Two-dimensional Lattice Gauge Theories with Superconducting Quantum Circuits

A quantum simulator of U(1) lattice gauge theories can be implemented with superconducting circuits. This allows the investigation of confined and deconfined phases in quantum link models, and of valence bond solid and spin liquid phases in quantum dimer models. Fractionalized confining strings and the real-time dynamics of quantum phase transitions are accessible as well. Here we show how state-of-the-art superconducting technology allows us to simulate these phenomena in relatively small circuit lattices. By exploiting the strong non-linear couplings between quantized excitations emerging when superconducting qubits are coupled, we show how to engineer gauge invariant Hamiltonians, including ring-exchange and four-body Ising interactions. We demonstrate that, despite decoherence and disorder effects, minimal circuit instances allow us to investigate properties such as the dynamics of electric flux strings, signaling confinement in gauge invariant field theories. The experimental realization of these models in larger superconducting circuits could address open questions beyond current computational capability.

Proof internalization in generalized Frege systems for classical logic

We present a general method for inserting proofs in Frege systems for classical logic that produces systems that can internalize their own proofs.

Censors for Boolean Description Logic

Protecting different kinds of information has become an important area of research. One aspect is to provide effective means to avoid that secrets can be deduced from the answers of legitimate queries. In the context of atomic propositional databases several methods have been developed to achieve this goal. However, in those databases it is not possible to formalize structural information. Also they are quite restrictive with respect to the specification of secrets. In this paper we extend those methods to match the much greater expressive power of Boolean description logics. In addition to the formal framework, we provide a discussion of various kinds of censors and establish different levels of security they can provide.

Neural circuits of emotion regulation: a comparison of mindfulness-based and cognitive reappraisal strategies

Dealing with one's emotions is a core skill in everyday life. Effective cognitive control strategies have been shown to be neurobiologically represented in prefrontal structures regulating limbic regions. In addition to cognitive strategies, mindfulness-associated methods are increasingly applied in psychotherapy. We compared the neurobiological mechanisms of these two strategies, i.e. cognitive reappraisal and mindfulness, during both the cued expectation and perception of negative and potentially negative emotional pictures. Fifty-three healthy participants were examined with functional magnetic resonance imaging (47 participants included in analysis). Twenty-four subjects applied mindfulness, 23 used cognitive reappraisal. On the neurofunctional level, both strategies were associated with comparable activity of the medial prefrontal cortex and the amygdala. When expecting negative versus neutral stimuli, the mindfulness group showed stronger activations in ventro- and dorsolateral prefrontal cortex, supramarginal gyrus as well as in the left insula. During the perception of negative versus neutral stimuli, the two groups only differed in an increased activity in the caudate in the cognitive group. Altogether, both strategies recruited overlapping brain regions known to be involved in emotion regulation. This result suggests that common neural circuits are involved in the emotion regulation by mindfulness-based and cognitive reappraisal strategies. Identifying differential activations being associated with the two strategies in this study might be one step towards a better understanding of differential mechanisms of change underlying frequently used psychotherapeutic interventions.

First steps towards probabilistic justification logic

In this article, we introduce the probabilistic justification logic PJ, a logic in which we can reason about the probability of justification statements. We present its syntax and semantics, and establish a strong completeness theorem. Moreover, we investigate the relationship between PJ and the logic of uncertain justifications.

Searching the hearts of graphene-like molecules for simplicity, sensitivity and logic

If quantum interference patterns in the hearts of polycyclic aromatic hydrocarbons (PAHs) could be isolated and manipulated, then a significant step towards realizing the potential of single-molecule electronics would be achieved. Here we demonstrate experimentally and theoretically that a simple, parameter-free, analytic theory of interference patterns evaluated at the mid-point of the HOMO-LUMO gap (referred to as M-functions) correctly predicts conductance ratios of molecules with pyrene, naphthalene, anthracene, anthanthrene or azulene hearts. M-functions provide new design strategies for identifying molecules with phase-coherent logic functions and enhancing the sensitivity of molecular-scale interferometers.

Reconsidering the logic of World Federation of Neurosurgical Societies grading in patients with severe subarachnoid hemorrhage.

OBJECT Current data show a favorable outcome in up to 50% of patients with World Federation of Neurosurgical Societies (WFNS) Grade V subarachnoid hemorrhage (SAH) and a rather poor prediction of worst cases. Thus, the usefulness of the current WFNS grading system for identifying the worst scenarios for clinical studies and for making treatment decisions is limited. One reason for this lack of differentiation is the use of "negative" or "silent" diagnostic signs as part of the WFNS Grade V definition. The authors therefore reevaluated the WFNS scale by using "positive" clinical signs and the logic of the Glasgow Coma Scale as a progressive herniation score. METHODS The authors performed a retrospective analysis of 182 patients with SAH who had poor grades on the WFNS scale. Patients were graded according to the original WFNS scale and additionally according to a modified classification, the WFNS herniation (hWFNS) scale (Grade IV, no clinical signs of herniation; Grade V, clinical signs of herniation). The prediction of poor outcome was compared between these two grading systems. RESULTS The positive predictive values of Grade V for poor outcome were 74.3% (OR 3.79, 95% CI 1.94-7.54) for WFNS Grade V and 85.7% (OR 8.27, 95% CI 3.78-19.47) for hWFNS Grade V. With respect to mortality, the positive predictive values were 68.3% (OR 3.9, 95% CI 2.01-7.69) for WFNS Grade V and 77.9% (OR 6.22, 95% CI 3.07-13.14) for hWFNS Grade V. CONCLUSIONS Limiting WFNS Grade V to the positive clinical signs of the Glasgow Coma Scale such as flexion, extension, and pupillary abnormalities instead of including "no motor response" increases the prediction of mortality and poor outcome in patients with severe SAH.

The Complexity of Non-Iterated Probabilistic Justification Logic

The logic PJ is a probabilistic logic defined by adding (noniterated) probability operators to the basic justification logic J. In this paper we establish upper and lower bounds for the complexity of the derivability problem in the logic PJ. The main result of the paper is that the complexity of the derivability problem in PJ remains the same as the complexity of the derivability problem in the underlying logic J, which is π[p/2] -complete. This implies that the probability operators do not increase the complexity of the logic, although they arguably enrich the expressiveness of the language.

Probabilistic Justification Logic

We present a probabilistic justification logic, PPJ, to study rational belief, degrees of belief and justifications. We establish soundness and completeness for PPJ and show that its satisfiability problem is decidable. In the last part we use PPJ to provide a solution to the lottery paradox.

THE LOGIC OF NOMINAL RECORD LINKAGE WITH A CASE STUDY FROM LAREDO, TEXAS

The Laredo Epidemiology Project is a study of the patterns of degenerative disease, particularly cancer, in the families of Laredo, Texas. The genealogical history of Laredo was reconstructed by the grouping of 350,000 individual church and civil vital event records into multi-generational families, with record linkage based on matching names. Mortality data from death records are mapped onto these pedigrees for analysis. This dissertation describes the construction of the data base and the logic upon which decisions were based. ^

POPULATION CODING IN LAMINAR CORTICAL CIRCUITS

One of the fundamental questions in neuroscience is to understand how encoding of sensory inputs is distributed across neuronal networks in cerebral cortex to influence sensory processing and behavioral performance. The fact that the structure of neuronal networks is organized according to cortical layers raises the possibility that sensory information could be processed differently in distinct layers. The goal of my thesis research is to understand how laminar circuits encode information in their population activity, how the properties of the population code adapt to changes in visual input, and how population coding influences behavioral performance. To this end, we performed a series of novel experiments to investigate how sensory information in the primary visual cortex (V1) emerges across laminar cortical circuits. First, it is commonly known that the amount of information encoded by cortical circuits depends critically on whether or not nearby neurons exhibit correlations. We examined correlated variability in V1 circuits from a laminar-specific perspective and observed that cells in the input layer, which have only local projections, encode incoming stimuli optimally by exhibiting low correlated variability. In contrast, output layers, which send projections to other cortical and subcortical areas, encode information suboptimally by exhibiting large correlations. These results argue that neuronal populations in different cortical layers play different roles in network computations. Secondly, a fundamental feature of cortical neurons is their ability to adapt to changes in incoming stimuli. Understanding how adaptation emerges across cortical layers to influence information processing is vital for understanding efficient sensory coding. We examined the effects of adaptation, on the time-scale of a visual fixation, on network synchronization across laminar circuits. Specific to the superficial layers, we observed an increase in gamma-band (30-80 Hz) synchronization after adaptation that was correlated with an improvement in neuronal orientation discrimination performance. Thus, synchronization enhances sensory coding to optimize network processing across laminar circuits. Finally, we tested the hypothesis that individual neurons and local populations synchronize their activity in real-time to communicate information about incoming stimuli, and that the degree of synchronization influences behavioral performance. These analyses assessed for the first time the relationship between changes in laminar cortical networks involved in stimulus processing and behavioral performance.