Probabilistic Mappings Research Articles

Global optimization problem and probabilistic distance

In this article, the probabilistic metric distance between two disjoint sets is utilised to define the essential criteria for the existence and uniqueness of the best proximity point, which takes into account the global optimization problem. In order to solve this problem, we pretend that we are trying to obtain the optimal approximation to the solution of a fixed point equation. Here, we introduce two types of probabilistic proximal contraction mappings and use a geometric property called Ω-property in the context of probabilistic metric spaces. We also obtain some consequences for self-mappings, which give the fixed point results. Some examples are provided to validate the findings. As an application, we obtain the solution to a second-order boundary value problem using a minimum t-norm in the context of probabilistic metric spaces.

Sonification of ocean data in art-science

ArtScience is a burgeoning field that promotes bi-directional collaboration between scientists and artists. Artists learn from scientists to inform the creation of new works based on scientific ideas and data. Scientists learn from artists to explore data in new ways and learn new ways of communicating. In 2022, Colin Malloy was the artist in residence for Ocean Networks Canada and created many new musical works based on ocean data. He explored many ways of sonifying ocean data using novel mappings in multiple original solo electroacoustic percussion compositions. Some mappings were more direct—such as using data for wavetables—while others were less so—such as probabilistic trigger mappings based using datasets as probability distributions. This paper presents his methods for sonifying ocean data used for sound production in these musical compositions.

Small steps for mankind: Modeling the emergence of cumulative culture from joint active inference communication.

Although the increase in the use of dynamical modeling in the literature on cultural evolution makes current models more mathematically sophisticated, these models have yet to be tested or validated. This paper provides a testable deep active inference formulation of social behavior and accompanying simulations of cumulative culture in two steps: First, we cast cultural transmission as a bi-directional process of communication that induces a generalized synchrony (operationalized as a particular convergence) between the belief states of interlocutors. Second, we cast social or cultural exchange as a process of active inference by equipping agents with the choice of who to engage in communication with. This induces trade-offs between confirmation of current beliefs and exploration of the social environment. We find that cumulative culture emerges from belief updating (i.e., active inference and learning) in the form of a joint minimization of uncertainty. The emergent cultural equilibria are characterized by a segregation into groups, whose belief systems are actively sustained by selective, uncertainty minimizing, dyadic exchanges. The nature of these equilibria depends sensitively on the precision afforded by various probabilistic mappings in each individual's generative model of their encultured niche.

Investigating developmental changes in scalp-to-cortex correspondence using diffuse optical tomography sensitivity in infancy.

.Significance: Diffuse optical tomography (DOT) uses near-infrared light spectroscopy (NIRS) to measure changes in cerebral hemoglobin concentration. Anatomical interpretations of NIRS data require accurate descriptions of the cranio-cerebral relations and DOT sensitivity to the underlying cortical structures. Such information is limited for pediatric populations because they undergo rapid head and brain development.Aim: We aim to investigate age-related differences in scalp-to-cortex distance and mapping between scalp locations and cortical regions of interest (ROIs) among infants (2 weeks to 24 months with narrow age bins), children (4 and 12 years), and adults (20 to 24 years).Approach: We used spatial scalp projection and photon propagation simulation methods with age-matched realistic head models based on MRIs.Results: There were age-group differences in the scalp-to-cortex distances in infancy. The developmental increase was magnified in children and adults. There were systematic age-related differences in the probabilistic mappings between scalp locations and cortical ROIs.Conclusions: Our findings have important implications in the design of sensor placement and making anatomical interpretations in NIRS and fNIRS research. Age-appropriate, realistic head models should be used to provide anatomical guidance for standalone DOT data in infants.

State anxiety biases estimates of uncertainty and impairs reward learning in volatile environments

Clinical and subclinical (trait) anxiety impairs decision making and interferes with learning. Less understood are the effects of temporary anxious states on learning and decision making in healthy populations, and whether these can serve as a model for clinical anxiety. Here we test whether anxious states in healthy individuals elicit a pattern of aberrant behavioural, neural, and physiological responses comparable with those found in anxiety disorders—particularly when processing uncertainty in unstable environments. In our study, both a state anxious and a control group learned probabilistic stimulus-outcome mappings in a volatile task environment while we recorded their electrophysiological (EEG) signals. By using a hierarchical Bayesian model of inference and learning, we assessed the effect of state anxiety on Bayesian belief updating with a focus on uncertainty estimates. State anxiety was associated with an underestimation of environmental uncertainty, and informational uncertainty about the reward tendency. Anxious individuals’ beliefs about reward contingencies were more precise (had smaller uncertainty) and thus more resistant to updating, ultimately leading to impaired reward-based learning. State anxiety was also associated with greater uncertainty about volatility. We interpret this pattern as evidence that state anxious individuals are less tolerant to informational uncertainty about the contingencies governing their environment and more willing to be uncertain about the level of stability of the world itself. Further, we tracked the neural representation of belief update signals in the trial-by-trial EEG amplitudes. In control participants, lower-level precision-weighted prediction errors (pwPEs) about reward tendencies were represented in the ERP signals across central and parietal electrodes peaking at 496 ms, overlapping with the late P300 in classical ERP analysis. The state anxiety group did not exhibit a significant representation of low-level pwPEs, and there were no significant differences between the groups. Smaller variance in low-level pwPE about reward tendencies in state anxiety could partially account for the null results. Expanding previous computational work on trait anxiety, our findings establish that temporary anxious states in healthy individuals impair reward-based learning in volatile environments, primarily through changes in uncertainty estimates, which play a central role in current Bayesian accounts of perceptual inference and learning.

Application of non-positional representation of information in the form of probabilistic mappings in control systems of unmanned vehicles

The paper considers the use of non-positional representation of information in the form of probabilistic displays in control systems of unmanned vehicles in order to solve the problem of ensuring the reliability and high bandwidth of information exchange channels (IEC) between unmanned vehicles (UMV) located in different environments and dispatch centers (DC). As shown in the paper, the use of probabilistic representation of information makes it possible to obtain combinations of the main characteristics of UMV control systems that are unattainable in a different form of information representation: speed, accuracy, reliability, and hardware volume.

Diffeological Statistical Models, the Fisher Metric and Probabilistic Mappings

We introduce the notion of a C k -diffeological statistical model, which allows us to apply the theory of diffeological spaces to (possibly singular) statistical models. In particular, we introduce a class of almost 2-integrable C k -diffeological statistical models that encompasses all known statistical models for which the Fisher metric is defined. This class contains a statistical model which does not appear in the Ay–Jost–Lê–Schwachhöfer theory of parametrized measure models. Then, we show that, for any positive integer k , the class of almost 2-integrable C k -diffeological statistical models is preserved under probabilistic mappings. Furthermore, the monotonicity theorem for the Fisher metric also holds for this class. As a consequence, the Fisher metric on an almost 2-integrable C k -diffeological statistical model P ⊂ P ( X ) is preserved under any probabilistic mapping T : X ⇝ Y that is sufficient w.r.t. P. Finally, we extend the Cramér–Rao inequality to the class of 2-integrable C k -diffeological statistical models.

Development of probabilistic inundation mapping for dam failure induced floods

A primary function of flood inundation mapping is to forecast flood hazards and assess potential losses. However, uncertainties limit the reliability of inundation hazard assessments. Major sources of uncertainty should be taken into consideration by an optimal flood management strategy. This study focuses on the 20 km reach downstream of the Shihmen Reservoir in Taiwan. In the modified dam failure model proposed in this study, the surface area of the water in the reservoir and water elevation are allowed to vary with the volume of the reservoir. A dam failure induced flood herein provides the upstream boundary conditions of flood routing. The two major sources of uncertainty that are considered in the hydraulic model and the flood inundation mapping herein are uncertainties in the dam break model and uncertainty of the roughness coefficient. The perturbance moments method is applied to a dam break model and the hydrosystem model to develop probabilistic flood inundation mapping. Uncertain variables such as roughness coefficient, breach width and reservoir surface area can be considered in these models and the variability of outputs can be quantified. The probabilistic flood inundation mapping for dam break induced floods can be developed with consideration of the variability of output using a hydraulic model. Two different probabilistic flood inundation mappings are discussed and compared. Probabilistic flood inundation mappings are hoped to provide improved insights in support of the evaluation of concerning reservoir flooded areas.

Towards A Neurological Model of Giftedness: A Conceptual Perspective

Event Abstract Back to Event Towards A Neurological Model of Giftedness: A Conceptual Perspective Maqsoud Kruse1* 1 British University in Dubai, United Arab Emirates The existing body of research concerning the neuroscience of giftedness is vast, diverse, and spread across the literature in the form of empirical findings of different neuroimaging techniques that attempt to examine a variety of research questions related to the different aspects of giftedness (See for example: Cropley, Westwell, & Gabriel, 2017; Jin et al 2006; Mrazik & Dombrowski, 2010; Shaw et al, 2006; Zhang, Cao, & Shi, 2016; Shen et al, 2018). Despite of all of these empirical findings, however, they tend to be “localized” and “narrow” in which they focus on either a “Technical Procedure” or a specific “Cognitive Function”, or a particular “Manifestation” of the different types of giftedness; and, hence, provide a “partial” and not an “all-inclusive” perspective (See for example: Geake, 2008; Zhang, et al, 2017). The question that presents itself, however, would it be possible to develop a new research direction geared towards the structuring of a novel conceptual model of giftedness based entirely on the analysis of the empirical findings of the neuroimaging research results of giftedness? Hence, attempt to systematically review, synthesize and organize such findings in a holistic, meaningful, and coherent manner that can paint a comprehensive framework towards the potential emergence of a “Neurological Model of Giftedness” (NMG). Unlike previous conceptual models of giftedness that are based - for instance - on psychological, cognitive, psychometric and educational frameworks; the proposed NMG will emerge as a result of a comprehensive Meta-Analysis and Neuroimaging Data Synthesis of existing empirical findings. Thus, create a “Giftedness Neurological Catalogue” (GNC) that can be developed further to produce a “Giftedness Neurological Mapping Guide” (GNMG) that can serve as a foundational text illustrating the “Neurological Terrain of Giftedness” (NTG) in the brain. Such an approach can be “ground breaking” in the sense that it will establish a new conceptual framework that can lead, potentially, to a “Paradigm Shift” - as described by Kuhn (1962) - in the current thinking and direction of mainstream research on giftedness. Consequently, it will provide a conceptual roadmap towards a possible development of a “Metamodel for Giftedness” (MfG) that is capable of explaining and defining the relationship between the different components of the NMG in a similar application of “Metamodeling” in the field of “Systems Engineering” (Garitselov et al, 2012; Sekaran & Bougie, 2010). One important method to conduct such an important research endeavor would be the “NeuroSynth”, in its capacity as “an instrumental step towards automated large-scale synthesis of the neuroimaging literature”, which was developed by Yarkoni, et al (2012, p.2). Moreover, the “NeuroSynth” is an online brain mapping framework that “combines test mining, meta-analysis, and machine learning techniques to generate probabilistic mappings between cognitive and neural states that can be used for a broad range of neuroimaging applications” (Yarkoni et al, 2012, p.2). Furthermore, the framework is based on an automated coordinate extraction from neuroimaging articles that are available in the single largest database containing (3,489) articles and (100, 953) foci (Yarkoni et al, 2012, p.9). Hence, provide a direct access to all existing literature on the neuroscience of giftedness in order to compare, analyze, infer and develop all sorts of conclusions, insights, frameworks and models via a set of sophisticated statistical analyses that are specifically designed to support researchers conducting neuroimaging synthesis research projects (See: http://neurosynth.org). Thus, provide unequivocal access to a systematic method of conducting a comprehensive literature review, conceptual modeling, and structured mapping. In conclusion, the proposed research direction aims at exploring a new approach towards the conceptualization, definition and identification of giftedness based on the advancements of Neuroimaging techniques within the growing hybrid domain of “Mind, Brain and Education” (Fischer, Daniel, Immordino-Yang, Stern, Battro, & Koizumi, 2007; Fischer, Immordino-Yang, & Waber, 2007; Fischer, 2009; Fischer, Goswami, & Geake, 2010; Zadina, 2015). Thus, utilizing the findings of “Educational Neuroscience” to inform the identification process of giftedness in order to insure the highest levels of validity, reliability and achieve trustworthiness in the outcome of the identification process (Carew & Magsamen, 2010; Kruse, 2017; Martin-Loeches, 2015; Stern, 2005). The success of this endeavor will contribute directly to the “Early Identification” of giftedness and at the same time provide a unique opportunity to identify giftedness amongst the “Twice Exceptional” and those whom their ability is masked by their disability. As a result, Neuroimaging will emerge as the prominent method of identification in comparison to current “Giftedness Identification Systems” (GIS’s). Thus, establishing what will be known as the “Neuro Giftedness Identification System” (NGIS) as a “fact-gathering” activity rather than a “theoretical” activity (Kuhn, 1962).

F2ConText: how to extract holistic contexts of persons of interest for enhancing exploratory analysis

A wide variety of publicly available heterogeneous data has provided us with an opportunity to meander through contextual snippets relevant to a particular event or persons of interest. One example of a heterogeneous source is online news articles where both images and text descriptions may co-exist in documents. Many of the images in a news article may contain faces of people. Names of many of the faces may not appear in the text. An expert on the topic may be able to identify people in images or at least recognize the context of the faces who are not widely known. However, it is difficult as well as expensive to employ topic experts of news topics to label every face of a massive news archive. In this paper, we describe an approach named F2ConText that helps analysts build contextual information, e.g., named entity context and geographical context of facial images found within news articles. Our approach extracts facial features of the faces detected in the images of publicly available news articles and learns probabilistic mappings between the features and the contents of the articles in an unsupervised manner. Afterward, it translates the mappings to geographical distributions and generates a contextual template for every face detected in the collection. This paper demonstrates three empirical studies—related to construction of context-based genealogy of events, tracking of a contextual phenomenon over time, and creation of contextual clusters of faces—to evaluate the effectiveness of the generated contexts.

Multivariate predictions of local reduced‐order‐model errors and dimensions

SummaryThis paper introduces multivariate input‐output models to predict the errors and bases dimensions of local parametric Proper Orthogonal Decomposition reduced‐order models. We refer to these mappings as the multivariate predictions of local reduced‐order model characteristics (MP‐LROM) models. We use Gaussian processes and artificial neural networks to construct approximations of these multivariate mappings. Numerical results with a viscous Burgers model illustrate the performance and potential of the machine learning‐based regression MP‐LROM models to approximate the characteristics of parametric local reduced‐order models. The predicted reduced‐order models errors are compared against the multifidelity correction and reduced‐order model error surrogates methods predictions, whereas the predicted reduced‐order dimensions are tested against the standard method based on the spectrum of snapshots matrix. Since the MP‐LROM models incorporate more features and elements to construct the probabilistic mappings, they achieve more accurate results. However, for high‐dimensional parametric spaces, the MP‐LROM models might suffer from the curse of dimensionality. Scalability challenges of MP‐LROM models and the feasible ways of addressing them are also discussed in this study.

The worldly constituents of perceptual presence.

The worldly constituents of perceptual presence.

Convergence of iterative methods for solving random operator equations

We discuss the concept of probabilistic quasi-nonexpansive mappings in connection with the mappings of Nishiura. We also prove a result regarding the convergence of the sequence of successive approximations for probabilistic quasi-nonexpansive mappings.

A diagnoser algorithm for anomaly detection in DEDS under partial and unreliable observations: characterization and inclusion in sensor configuration optimization

Complex engineering systems have to be carefully monitored to meet demanding performance requirements, including detecting anomalies in their operations. There are two major monitoring challenges for these systems. The first challenge is that information collected from the monitored system is often partial and/or unreliable, in the sense that some occurred events may not be reported and/or may be reported incorrectly (e.g., reported as another event). The second is that anomalies often consist of sequences of event patterns separated in space and time. This paper introduces and analyzes a diagnoser algorithm that meets these challenges for detecting and counting occurrences of anomalies in engineering systems. The proposed diagnoser algorithm assumes that models are available for characterizing plant operations (via stochastic automata) and sensors (via probabilistic mappings) used for reporting partial and unreliable information. Methods for analyzing the effects of model uncertainties on the diagnoser performance are also discussed. In order to select configurations that reduce sensor costs, while satisfying diagnoser performance requirements, a sensor configuration selection algorithm developed in previous work is then extended for the proposed diagnoser algorithm. The proposed algorithms and methods are then applied to a multi-unit-operation system, which is derived from an actual facility application. Results show that the proposed diagnoser algorithm is able to detect and count occurrences of anomalies accurately and that its performance is robust to model uncertainties. Furthermore, the sensor configuration selection algorithm is able to suggest optimal sensor configurations with significantly reduced costs, while still yielding acceptable performance for counting the occurrences of anomalies.

Bounding the coarse graining error in hidden Markov dynamics

Lumping a Markov process introduces a coarser level of description that is useful in many contexts and applications. The dynamics on the coarse grained states is often approximated by its Markovian component. In this paper we derive finite-time bounds on the error in this approximation. These results hold for non-reversible dynamics and for probabilistic mappings between microscopic and coarse grained states.

Data integration with uncertainty

This paper reports our first set of results on managing uncertainty in data integration. We posit that data-integration systems need to handle uncertainty at three levels, and do so in a principled fashion. First, the semantic mappings between the data sources and the mediated schema may be approximate because there may be too many of them to be created and maintained or because in some domains (e.g., bioinformatics) it is not clear what the mappings should be. Second, queries to the system may be posed with keywords rather than in a structured form. Third, the data from the sources may be extracted using information extraction techniques and so may yield imprecise data. As a first step to building such a system, we introduce the concept of probabilistic schema mappings and analyze their formal foundations. We show that there are two possible semantics for such mappings: by-table semantics assumes that there exists a correct mapping but we don't know what it is; by-tuple semantics assumes that the correct mapping may depend on the particular tuple in the source data. We present the query complexity and algorithms for answering queries in the presence of approximate schema mappings, and we describe an algorithm for efficiently computing the top-k answers to queries in such a setting.

AN EXTENDED FRAMEWORK FOR EVIDENTIAL REASONING SYSTEMS

Use of the Dempster-Shafer (D-S) theory of evidence to deal with uncertainty in knowledge-based systems has been widely addressed. Several AI implementations have been undertaken based on the D-S theory of evidence or the extended theory. But the representation of uncertain relationships between evidence and hypothesis groups (heuristic knowledge) is still a major problem. This paper presents an approach to representing such knowledge, in which Yen’s probabilistic multi-set mappings have been extended to evidential mappings, and Shafer’s partition technique is used to get the mass function in a complex evidence space. Then, a new graphic method for describing the knowledge is introduced which is an extension of the graphic model by Lowrance et al. Finally, an extended framework for evidential reasoning systems is specified.

Morphological filters: Statistics and further syntactic properties

Mathematical morphology has recently been introduced as a powerful tool for studying the geometrical properties of signals and systems. These techniques have been applied very successfully to the smoothing of noisy data. In this paper, we first derive some new mathematical morphology results for function and set processing (FSP) systems. Using these results we derive several statistical results for the (FSP) morphological filtering of random signals, by deriving probabilistic mappings between input and output signals. Finally, we introduce a two-dimensional filter for image restoration which has desirable structure preserving properties.

Concepts of probabilistic sets

In the field of pattern recognition or decision making theory, the important subjects are as follows: (1) ambiguity of property of objects, (2) variety of character of objects, (3) subjectivity of observers, (4) evolution of knowledge of observers (i.e. learning). Considering these points, the concept of probabilistic set is proposed. It is based on both probability theory and fuzzy concepts. A probabilistic set on a total space is defined by a point wise measurable function from a parameter space (which is a probability space) to a characteristic space (which is a measurable space). It is shown that the family of all probabilistic sets constitutes a complete pseudo-Boolean algebra. Moment analysis is possible by using a probability measure of the parameter space. Other useful concepts are also mentioned such as probabilistic mappings and expected cardinal numbers.