Potentiality and Contradiction in Quantum Mechanics

Following J.-Y.B\'eziau in his pioneer work on non-standard interpretations of the traditional square of opposition, we have applied the abstract structure of the square to study the relation of opposition between states in superposition in orthodox quantum mechanics in \cite{are14}. Our conclusion was that such states are \ita{contraries} (\ita{i.e.} both can be false, but both cannot be true), contradicting previous analyzes that have led to different results, such as those claiming that those states represent \ita{contradictory} properties (\ita{i. e.} they must have opposite truth values). In this chapter we bring the issue once again into the center of the stage, but now discussing the metaphysical presuppositions which underlie each kind of analysis and which lead to each kind of result, discussing in particular the idea that superpositions represent potential contradictions. We shall argue that the analysis according to which states in superposition are contrary rather than contradictory is still more plausible

Axiomatization and Models of Scientific Theories

In this paper we discuss two approaches to the axiomatization of scien- tific theories in the context of the so called semantic approach, according to which (roughly) a theory can be seen as a class of models. The two approaches are associated respectively to Suppes’ and to da Costa and Chuaqui’s works. We argue that theories can be developed both in a way more akin to the usual mathematical practice (Suppes), in an informal set theoretical environment, writing the set theoretical predicate in the language of set theory itself or, more rigorously (da Costa and Chuaqui), by employing formal languages that help us in writing the postulates to define a class of structures. Both approaches are called internal, for we work within a mathematical framework, here taken to be first-order ZFC. We contrast these approaches with an external one, here discussed briefly. We argue that each one has its strong and weak points, whose discussion is relevant for the philosophical foundations of science

Impact and Recovery Process of Mini Flash Crashes: An Empirical Study

In an Ultrafast Extreme Event (or Mini Flash Crash), the price of a traded stock increases or decreases strongly within milliseconds. We present a detailed study of Ultrafast Extreme Events in stock market data. In contrast to popular belief, our analysis suggests that most of the Ultrafast Extreme Events are not primarily due to High Frequency Trading. In at least 60 percent of the observed Ultrafast Extreme Events, the main cause for the events are large market orders. In times of financial crisis, large market orders are more likely which can be linked to the significant increase of Ultrafast Extreme Events occurrences. Furthermore, we analyze the 100 trades following each Ultrafast Extreme Events. While we observe a tendency of the prices to partially recover, less than 40 percent recover completely. On the other hand we find 25 percent of the Ultrafast Extreme Events to be almost recovered after only one trade which differs from the usually found price impact of market orders

Identical particles in quantum mechanics: favouring the Received View

The so-called Received View (RV) on quantum non-individuality states, basically, that quantum particles are not individuals. It has received an amount of criticism in the recent literature, most of it concerning the relation between the RV and the relation of identity. In this chapter we carefully characterise a family of concepts involved in clarifying the view, indicating how the very idea of failure of identity, commonly used to define the RV, may be understood. By doing so, we hope to dissipate some misunderstandings about the RV, which shall also be seen as evidence of its tenability

Identical particles in quantum mechanics: favouring the Received View

The so-called Received View (RV) on quantum non-individuality states, basically, that quantum particles are not individuals. It has received an amount of criticism in the recent literature, most of it concerning the relation between the RV and the relation of identity. In this chapter we carefully characterise a family of concepts involved in clarifying the view, indicating how the very idea of failure of identity, commonly used to define the RV, may be understood. By doing so, we hope to dissipate some misunderstandings about the RV, which shall also be seen as evidence of its tenability

Polygonic spectra and TR with coefficients

We introduce the notion of a polygonic spectrum which is designed to axiomatize the structure on topological Hochschild homology $\mathrm{THH}(R,M)$ of an $\mathbb{E}_1$-ring $R$ with coefficients in an $R$-bimodule $M$. For every polygonic spectrum $X$, we define a spectrum $\mathrm{TR}(X)$ as the mapping spectrum from the polygonic version of the sphere spectrum $\mathbb{S}$ to $X$. In particular if applied to $X = \mathrm{THH}(R,M)$ this gives a conceptual definition of $\mathrm{TR}(R,M)$. Every cyclotomic spectrum gives rise to a polygonic spectrum and we prove that TR agrees with the classical definition of TR in this case. We construct Frobenius and Verschiebung maps on $\mathrm{TR}(X)$ by exhibiting $\mathrm{TR}(X)$ as the $\mathbb{Z}$-fixedpoints of a quasifinitely genuine $\mathbb{Z}$-spectrum. The notion of quasifinitely genuine $\mathbb{Z}$-spectra is a new notion that we introduce and discuss inspired by a similar notion over $\mathbb{Z}$ introduced by Kaledin. Besides the usual coherences for genuine spectra, this notion additionally encodes that $\mathrm{TR}(X)$ admits certain infinite sums of Verschiebung maps.Comment: 61 pages, comments are welcom

Towards a hybrid parallelization of lattice Boltzmann methods

AbstractOngoing research towards the development of a hybrid parallelization concept for lattice Boltzmann methods is presented. It allows coping with platforms sharing both the properties of shared and distributed architectures. The proposed approach relies on spatial domain decomposition where each domain represents a basic block entity which is solved on a symmetric multi-processing (SMP) system. Emphasis is placed on the software design and the reworking needed to achieve good performance using OpenMP in that context. Those ideas are implemented in the C++ project OpenLB, which is also sketched in this article. The efficiency of the proposed approaches is tested on a 3D benchmark problem and compared with a purely MPI based approach

Bússola homilética: indicando princípios orientadores para o labor homilético

Preaching the word of God has always been challenging. It is even more challenging at present because of the influences to which members of the Christian churches are exposed on a daily basis. Those who want to preach the word of God must do their best, show that they have knowledge about God and their hearers. The greater their intimacy with God's word and the people hearing the sermon, the greater are the chances that the preacher will bring a message that is relevant to their audience. God is revealed in the cultivation of spirituality. One can get to know the people through visits, surveys (with specific foci), by listening, through dialogue. The preparation of the sermon has to take the homiletic methods into account. Spirituality will shape the sermon, and the joys and worries of the hearers have to be taken into account. The hearer's participation is so essential that the sermon is concluded in their ears and heart. (One should not bring ready-made truths, but help the hearer to draw their own conclusions. One should allow the hearer to join the reflection and to withdraw from it at the right time.)Pregar a palavra de Deus sempre foi algo desafiador. Na atualidade, é mais ainda, devido às influências que os membros das igrejas cristãs recebem diariamente. Quem quiser pregar a palavra de Deus, deverá esmerar-se para tal tarefa, mostrar que tem conhecimento acerca de Deus e também, de seus ouvintes. Quanto mais intimidade com Deus e com as pessoas ouvintes das prédicas, mais chance a pessoa do/a pregador/a tem de trazer uma mensagem relevante para o seu público. Deus se dá a conhecer no cultivo da espiritualidade. Já as pessoas, conhece-se fazendo visitas, pesquisas (com enfoques específicos), ouvindo, dialogando. A confecção da prédica deverá levar em conta os métodos homiléticos. A espiritualidade moldará a prédica, bem como o que alegra e o que preocupa os/as ouvintes deverá ser levado em conta. A participação do ouvinte é tamanha que a prédica é finalizada nos ouvidos e no coração do ouvinte. (Não trazer verdades prontas, mas conduzir o/a ouvinte a tirar as suas próprias conclusões. Permitir que o/a ouvinte embarque e desembarque da reflexão no seu devido tempo.

Scalable PAC-Bayesian Meta-Learning via the PAC-Optimal Hyper-Posterior: From Theory to Practice

Meta-Learning aims to speed up the learning process on new tasks by acquiring useful inductive biases from datasets of related learning tasks. While, in practice, the number of related tasks available is often small, most of the existing approaches assume an abundance of tasks; making them unrealistic and prone to overfitting. A central question in the meta-learning literature is how to regularize to ensure generalization to unseen tasks. In this work, we provide a theoretical analysis using the PAC-Bayesian theory and present a generalization bound for meta-learning, which was first derived by Rothfuss et al. (2021). Crucially, the bound allows us to derive the closed form of the optimal hyper-posterior, referred to as PACOH, which leads to the best performance guarantees. We provide a theoretical analysis and empirical case study under which conditions and to what extent these guarantees for meta-learning improve upon PAC-Bayesian per-task learning bounds. The closed-form PACOH inspires a practical meta-learning approach that avoids the reliance on bi-level optimization, giving rise to a stochastic optimization problem that is amenable to standard variational methods that scale well. Our experiments show that, when instantiating the PACOH with Gaussian processes and Bayesian Neural Networks models, the resulting methods are more scalable, and yield state-of-the-art performance, both in terms of predictive accuracy and the quality of uncertainty estimates.Comment: 61 pages. arXiv admin note: text overlap with arXiv:2002.0555

Making Sense of Non-Individuals in Quantum Mechanics

In this work, we focus on a very specific case study: assuming that quantum theories deal with “particles” of some kind (point particles in orthodox non-relativistic quantum mechanics, field excitations in quantum field theories), what kind of entity can such particles be? One possible answer, the one we shall examine here, is that they are not the usual kind of object found in daily life: individuals. Rather, we follow a suggestion by Erwin Schrödinger, according to which quantum mechanics poses a revolutionary kind of entity: non-individuals. While physics, as a scientific field, is not concerned with whether entities posited by a specific physical theory are individuals or not, answering this question is part of the quest for a better understanding of physical reality. Here lies, in large measure, the relevance of ontology