Calibrating Einstein field equations using rippling 3-Riemannian structure for gravity with dark matter effects

The paper presents modifications to Einstein field equations (EFEs) based on the model proposed in the working paper, 'Rippling 3-Riemannian structure describing gravity with dark matter effects'. The model proposes matter and energy are separate entities and energy is a property of three dimensional probabilistic structure spanning space. Mass interacts by binding energy density causing variations in length and time scales, mathematically equivalent to spacetime curvature in general relativity. Gravity is thus described as flow and distribution of energy density. Bounded energy density is the additional source of gravity leading to dark matter observations. The results of the model proposes two EFEs for large and largest scales and further predicts dependence of cosmological constant on space and time coordinates.

Quantum Fields as Category Algebras

In the present paper, we propose a new approach to quantum fields in terms of category algebras and states on categories. We define quantum fields and their states as category algebras and states on causal categories with partial involution structures. By utilizing category algebras and states on categories instead of simply considering categories, we can directly integrate relativity as a category theoretic structure and quantumness as a noncommutative probabilistic structure. Conceptual relationships with conventional approaches to quantum fields, including Algebraic Quantum Field Theory (AQFT) and Topological Quantum Field Theory (TQFT), are also be discussed.

Cluster’s Number Free Bayes Prediction of General Framework on Mixture of Regression Models

Prediction based on a single linear regression model is one of the most common way in various field of studies. It enables us to understand the structure of data, but might not be suitable to express the data whose structure is complex. To express the structure of data more accurately, we make assumption that the data can be divided in clusters, and has a linear regression model in each cluster. In this case, we can assume that each explanatory variable has their own role; explaining the assignment to the clusters, explaining the regression to the target variable, or being both of them. Introducing probabilistic structure to the data generating process, we derive the optimal prediction under Bayes criterion and the algorithm which calculates it sub-optimally with variational inference method. One of the advantages of our algorithm is that it automatically weights the probabilities of being each number of clusters in the process of the algorithm, therefore it solves the concern about selection of the number of clusters. Some experiments are performed on both synthetic and real data to demonstrate the above advantages and to discover some behaviors and tendencies of the algorithm.

Connecting Social Psychology and Deep Reinforcement Learning: A Probabilistic Predictor on the Intention to Do Home-Based Physical Activity After Message Exposure

Previous research has shown that sending personalized messages consistent with the recipient's psychological profile is essential to activate the change toward a healthy lifestyle. In this paper we present an example of how artificial intelligence can support psychology in this process, illustrating the development of a probabilistic predictor in the form of a Dynamic Bayesian Network (DBN). The predictor regards the change in the intention to do home-based physical activity after message exposure. The data used to construct the predictor are those of a study on the effects of framing in communication to promote physical activity at home during the Covid-19 lockdown. The theoretical reference is that of psychosocial research on the effects of framing, according to which similar communicative contents formulated in different ways can be differently effective depending on the characteristics of the recipient. Study participants completed a first questionnaire aimed at measuring the psychosocial dimensions involved in doing physical activity at home. Next, they read recommendation messages formulated with one of four different frames (gain, non-loss, non-gain, and loss). Finally, they completed a second questionnaire measuring their perception of the messages and again the intention to exercise at home. The collected data were analyzed to elicit a DBN, i.e., a probabilistic structure representing the interrelationships between all the dimensions considered in the study. The adopted procedure was aimed to achieve a good balance between explainability and predictivity. The elicited DBN was found to be consistent with the psychosocial theories assumed as reference and able to predict the effectiveness of the different messages starting from the relevant psychosocial dimensions of the recipients. In the next steps of our project, the DBN will form the basis for the training of a Deep Reinforcement Learning (DRL) system for the synthesis of automatic interaction strategies. In turn, the DRL system will train a Deep Neural Network (DNN) that will guide the online interaction process. The discussion focuses on the advantages of the proposed procedure in terms of interpretability and effectiveness.

Estimating the class prior for positive and unlabelled data via logistic regression

In the paper, we revisit the problem of class prior probability estimation with positive and unlabelled data gathered in a single-sample scenario. The task is important as it is known that in positive unlabelled setting, a classifier can be successfully learned if the class prior is available. We show that without additional assumptions, class prior probability is not identifiable and thus the existing non-parametric estimators are necessarily biased in general if extra assumptions are not imposed. The magnitude of their bias is also investigated. The problem becomes identifiable when the probabilistic structure satisfies mild semi-parametric assumptions. Consequently, we propose a method based on a logistic fit and a concave minorization of its (non-concave) log-likelihood. The experiments conducted on artificial and benchmark datasets as well as on a large clinical database MIMIC indicate that the estimation errors for the proposed method are usually lower than for its competitors and that it is robust against departures from logistic settings.

How dynamics constrains probabilities in general probabilistic theories

We introduce a general framework for analysing general probabilistic theories, which emphasises the distinction between the dynamical and probabilistic structures of a system. The dynamical structure is the set of pure states together with the action of the reversible dynamics, whilst the probabilistic structure determines the measurements and the outcome probabilities. For transitive dynamical structures whose dynamical group and stabiliser subgroup form a Gelfand pair we show that all probabilistic structures are rigid (cannot be infinitesimally deformed) and are in one-to-one correspondence with the spherical representations of the dynamical group. We apply our methods to classify all probabilistic structures when the dynamical structure is that of complex Grassmann manifolds acted on by the unitary group. This is a generalisation of quantum theory where the pure states, instead of being represented by one-dimensional subspaces of a complex vector space, are represented by subspaces of a fixed dimension larger than one. We also show that systems with compact two-point homogeneous dynamical structures (i.e. every pair of pure states with a given distance can be reversibly transformed to any other pair of pure states with the same distance), which include systems corresponding to Euclidean Jordan Algebras, all have rigid probabilistic structures.

Prefaces, Sorites and Guides to Reasoning

Is there an interesting relation between the Preface paradox and the Sorites paradox that might be used to illuminate either or both of those paradoxes and the phenomena of rationality and vagueness with which they, respectively, are bound up? In particular, if we consider the analogy alongside a familiar response to the Preface Paradox that employs degrees of belief, does this give any support to the thought that we should adopt some kind of degree-theoretic treatment of vagueness and the sorites? This chapter argues that it does not; indeed exploring the disanalogies contributes to a case against such a treatment of vagueness more generally. Among other views, it considers Edgington’s account of vagueness that employs a probabilistic structure of ‘verities’. It then contends that appeal to the framework of supervaluationism yields a better guide to reasoning in vague language than the degree-theoretic treatment can sustain.

Viability and Arbitrage Under Knightian Uncertainty

We reconsider the microeconomic foundations of financial economics. Motivated by the importance of Knightian uncertainty in markets, we present a model that does not carry any probabilistic structure ex ante, yet is based on a common order. We derive the fundamental equivalence of economic viability of asset prices and absence of arbitrage. We also obtain a modified version of the fundamental theorem of asset pricing using the notion of sublinear pricing measures. Different versions of the efficient market hypothesis are related to the assumptions one is willing to impose on the common order.