Group completion in the K-theory and Grothendieck-Witt theory of proto-exact categories

We study the algebraic $K$-theory and Grothendieck-Witt theory of proto-exact categories, with a particular focus on classes of examples of $\mathbb{F}_1$-linear nature. Our main results are analogues of theorems of Quillen and Schlichting, relating the $K$-theory or Grothendieck-Witt theories of proto-exact categories defined using the (hermitian) $Q$-construction and group completion

Algebraic KK-theory and Grothendieck-Witt theory of monoid schemes

We study the algebraic $K$-theory and Grothendieck-Witt theory of proto-exact categories of vector bundles over monoid schemes. Our main results are the complete description of the algebraic $K$-theory space of an integral monoid scheme $X$ in terms of its Picard group $\operatorname{Pic}(X)$ and pointed monoid of regular functions $\Gamma(X, \mathcal{O}_X)$ and a description of the Grothendieck-Witt space of $X$ in terms of an additional involution on $\operatorname{Pic}(X)$. We also prove space-level projective bundle formulae in both settings

Experiment Selection for Causal Discovery

Randomized controlled experiments are often described as the most reliable tool available to scientists for discovering causal relationships among quantities of interest. However, it is often unclear how many and which different experiments are needed to identify the full (possibly cyclic) causal structure among some given (possibly causally insufficient) set of variables. Recent results in the causal discovery literature have explored various identifiability criteria that depend on the assumptions one is able to make about the underlying causal process, but these criteria are not directly constructive for selecting the optimal set of experiments. Fortunately, many of the needed constructions already exist in the combinatorics literature, albeit under terminology which is unfamiliar to most of the causal discovery community. In this paper we translate the theoretical results and apply them to the concrete problem of experiment selection. For a variety of settings we give explicit constructions of the optimal set of experiments and adapt some of the general combinatorics results to answer questions relating to the problem of experiment selection

Noisy-OR Models with Latent Confounding

Given a set of experiments in which varying subsets of observed variables are subject to intervention, we consider the problem of identifiability of causal models exhibiting latent confounding. While identifiability is trivial when each experiment intervenes on a large number of variables, the situation is more complicated when only one or a few variables are subject to intervention per experiment. For linear causal models with latent variables Hyttinen et al. (2010) gave precise conditions for when such data are sufficient to identify the full model. While their result cannot be extended to discrete-valued variables with arbitrary cause-effect relationships, we show that a similar result can be obtained for the class of causal models whose conditional probability distributions are restricted to a `noisy-OR' parameterization. We further show that identification is preserved under an extension of the model that allows for negative influences, and present learning algorithms that we test for accuracy, scalability and robustness

Combining experiments to discover linear cyclic models with latent variables

Volume: Vol 9 : AISTATS 2010 Host publication title: Proceedings of the 13th International Conference on Artificial Intelligence and StatisticsPeer reviewe

Discovering Cyclic Causal Models with Latent Variables: A General SAT-Based Procedure

We present a very general approach to learning the structure of causal models based on d-separation constraints, obtained from any given set of overlapping passive observational or experimental data sets. The procedure allows for both directed cycles (feedback loops) and the presence of latent variables. Our approach is based on a logical representation of causal pathways, which permits the integration of quite general background knowledge, and inference is performed using a Boolean satisfiability (SAT) solver. The procedure is complete in that it exhausts the available information on whether any given edge can be determined to be present or absent, and returns "unknown" otherwise. Many existing constraint-based causal discovery algorithms can be seen as special cases, tailored to circumstances in which one or more restricting assumptions apply. Simulations illustrate the effect of these assumptions on discovery and how the present algorithm scales.Comment: Appears in Proceedings of the Twenty-Ninth Conference on Uncertainty in Artificial Intelligence (UAI2013

Magnetism and interlayer coupling in fcc Fe/Co films

The magnetism of epitaxial fee Fe films deposited on Co(100) and sandwiched between two Co(100) films was investigated by x-ray magnetic circular dichroism. The dependence of the Fe magnetism on the film thickness is complex and qualitatively similar on Co(100) and in fee Co/Fe/Co(100) trilayers. The fee Fe film magnetization presents a pronounced oscillation, suggesting a partial antiferromagnetic ordering in the 5-10 monolayer thickness range. The fee Fe films mediate an oscillatory, indirect coupling in Co/Fe/Co(100) structures that alternates in correspondence with the changes of the Fe magnetization

Enhancing mental health with Artificial Intelligence: Current trends and future prospects

Artificial Intelligence (AI) has emerged as a transformative force in various fields, and its application in mental healthcare is no exception. Hence, this review explores the integration of AI into mental healthcare, elucidating current trends, ethical considerations, and future directions in this dynamic field. This review encompassed recent studies, examples of AI applications, and ethical considerations shaping the field. Additionally, regulatory frameworks and trends in research and development were analyzed. We comprehensively searched four databases (PubMed, IEEE Xplore, PsycINFO, and Google Scholar). The inclusion criteria were papers published in peer-reviewed journals, conference proceedings, or reputable online databases, papers that specifically focus on the application of AI in the field of mental healthcare, and review papers that offer a comprehensive overview, analysis, or integration of existing literature published in the English language. Current trends reveal AI's transformative potential, with applications such as the early detection of mental health disorders, personalized treatment plans, and AI-driven virtual therapists. However, these advancements are accompanied by ethical challenges concerning privacy, bias mitigation, and the preservation of the human element in therapy. Future directions emphasize the need for clear regulatory frameworks, transparent validation of AI models, and continuous research and development efforts. Integrating AI into mental healthcare and mental health therapy represents a promising frontier in healthcare. While AI holds the potential to revolutionize mental healthcare, responsible and ethical implementation is essential. By addressing current challenges and shaping future directions thoughtfully, we may effectively utilize the potential of AI to enhance the accessibility, efficacy, and ethicality of mental healthcare, thereby helping both individuals and communities

About the strength of correlation effects in the electronic structure of iron

The strength of electronic correlation effects in the spin-dependent electronic structure of ferromagnetic bcc Fe(110) has been investigated by means of spin and angle-resolved photoemission spectroscopy. The experimental results are compared to theoretical calculations within the three-body scattering approximation and within the dynamical mean-field theory, together with one-step model calculations of the photoemission process. This comparison indicates that the present state of the art many-body calculations, although improving the description of correlation effects in Fe, give too small mass renormalizations and scattering rates thus demanding more refined many-body theories including non-local fluctuations.Comment: 4 pages, 4 figure