This paper describes an intelligent algorithm for traffic sign recognition which converges quickly, is accurate in its segmentation and adaptive in its behaviour. The proposed approach can segment images of traffic signs in different lighting and environmental conditions and in different countries. It is based on using Kohonen's Self-Organizing Maps as a clustering tool and it is developed for Intelligent Vehicle applications. The current approach does not need any prior training. Instead, a slight portion, which is about 1% (...) of the image under investigation, is used for training. This is a key issue to ensure fast convergence and high adaptability. The current approach was tested by using 442 images which were collected under different environmental conditions and from different countries. The proposed approach shows promising results; good improvement of 73% is observed in faded traffic sign images compared with 53.3% using the traditional algorithm. The adaptability of the system is evident from the segmentation of the traffic sign images from various countries where the result is 96% for the nine countries included in the test. (shrink)

Статья посвящена исследованию финансового состояния предприятия сферы услуг. Стабилизация финансового состояния является приоритетным направлением отдельно взятого предприятия и экономической системы в целом. Предлагается решить обеспечение стабильности финансовой деятельности предприятия с помощью нейронной сетевой модели кластеризации - самоорганизующихся карт Кохонена - мощного механизма кластеризации, что позволяет отобразить результаты финансового анализа в виде компактных и удобных для интерпретации двумерных карт. В работе проанализированы услуги предприятия и проведена сегментация базы посетителей, построены профили пользователей услуг путем выявления их похожего поведения в плане частоты, типа (...) заказанных услуг, проведена оценка наиболее и наименее прибыльных сегментов. Сегментация посетителей отеля-ресторана проведена с помощью подхода, основанного на алгоритме Кохонена, и кластеризации объектов по алгоритму Кохонена. Данный интерфейс используется для поиска закономерностей в больших массивах данных, что позволяет проводить разведывательный анализ данных, который отличается от классических статистических процедур. (shrink)

In this paper I shall compare two models of concept formation, both inspired by basic convictions of philosophical empiricism. The first, the connectionist model, will be exemplified by Kohonen maps, and the second will be my own dynamic theory of concept formation. Both can be understood in probabilistic terms, both use a notion of convergence or stabilization in modelling how concepts are built up. Both admit destabilization of concepts and conceptual change. Both do not use a notion of (...) representation in some pregiven language, such as a language of thought or some logical language. Representation in a formal language only plays a role on the meta-level, namely within the theory about concept formation. (shrink)

The objective of this work is to categorize the available fly ashes in different parts of the world into distinct groups based on its compositional attributes. Kohonen's self-organizing feature map and radial basis function networks are applied in a cascading fashion for the classification of fly ashes in terms of its chemical parameters. The basic procedure of the methodology consists of three stages: apply self-organizing neural net to ascertain possible number of groups, delineate them and identify the group sensitive (...) attributes; find mean values of sensitive attributes of the elicited groups and augment them as start-up prototypes in k-means algorithm and find the refined centroids of these groups; incorporate the centroids in a two layer radial basis function network and fine-tune the delineated groups and develop an indexing equation using the weights of the stabilized network. Further, to demonstrate the utility of this classification scheme, the so formed groups were correlated with their performance in High Volume Fly Ash Concrete System [HVFAC]. The categorization was found to be excellent and compares well with Canadian Standard Association's [CSA A 3000] classification scheme. (shrink)

The matter of enterprise labor resource management explaining the enterprise's staff potential increase or reduction is considered. That is to say the problem of efficiency of staff potential employment is researched. The author determines a general aim of the enterprise staff potential management in current terms of functioning, which refers to the purposeful performance of certain steps resulting in effective appliance. Factors of degree of staff potential and its effective appliance are determined as followed: qualified staff development; involvement of qualified (...) professionals; optimal conditions for staff operation support. The mechanism of unit staff potential management being able to adjust to changes in a structure of interrelated elements, production and the technological interaction organization, terms of working, the performance of professional competiveness and the staff rotation within the branches as well as between them is suggested. Criteria of effective realization of the mechanism of staff potential management by the working efficiency increase, the staff and manager competiveness increase, the rotations possibility, the produced goods and services quality increase. A procedure of enterprise staff rating is considered. To motivate qualified workers of organizational and functional units of an enterprise and to stimulate them for better further working, the monitoring of their activity compensation by certain bonuses is proposed. A model of premium distribution between co-workers of functional units of an enterprise, based on the Kohonen self-organized maps method implementation, is represented. Characteristics of informational and analytical systems of the enterprise staff potential management functioning in the unified informational environment are determined. The implementation of proposed mechanism provides high level of the enterprise staff potential realization as well as the permanent development of labor resources during a business activity process. (shrink)

Walter Map was a twelfth-century courtier and royal servant. He was a prolific writer, but De Nugis Curialium is the only surviving work confidently attributed to him. The book is a collection of short stories and anecdotes about the court, religion and history. Map's references demonstrate that he read widely, not only biblical and theological works, but also classical authors such as Horace, Virgil, Ovid and Juvenal. The only surviving manuscript of the work is a fourteenth-century copy once belonging to (...) the monk John Wells of Ramsey Abbey. The Cambridge bibliographer M. R. James would have been attracted to the breadth of Map's referencing, and the author's light-hearted writing style which was intended to entertain. James' 1914 Oxford publication corrected the earlier work of Thomas Wright who published an edition for the Camden Society in 1850. (shrink)

Neonatal brain monitoring in the neonatal intensive care units (NICU) requires a continuous review of the spontaneous cortical activity, i.e., the electroencephalograph (EEG) background activity. This needs development of bedside methods for an automated assessment of the EEG background activity. In this paper, we present development of the key components of a neonatal EEG background classifier, starting from the visual background scoring to classifier design, and finally to possible bedside visualization of the classifier results. A dataset with 13,200 5-minute EEG (...) epochs (8–16 channels) from 27 infants with birth asphyxia was used for classifier training after scoring by two independent experts. We tested three classifier designs based on 98 computational features, and their performance was assessed with respect to scoring system, pre- and post-processing of labels and outputs, choice of channels, and visualization in monitor displays. The optimal solution achieved an overall classification accuracy of 97% with a range across subjects of 81–100%. We identified a set of 23 features that make the classifier highly robust to the choice of channels and missing data due to artefact rejection. Our results showed that an automated bedside classifier of EEG background is achievable, and we publish the full classifier algorithm to allow further clinical replication and validation studies. (shrink)

Most of us create and use a panoply of non-sentential representations throughout our ordinary lives: we regularly use maps to navigate, charts to keep track of complex patterns of data, and diagrams to visualize logical and causal relations among states of affairs. But philosophers typically pay little attention to such representations, focusing almost exclusively on language instead. In particular, when theorizing about the mind, many philosophers assume that there is a very tight mapping between language and thought. Some analyze (...) utterances as the outer vocalizations of inner thoughts (e.g. Grice 1957, Devitt 2005), while others treat thought as a form of inner speech (e.g. Sellars 1956/1997, Carruthers 2002). But even philosophers who take no stand on the relative priority of language and thought still tend to individuate mental states in terms of the sentences we use to ascribe them. Indeed, Dummett (1993) claims that it is constitutive of analytic philosophy that it approaches the mind by way of language. In many ways, this linguistic model is salutary. Our thoughts are often intimately intertwined with their linguistic expression, and public language does provide a comparatively tractable proxy for, and a window into, the messier realm of thought. However, an exclusive focus on thought as it is expressed in language threatens to leave other sorts of thought unexplained, or even to blind us to their possibility. In particular, many cognitive ethologists and psychologists find it useful to talk about humans, chimpanzees, birds, rats, and even bees as employing cognitive maps. We need to make sense of this way of talking about minds as well as more familiar sentential descriptions. In what follows, I investigate the theoretical and practical possibility of non-sentential thought. Ultimately, I am most interested in the contours of distinctively human thought: what forms does human thought take, and how do those different forms interact? How does human thought compare with that of other animals? In this essay, however, I focus on a narrower and more basic theoretical question: could thought occur in maps? Many philosophers are convinced that in some important sense, thought per se must be language-like.. (shrink)

Contemporary philosophy of technology after the empirical turn has surprisingly little to say on the relation between language and technology. This essay describes this gap, offers a preliminary discussion of how language and technology may be related to show that there is a rich conceptual space to be gained, and begins to explore some ways in which the gap could be bridged by starting from within specific philosophical subfields and traditions. One route starts from philosophy of language (both ‘‘analytic’’ and (...) ‘‘continental’’: Searle and Heidegger) and discusses some potential implications for thinking about technology; another starts from artefact-oriented approaches in philosophy of technology and STS and shows that these approaches might helpfully be extended by theorizing relationships between language and techno- logical artefacts. The essay concludes by suggesting a research agenda, which invites more work on the relation between language and technology. (shrink)

We propose that children employ specialized cognitive systems that allow them to recover an accurate “causal map” of the world: an abstract, coherent, learned representation of the causal relations among events. This kind of knowledge can be perspicuously understood in terms of the formalism of directed graphical causal models, or “Bayes nets”. Children’s causal learning and inference may involve computations similar to those for learning causal Bayes nets and for predicting with them. Experimental results suggest that 2- to 4-year-old children (...) construct new causal maps and that their learning is consistent with the Bayes net formalism. (shrink)

A judge springs out of his car on the way to court in downtown Chicago and takes photographs of an inflatable rat. A while later he inserts these photographs into a decision involving another inflatable rodent. Judges now regularly insert pictures in judgments, but there is no study either of the genres or the precedential status of these modern visual emblemata, these pictorial interventions in the record. Using a comparative visual corpus of over three hundred images extracted from diverse common (...) law jurisdictions, the practice of retinal justice, the novelty of vision in decision, is here anatomized, choreographed, and critically classified. (shrink)

Background: Although convolutional neural networks (CNNs) achieve high diagnostic accuracy for detecting Alzheimer’s disease (AD) dementia based on magnetic resonance imaging (MRI) scans, they are not yet applied in clinical routine. One important reason for this is a lack of model comprehensibility. Recently developed visualization methods for deriving CNN relevance maps may help to fill this gap as they allow the visualization of key input image features that drive the decision of the model. We investigated whether models with higher (...) accuracy also rely more on discriminative brain regions predefined by prior knowledge. Methods: We trained a CNN for the detection of AD in N = 663 T1-weighted MRI scans of patients with dementia and amnestic mild cognitive impairment (MCI) and verified the accuracy of the models via cross-validation and in three independent samples including in total N = 1655 cases. We evaluated the association of relevance scores and hippocampus volume to validate the clinical utility of this approach. To improve model comprehensibility, we implemented an interactive visualization of 3D CNN relevance maps, thereby allowing intuitive model inspection. Results: Across the three independent datasets, group separation showed high accuracy for AD dementia versus controls (AUC ≥ 0.91) and moderate accuracy for amnestic MCI versus controls (AUC ≈ 0.74). Relevance maps indicated that hippocampal atrophy was considered the most informative factor for AD detection, with additional contributions from atrophy in other cortical and subcortical regions. Relevance scores within the hippocampus were highly correlated with hippocampal volumes (Pearson’s r ≈ −0.86, p < 0.001). Conclusion: The relevance maps highlighted atrophy in regions that we had hypothesized a priori. This strengthens the comprehensibility of the CNN models, which were trained in a purely data-driven manner based on the scans and diagnosis labels. The high hippocampus relevance scores as well as the high performance achieved in independent samples support the validity of the CNN models in the detection of AD-related MRI abnormalities. The presented data-driven and hypothesis-free CNN modeling approach might provide a useful tool to automatically derive discriminative features for complex diagnostic tasks where clear clinical criteria are still missing, for instance for the differential diagnosis between various types of dementia. (shrink)

This paper investigates structural properties of monotone function classes within the framework of three-valued logic (3VL), aiming to characterize dependencies and constraints that ensure structural finiteness and order-preserving properties. This research delves into characteristics of structurally finite classes of order-preserving 3VL map. Monotonicity plays a critical role in understanding functional behaviour, which is essential for structuring closed logical operations within $ P_{k} $. We define $ F $ as a closed class in $ P_{k} $, consisting only of mappings that (...) comply with specified operations and are strictly confined to $ P_{k} $. The notation $ F(n) $ represents the subset of mappings in $ F $ dependent on $ n $ variables, highlighting the limited scope of inputs and their respective outputs. Further analysis through $ CR(F) $ facilitates the identification of precursor subclasses within $ F $, which have not yet achieved closure under all necessary operations—a pivotal step in constructing intermediate mapping classes. Within the framework of 3VL, the study examines order-preserving maps $ f_{D}, f_{K}, f_{M^{(2)}}, f_{DM^{(2)}}, f_{KM^{(2)}} $, deliberately excluding the sets $ D, K, M^{(2)} $, where $ DM^{(2)} $ is defined as $ D \cap M^{(2)} $ and $ KM^{(2)} $ as $ K \cap M^{(2)} $. The lattice framework in $ P_{k}(1) $ for $ k = 3 $ systematically organizes these mapping classes based on their completeness properties, with particular emphasis on classes such as $ M $, which is characterized as a comprehensive set governed by the operations of maximum and minimum. Our theorems establish structural finiteness for classes of unary order-preserving maps, emphasizing their two-variable dependency in class construction. This study extends existing findings on single-variable monotonic functions within 3VL by integrating criteria of linear order. Key results include the classification of mapping classes $ F \subseteq M $ containing $ M^{(1)}_{3} $, categorized into distinct groups: $ M^{(1)}_{3}, KM^{(2)}, DM^{(2)}, M^{(2)}, K, D, M $. Inclusion relations are visualized diagrammatically, showing the hierarchical structure of these monotone classes, ultimately validating the structural finiteness of classes incorporating all unary order-preserving maps within the broader context of 3VL. (shrink)

How can one investigate phenomenal consciousness? As in other areas of science, the investigation of consciousness aims for a more precise knowledge of its phenomena, and the discovery of general truths about their nature. This requires the development of appropriate first-person, second-person and third-person methods. This book introduces some of the creative ways in which these methods can be applied to different purposes, e.g. to understanding the relation of consciousness to brain, to examining or changing consciousness as such, and to (...) understanding the way consciousness is influenced by social, clinical and therapeutic contexts. To clarify the strengths and weaknesses of different methods and to demonstrate the interplay of methodology and epistemology, the book also suggests a number of “maps” of the consciousness studies terrain that place different approaches to the study of consciousness into a broader, interdisciplinary context. (shrink)

We propose the notion of partial recursiveness and strong partial recursiveness for fuzzy maps. We prove that a fuzzy map f is partial recursive if and only if it is computable by a Turing fuzzy machine and that f is strongly partial recursive and deterministic if and only if it is computable via a deterministic Turing fuzzy machine. This gives a simple and manageable tool to investigate about the properties of the fuzzy machines.

The identification and analysis of the spatiotemporal dynamic traffic patterns in citywide road networks constitute a crucial process for complex traffic management and control. However, city-scale and synchronal traffic data pose challenges for such kind of quantification, especially during peak hours. Traditional studies rely on data from road-based detectors or multiple communication systems, which are limited in not only access but also coverage. To avoid these limitations, we introduce real-time, traffic condition digital maps as our input. The digital (...) class='Hi'>maps keep spatiotemporal urban traffic information in nature and are open to access. Their pixel colors represent traffic conditions on corresponding road segments. We propose a stacked convolutional autoencoder-based method to extract a low-dimension feature vector for each input. We compute and analyze the distances between vectors. The statistical results show different traffic patterns during given periods. With the actual data of Chongqing city, we compare the feature extraction performance between our proposed method and histogram. The result shows our proposed method can extract spatiotemporal features better. For the same data set, there is little difference in the number distribution of red pixels found in the statistics result of the histogram, while differences do exist in the results of our proposed method. We find the most fluctuated morning is on Friday; the most fluctuated evening is on Tuesday; and the most stable evening is on Wednesday. The distance captured by our method can represent the evolution of different traffic conditions during the morning and evening peak hours. Our proposed method provides managers with assistance to sense the dynamics of citywide traffic conditions in quantity. (shrink)

Neuroethics to date has tended to focus on social and ethical implications of developments in brain science, especially in functional neuroimaging. Within clinical neuroethics, the emphasis has been on ethical issues in clinical neuroscience practice, including informed consent to neuroimaging; the development of ethical research protocols for functional magnetic resonance imaging especially, and especially in children; and the ethical clinical management of incidental findings. Within normative neuroethics, we have witnessed the more philosophical and/or social scientific study of the meanings of (...) developments in neuroscience, including concerns about the impact of neuroimaging on privacy, freedom of thought, moral culpability, and sense of self. In this piece, I argue for an expansion of neuroethical attention to the interface of neuroscience and psychiatry, where brain science meets the clinical sciences of the mind. My particular focus is the development of psychiatric classification systems. (shrink)

The aim of this paper is to characterize the various structuralist reduction concepts as structure-preserving maps in a succinct and unifying way. To begin with, some important intuitive adequacy conditions are discussed that a good (structuralist) reduction concept should satisfy. Having reconstructed these intuitive conditions in the structuralist framework, it turns out that they divide into two mutually incompatible sets of requirements. Accordingly there exist (at least) two essentially different types of structuralist reduction concepts: the first type stresses the (...) existence of a deductive or inferential link between the reducing and the reduced theory; the second type emphasizes the greater explanatory power the reducing theory should have in comparison with the reduced theory. The problem of the incompatibility of equally plausible reduction concepts is treated in the last section and a proposal is made for its solution consisting in the definition of a multiple synthetizing reduction relation. (shrink)

Ability to recall the timing of events is a crucial aspect of associative learning. Yet, traditional theories of associative learning have often overlooked the role of time in learning association and shaping the behavioral outcome. They address temporal learning as an independent and parallel process. Temporal Coding Hypothesis is an attempt to bringing together the associative and non-associative aspects of learning. This account proposes temporal maps, a representation that encodes several aspects of a learned association, but attach considerable importance (...) to the temporal aspect. A temporal map helps an agent to make inferences about missing information by applying an integration mechanism over a common element present in independently acquired temporal maps. We review the empirical evidence demonstrating the construct of temporal maps and discuss the importance of this concept in clinical and behavioral interventions. (shrink)

The presumption that navigation requires a cognitive map leads to its conception as an abstract computational problem. Instead of loading the question in favor of an inquiry into the metric structure and evolutionary origin of cognitive maps, the task should first be to establish that a map-like representation actually is operative in real animals navigating real environments.

Weakly interacting lattices of coupled maps can be modeled as ordinary coupled map lattices separated from each other by boundary regions with small coupling parameters. We demonstrate that such weakly interacting lattices can nevertheless have unexpected and striking effects on each other. Under specific conditions, particular stability properties of the lattices are significantly influenced by their weak mutual interaction. This observation is tantamount to an efficacious information flow across the boundary.

A classic result in the foundations of Yang-Mills theory, due to J. W. Barrett ["Holonomy and Path Structures in General Relativity and Yang-Mills Theory." Int. J. Th. Phys. 30, ], establishes that given a "generalized" holonomy map from the space of piece-wise smooth, closed curves based at some point of a manifold to a Lie group, there exists a principal bundle with that group as structure group and a principal connection on that bundle such that the holonomy map corresponds to (...) the holonomies of that connection. Barrett also provided one sense in which this "recovery theorem" yields a unique bundle, up to isomorphism. Here we show that something stronger is true: with an appropriate definition of isomorphism between generalized holonomy maps, there is an equivalence of categories between the category whose objects are generalized holonomy maps on a smooth, connected manifold and whose arrows are holonomy isomorphisms, and the category whose objects are principal connections on principal bundles over a smooth, connected manifold. This result clarifies, and somewhat improves upon, the sense of "unique recovery" in Barrett's theorems; it also makes precise a sense in which there is no loss of structure involved in moving from a principal bundle formulation of Yang-Mills theory to a holonomy, or "loop", formulation. (shrink)

In “The Blessing of Departure—Exchange of Populated Territories The Lieberman Plan as anExercise in Demographic Transformation,” Prof. Timothy Waters offers a strong endorsement of the right of ethnic majorities within a state to redefine their state's boundaries in ways consistent with the majority's right to self-determination and to opt out of a political union with minority groups, regardless of the latter's' political preferences. Applied to the Israeli context, Waters concludes that parts of the Lieberman Plan—a plan advocating the redrawing of (...) Israel borders, inter alia, in ways which exclude some areas populated by Israeli citizens belonging to the Arab-Palestinian minority —does not run afoul of international law . This short response challenges two points that are central to Waters’s analysis. First, that the right to self-determination of peoples—in particular, the right to external self-determination —is subject to temporal or contextual limitations. The right is fully applicable only in exceptional and formative moments in the life of a nation—e.g., during the formation of a new polity or the collapse of an existing political arrangement , and when states systematically fail to respect the basic interest of some of the groups that comprise its populace—i.e., in response to extraordinary situations of groups exclusion or oppression. Second, even if Waters is correct and an ongoing right to self-determination—including, a right to secede from existing states—is available to ethnic groups comprising diverse national societies, the invocation of such a right must necessarily be limited by other positive rules of international law designed to protect group and individual interests. Specifically, Waters’s concept of self-determination as a right of a preliminary nature, that overrides other human rights , is debatable. (shrink)

Philosophers and psychologists acclaim Edward C. Tolman's “Cognitive Maps in Rats and Men” as an early, transformative instance of representationalist explanation. The article is said to mark a move by Tolman to renounce his behaviorism and to herald a new, cognitivist psychology. I argue, opposingly, that framing the text with reference to later psychology badly distorts its meaning. The text is better understood with respect to the contexts of its age and deeper currents in the history of psychology. Tolman (...) is not upturning behaviorism; he is re-litigating an intramural debate between behaviorists pertaining to the place of physiology in psychology. (shrink)

This article describes how the City of Los Angeles is showcasing data-driven services to the public through dynamic visualisations of open data. I frame an analysis of this aspect of datafication in local government through linguistics and cultural theory; drawing on this set of literature I theorise the use of public data as both a performative tool and a performance of data-driven city services. I then discuss examples of interactive maps on the City of Los Angeles’ open data websites, (...) produced by the Bureau of Sanitation, the Controller’s Office, and the Department of Transportation. The article concludes with some general thoughts on how open data maps are a new form of impression management; they set up a relationship in which government and citizens are in alignment, sharing an orientation towards administrative problems that begins at the same point, framed by an administration’s datasets. (shrink)

24 undergraduates were blindfolded and walked through paths laid out on a floor to investigate whether the orientation of Ss' cognitive maps (CMs) could be determined after they had learned a path by walking through it. Given the assumption that the CM is picturelike, it was predicted that it has a specific orientation, which implies that tests in which the CM is assumed to be aligned with the path should be less difficult than tests in which the CM is (...) hypothesized to be contraligned. In Exp I (8 Ss), Ss were required to draw a picture of the path they had walked through; in Exp II (14 Ss), Ss were required to locate targets in the path under conditions in which their presumed CMs were either aligned or contraligned with the path. Results show that, in Exp I, all Ss drew the 1st line segment of the path upward, suggesting that this part of the path was fixed in an upward direction in memory. In Exp II, Ss were more accurate and faster in locating points on the path when the CM was hypothesized to be aligned with the path than when it was hypothesized to be contraligned. (shrink)

“Scientific theories are maps of the natural world.” This metaphor is often used as part of a deflationary argument for a weak but relatively global version of scientific realism, a version that recognizes the place of conventions, goals, and contingencies in scientific representations, while maintaining that they are typically true in a clear and literal sense. By examining, in a naturalistic way, some relationships between maps and what they map, we question the scope and value of realist construals (...) of maps—and by extension of scientific representations. Deflationary philosophy of science requires more variegated stances. (shrink)

This article begins with a review of the framework of fuzzy probability theory. The basic structure is given by the σ-effect algebra of effects (fuzzy events) $\mathcal{E}{\text{ }}\left( {\Omega ,\mathcal{A}} \right)$ and the set of probability measures $M_1^ + {\text{ }}\left( {\Omega ,\mathcal{A}} \right)$ on a measurable space $\left( {\Omega ,\mathcal{A}} \right)$ . An observable $X:\mathcal{B} \to {\text{ }}\mathcal{E}{\text{ }}\left( {\Omega ,\mathcal{A}} \right)$ is defined, where $\begin{gathered} X:\mathcal{B} \to {\text{ }}\mathcal{E}{\text{ }}\left( {\Omega ,\mathcal{A}} \right) \\ \left( {\Lambda ,{\text{ }}\mathcal{B}} \right) (...) \\ \end{gathered} $ is the value space of X. It is noted that there exists a one-to-one correspondence between states on $\mathcal{E} \left( {\Omega ,\mathcal{A} } \right)$ and elements of $M_1^ + {\text{ }}\left( {\Omega ,\mathcal{A} } \right)$ and between observables $X:\mathcal{B} \to \mathcal{E} \left( {\Omega ,\mathcal{A} } \right)$ and σ-morphisms from $\mathcal{E} \left( {\Lambda , \mathcal{B}} \right)$ to $\mathcal{E} \left( {\Omega , \mathcal{A}} \right)$ . Various combinations of observables are discussed. These include compositions, products, direct products, and mixtures. Fuzzy stochastic processes are introduced and an application to quantum dynamics is considered. Quantum effects are characterized from among a more general class of effects. An alternative definition of a statistical map $M_1^ + {\text{ }}\left( {\Lambda ,\mathcal{B} } \right)$ is given and it is shown that any statistical map has a unique extension to a statistical operator. Finally, various combinations of statistical maps are discussed and their relationships to the corresponding combinations of observables are derived. (shrink)