Towards Verifying Nonlinear Integer Arithmetic

We eliminate a key roadblock to efficient verification of nonlinear integer arithmetic using CDCL SAT solvers, by showing how to construct short resolution proofs for many properties of the most widely used multiplier circuits. Such short proofs were conjectured not to exist. More precisely, we give n^{O(1)} size regular resolution proofs for arbitrary degree 2 identities on array, diagonal, and Booth multipliers and quasipolynomial- n^{O(\log n)} size proofs for these identities on Wallace tree multipliers.Comment: Expanded and simplified with improved result

Attention bias dynamics and symptom severity during and following CBT for social anxiety disorder

Objective: Threat-related attention bias figures prominently in contemporary accounts of the maintenance of anxiety disorders, yet longitudinal intervention research relating attention bias to anxiety symptom severity is limited. Capitalizing on recent advances in the conceptualization and measurement of attention bias, we aimed to examine the relation between attention bias, indexed using trial-level bias scores (TLBSs) to quantify temporal dynamics reflecting dysregulation of attentional processing of threat (as opposed to aggregated mean bias scores) and social anxiety symptom severity over the course of cognitive-behavioral therapy (CBT) and 1-month follow-up. Method: Adults with social anxiety disorder (N = 39) assigned to either yohimbine-or placebo-augmented CBT completed measures of attention bias and social anxiety symptom severity weekly throughout CBT (5 sessions) and at 1-week and 1-month posttreatment. Results: TLBSs of attention bias temporal dynamics showed stronger psychometric properties than mean aggregated scores and were highly interrelated, in line with within-subject temporal variability fluctuating in time between attentional overengagement and strategic avoidance from threat. Attention bias toward threat and temporal variability in attention bias (i.e., attentional dysregulation), but not attention bias away from threat, significantly reduced over the course of CBT. Cross-lag analyses revealed no evidence of a causal relation between reductions in attentional dysregulation leading to symptom severity reduction, or vice versa. Observed relations did not vary as a function of time. Conclusions: We found no evidence for attentional dysregulation as a causal mechanism for symptom reduction in CBT for social anxiety disorders. Implications for future research are discussed

Sporormiella as a tool for detecting the presence of large herbivores in the Neotropics

The reliability of using the abundance of Sporormiella spores as a proxy for the presence and abundance of megaherbivores was tested in southern Brazil. Mud-water interface samples from nine lakes, in which cattle-use was categorized as high, medium, or low, were assayed for Sporormiella representation. The sampling design allowed an analysis of both the influence of the number of animals using the shoreline and the distance of the sampling site from the nearest shoreline. Sporormiella was found to be a reliable proxy for the presence of large livestock. The concentration and abundance of spores declined from the edge of the lake toward the center, with the strongest response being in sites with high livestock use. Consistent with prior studies in temperate regions, we find that Sporormiella spores are a useful proxy to study the extinction of Pleistocene megafauna or the arrival of European livestock in Neotropical landscapes

Pfaffian representations of cubic surfaces

Let K be a field of characteristic zero. We describe an algorithm which requires a homogeneous polynomial F of degree three in K[x_0,x_1,x_2,x_3] and a zero A of F in P^3_K and ensures a linear pfaffian representation of V(F) with entries in K[x_0,x_1,x_2,x_3], under mild assumptions on F and A. We use this result to give an explicit construction of (and to prove the existence of) a linear pfaffian representation of V(F), with entries in K'[x_0,x_1,x_2,x_3], being K' an algebraic extension of K of degree at most six. An explicit example of such a construction is given.Comment: 17 pages. Expanded with some remarks. Published with minor corrections in Geom. Dedicat

Minsky machines and algorithmic problems

This is a survey of using Minsky machines to study algorithmic problems in semigroups, groups and other algebraic systems.Comment: 19 page

Divergent mathematical treatments in utility theory

In this paper I study how divergent mathematical treatments affect mathematical modelling, with a special focus on utility theory. In particular I examine recent work on the ranking of information states and the discounting of future utilities, in order to show how, by replacing the standard analytical treatment of the models involved with one based on the framework of Nonstandard Analysis, diametrically opposite results are obtained. In both cases, the choice between the standard and nonstandard treatment amounts to a selection of set-theoretical parameters that cannot be made on purely empirical grounds. The analysis of this phenomenon gives rise to a simple logical account of the relativity of impossibility theorems in economic theory, which concludes the paper

Propagation of an Earth-directed coronal mass ejection in three dimensions

Solar coronal mass ejections (CMEs) are the most significant drivers of adverse space weather at Earth, but the physics governing their propagation through the heliosphere is not well understood. While stereoscopic imaging of CMEs with the Solar Terrestrial Relations Observatory (STEREO) has provided some insight into their three-dimensional (3D) propagation, the mechanisms governing their evolution remain unclear due to difficulties in reconstructing their true 3D structure. Here we use a new elliptical tie-pointing technique to reconstruct a full CME front in 3D, enabling us to quantify its deflected trajectory from high latitudes along the ecliptic, and measure its increasing angular width and propagation from 2-46 solar radii (approximately 0.2 AU). Beyond 7 solar radii, we show that its motion is determined by an aerodynamic drag in the solar wind and, using our reconstruction as input for a 3D magnetohydrodynamic simulation, we determine an accurate arrival time at the Lagrangian L1 point near Earth.Comment: 5 figures, 2 supplementary movie

Direct Observation of the Superfluid Phase Transition in Ultracold Fermi Gases

Water freezes into ice, atomic spins spontaneously align in a magnet, liquid helium becomes superfluid: Phase transitions are dramatic phenomena. However, despite the drastic change in the system's behaviour, observing the transition can sometimes be subtle. The hallmark of Bose-Einstein condensation (BEC) and superfluidity in trapped, weakly interacting Bose gases is the sudden appearance of a dense central core inside a thermal cloud. In strongly interacting gases, such as the recently observed fermionic superfluids, this clear separation between the superfluid and the normal parts of the cloud is no longer given. Condensates of fermion pairs could be detected only using magnetic field sweeps into the weakly interacting regime. The quantitative description of these sweeps presents a major theoretical challenge. Here we demonstrate that the superfluid phase transition can be directly observed by sudden changes in the shape of the clouds, in complete analogy to the case of weakly interacting Bose gases. By preparing unequal mixtures of the two spin components involved in the pairing, we greatly enhance the contrast between the superfluid core and the normal component. Furthermore, the non-interacting wings of excess atoms serve as a direct and reliable thermometer. Even in the normal state, strong interactions significantly deform the density profile of the majority spin component. We show that it is these interactions which drive the normal-to-superfluid transition at the critical population imbalance of 70(5)%.Comment: 16 pages (incl. Supplemental Material), 5 figure

Identifying component modules

A computer-based system for modelling component dependencies and identifying component modules is presented. A variation of the Dependency Structure Matrix (DSM) representation was used to model component dependencies. The system utilises a two-stage approach towards facilitating the identification of a hierarchical modular structure. The first stage calculates a value for a clustering criterion that may be used to group component dependencies together. A Genetic Algorithm is described to optimise the order of the components within the DSM with the focus of minimising the value of the clustering criterion to identify the most significant component groupings (modules) within the product structure. The second stage utilises a 'Module Strength Indicator' (MSI) function to determine a value representative of the degree of modularity of the component groupings. The application of this function to the DSM produces a 'Module Structure Matrix' (MSM) depicting the relative modularity of available component groupings within it. The approach enabled the identification of hierarchical modularity in the product structure without the requirement for any additional domain specific knowledge within the system. The system supports design by providing mechanisms to explicitly represent and utilise component and dependency knowledge to facilitate the nontrivial task of determining near-optimal component modules and representing product modularity

Delineation of individual human chromosomes in metaphase and interphase cells by in situ suppression hybridization using recombinant DNA libraries

A method of in situ hybridization for visualizing individual human chromosomes from pter to qter, both in metaphase spreads and interphase nuclei, is reported. DNA inserts from a single chromosomal library are labeled with biotin and partially preannealed with a titrated amount of total human genomic DNA prior to hybridization with cellular or chromosomal preparations. The cross-hybridization of repetitive sequences to nontargeted chromosomes can be markedly suppressed under appropriate preannealing conditions. The remaining single-stranded DNA is hybridized to specimens of interest and detected with fluorescent or enzymelabeled avidin conjugates following post-hybridization washes. DNA inserts from recombinant libraries for chromosomes 1, 4, 7, 8, 13, 14, 18, 20, 21, 22, and X were assessed for their ability to decorate specifically their cognate chromosome; most libraries proved to be highly specific. Quantitative densitometric analyses indicated that the ratio of specific to nonspecific hybridization signal under optimal preannealing conditions was at least 8:1. Interphase nuclei showed a cohesive territorial organization of chromosomal domains, and laserscanning confocal fluorescence microscopy was used to aid the 3-D visualization of these domains. This method should be useful for both karyotypic studies and for the analysis of chromosome topography in interphase cells