Accumulating data suggest that the eukaryotic cell originated from a merger of two prokaryotes, an archaeal host and a bacterial endosymbiont. However, since prokaryotes are unable to perform phagocytosis, the means by which the endosymbiont entered its host is an enigma. We suggest that a predatory or parasitic interaction between prokaryotes provides a reasonable explanation for this conundrum. According to the model presented here, the host in this interaction was an anaerobic archaeon with a periplasm‐like space. The predator was a (...) small (facultative) aerobic α‐proteobacterium, which penetrated and replicated within the host periplasm, and later became the mitochondria. Plausible conditions under which this interaction took place and circumstances that may have led to the contemporary complex eukaryotic cell are discussed. (shrink)

This is a comprehensive study of the dynamics that underlie information processing in foreign policy decision-making, the resultant biases and errors, and the implications for the quality of decisions. The World in Their Minds is a compendium of the manifold ways that misperception and, hence, miscalculation can enter into seemingly rational policy choice. The cases of Vietnam for the Americans and the Yom Kippur War for the Israelis constitute the primary database for the number of illustrations cited.

In this paper, we distinguish between different sorts of assessments of algorithmic systems, describe our process of assessing such systems for ethical risk, and share some key challenges and lessons for future algorithm assessments and audits. Given the distinctive nature and function of a third-party audit, and the uncertain and shifting regulatory landscape, we suggest that second-party assessments are currently the primary mechanisms for analyzing the social impacts of systems that incorporate artificial intelligence. We then discuss two kinds of as-sessments: (...) an ethical risk assessment and a narrower, technical algo-rithmic bias assessment. We explain how the two assessments depend on each other, highlight the importance of situating the algorithm within its particular socio-technical context, and discuss a number of lessons and challenges for algorithm assessments and, potentially, for algorithm audits. The discussion builds on our team’s experience of advising and conducting ethical risk assessments for clients across dif-ferent industries in the last four years. Our main goal is to reflect on the key factors that are potentially ethically relevant in the use of algo-rithms, and draw lessons for the nascent algorithm assessment and audit industry, in the hope of helping all parties minimize the risk of harm from their use. (shrink)

We prove that under reasonable assumptions, every cat (compact abstract theory) is metric, and develop some of the theory of metric cats. We generalise Morley's theorem: if a countable Hausdorff cat T has a unique complete model of density character Λ ≥ ω₁, then it has a unique complete model of density character Λ for every Λ ≥ ω₁.

We give a general framework for the treatment of perturbations of types and structures in continuous logic, allowing to specify which parts of the logic may be perturbed. We prove that separable, elementarily equivalent structures which are approximately $aleph_0$-saturated up to arbitrarily small perturbations are isomorphic up to arbitrarily small perturbations. As a corollary, we obtain a Ryll-Nardzewski style characterisation of complete theories all of whose separable models are isomorphic up to arbitrarily small perturbations.

We develop the general theory of topometric spaces, i.e., topological spaces equipped with a well-behaved lower semi-continuous metric. Spaces of global and local types in continuous logic are the motivating examples for the study of such spaces. In particular, we develop Cantor-Bendixson analysis of topometric spaces, which can serve as a basis for the study of local stability (extending the ad hoc development in Ben Yaacov I and Usvyatsov A, Continuous first order logic and local stability. Trans Am Math (...) Soc, in press), as well as of global ${\aleph_0}$ -stability. We conclude with a study of perturbation systems (see Ben Yaacov I, On perturbations of continuous structures, submitted) in the formalism of topometric spaces. In particular, we show how the abstract development applies to ${\aleph_0}$ -stability up to perturbation. (shrink)

We revisit the foundations of positive model theory, introducing h-inductive sentences. These allow a considerably simplified presentation of positive model theory, as well as a characterisation of Hausdorff cats by an amalgamation property of their h-inductive theory.

We present an adaptation of continuous first order logic to unbounded metric structures. This has the advantage of being closer in spirit to C. Ward Henson's logic for Banach space structures than the unit ball approach, as well as of applying in situations where the unit ball approach does not apply. We also introduce the process of single point emph{emboundment}, allowing to bring unbounded structures back into the setting of bounded continuous first order logic. Together with results from cite{BenYaacov:Perturbations} regarding (...) perturbations of bounded metric structures, we prove a Ryll-Nardzewski style characterisation of theories of Banach spaces which are separably categorical up to small perturbation of the norm. This last result is motivated by an unpublished result of Henson. (shrink)

In recent years, the ethical impact of AI has been increasingly scrutinized, with public scandals emerging over biased outcomes, lack of transparency, and the misuse of data. This has led to a growing mistrust of AI and increased calls for mandated ethical audits of algorithms. Current proposals for ethical assessment of algorithms are either too high level to be put into practice without further guidance, or they focus on very specific and technical notions of fairness or transparency that do not (...) consider multiple stakeholders or the broader social context. In this article, we present an auditing framework to guide the ethical assessment of an algorithm. The audit instrument itself is comprised of three elements: a list of possible interests of stakeholders affected by the algorithm, an assessment of metrics that describe key ethically salient features of the algorithm, and a relevancy matrix that connects the assessed metrics to stakeholder interests. The proposed audit instrument yields an ethical evaluation of an algorithm that could be used by regulators and others interested in doing due diligence, while paying careful attention to the complex societal context within which the algorithm is deployed. (shrink)

In Israel, whistleblowing in the nursing profession has been largely ignored. This topic is neither part of the professional—ethical discourse nor a subject for research. Focusing on the divide between internal and external whistleblowing, this article presents a study that explores nurses’ willingness to disclose an act that could jeopardize the rights or safety of patients. Internal disclosure entails reporting wrongdoing to an authority within the organization. External disclosure involves reporting the offense to an outside agency, such as a professional (...) organization or the press. The study’s findings indicate that the nurse respondents viewed both the harmful misconduct of a colleague and that of a manager as being very serious. In such dilemmas the nurses reported a desire to correct the wrongdoing and a concomitant willingness to act. They were, however, much more likely to whistleblow internally rather than externally. This study revealed a pattern of nurses’ progressive retraction as the circle of disclosure widened. (shrink)

We develop positive model theory, which is a non first order analogue of classical model theory where compactness is kept at the expense of negation. The analogue of a first order theory in this framework is a compact abstract theory: several equivalent yet conceptually different presentations of this notion are given. We prove in particular that Banach and Hilbert spaces are compact abstract theories, and in fact very well-behaved as such.

We continue [2], developing simplicity in the framework of compact abstract theories. Due to the generality of the context we need to introduce definitions which differ somewhat from the ones use in first order theories. With these modified tools we obtain more or less classical behaviour: simplicity is characterized by the existence of a certain notion of independence, stability is characterized by simplicity and bounded multiplicity, and hyperimaginary canonical bases exist.

We introduce the notion of a lovely pair of models of a simple theory T, generalizing Poizat's “belles paires” of models of a stable theory and the third author's “generic pairs” of models of an SU-rank 1 theory. We characterize when a saturated model of the theory TP of lovely pairs is a lovely pair , finding an analog of the nonfinite cover property for simple theories. We show that, under these hypotheses, TP is also simple, and we study forking (...) and canonical bases in TP. We also prove that assuming only that T is low, the existentially universal models of the universal part of a natural expansion TP+ of TP, are lovely pairs, and “simple Robinson universal domains”. (shrink)

-/- Continuous first-order logic has found interest among model theorists who wish to extend the classical analysis of “algebraic” structures (such as fields, group, and graphs) to various natural classes of complete metric structures (such as probability algebras, Hilbert spaces, and Banach spaces). With research in continuous first-order logic preoccupied with studying the model theory of this framework, we find a natural question calls for attention. Is there an interesting set of axioms yielding a completeness result? -/- The primary purpose (...) of this article is to show that a certain, interesting set of axioms does indeed yield a completeness result for continuous first-order logic. In particular, we show that in continuous first-order logic a set of formulae is (completely) satisfiable if (and only if) it is consistent. From this result it follows that continuous first-order logic also satisfies an approximated form of strong completeness, whereby Σ⊧φ (if and) only if Σ⊢φ ∸2−n for all n < ω. This approximated form of strong completeness asserts that if Σ⊧φ, then proofs from Σ, being finite, can provide arbitrarily better approximations of the truth of φ. -/- Additionally, we consider a different kind of question traditionally arising in model theory—that of decidability. When is the set of all consequences of a theory (in a countable, recursive language) recursive? Say that a complete theory T is decidable if for every sentence φ, the value φ T is a recursive real, and moreover, uniformly computable from φ. If T is incomplete, we say it is decidable if for every sentence φ the real number φ T o is uniformly recursive from φ, where φ T o is the maximal value of φ consistent with T. As in classical first-order logic, it follows from the completeness theorem of continuous first-order logic that if a complete theory admits a recursive (or even recursively enumerable) axiomatization then it is decidable. (shrink)

1. We show that if p is a real type which is internal in a set $\sigma$ of partial types in a simple theory, then there is a type p' interbounded with p, which is finitely generated over $\sigma$ , and possesses a fundamental system of solutions relative to $\sigma$ . 2. If p is a possibly hyperimaginary Lascar strong type, almost \sigma-internal$ , but almost orthogonal to $\sigma^{\omega}$ , then there is a canonical non-trivial almost hyperdefinable polygroup which multi-acts (...) on p while fixing $\sigma$ generically. In case p is $\sigma-internal$ and T is stable, this is the binding group of p over \sigma$. (shrink)

In recent years, scientists have increasingly taken to investigate the predictive nature of cognition. We argue that prediction relies on abstraction, and thus theories of predictive cognition need an explicit theory of abstract representation. We propose such a theory of the abstract representational capacities that allow humans to transcend the “here-and-now.” Consistent with the predictive cognition literature, we suggest that the representational substrates of the mind are built as ahierarchy, ranging from the concrete to the abstract; however, we argue that (...) there are qualitative differences between elements along this hierarchy, generating meaningful, often unacknowledged,diversity.Echoing views from philosophy, we suggest that the representational hierarchy can be parsed into:modality-specificrepresentations, instantiated on perceptual similarity;multimodalrepresentations, instantiated primarily on the discovery of spatiotemporal contiguity; andcategoricalrepresentations, instantiated primarily on social interaction. These elements serve as the building blocks ofcomplex structures discussed in cognitive psychology (e.g., episodes, scripts) and are the inputs for mental representations that behave like functions, typically discussed in linguistics (i.e.,predicators). We support our argument for representational diversity by explaining how the elements in our ontology are all required to account for humans’ predictive cognition (e.g., in subserving logic-based prediction; in optimizing the trade-off between accurate and detailed predictions) and by examining how the neuroscientific evidence coheres with our account. In doing so, we provide a testable model of the neural bases of conceptual cognition and highlight several important implications to research on self-projection, reinforcement learning, and predictive-processing models of psychopathology. (shrink)

We point out how the "Fundamental Theorem of Stability Theory", namely the equivalence between the "non order property" and definability of types, proved by Shelah in the 1970s, is in fact an immediate consequence of Grothendieck's "Criteres de compacite" from 1952. The familiar forms for the defining formulae then follow using Mazur's Lemma regarding weak convergence in Banach spaces.

Continuous first-order logic has found interest among model theorists who wish to extend the classical analysis of “algebraic” structures to various natural classes of complete metric structures. With research in continuous first-order logic preoccupied with studying the model theory of this framework, we find a natural question calls for attention. Is there an interesting set of axioms yielding a completeness result?The primary purpose of this article is to show that a certain, interesting set of axioms does indeed yield a completeness (...) result for continuous first-order logic. In particular, we show that in continuous first-order logic a set of formulae is satisfiable if it is consistent. From this result it follows that continuous first-order logic also satisfies an approximated form of strong completeness, whereby Σ⊨φ only if Σ⊢φ∸ 2-n for all n < ω. This approximated form of strong completeness asserts that if Σ⊨φ, then proofs from Σ, being finite, can provide arbitrarily better approximations of the truth of φ.Additionally, we consider a different kind of question traditionally arising in model theory—that of decidability. When is the set of all consequences of a theory recursive? Say that a complete theory T is decidable if for every sentence φ, the value φT is a recursive real, and moreover, uniformly computable from φ. If T is incomplete, we say it is decidable if for every sentence φ the real number φT∘ is uniformly recursive from φ, where φT∘is the maximal value of φ consistent with T. As in classical first-order logic, it follows from the completeness theorem of continuous first-order logic that if a complete theory admits a recursive axiomatization then it is decidable. (shrink)

We prove that the definition of supersimplicity in metric structures from [7] is equivalent to an a priori stronger variant. This stronger variant is then used to prove that if T is a supersimple Hausdorff cat then so is its theory of lovely pairs.

ʻUmar II’s vast correspondence with governors is examined for the discussion of Islamization and acculturation. From the caliph’s point of view, these two processes had to be regulated and the dilemma was how to formulate a policy that was both in line with Islamic ethics and, at the same time, controlling Islamization by setting a high entrance bar for the converts. The struggle against acculturation attempted to preserve Muslim political dominance by controlling the administration.

This paper focuses on the image the Fāṭimids propagated and disseminated about themselves as is depicted in literary and documentary sources. The narrative the Fāṭimids constructed about their right to rule and the characteristics of their rule are also discussed.

We present a framework for model theoretic forcing in a non first order context, and present some applications of this framework to Banach space theory.

This article is a result of a unique project that brought together academics and military practitioners with a mind to addressing difficult moral questions in a way that is philosophically careful,...

Lagrangian formulation of quantum mechanical Schrödinger equation is developed in general and illustrated in the eigenbasis of the Hamiltonian and in the coordinate representation. The Lagrangian formulation of physically plausible quantum system results in a well defined second order equation on a real vector space. The Klein–Gordon equation for a real field is shown to be the Lagrangian form of the corresponding Schrödinger equation.