Splitting Proofs for Interpolation

We study interpolant extraction from local first-order refutations. We present a new theoretical perspective on interpolation based on clearly separating the condition on logical strength of the formula from the requirement on the com- mon signature. This allows us to highlight the space of all interpolants that can be extracted from a refutation as a space of simple choices on how to split the refuta- tion into two parts. We use this new insight to develop an algorithm for extracting interpolants which are linear in the size of the input refutation and can be further optimized using metrics such as number of non-logical symbols or quantifiers. We implemented the new algorithm in first-order theorem prover VAMPIRE and evaluated it on a large number of examples coming from the first-order proving community. Our experiments give practical evidence that our work improves the state-of-the-art in first-order interpolation.Comment: 26th Conference on Automated Deduction, 201

The lifecycle of axisymmetric internal solitary waves

The generation and evolution of solitary waves by intrusive gravity currents in an approximate two-layer fluid with equal upper- and lower-layer depths is examined in a cylindrical geometry by way of theory and numerical simulations. The study is limited to vertically symmetric cases in which the density of the intruding fluid is equal to the average density of the ambient. We show that even though the head height of the intrusion decreases, it propagates at a constant speed well beyond 3 lock radii. This is because the strong stratification at the interface supports the formation of a mode-2 solitary wave that surrounds the intrusion head and carries it outwards at a constant speed. The wave and intrusion propagate faster than a linear long wave; therefore, there is strong supporting evidence that the wave is indeed nonlinear. Rectilinear Korteweg-de Vries theory is extended to allow the wave amplitude to decay as <i>r<sup>-p</sup></I> with <i>p</i>=½ and the theory is compared to the observed waves to demonstrate that the width of the wave scales with its amplitude. After propagating beyond 7 lock radii the intrusion runs out of fluid. Thereafter, the wave continues to spread radially at a constant speed, however, the amplitude decreases sufficiently so that linear dispersion dominates and the amplitude decays with distance as <i>r</i><sup>-1</sup>

From model system to clinical medicine: pathophysiologic links of common proteinopathies

Recent clinical evidence suggests that Alzheimer disease (AD), Parkinson disease (PD), and dementia with Lewy bodies (DLB), though distinct neurological disorders, have some common pathological features that may have an impact on the clinical characteristics of these diseases. However, the question of whether these disorders have a common pathophysiology remains. Clinton and colleagues recently reported a mouse model that exhibits the combined pathologies of AD, PD, and DLB, a finding that may shed some light on this issue. Using this mouse model, the authors demonstrate that the pathogenic proteins amyloid beta, tau, and alpha-synuclein interact synergistically to enhance the accumulation of one another and accelerate cognitive decline. These data indicate shared pathogenic mechanisms and suggest the possibility that therapeutic interventions successfully targeting one of these pathogenic proteins have implications for a number of related neurodegenerative disorders

Anatomy and Physiology of Artificial Intelligence in PET Imaging

The influence of artificial intelligence (AI) within the field of nuclear medicine has been rapidly growing. Many researchers and clinicians are seeking to apply AI within PET, and clinicians will soon find themselves engaging with AI-based applications all along the chain of molecular imaging, from image reconstruction to enhanced reporting. This expanding presence of AI in PET imaging will result in greater demand for educational resources for those unfamiliar with AI. The objective of this article to is provide an illustrated guide to the core principles of modern AI, with specific focus on aspects that are most likely to be encountered in PET imaging. We describe convolutional neural networks, algorithm training, and explain the components of the commonly used U-Net for segmentation and image synthesis

Tunneling spectra of strongly coupled superconductors: Role of dimensionality

We investigate numerically the signatures of collective modes in the tunneling spectra of superconductors. The larger strength of the signatures observed in the high-Tc superconductors, as compared to classical low-Tc materials, is explained by the low dimensionality of these layered compounds. We also show that the strong-coupling structures are dips (zeros in the d2I/dV2 spectrum) in d-wave superconductors, rather than the steps (peaks in d2I/dV2) observed in classical s-wave superconductors. Finally we question the usefulness of effective density of states models for the analysis of tunneling data in d-wave superconductors.Comment: 8 pages, 6 figure

Properties of the superconducting state in a two-band model

Eliashberg theory is used to investigate the range of thermodynamic properties possible within a two-band model for s-wave superconductivity and to identify signatures of its two-band nature. We emphasize dimensionless BCS ratios (those for the energy gaps, the specific heat jump and the negative of its slope near Tc, the thermodynamic critical field Hc(0), and the normalized slopes of the critical field and the penetration depth near Tc), which are no longer universal even in weak coupling. We also give results for temperature-dependent quantities, such as the penetration depth and the energy gap. Results are presented both for microscopic parameters appropriate to MgB2 and for variations away from these. Strong coupling corrections are identified and found to be significant. Analytic formulas are provided which show the role played by the anisotropy in coupling in some special limits. Particular emphasis is placed on small interband coupling and on the opposite limit of no diagonal coupling. The effect of impurity scattering is considered, particularly for the interband case.Comment: 20 pages, 14 figures, final version accepted in PR

Experimentally exploring compressed sensing quantum tomography

In the light of the progress in quantum technologies, the task of verifying the correct functioning of processes and obtaining accurate tomographic information about quantum states becomes increasingly important. Compressed sensing, a machinery derived from the theory of signal processing, has emerged as a feasible tool to perform robust and significantly more resource-economical quantum state tomography for intermediate-sized quantum systems. In this work, we provide a comprehensive analysis of compressed sensing tomography in the regime in which tomographically complete data is available with reliable statistics from experimental observations of a multi-mode photonic architecture. Due to the fact that the data is known with high statistical significance, we are in a position to systematically explore the quality of reconstruction depending on the number of employed measurement settings, randomly selected from the complete set of data, and on different model assumptions. We present and test a complete prescription to perform efficient compressed sensing and are able to reliably use notions of model selection and cross-validation to account for experimental imperfections and finite counting statistics. Thus, we establish compressed sensing as an effective tool for quantum state tomography, specifically suited for photonic systems.Comment: 12 pages, 5 figure

Numerical study of surface-induced reorientation and smectic layering in a nematic liquid crystal

Surface-induced profiles of both nematic and smectic order parameters in a nematic liquid crystal, ranging from an orienting substrate to "infinity", were evaluated numerically on base of an extended Landau theory. In order to obtain a smooth behavior of the solutions at "infinity" a boundary energy functional was derived by linearizing the Landau energy around its equilibrium solutions. We find that the intrinsic wave number of the smectic structure, which plays the role of a coupling between nematic and smectic order, strongly influences the director reorientation. Whereas the smectic order is rapidly decaying when moving away from the surface, the uniaxial nematic order parameter shows an oscillatory behavior close to the substrate, accompanied by a non-zero local biaxiality.Comment: LaTeX, 17 pages, with 4 postscript figure

Candidatus Bartonella merieuxii, a potential new zoonotic Bartonella species in canids from Iraq.

Bartonellae are emerging vector-borne pathogens infecting erythrocytes and endothelial cells of various domestic and wild mammals. Blood samples were collected from domestic and wild canids in Iraq under the United States Army zoonotic disease surveillance program. Serology was performed using an indirect immunofluorescent antibody test for B. henselae, B. clarridgeiae, B. vinsonii subsp. berkhoffii and B. bovis. Overall seroprevalence was 47.4% in dogs (n = 97), 40.4% in jackals (n = 57) and 12.8% in red foxes (n = 39). Bartonella species DNA was amplified from whole blood and representative strains were sequenced. DNA of a new Bartonella species similar to but distinct from B. bovis, was amplified from 37.1% of the dogs and 12.3% of the jackals. B. vinsonii subsp. berkhoffii was also amplified from one jackal and no Bartonella DNA was amplified from foxes. Adjusting for age, the odds of dogs being Bartonella PCR positive were 11.94 times higher than for wild canids (95% CI: 4.55-31.35), suggesting their role as reservoir for this new Bartonella species. This study reports on the prevalence of Bartonella species in domestic and wild canids of Iraq and provides the first detection of Bartonella in jackals. We propose Candidatus Bartonella merieuxii for this new Bartonella species. Most of the Bartonella species identified in sick dogs are also pathogenic for humans. Therefore, seroprevalence in Iraqi dog owners and bacteremia in Iraqi people with unexplained fever or culture negative endocarditis requires further investigation as well as in United States military personnel who were stationed in Iraq. Finally, it will also be essential to test any dog brought back from Iraq to the USA for presence of Bartonella bacteremia to prevent any accidental introduction of a new Bartonella species to the New World