974 resultados para continuous representations
Resumo:
Two forms of continuity are defined for Pareto representations of preferences. They are designated continuity and coordinate continuity. Characterizations are given of those Pareto representable preferences that are continuously representable and, in dimension two, of those that are coordinate-continuously representable.
Resumo:
Deep belief networks are a powerful way to model complex probability distributions. However, learning the structure of a belief network, particularly one with hidden units, is difficult. The Indian buffet process has been used as a nonparametric Bayesian prior on the directed structure of a belief network with a single infinitely wide hidden layer. In this paper, we introduce the cascading Indian buffet process (CIBP), which provides a nonparametric prior on the structure of a layered, directed belief network that is unbounded in both depth and width, yet allows tractable inference. We use the CIBP prior with the nonlinear Gaussian belief network so each unit can additionally vary its behavior between discrete and continuous representations. We provide Markov chain Monte Carlo algorithms for inference in these belief networks and explore the structures learned on several image data sets.
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Computational research with continuous representations depends on obtaining continuous representations from human labellers. The main method used for that purpose is tracing. Tracing raises a range of challenging issues, both psychological and statistical. Naive assumptions about these issues are easy to make, and can lead to inappropriate requirements and uses. The natural function of traces is to capture perceived affect, and as such they belong in long traditions of research on both perception and emotion. Experiments on several types of material provide information about their characteristics, particularly the ratings on which people tend to agree. Disagreement is not necessarily a problem in the technique. It may correctly show that people’s impressions of emotion diverge more than commonly thought. A new system, Gtrace, is designed to let rating studies capitalise on a decade of experience and address the research questions that are opened up by the data now available.
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RatSLAM is a system for vision-based Simultaneous Localisation and Mapping (SLAM) inspired by models of the rodent hippocampus. The system can produce stable representations of large complex environments during robot experiments in both indoor and outdoor environments. These representations are both topological and metric in nature, and can involve multiple representations of the same place as well as discontinuities. In this paper we describe a new technique known as experience mapping that can be used online with the RatSLAM system to produce world representations known as experience maps. These maps group together multiple place representations and are spatially continuous. A number of experiments have been conducted in simulation and a real world office environment. These experiments demonstrate the high degree to which experience maps are representative of the spatial arrangement of the environment.
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The study of data modelling with elementary students involves the analysis of a developmental process beginning with children’s investigations of meaningful contexts: visualising, structuring, and representing data and displaying data in simple graphs (English, 2012; Lehrer & Schauble, 2005; Makar, Bakker, & Ben-Zvi, 2011). A 3-year longitudinal study investigated young children’s data modelling, integrating mathematical and scientific investigations. One aspect of this study involved a researcher-led teaching experiment with 21 mathematically able Grade 1 students. The study aimed to describe explicit developmental features of students’ representations of continuous data...
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Appearance-based localization can provide loop closure detection at vast scales regardless of accumulated metric error. However, the computation time and memory requirements of current appearance-based methods scale not only with the size of the environment but also with the operation time of the platform. Additionally, repeated visits to locations will develop multiple competing representations, which will reduce recall performance over time. These properties impose severe restrictions on long-term autonomy for mobile robots, as loop closure performance will inevitably degrade with increased operation time. In this paper we present a graphical extension to CAT-SLAM, a particle filter-based algorithm for appearance-based localization and mapping, to provide constant computation and memory requirements over time and minimal degradation of recall performance during repeated visits to locations. We demonstrate loop closure detection in a large urban environment with capped computation time and memory requirements and performance exceeding previous appearance-based methods by a factor of 2. We discuss the limitations of the algorithm with respect to environment size, appearance change over time and applications in topological planning and navigation for long-term robot operation.
Resumo:
Animals repeat rewarded behaviors, but the physiological basis of reward-based learning has only been partially elucidated. On one hand, experimental evidence shows that the neuromodulator dopamine carries information about rewards and affects synaptic plasticity. On the other hand, the theory of reinforcement learning provides a framework for reward-based learning. Recent models of reward-modulated spike-timing-dependent plasticity have made first steps towards bridging the gap between the two approaches, but faced two problems. First, reinforcement learning is typically formulated in a discrete framework, ill-adapted to the description of natural situations. Second, biologically plausible models of reward-modulated spike-timing-dependent plasticity require precise calculation of the reward prediction error, yet it remains to be shown how this can be computed by neurons. Here we propose a solution to these problems by extending the continuous temporal difference (TD) learning of Doya (2000) to the case of spiking neurons in an actor-critic network operating in continuous time, and with continuous state and action representations. In our model, the critic learns to predict expected future rewards in real time. Its activity, together with actual rewards, conditions the delivery of a neuromodulatory TD signal to itself and to the actor, which is responsible for action choice. In simulations, we show that such an architecture can solve a Morris water-maze-like navigation task, in a number of trials consistent with reported animal performance. We also use our model to solve the acrobot and the cartpole problems, two complex motor control tasks. Our model provides a plausible way of computing reward prediction error in the brain. Moreover, the analytically derived learning rule is consistent with experimental evidence for dopamine-modulated spike-timing-dependent plasticity.
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This paper proves a new representation theorem for domains with both discrete and continuous variables. The result generalizes Debreu's well-known representation theorem on connected domains. A strengthening of the standard continuity axiom is used in order to guarantee the existence of a representation. A generalization of the main theorem and an application of the more general result are also presented.
Resumo:
This paper derives exact discrete time representations for data generated by a continuous time autoregressive moving average (ARMA) system with mixed stock and flow data. The representations for systems comprised entirely of stocks or of flows are also given. In each case the discrete time representations are shown to be of ARMA form, the orders depending on those of the continuous time system. Three examples and applications are also provided, two of which concern the stationary ARMA(2, 1) model with stock variables (with applications to sunspot data and a short-term interest rate) and one concerning the nonstationary ARMA(2, 1) model with a flow variable (with an application to U.S. nondurable consumers’ expenditure). In all three examples the presence of an MA(1) component in the continuous time system has a dramatic impact on eradicating unaccounted-for serial correlation that is present in the discrete time version of the ARMA(2, 0) specification, even though the form of the discrete time model is ARMA(2, 1) for both models.
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Models of root system growth emerged in the early 1970s, and were based on mathematical representations of root length distribution in soil. The last decade has seen the development of more complex architectural models and the use of computer-intensive approaches to study developmental and environmental processes in greater detail. There is a pressing need for predictive technologies that can integrate root system knowledge, scaling from molecular to ensembles of plants. This paper makes the case for more widespread use of simpler models of root systems based on continuous descriptions of their structure. A new theoretical framework is presented that describes the dynamics of root density distributions as a function of individual root developmental parameters such as rates of lateral root initiation, elongation, mortality, and gravitropsm. The simulations resulting from such equations can be performed most efficiently in discretized domains that deform as a result of growth, and that can be used to model the growth of many interacting root systems. The modelling principles described help to bridge the gap between continuum and architectural approaches, and enhance our understanding of the spatial development of root systems. Our simulations suggest that root systems develop in travelling wave patterns of meristems, revealing order in otherwise spatially complex and heterogeneous systems. Such knowledge should assist physiologists and geneticists to appreciate how meristem dynamics contribute to the pattern of growth and functioning of root systems in the field.
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[EN]This work presents experimental mixing properties, hEand vE, at several temperatures and the iso-baric vapor–liquid equilibria (iso-p VLE) at 101.32 kPa for four binaries containing pentane and four alkyl(methyl to butyl) methanoates. Particular conditions are established to work with these solutions withhighly volatile compounds, especially for the case of methyl methanoate + pentane system, for whicha continuous feeding device is designed and constructed for measuring the densities.
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We study representations of MV-algebras -- equivalently, unital lattice-ordered abelian groups -- through the lens of Stone-Priestley duality, using canonical extensions as an essential tool. Specifically, the theory of canonical extensions implies that the (Stone-Priestley) dual spaces of MV-algebras carry the structure of topological partial commutative ordered semigroups. We use this structure to obtain two different decompositions of such spaces, one indexed over the prime MV-spectrum, the other over the maximal MV-spectrum. These decompositions yield sheaf representations of MV-algebras, using a new and purely duality-theoretic result that relates certain sheaf representations of distributive lattices to decompositions of their dual spaces. Importantly, the proofs of the MV-algebraic representation theorems that we obtain in this way are distinguished from the existing work on this topic by the following features: (1) we use only basic algebraic facts about MV-algebras; (2) we show that the two aforementioned sheaf representations are special cases of a common result, with potential for generalizations; and (3) we show that these results are strongly related to the structure of the Stone-Priestley duals of MV-algebras. In addition, using our analysis of these decompositions, we prove that MV-algebras with isomorphic underlying lattices have homeomorphic maximal MV-spectra. This result is an MV-algebraic generalization of a classical theorem by Kaplansky stating that two compact Hausdorff spaces are homeomorphic if, and only if, the lattices of continuous [0, 1]-valued functions on the spaces are isomorphic.
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We introduce a type of 2-tier convolutional neural network model for learning distributed paragraph representations for a special task (e.g. paragraph or short document level sentiment analysis and text topic categorization). We decompose the paragraph semantics into 3 cascaded constitutes: word representation, sentence composition and document composition. Specifically, we learn distributed word representations by a continuous bag-of-words model from a large unstructured text corpus. Then, using these word representations as pre-trained vectors, distributed task specific sentence representations are learned from a sentence level corpus with task-specific labels by the first tier of our model. Using these sentence representations as distributed paragraph representation vectors, distributed paragraph representations are learned from a paragraph-level corpus by the second tier of our model. It is evaluated on DBpedia ontology classification dataset and Amazon review dataset. Empirical results show the effectiveness of our proposed learning model for generating distributed paragraph representations.