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In linear regression, the coefficients are simple to estimate using the least squares method with a known design matrix for the observed measurements. However, real-world applications may encounter complications such as an unknown design matrix and complex-valued parameters. The design matrix can be estimated from prior information but can potentially cause an inverse problem when multiplying by the transpose as it is generally ill-conditioned. This can be combat by adding regularizers to the model but does not always mitigate the issues. Here, we propose our Bayesian approach to a complex-valued latent variable linear model with an application to functional magnetic resonance imaging (fMRI) image reconstruction. The complex-valued linear model and our Bayesian model are evaluated through extensive simulations and applied to experimental fMRI data. [ABSTRACT FROM AUTHOR]

Functional magnetic resonance imaging (fMRI) enables indirect detection of brain activity changes via the blood-oxygen-level-dependent (BOLD) signal. Conventional analysis methods mainly rely on the real-valued magnitude of these signals. In contrast, research suggests that analyzing both real and imaginary components of the complex-valued fMRI (cv-fMRI) signal provides a more holistic approach that can increase power to detect neuronal activation. We propose a fully Bayesian model for brain activity mapping with cv-fMRI data. Our model accommodates temporal and spatial dynamics. Additionally, we propose a computationally efficient sampling algorithm, which enhances processing speed through image partitioning. Our approach is shown to be computationally efficient via image partitioning and parallel computation while being competitive with state-of-the-art methods. We support these claims with both simulated numerical studies and an application to real cv-fMRI data obtained from a finger-tapping experiment. [ABSTRACT FROM AUTHOR]

The ongoing mixed-tenure redevelopment of Toronto's Regent Park neighbourhood is a multi-decade effort to rebuild the aging community's stock of post-war public housing and radically reshape the social composition of the community with the introduction of market owners and renters. This research provides a useful quantitative complement to the now extensive body of qualitative research concerning the neighbourhood's redevelopment, specifically investigating perceptions of stigma among both public housing and market residents using Pinel's Stigma Consciousness Questionnaire. We find that respondents of all tenures report relatively low levels of stigma consciousness. Unexpectedly, the largest observed difference between discrete tenure groups was between market owners and renters within the market units. Additionally, we find that non-native speakers of English report lower levels of stigma consciousness while the largest source of variation, by a wide margin, is between individuals. [ABSTRACT FROM AUTHOR]

In the variety of not necessarily associative rings, we show that the sixty Bol-Moufang identities determine exactly thirteen subvarieties, and we determine all inclusions and necessary counterexamples. We make use of the concepts of magma rings and linear identities. The result is analogous to the classification of varieties of loops or quasigroups of Bol-Moufang type (Phillips, Vojtěchovský-2005) and was motivated by the study of tangent algebras to smooth loops of Bol-Moufang type (Mal'cev-1955, Sagle-1961, Nagy-1992, Bremner, Madariaga-2014). [ABSTRACT FROM AUTHOR]

In the field of Talmudic Temporal logic, an important question has been how to model the approach known in one paper as 'Shkop logic' (after the 19th-20th century philosopher of Jewish law, Rabbi Shimon Shkop). Previous suggestions have included a model that involved a 'Dual-time' account. In this paper we first analyse the Dual time approach, including the logical language, its motivation and mechanism for diffusing legal contrary-to-time paradoxes. We compare the Dual time approach to a logic whose semantics need not appeal to Dual-time, but that employs a combination of trivalent truth function for the future, together with legal-functions designed to achieve the same conclusion. We show why such an approach would be inadequate, but then claim that a similar objection can be raised against the 'Dual-time' account. We then offer our own proposal, which involves a two-dimensional temporal model, thus permitting truth-valuations for events at moments in time to shift relative to other moments without any temporal loops. The language in which the model is expressed is sufficiently context-sensitive to permit a shift in perspective form the antecedent of a condition to its consequent. We argue that such an approach has significant benefits both in terms of being truer to the Talmudic sources, and in terms of its ability to diffuse legal paradoxes. We anticipate criticisms of the approach and argue that it can meet those criticisms. This is a part of a series of papers, and in future papers we intend to demonstrate the potential for this Perspectival 2-D Talmudic Temporal logic to resolve paradoxes such as Liar Paradoxes. [ABSTRACT FROM AUTHOR]

This paper explores the underlying logical framework of a legal approach to backwards causation in Talmudic (ancient Jewish) law. The Talmudic cases involve legal constructions such as purchases, marriages, or divorces, whereby the action is stipulated to be conditional upon a future occurrence (or non-occurrence) of an event. The Talmud accepts the principle of future causation, though there are different approaches that appear to involve different metaphysical and logical philosophies. One approach takes a future state of affairs to be considered an objective fact in the present moment. On this approach the future-condition is fulfilled (or not) as soon as it is made, although the facts remain epistemically inaccessible to the agents themselves until the later time. A second approach takes future facts to be non-facts until they become true. On this approach, when the later event occurs it causes a contrary-to-time effect to take place. Although we briefly discuss the second approach, our primary focus is the former approach. We analyse and elaborate upon the Abraham-Gabbay-Schild Talmudic language L, which is an executable temporal language, flexible enough to handle reference to absolute moments in time, and also to the subjective present as it changes for agents travelling through time. We then critically assess their Parallel-histories model for the approach that takes future facts to be present facts. In this paper we raise an alternative to the Parallel-Histories approach. We argue that to truly represent the Talmudic position, there is a need for a function F that is not a part of the language L, but operates at a meta-level, permitting or cancelling the conditional statements. We argue that once this function is introduced, then the potency of the language L makes the need for Parallel-Histories redundant (though we accept that it may serve as a useful heuristic). We argue further that the Parallel-Histories applied to paradoxical cases (temporal loops) does not have sufficient resources to fully unravel the loop alone, whereas the language L augmented by the function F indeed has the resources to diffuse such paradoxical constructions. [ABSTRACT FROM AUTHOR]

In the two subvarieties of commutative not necessarily associative rings, and 2-divisible not necessarily associative rings, we show that the sixty Bol-Moufang identities determine exactly five subvarieties in each case, and we completely determine all inclusions and necessary counterexamples. The historically important nonassociative rings of octonions and sedenions may be used as counterexamples in our classification. We utilize both associator and linear forms of each Bol-Moufang identity. The results are analogous to the classification of varieties of loops or quasigroups of Bol-Moufang type (Phillips, Vojtechovský-2005). [ABSTRACT FROM AUTHOR]

We propose a model‐based approach that combines Bayesian variable selection tools, a novel spatial kernel convolution structure, and autoregressive processes for detecting a subject's brain activation at the voxel level in complex‐valued functional magnetic resonance imaging (CV‐fMRI) data. A computationally efficient Markov chain Monte Carlo algorithm for posterior inference is developed by taking advantage of the dimension reduction of the kernel‐based structure. The proposed spatiotemporal model leads to more accurate posterior probability activation maps and less false positives than alternative spatial approaches based on Gaussian process models, and other complex‐valued models that do not incorporate spatial and/or temporal structure. This is illustrated in the analysis of simulated data and human task‐related CV‐fMRI data. In addition, we show that complex‐valued approaches dominate magnitude‐only approaches and that the kernel structure in our proposed model considerably improves sensitivity rates when detecting activation at the voxel level. [ABSTRACT FROM AUTHOR]