Positivity, entanglement entropy, and minimal surfaces

The path integral representation for the Renyi entanglement entropies of integer index n implies these information measures define operator correlation functions in QFT. We analyze whether the limit $n\rightarrow 1$, corresponding to the entanglement entropy, can also be represented in terms of a path integral with insertions on the region's boundary, at first order in $n-1$. This conjecture has been used in the literature in several occasions, and specially in an attempt to prove the Ryu-Takayanagi holographic entanglement entropy formula. We show it leads to conditional positivity of the entropy correlation matrices, which is equivalent to an infinite series of polynomial inequalities for the entropies in QFT or the areas of minimal surfaces representing the entanglement entropy in the AdS-CFT context. We check these inequalities in several examples. No counterexample is found in the few known exact results for the entanglement entropy in QFT. The inequalities are also remarkable satisfied for several classes of minimal surfaces but we find counterexamples corresponding to more complicated geometries. We develop some analytic tools to test the inequalities, and as a byproduct, we show that positivity for the correlation functions is a local property when supplemented with analyticity. We also review general aspects of positivity for large N theories and Wilson loops in AdS-CFT.Comment: 36 pages, 10 figures. Changes in presentation and discussion of Wilson loops. Conclusions regarding entanglement entropy unchange

Stringy effects in black hole decay

We compute the low energy decay rates of near-extremal three(four) charge black holes in five(four) dimensional N=4 string theory to sub-leading order in the large charge approximation. This involves studying stringy corrections to scattering amplitudes of a scalar field off a black hole. We adapt and use recently developed techniques to compute such amplitudes as near-horizon quantities. We then compare this with the corresponding calculation in the microscopic configuration carrying the same charges as the black hole. We find perfect agreement between the microscopic and macroscopic calculations; in the cases we study, the zero energy limit of the scattering cross section is equal to four times the Wald entropy of the black hole.Comment: 32 page

Holographic c-theorems in arbitrary dimensions

We re-examine holographic versions of the c-theorem and entanglement entropy in the context of higher curvature gravity and the AdS/CFT correspondence. We select the gravity theories by tuning the gravitational couplings to eliminate non-unitary operators in the boundary theory and demonstrate that all of these theories obey a holographic c-theorem. In cases where the dual CFT is even-dimensional, we show that the quantity that flows is the central charge associated with the A-type trace anomaly. Here, unlike in conventional holographic constructions with Einstein gravity, we are able to distinguish this quantity from other central charges or the leading coefficient in the entropy density of a thermal bath. In general, we are also able to identify this quantity with the coefficient of a universal contribution to the entanglement entropy in a particular construction. Our results suggest that these coefficients appearing in entanglement entropy play the role of central charges in odd-dimensional CFT's. We conjecture a new c-theorem on the space of odd-dimensional field theories, which extends Cardy's proposal for even dimensions. Beyond holography, we were able to show that for any even-dimensional CFT, the universal coefficient appearing the entanglement entropy which we calculate is precisely the A-type central charge.Comment: 62 pages, 4 figures, few typo's correcte

Behavioral Modernity and the Cultural Transmission of Structured Information: The Semantic Axelrod Model

Cultural transmission models are coming to the fore in explaining increases in the Paleolithic toolkit richness and diversity. During the later Paleolithic, technologies increase not only in terms of diversity but also in their complexity and interdependence. As Mesoudi and O'Brien (2008) have shown, selection broadly favors social learning of information that is hierarchical and structured, and multiple studies have demonstrated that teaching within a social learning environment can increase fitness. We believe that teaching also provides the scaffolding for transmission of more complex cultural traits. Here, we introduce an extension of the Axelrod (1997} model of cultural differentiation in which traits have prerequisite relationships, and where social learning is dependent upon the ordering of those prerequisites. We examine the resulting structure of cultural repertoires as learning environments range from largely unstructured imitation, to structured teaching of necessary prerequisites, and we find that in combination with individual learning and innovation, high probabilities of teaching prerequisites leads to richer cultural repertoires. Our results point to ways in which we can build more comprehensive explanations of the archaeological record of the Paleolithic as well as other cases of technological change.Comment: 24 pages, 7 figures. Submitted to "Learning Strategies and Cultural Evolution during the Paleolithic", edited by Kenichi Aoki and Alex Mesoudi, and presented at the 79th Annual Meeting of the Society for American Archaeology, Austin TX. Revised 5/14/1

DNA Barcoding Identifies Argentine Fishes from Marine and Brackish Waters

DNA barcoding has been advanced as a promising tool to aid species identification and discovery through the use of short, standardized gene targets. Despite extensive taxonomic studies, for a variety of reasons the identification of fishes can be problematic, even for experts. DNA barcoding is proving to be a useful tool in this context. However, its broad application is impeded by the need to construct a comprehensive reference sequence library for all fish species. Here, we make a regional contribution to this grand challenge by calibrating the species discrimination efficiency of barcoding among 125 Argentine fish species, representing nearly one third of the known fauna, and examine the utility of these data to address several key taxonomic uncertainties pertaining to species in this region..This study constitutes a significant contribution to the global barcode reference sequence library for fishes and demonstrates the utility of barcoding for regional species identification. As an independent assessment of alpha taxonomy, barcodes provide robust support for most morphologically based taxon concepts and also highlight key areas of taxonomic uncertainty worthy of reappraisal

The Quantum Mind: Alternative Ways of Reasoning with Uncertainty

© 2018, Ontario Institute for Educational Studies (OISE). Human reasoning about and with uncertainty is often at odds with the principles of classical probability. Order effects, conjunction biases, and sure-thing inclinations suggest that an entirely different set of probability axioms could be developed and indeed may be needed to describe such habits. Recent work in diverse fields, including cognitive science, economics, and information theory, explores alternative approaches to decision theory. This work considers more expansive theories of reasoning with uncertainty while continuing to recognize the value of classical probability. In this paper, we discuss one such alternative approach, called quantum probability, and explore its applications within decision theory. Quantum probability is designed to formalize uncertainty as an ontological feature of the state of affairs, offering a mathematical model for entanglement, de/coherence, and interference, which are all concepts with unique onto-epistemological relevance for social theorists working in new and trans-materialisms. In this paper, we suggest that this work be considered part of the quantum turn in the social sciences and humanities. Our aim is to explore different models and formalizations of decision theory that attend to the situatedness of judgment. We suggest that the alternative models of reasoning explored in this article might be better suited to queries about entangled mathematical concepts and, thus, be helpful in rethinking both curriculum and learning theory