Constraint-Based Causal Discovery using Partial Ancestral Graphs in the presence of Cycles

While feedback loops are known to play important roles in many complex systems, their existence is ignored in a large part of the causal discovery literature, as systems are typically assumed to be acyclic from the outset. When applying causal discovery algorithms designed for the acyclic setting on data generated by a system that involves feedback, one would not expect to obtain correct results. In this work, we show that---surprisingly---the output of the Fast Causal Inference (FCI) algorithm is correct if it is applied to observational data generated by a system that involves feedback. More specifically, we prove that for observational data generated by a simple and $\sigma$-faithful Structural Causal Model (SCM), FCI is sound and complete, and can be used to consistently estimate (i) the presence and absence of causal relations, (ii) the presence and absence of direct causal relations, (iii) the absence of confounders, and (iv) the absence of specific cycles in the causal graph of the SCM. We extend these results to constraint-based causal discovery algorithms that exploit certain forms of background knowledge, including the causally sufficient setting (e.g., the PC algorithm) and the Joint Causal Inference setting (e.g., the FCI-JCI algorithm).Comment: Major revision. To appear in Proceedings of the 36 th Conference on Uncertainty in Artificial Intelligence (UAI), PMLR volume 124, 202

Nondegeneracy and Stability of Antiperiodic Bound States for Fractional Nonlinear Schr\"odinger Equations

We consider the existence and stability of real-valued, spatially antiperiodic standing wave solutions to a family of nonlinear Schr\"odinger equations with fractional dispersion and power-law nonlinearity. As a key technical result, we demonstrate that the associated linearized operator is nondegenerate when restricted to antiperiodic perturbations, i.e. that its kernel is generated by the translational and gauge symmetries of the governing evolution equation. In the process, we provide a characterization of the antiperiodic ground state eigenfunctions for linear fractional Schr\"odinger operators on $\mathbb{R}$ with real-valued, periodic potentials as well as a Sturm-Liouville type oscillation theory for the higher antiperiodic eigenfunctions.Comment: 46 pages, 2 figure

Ancestral Causal Inference

Constraint-based causal discovery from limited data is a notoriously difficult challenge due to the many borderline independence test decisions. Several approaches to improve the reliability of the predictions by exploiting redundancy in the independence information have been proposed recently. Though promising, existing approaches can still be greatly improved in terms of accuracy and scalability. We present a novel method that reduces the combinatorial explosion of the search space by using a more coarse-grained representation of causal information, drastically reducing computation time. Additionally, we propose a method to score causal predictions based on their confidence. Crucially, our implementation also allows one to easily combine observational and interventional data and to incorporate various types of available background knowledge. We prove soundness and asymptotic consistency of our method and demonstrate that it can outperform the state-of-the-art on synthetic data, achieving a speedup of several orders of magnitude. We illustrate its practical feasibility by applying it on a challenging protein data set.Comment: In Proceedings of Advances in Neural Information Processing Systems 29 (NIPS 2016

OVID'S EXILIC VOCABULARY

Introduction Ovid's artistry with words has been called "logodaedaly", creative word magic.2 His "painting with words" lies partly in a controlled use of synonyms.3 The poet's originality in creating new words has also been much commented upon.4 His artistry with words when in exile offers continued pleasure. Words were of paramount importance for an exiled poet who was reaching out to his friends and to the enemy who exiled him. In the process he created a word-portrait of himself as suppliant; as Downing (1993:13) puts it: "The author makes a self, while the self makes a book of the self." Ovid's readership in Rome would have been familiar with the whole of his earlier oeuvre as context for a particular diction. In the context of his exile, the poet's choice of words and the uses to which he put his vocabulary were a powerful means of influencing public thought. Augustus, as very particular member of the more general readership, had to be persuaded that his previous works were innocuous, if ever the exile were to be allowed to return. At the same time the poet seems to have sought a means of criticizing the emperor without antagonising him

FRONTO AVUS: THE TALE OF A GRANDFATHER

This paper examines some examples from the correspondence of the secondcentury rhetor, the Romanised African M. Cornelius Fronto, in particular letters that relate to the death of his grandson, drawing conclusions about Fronto as grandfather and as a person who had sustained previous bereavements. His attitude to his daughter Cratia2 and son-in-law Aufidius Victorinus receives special attention. The question of why Fronto seems to favour Victorinus over his own daughter when both are plunged into grief is addressed. It seems that in the grief of the younger man the older relives the agonies of his own youth, when he and his wife lost a series of children before bringing up Cratia as an only child

RENDERING CAESAR: THOUGHTS ON THE TRANSLATION INTO ENGLISH OF N P VAN WYK LOUW’S GERMANICUS

This paper discusses its author’s attempt to translate into English the verse drama Germanicus by the Afrikaans poet NP Van Wyk Louw, which is based on Tacitus’ Annales 1-3. After a general discussion of translation theory and of Louw’s theories relating to the classical tradition, the paper highlights, with examples, problems encountered on the levels of prosody, of register and of equivalence of meaning. Louw’s poetic Afrikaans is so concise that it requires an effort to be as brief in English. “Shakespearian English”, both lexis and wordorder, is closer to the Germanic Afrikaans, but would be unacceptable in a modern translation. Louw’s idiosyncratic use of Afrikaans, deliberate archaisms and occasional neologisms call for interpretative reading before these can be translated. The paper ends with a short reference to the place of Louw’s Germanicus in the international Classical tradition

LATIN FOR STUDENTS WITH AN AFRICAN HOME LANGUAGE

One of my favourite quotations has always been Tennyson's "The old order changeth, yielding place to new / and God fulfils himself in many ways, / lest one good custom should corrupt the world." That means, essentially, "Change is good, and we should not fear it"