environments which cannot be adequately modeled by either of the individual representations. [Copyright &y& Elsevier]

Abstract: Whenever a functional is concave it is natural to ask whether its sendograph is a closed convex set. If so, the Hahn–Banach theory implies that the functional can be represented as the infimum of all continuous linear functionals greater than or equal to it. We refer to such representation as a dual representation. Dominated convergence of the concave integral for capacities is characterized in terms of dual representation whenever sequences of functions converge pointwise outside a set of zero capacity. [Copyright &y& Elsevier]

Abstract: It is shown that polynomial (or rational) parametric surfaces with a linear field of normal vectors are dual to graphs bivariate polynomials (or rational functions). We discuss the geometric properties of these surfaces. In particular, using the dual representation it is shown that the convolution with general rational surfaces yields again rational surfaces. Similar results hold in the case of curves. [Copyright &y& Elsevier]

Two experiments were conducted to determine whether very young children have difficulty with dual representations when change in perspective has been eliminated, that is, the task no longer requires transfer between a traversable and surveyable array. In a preliminary experiment children 30 and 36 months of age attempted to transfer an action observed with one of four tools associated with a child-size workbench to a miniature replica of that workbench or vice versa. Children at both ages exhibited limited success on both transfer and memory trials; the demands of selecting a tool and transferring the appropriate imitative response were hypothesized to exceed their processing capacity. A second experiment using an object-retrieval procedure involving the two workbenches revealed successful transfer by 36-month-olds, but not 30-month-olds. The results confirm that limitations in dual representation extend to contexts other than the room and model of the room paradigm where spatial perspective differs. The results are discussed in terms of procedures that support or interfere with children’s ability to demonstrate symbolic insight. [Copyright &y& Elsevier]

Abstract: Various theories have been proposed to explain the development and maintenance of post-traumatic stress disorder (PTSD). This article reviews psychological and social theories that have been influential. The most prominent current theories – emotional processing, dual representation, and the cognitive model of PTSD – draw on earlier work, in particular conditioning, information processing, and classical cognitive theory. Psychodynamic and attachment theory have also influenced thinking in this area. The latest theories combine stimulus and response elements with meaning, interpretation, and appraisal; they argue that successful processing depends on being able to access and assimilate new information within pre-existing schemas. Social factors are also recognized as playing a significant role in the development and maintenance of PTSD. These are considered along with the contention that PTSD is a socio-political construct as opposed to a true disease. [Copyright &y& Elsevier]