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Reducing wealth inequality and disparity is a global challenge. The economic system is mainly divided into (1) gift and reciprocity, (2) power and redistribution, (3) market exchange, and (4) mutual aid without reciprocal obligations. The current inequality stems from a capitalist economy consisting of (2) and (3). To sublimate (1), which is the human economy, to (4), the concept of a "mixbiotic society" has been proposed in the philosophical realm. This is a society in which free and diverse individuals, "I," mix with each other, recognize their respective "fundamental incapability" and sublimate them into "WE" solidarity. The economy in this society must have moral responsibility as a coadventurer and consideration for vulnerability to risk. Therefore, I focus on two factors of mind perception: moral responsibility and risk vulnerability, and propose a novel model of wealth distribution following an econophysical approach. Specifically, I developed a joint-venture model, a redistribution model in the joint-venture model, and a "WE economy" model. A simulation comparison of a combination of the joint ventures and redistribution with the WE economies reveals that WE economies are effective in reducing inequality and resilient in normalizing wealth distribution as advantages, and susceptible to free riders as disadvantages. However, this disadvantage can be compensated for by fostering consensus and fellowship, and by complementing it with joint ventures. This study essentially presents the effectiveness of moral responsibility, the complementarity between the WE economy and the joint economy, and the direction of the economy toward reducing inequality. Future challenges are to develop the WE economy model based on real economic analysis and psychology, as well as to promote WE economy fieldwork for worker coops and platform cooperatives to realize a desirable mixbiotic society.

In several branches of the social sciences and humanities, surveys based on standardized questionnaires are a prominent research tool. While there are a variety of ways to analyze the data, some standard procedures have become established. When those surveys want to analyze differences in the answer patterns of different groups (e.g., countries, gender, age, ...), these procedures can only be carried out in a meaningful way if there is measurement invariance, i.e., the measured construct has psychometric equivalence across groups. As recently raised as an open problem by Sauerwein et al. (2021), new evaluation methods that work in the absence of measurement invariance are needed. This paper promotes an unsupervised learning-based approach to such research data by proposing a procedure that works in three phases: data preparation, clustering of questionnaires, and measuring similarity based on the obtained clustering and the properties of each group. We generate synthetic data in three data sets, which allows us to compare our approach with the PCA approach under measurement invariance and under violated measurement invariance. As a main result, we obtain that the approach provides a natural comparison between groups and a natural description of the response patterns of the groups. Moreover, it can be safely applied to a wide variety of data sets, even in the absence of measurement invariance. Finally, this approach allows us to translate (violations of) measurement invariance into a meaningful measure of similarity.

Large Language Models (LLMs) have emerged as powerful generative Artificial Intelligence solutions which can be applied to several fields and areas of work. This paper presents results and reflection of an experiment done to use the model GPT 3.5-Turbo to emulate some aspects of an inductive Thematic Analysis. Previous research on this subject has largely worked on conducting deductive analysis. Thematic Analysis is a qualitative method for analysis commonly used in social sciences and it is based on interpretations made by the human analyst(s) and the identification of explicit and latent meanings in qualitative data. Attempting an analysis based on human interpretation with an LLM clearly is a provocation but also a way to learn something about how these systems can or cannot be used in qualitative research. The paper presents the motivations for attempting this emulation, it reflects on how the six steps to a Thematic Analysis proposed by Braun and Clarke can at least partially be reproduced with the LLM and it also reflects on what are the outputs produced by the model. The paper used two existing datasets of open access semi-structured interviews, previously analysed with Thematic Analysis by other researchers. It used the previously produced analysis (and the related themes) to compare with the results produced by the LLM. The results show that the model can infer at least partially some of the main Themes. The objective of the paper is not to replace human analysts in qualitative analysis but to learn if some elements of LLM data manipulation can to an extent be of support for qualitative research.

We adopt the integral definition of the fractional Laplace operator and study an optimal control problem on Lipschitz domains that involves a fractional elliptic partial differential equation (PDE) as state equation and a control variable that enters the state equation as a coefficient; pointwise constraints on the control variable are considered as well. We establish the existence of optimal solutions and analyze first and, necessary and sufficient, second order optimality conditions. Regularity estimates for optimal variables are also analyzed. We develop two finite element discretization strategies: a semidiscrete scheme in which the control variable is not discretized, and a fully discrete scheme in which the control variable is discretized with piecewise constant functions. For both schemes, we analyze the convergence properties of discretizations and derive error estimates.

In this study, we present a precise anisotropic interpolation error estimate for the Morley finite element method (FEM) and apply it to fourth-order elliptical equations. We did not impose a shape-regularity mesh condition for the analysis. Therefore, anisotropic meshes can be used. The main contributions of this study include providing new proof of the consistency term. This enabled us to obtain an anisotropic consistency error estimate. The core idea of the proof involves using the relationship between the Raviart--Thomas and Morley finite element spaces. Our results show optimal convergence rates and imply that the modified Morley FEM may be effective for errors.

We present a new stability and error analysis of fully discrete approximation schemes for the transient Stokes equation. For the spatial discretization, we consider a wide class of Galerkin finite element methods which includes both inf-sup stable spaces and symmetric pressure stabilized formulations. We extend the results from Burman and Fern\'andez [\textit{SIAM J. Numer. Anal.}, 47 (2009), pp. 409-439] and provide a unified theoretical analysis of backward difference formulae (BDF methods) of order 1 to 6. The main novelty of our approach lies in the use of Dahlquist's G-stability concept together with multiplier techniques introduced by Nevannlina-Odeh and recently by Akrivis et al. [\textit{SIAM J. Numer. Anal.}, 59 (2021), pp. 2449-2472] to derive optimal stability and error estimates for both the velocity and the pressure. When combined with a method dependent Ritz projection for the initial data, unconditional stability can be shown while for arbitrary interpolation, pressure stability is subordinate to the fulfillment of a mild inverse CFL-type condition between space and time discretizations.

To successfully navigate its environment, an agent must construct and maintain representations of the other agents that it encounters. Such representations are useful for many tasks, but they are not without cost. As a result, agents must make decisions regarding how much information they choose to store about the agents in their environment. Using selective social learning as an example task, we motivate the problem of finding agent representations that optimally trade off between downstream utility and information cost, and illustrate two example approaches to resource-constrained social representation.

The goal of explainable Artificial Intelligence (XAI) is to generate human-interpretable explanations, but there are no computationally precise theories of how humans interpret AI generated explanations. The lack of theory means that validation of XAI must be done empirically, on a case-by-case basis, which prevents systematic theory-building in XAI. We propose a psychological theory of how humans draw conclusions from saliency maps, the most common form of XAI explanation, which for the first time allows for precise prediction of explainee inference conditioned on explanation. Our theory posits that absent explanation humans expect the AI to make similar decisions to themselves, and that they interpret an explanation by comparison to the explanations they themselves would give. Comparison is formalized via Shepard's universal law of generalization in a similarity space, a classic theory from cognitive science. A pre-registered user study on AI image classifications with saliency map explanations demonstrate that our theory quantitatively matches participants' predictions of the AI.

Forecasting has always been at the forefront of decision making and planning. The uncertainty that surrounds the future is both exciting and challenging, with individuals and organisations seeking to minimise risks and maximise utilities. The large number of forecasting applications calls for a diverse set of forecasting methods to tackle real-life challenges. This article provides a non-systematic review of the theory and the practice of forecasting. We provide an overview of a wide range of theoretical, state-of-the-art models, methods, principles, and approaches to prepare, produce, organise, and evaluate forecasts. We then demonstrate how such theoretical concepts are applied in a variety of real-life contexts. We do not claim that this review is an exhaustive list of methods and applications. However, we wish that our encyclopedic presentation will offer a point of reference for the rich work that has been undertaken over the last decades, with some key insights for the future of forecasting theory and practice. Given its encyclopedic nature, the intended mode of reading is non-linear. We offer cross-references to allow the readers to navigate through the various topics. We complement the theoretical concepts and applications covered by large lists of free or open-source software implementations and publicly-available databases.

This paper does not describe a working system. Instead, it presents a single idea about representation which allows advances made by several different groups to be combined into an imaginary system called GLOM. The advances include transformers, neural fields, contrastive representation learning, distillation and capsules. GLOM answers the question: How can a neural network with a fixed architecture parse an image into a part-whole hierarchy which has a different structure for each image? The idea is simply to use islands of identical vectors to represent the nodes in the parse tree. If GLOM can be made to work, it should significantly improve the interpretability of the representations produced by transformer-like systems when applied to vision or language