We study active set methods for optimization problems in Block Angular Form (BAF). We begin by reviewing some standard basis factorizations, including Saunders' orthogonal factorization and updates for the simplex method that do not impose any restriction on the pivot sequence and maintain the basis factorization structured in BAF throughout the algorithm. We then suggest orthogonal factorization and updating procedures that allow coarse grain parallelization, pivot updates local to the affected blocks, and independent block reinversion. A simple parallel environment appropriate (...) to the description and complexity analysis of test procedures is defined in Section 5. The factorization and updating procedures are presented in Sections 6 and 7. Our update procedure outperforms conventional Updating procedures even in a purely sequential environment. (shrink)

The authors propose a nested dissection approach to finding a fundamental cycle basis in a planar graph. The cycle basis corresponds to a fundamental null-space basis of the adjacency matrix. This problem is meant to model sparse null-space basis computations occurring in a variety of settings. An O(n3/2) bound is achieved on the nullspace basis size (i.e., the number of nonzero entries in the basis), and an O(n log n) bound on the size in the special case of grid graphs.

Inauguration speech at chair number 18 of the Brasilian Academy of Philosophy.

This article presents a simple derivation of optimization models for reaction networks leading to a generalized form of the mass-action law, and compares the formal structure of Minimum Information Divergence, Quadratic Programming and Kirchhoff type network models. These optimization models are used in related articles to develop and illustrate the operation of ontology alignment algorithms and to discuss closely connected issues concerning the epistemological and statistical significance of sharp or precise hypotheses in empirical science.

Kim’s causal exclusion argument purports to demonstrate that the non-reductive physicalist must treat mental properties (and macro-level properties in general) as causally inert. A number of authors have attempted to resist Kim’s conclusion by utilizing the conceptual resources of Woodward’s interventionist conception of causation. The viability of these responses has been challenged by Gebharter, who argues that the causal exclusion argument is vindicated by the theory of causal Bayesian networks (CBNs). Since the interventionist conception of causation relies crucially on CBNs (...) for its foundations, Gebharter’s argument appears to cast significant doubt on interventionism’s anti-reductionist credentials. In the present article, we both (1) demonstrate that Gebharter’s CBN-theoretic formulation of the exclusion argument relies on some unmotivated and philosophically significant assumptions (especially regarding the relationship between CBNs and the metaphysics of causal relevance), and (2) use Bayesian networks to develop a general theory of causal inference for multi-level systems that can serve as the foundation for an anti-reductionist interventionist account of causation.1. (shrink)

Simultaneous hypothesis tests can fail to provide results that meet logical requirements. For example, if A and B are two statements such that A implies B, there exist tests that, based on the same data, reject B but not A. Such outcomes are generally inconvenient to statisticians (who want to communicate the results to practitioners in a simple fashion) and non-statisticians (confused by conflicting pieces of information). Based on this inconvenience, one might want to use tests that satisfy logical requirements. (...) However, Izbicki and Esteves shows that the only tests that are in accordance with three logical requirements (monotonicity, invertibility and consonance) are trivial tests based on point estimation, which generally lack statistical optimality. As a possible solution to this dilemma, this paper adapts the above logical requirements to agnostic tests, in which one can accept, reject or remain agnostic with respect to a given hypothesis. Each of the logical requirements is characterized in terms of a Bayesian decision theoretic perspective. Contrary to the results obtained for regular hypothesis tests, there exist agnostic tests that satisfy all logical requirements and also perform well statistically. In particular, agnostic tests that fulfill all logical requirements are characterized as region estimator-based tests. Examples of such tests are provided. (shrink)

Decoupling is a general principle that allows us to separate simple components in a complex system. In statistics, decoupling is often expressed as independence, no association, or zero covariance relations. These relations are sharp statistical hypotheses, that can be tested using the FBST - Full Bayesian Significance Test. Decoupling relations can also be introduced by some techniques of Design of Statistical Experiments, DSEs, like randomization. This article discusses the concepts of decoupling, randomization and sparsely connected statistical models in the epistemological (...) framework of cognitive constructivism. (shrink)

Sparsity, Structure, Scaling and Stability in Computational Linear Algebra. Tutorial book for the IX Brazilian Computer Science School, held at Recife, in 1994.

Although logical consistency is desirable in scientific research, standard statistical hypothesis tests are typically logically inconsistent. To address this issue, previous work introduced agnostic hypothesis tests and proved that they can be logically consistent while retaining statistical optimality properties. This article characterizes the credal modalities in agnostic hypothesis tests and uses the hexagon of oppositions to explain the logical relations between these modalities. Geometric solids that are composed of hexagons of oppositions illustrate the conditions for these modalities to be logically (...) consistent. Prisms composed of hexagons of oppositions show how the credal modalities obtained from two agnostic tests vary according to their threshold values. Nested hexagons of oppositions summarize logical relations between the credal modalities in these tests and prove new relations. (shrink)

Optimization and Stochastic Processes Applied to Economy and Finance. Textbook for the BM&F-USP (Brazilian Mercantile and Futures Exchange - University of Sao Paulo) Master's degree program in Finance.

The reader of RTP is granted just a few paragraphs before habit is introduced: Habit! That able but slow-moving arranger who begins by letting our minds sufer for weeks on end in temporary quarters, but whom our mind is nonetheless only too happy to fnd, for without it, reduced to its own devices, it would be powerless to make any room habitable. (SW, 9, translation altered; I 8) Implied is a view of mind: powerless to interfere with habit’s course, but (...) equally powerless to reconcile us even to something as innocuous as a room, were it not for habit’s work. Corresponding to this is a view of the world: hostile. The objects are nasty, imposing, menacing: a ‘mentally poisoning’ smell, malicious curtains and a cruel mirror (SW, 9; I 8). Habit, unbidden but welcome, steps in. The mirror becomes compassionate. Habit is a central aspect of the narrator’s worldview. It appears both at major plot points and in signifcant theoretical passages. Proust had already thematised habit in some of his earliest published work – notably in ‘Violante ou la Mondanité’ (1892) (‘Violante, or High Society’) – as well as in unpublished material (see II 1352 fn. 2). His ideas have their roots in his philosophical education, where habit formed a key part of the syllabus. Indeed, in retrospect, we can say that Proust may have been taught philosophy at a time and place where habit, as a philosophical topic, was approaching its high watermark, as a major theme in French philosophical thought. Another major theme, of course, was time. (shrink)

We show how the Full Bayesian Significance Test (FBST) can be used as a model selection criterion. The FBST was presented by Pereira and Stern as a coherent Bayesian significance test. Key Words: Bayesian test; Evidence; Global optimization; Information; Model selection; Numerical integration; Posterior density; Precise hypothesis; Regularization. AMS: 62A15; 62F15; 62H15.

This article explores the metaphor of Science as provider of sharp images of our environment, using the epistemological framework of Objective Cognitive Constructivism. These sharp images are conveyed by precise scientific hypotheses that, in turn, are encoded by mathematical equations. Furthermore, this article describes how such knowledge is pro-duced by a cyclic and recursive development, perfection and reinforcement process, leading to the emergence of eigen-solutions characterized by the four essential properties of precision, stability, separability and composability. Finally, this article discusses (...) the role played by ontology and metaphysics in the scientific production process, and in which sense the resulting knowledge can be considered objective. (shrink)

In this article, we discuss some issues concerning magical thinking—forms of thought and association mechanisms characteristic of early stages of mental development. We also examine good reasons for having an ambivalent attitude concerning the later permanence in life of these archaic forms of association, and the coexistence of such intuitive but informal thinking with logical and rigorous reasoning. At the one hand, magical thinking seems to serve the creative mind, working as a natural vehicle for new ideas and innovative insights, (...) and giving form to heuristic arguments. At the other hand, it is inherently difficult to control, lacking effective mechanisms needed for rigorous manipulation. Our discussion is illustrated with many examples from the Hebrew Bible, and some final examples from modern science. (shrink)

This article discusses some continuous limit cases of Susan Haack’s crossword puzzle metaphor for the coherent development and foundation of science. The main objective of this discussion is to build a bridge between Haack’s foundherentism and the epistemological framework of objective cognitive constructivism, including its key metaphor of objects as tokens for eigen-solutions. The historical development of chemical affinity tables is used to illustrate our arguments.

This paper presents affirmation as the central normative category of Nietzsche’s positive ethics. The paper argues in particular for two interpretive claims: first, that from Beyond Good and Evil onwards, we find a new variety of Nietzschean affirmation (‘natural affirmation’), which is crucial to the strategy of his later works; and second, for reasons internal to his own philosophical aims, Nietzsche’s new variety of affirmation is seriously flawed. The author argues for the second claim on the basis that Nietzsche himself (...) requires that affirmation not perform exactly the role he requires that it perform. The author contends that we are thus faced with a major challenge to Nietzsche’s late philosophical project—that (late) Nietzschean affirmation fails by Nietzsche’s own standards. (shrink)

A critical comment on methods in Nietzsche scholarship, and some suggestions about how to improve things.

This article considers distinct ways of understanding the world, referred to in psychology as Functions of Consciousness or as Cognitive Modes, having as the scope of interest epistemology and natural sciences. Inspired by C.G. Jung's Simile of the Spectrum, we consider three basic cognitive modes associated to: (R) embodied instinct, experience, and action; (G) reality perception and learning; and (B) concept abstraction, rational thinking, and language. RGB stand for the primary colors: red, green, and blue. Accordingly, a conceptual map between (...) cognitive modes and primary and secondary colors is built based on the physics and physiology of color perception and epistemological characteristics of the aforementioned cognitive modes, leading to logical relations structured as an Hexagon of Opposition. Finally, this model of cognitive modes is applied to the analysis and interpretation of some important episodes in the historical development of physics and technology. (shrink)

Clearing algorithms are at the core of modern payment systems, facilitating the settling of multilateral credit messages with (near) minimum transfers of currency. Traditional clearing procedures use batch processing based on MILP - mixed-integer linear programming algorithms. The MILP approach demands intensive computational resources; moreover, it is also vulnerable to operational risks generated by possible defaults during the inter-batch period. This paper presents TORC3 - the Token-Ring Clearing Algorithm for Currency Circulation. In contrast to the MILP approach, TORC3 is a (...) real time heuristic procedure, demanding modest computational resources, and able to completely shield the clearing operation against the participating agents’ risk of default. (shrink)

We describe a software system for the analysis of defined benefit actuarial plans. The system uses a recursive formulation of the actuarial stochastic processes to implement precise and efficient computations of individual and group cash flows.

This paper presents REAL, a Real-Valued Attribute Classification Tree Learning Algorithm. Several of the algorithm's unique features are explained by úe users' demands for a decision support tool to be used for evaluating financial operations strategies. Compared to competing algorithms, in our applications, REAL presents maj or advantages : (1) The REAL classification trees usually have smaller error rates. (2) A single conviction (or trust) measure at each leaf is more convenient than the traditional (probability, confidence-level) pair. (3) No need (...) for an external pruning criterion. (shrink)

This paper has three main objectives: (a) Discuss the formal analogy between some important symmetry-invariance arguments used in physics, probability and statistics. Specifically, we will focus on Noether’s theorem in physics, the maximum entropy principle in probability theory, and de Finetti-type theorems in Bayesian statistics; (b) Discuss the epistemological and ontological implications of these theorems, as they are interpreted in physics and statistics. Specifically, we will focus on the positivist (in physics) or subjective (in statistics) interpretations vs. objective interpretations that (...) are suggested by symmetry and invariance arguments; (c) Introduce the cognitive constructivism epistemological framework as a solution that overcomes the realism-subjectivism dilemma and its pitfalls. The work of the physicist and philosopher Max Born will be particularly important in our discussion. (shrink)

Comments presented at the 35th International Seminar on the -- New Institutional Economics -- Empirical Methods for the Law; Syracuse, 2018.

ABSTRACT ABSTRACT: Nietzsche, we are often told, had an account of 'self' or 'mind' or a 'philosophical psychology', in which what he calls our 'drives' play a highly significant role. This underpins not merely his understanding of mind, in particular, of consciousness and action. but also his positive ethics, be they understood as authenticity, freedom, knowledge, autonomy, self-creation, or power. But Nietzsche did not have anything like a coherent account of 'the drives' according to which the self, the relationship between (...) thought and action, or consciousness could be explained; consequently, he did not have a stable account of drives on which his positive ethics could rest. By this, I do not mean that his account is incomplete or that it is philosophically indefensible: both would leave open, misleadingly, the possibility of a rational reconstruction of Nietzsche’s views; both would already assume more unity and coherence than we find in his texts. Specifically, as I show through detailed analysis, Nietzsche provides varied and inconsistent accounts of what a 'drive' is, how much we can know about drives, and the relationship between drives and conscious deliberations about action. I conclude by questioning the hunt for a Nietzschean theory: is this the best way to be reading him? (shrink)

Nietzsche writes a great deal about freedom throughout his work, but never more explicitly than in Twiling of the Idols, a book he described as 'my philosophy in a nutshell'. This paper offers an analysis of Nietzsche's conception freedom and the role it plays within Twilight.

The main goal of this article is to use the epistemological framework of a specific version of Cognitive Constructivism to address Piaget’s central problem of knowledge construction, namely, the re-equilibration of cognitive structures. The distinctive objective character of this constructivist framework is supported by formal inference methods of Bayesian statistics, and is based on Heinz von Foerster’s fundamental metaphor of objects as tokens for eigen-solutions. This epistemological perspective is illustrated using some episodes in the history of chemistry concerning the definition (...) or identification of chemical elements. Some of von Foerster’s epistemological imperatives provide general guidelines of development and argumentation. (shrink)

The aim of this paper is to begin a conversation about how we read and write about Nietzsche and, related to this, other figures in the history of philosophy. The principle of charity can appear to be a way to bridge two dif-ferent interpretative goals: getting the meaning of the text right and offering the best philosophy. I argue that the principle of charity is multiply ambiguous along three different dimensions, which I call “unit,” “mode,” and “strength”: consequently, it is (...) not a single, neutral or independent principle to which we can helpfully appeal and it cannot, in itself, perform this bridging function. Nietzsche, I suggest, is particularly ill suited to some forms of charitable reading. I compare charity to what I call “misreporting” a philosopher’s words, in order to highlight some problematic structural similarities. Finally, I assess what charity might be doing instead, if it is not intended to bridge meaning and best philosophy. (shrink)

In this paper epistemological, ontological and sociological questions concerning the statistical significance of sharp hypotheses in scientific research are investigated within the framework provided by Cognitive Constructivism and the FBST (Full Bayesian Significance Test). The constructivist framework is contrasted with the traditional epistemological settings for orthodox Bayesian and frequentist statistics provided by Decision Theory and Falsificationism.

This article explores some open questions related to the problem of verification of theories in the context of empirical sciences by contrasting three epistemological frameworks. Each of these epistemological frameworks is based on a corresponding central metaphor, namely: (a) Neo-empiricism and the gambling metaphor; (b) Popperian falsificationism and the scientific tribunal metaphor; (c) Cognitive constructivism and the object as eigen-solution metaphor. Each of one of these epistemological frameworks has also historically co-evolved with a certain statistical theory and method for testing (...) scientific hypotheses, respectively: (a) Decision theoretic Bayesian statistics and Bayes factors; (b) Frequentist statistics and p-values; (c) Constructive Bayesian statistics and e-values. This article examines with special care the Zero Probability Paradox (ZPP), related to the verification of sharp or precise hypotheses. Finally, this article makes some remarks on Lakatos’ view of mathematics as a quasi-empirical science. (shrink)

This paper introduces pragmatic hypotheses and relates this concept to the spiral of scientific evolution. Previous works determined a characterization of logically consistent statistical hypothesis tests and showed that the modal operators obtained from this test can be represented in the hexagon of oppositions. However, despite the importance of precise hypothesis in science, they cannot be accepted by logically consistent tests. Here, we show that this dilemma can be overcome by the use of pragmatic versions of precise hypotheses. These pragmatic (...) versions allow a level of imprecision in the hypothesis that is small relative to other experimental conditions. The introduction of pragmatic hypotheses allows the evolution of scientific theories based on statistical hypothesis testing to be interpreted using the narratological structure of hexagonal spirals, as defined by Pierre Gallais. (shrink)

This Element explains Nietzsche's ethics in his late works, from 1886 onwards. The first three sections explain the basics of his ethical theory – its context and presuppositions, its scope and its central tension. The next three sections explore Nietzsche's goals in writing a history of Christian morality, the content of that history, and whether he achieves his goals. The last two sections take a broader look, respectively, at Nietzsche's wider philosophy in light of his ethics and at the prospects (...) for a Nietzschean ethics after Nietzsche. (shrink)

The full Bayesian signi/cance test (FBST) for precise hypotheses is presented, with some illustrative applications. In the FBST we compute the evidence against the precise hypothesis. We discuss some of the theoretical properties of the FBST, and provide an invariant formulation for coordinate transformations, provided a reference density has been established. This evidence is the probability of the highest relative surprise set, “tangential” to the sub-manifold (of the parameter space) that defines the null hypothesis.

Heinz Von Forester characterizes the objects “known” by an autopoietic system as eigen-solutions, that is, as discrete, separable, stable and composable states of the interaction of the system with its environment. Previous articles have presented the FBST, Full Bayesian Significance Test, as a mathematical formalism specifically designed to access the support for sharp statistical hypotheses, and have shown that these hypotheses correspond, from a constructivist perspective, to systemic eigen-solutions in the practice of science. In this article several issues related to (...) the role played by language in the emergence of eigen-solutions are analyzed. The last sections also explore possible connections with the semiotic theory of Charles Sanders Peirce. (shrink)

Wittgenstein’s writings and lectures during the first half of the 1930s play a crucial role in any interpretation of the relationship between the Tractatus and the Philosophical Investigations . G. E. Moore’s notes of Wittgenstein’s Cambridge lectures, 1930-1933, offer us a remarkably careful and conscientious record of what Wittgenstein said at the time, and are much more detailed and reliable than previously published notes from those lectures. The co-authors are currently editing these notes of Wittgenstein’s lectures for a book to (...) be published by Cambridge University Press. We describe the materials that make up Moore’s notes, explain their unique value, review the principal editorial challenges that these materials present, and provide a brief outline of our editorial project. (shrink)

In this paper, the notion of degree of inconsistency is introduced as a tool to evaluate the sensitivity of the Full Bayesian Significance Test (FBST) value of evidence with respect to changes in the prior or reference density. For that, both the definition of the FBST, a possibilistic approach to hypothesis testing based on Bayesian probability procedures, and the use of bilattice structures, as introduced by Ginsberg and Fitting, in paraconsistent logics, are reviewed. The computational and theoretical advantages of using (...) the proposed degree of inconsistency based sensitivity evaluation as an alternative to traditional statistical power analysis is also discussed. (shrink)

A new Evidence Test is applied to the problem of testing whether two Poisson random variables are dependent. The dependence structure is that of Holgate’s bivariate distribution. These bivariate distribution depends on three parameters, 0 < theta_1, theta_2 < infty, and 0 < theta_3 < min(theta_1, theta_2). The Evidence Test was originally developed as a Bayesian test, but in the present paper it is compared to the best known test of the hypothesis of independence in a frequentist framework. It is (...) shown that the Evidence Test is considerably more powerful when the correlation is not too close to zero, even for small samples. (shrink)

Sortition, i.e. random appointment for public duty, has been employed by societies throughout the years as a firewall designated to prevent illegitimate interference between parties in a legal case and agents of the legal system. In judicial systems of modern western countries, random procedures are mainly employed to select the jury, the court and/or the judge in charge of judging a legal case. Therefore, these random procedures play an important role in the course of a case, and should comply with (...) some principles, such as transparency and complete auditability. Nevertheless, these principles are neglected by random procedures in some judicial systems, which are performed in secrecy and are not auditable by the involved parties. The assignment of cases in the Brazilian Supreme Court is an example of such a procedure, for it is performed using procedures unknown to the parties involved in the judicial cases. This article presents a review of how sortition has been historically employed by societies and discusses how Mathematical Statistics may be applied to random procedures of the judicial system, as it has been applied for almost a century on clinical trials, for example. A statistical model for assessing randomness in case assignment is proposed and applied to the Brazilian Supreme Court. As final remarks, guidelines for the development of good randomization procedures are outlined. (shrink)

We review the definition of the Full Bayesian Significance Test (FBST), and summarize its main statistical and epistemological characteristics. We review also the Abstract Belief Calculus (ABC) of Darwiche and Ginsberg, and use it to analyze the FBST’s value of evidence. This analysis helps us understand the FBST properties and interpretation. The definition of value of evidence against a sharp hypothesis, in the FBST setup, was motivated by applications of Bayesian statistical reasoning to legal matters where the sharp hypotheses were (...) defendants statements, to be judged according to the Onus Probandi juridical principle. (shrink)

The goal of this paper is to show that the information carried by a structural representation can be decomposed into the information carried by its component parts. In particular, the relations between the components of a structural representation carry quantifiable information about the relations between components of their signifieds. It follows that the information carried by cognitive structural representations, including cognitive maps, can in principle be quantified and decomposed. This is perhaps surprising given that the formal tools of communication theory (...) have typically only been applied to simpler representation-like states without significant structure, such as detectors or indicators. In the final section I consider using computational complexity theory to capture the processing advantages afforded by structural representation. (shrink)

It has long been known that in the context of axiomatic second-order logic (SOL), Hume's Principle (HP) is mutually interpretable with "the universe is Dedekind infinite" (DI). I offer a more fine-grained analysis of the logical strength of HP, measured by deductive implications rather than interpretability. The main result is that HP is not deductively conservative over SOL + DI. That is, SOL + HP proves additional theorems in the language of pure second-order logic that are not provable from SOL (...) + DI alone. Arguably, then, HP is not just a pure axiom of infinity, but rather it carries additional logical content. On the other hand, I show that HP is $\Pi^1_1$ conservative over SOL + DI, and that HP is conservative over SOL + DI + "the universe is well ordered" (WO). Next, I show that SOL + HP does not prove any of the simplest and most natural versions of the axiom of choice, including WO and weaker principles. Lastly, I discuss other axioms of infinity. I show that HP does not prove the Splitting or Pairing principles (axioms of infinity stronger than DI). (shrink)

Many authors have proposed constraining the behaviour of intelligent systems with ‘machine ethics’ to ensure positive social outcomes from the development of such systems. This paper critically analyses the prospects for machine ethics, identifying several inherent limitations. While machine ethics may increase the probability of ethical behaviour in some situations, it cannot guarantee it due to the nature of ethics, the computational limitations of computational agents and the complexity of the world. In addition, machine ethics, even if it were to (...) be ‘solved’ at a technical level, would be insufficient to ensure positive social outcomes from intelligent systems. (shrink)

Now that she is old enough to be taken to boring, so-called “cultural” events by her aging, academic relatives, we have just taken Anya to see a performance of Julius Caesar. When it’s over, we discuss the acting, the poetry, the famous lines. At some point, Anya asks: “I wonder if it happened like that?” Anya has not radically misunderstood what we just watched; she did not, for example, rush down and yell at Caesar that he’d better read that scroll. (...) Her question is not uncommon as a response to a history play, from audience members both young and old. It is perfectly intelligible; I would like to give her an answer. Before I sketch some possible answers, it is worth saying something more about Anya’s. (shrink)

This paper offers a reading of Thus Spoke Zarathustra, arguing that there is a conflict between Zarathustra's hope for something greater (in the form of the Übermensch) and his conception of the eternal recurrence.

Over the last fifteen years, an ambitious explanatory framework has been proposed to unify explanations across biology and cognitive science. Active inference, whose most famous tenet is the free energy principle, has inspired excitement and confusion in equal measure. Here, we lay the ground for proper critical analysis of active inference, in three ways. First, we give simplified versions of its core mathematical models. Second, we outline the historical development of active inference and its relationship to other theoretical approaches. Third, (...) we describe three different kinds of claim -- labelled mathematical, empirical and general -- routinely made by proponents of the framework, and suggest dialectical links between them. Overall, we aim to increase philosophical understanding of active inference so that it may be more readily evaluated. -/- This the final submitted version of the Introduction to the Topical Collection "The Free Energy Principle: From Biology to Cognition", forthcoming in Biology & Philosophy. (shrink)

This article analyzes the role of entropy in Bayesian statistics, focusing on its use as a tool for detection, recognition and validation of eigen-solutions. “Objects as eigen-solutions” is a key metaphor of the cognitive constructivism epistemological framework developed by the philosopher Heinz von Foerster. Special attention is given to some objections to the concepts of probability, statistics and randomization posed by George Spencer-Brown, a figure of great influence in the field of radical constructivism.