Some observations on the logical foundations of inductive theorem proving

In this paper we study the logical foundations of automated inductive theorem proving. To that aim we first develop a theoretical model that is centered around the difficulty of finding induction axioms which are sufficient for proving a goal. Based on this model, we then analyze the following aspects: the choice of a proof shape, the choice of an induction rule and the language of the induction formula. In particular, using model-theoretic techniques, we clarify the relationship between notions of inductiveness that have been considered in the literature on automated inductive theorem proving. This is a corrected version of the paper arXiv:1704.01930v5 published originally on Nov.~16, 2017

Initial segments and end-extensions of models of arithmetic

This thesis is organized into two independent parts. In the first part, we extend the recent work on generic cuts by Kaye and the author. The focus here is the properties of the pairs (M, I) where I is a generic cut of a model M. Amongst other results, we characterize the theory of such pairs, and prove that they are existentially closed in a natural category. In the second part, we construct end-extensions of models of arithmetic that are at least as strong as ATR$_0$. Two new constructions are presented. The first one uses a variant of Fodor’s Lemma in ATR$_0$ to build an internally rather classless model. The second one uses some weak versions of the Galvin–Prikry Theorem in adjoining an ideal set to a model of second-order arithmetic

Prediction and Control of Asymmetric Vortical Flows Around Slender Bodies Using Navier-Stokes Equations

Steady and unsteady vortex-dominated flows around slender bodies at high angles of attack are solved using the unsteady, compressible Navier-Stokes equations. An implicit upwind, finite-volume scheme is used for the numerical computations. For supersonic flows past pointed bodies, the locally-conical flow assumption has been used. Asymmetric flows past five-degree semiapex cones using the thin-layer Navier-Stokes equations at different angles of attack, freestream Mach numbers, Reynolds numbers, grid fineness, computational domain size, sources of disturbances and cross-section shapes have been studied. The onset of flow asymmetry occurs when the relative incidence of pointed forebodies exceeds certain critical values. At these critical values of relative incidence, asymmetric flow develops irrespective of the sources of disturbances. The results of unsteady asymmetric flows show that periodic vortex shedding exists at larger angles of attack and it is independent of the numerical schemes used. Passive control of steady and unsteady asymmetric vortical flows around cones using vertical fins and side-strakes have also been studied. Side-strikes control of flow asymmetry over a wide range of angles of attack requires shorter strake heights than those of the vertical-fin control and produces higher lift for the same cone. Three-dimensional, incompressible flows past a prolate spheroid and a tangent-ogive cylinder are solved and compared with experimental data for validation of the numerical scheme. Three-dimensional supersonic asymmetric flows around a five degree semiapex angle circular cone at different angles of attack and Reynolds numbers are presented. Flow asymmetry has been obtained using short-duration disturbances. The flow asymmetry becomes stronger as the Reynolds number and angle of attack are increased. The asymmetric solutions show spatial vortex shedding which is qualitatively similar to the temporal vortex shedding of the unsteady locally-conical flow

The Role of the Lateral Habenula in inhibitory-driven action selection

In order to behave adaptively, animals are required to use cues that predicts the presence or the absence of the desired outcome to guide their selection of actions. Previous studies of how cue influences on choice, using the Specific Pavlovian Instrumental Transfer (S-PIT) paradigm, have yielded considerable progress in our understanding of the underlying mechanism. However, most of them focused on the influence from the excitatory association, where the cue is signalling the presence of outcome. While some pioneering studies have demonstrated the possibility of a cue predicting the absence of outcome affecting the animal's choice behaviour, the neural mechanism that specific to this effect is still largely unexplored. Therefore, the aim of the current thesis was to investigate the role of the Lateral Habenula (LHb) in this type of inhibitory-driven action selection process, as there is reasonable evidences suggesting that this region involved heavily in processing cue that signal the absence of outcome. Our result has shown that the LHb lesion i) weakened the effect of conditioned inhibition, ii) abolished the reversed S-PIT effect that caused by the negative predicting cue, but iii) not affected the normal S-PIT that elicited by the positive predicting cue nor the choice bias that based on the value of the outcomes. Overall speaking, it suggested that the LHb is essential for stimulus-based, and not value-based, choice in situations where the stimuli have been trained as negative, but not positive, predictors of their associated outcomes

Numerical simulation of steady and unsteady asymmetric vortical flow

The unsteady, compressible, thin-layer, Navier-Stokes (NS) equations are solved to simulate steady and unsteady, asymmetric, vortical laminar flow around cones at high incidences and supersonic Mach numbers. The equations are solved by using an implicit, upwind, flux-difference splitting (FDS), finite-volume scheme. The locally conical flow assumption is used and the solutions are obtained by forcing the conserved components of the flowfield vector to be equal at two axial stations located at 0.95 and 1.0. Computational examples cover steady and unsteady asymmetric flows around a circular cone and its control using side strakes. The unsteady asymmetric flow solution around the circular cone has also been validated using the upwind, flux-vector splitting (FVS) scheme with the thin-layer NS equations and the upwind FDS with the full NS equations. The results are in excellent agreement with each other. Unsteady asymmetric flows are also presented for elliptic- and diamond-section cones, which model asymmetric vortex shedding around round- and sharp-edged delta winds

High-resolution detection of recurrent aberrations in lung adenocarcinomas by array comparative genomic hybridization and expression analysis of selective genes by quantitative PCR

Genomic abnormalities are the hallmark of cancers and may harbor potential candidate genes important for cancer development and progression. We performed array comparative genomic hybridization (array CGH) on 36 cases of primary lung adenocarcinoma (AD) using an array containing 2621 BAC or PAC clones spanning the genome at an average interval of 1 Mb. Array CGH identified the commonest aberrations consisting of DNA gains within 1p, 1q, 5p, 5q, 7p, 7q, 8q, 11q, 12p, 13q, 16p, 17q, 20q, and losses with 6q, 9p, 10q and 18q. High-level copy gains involved mainly 7p21-p15 and 20q13.3. Dual color fluorescence in situ hybridization (FISH) was performed on a selective locus for validation of array CGH results. Genomic aberrations were compared with different clinicopathological features and a trend of higher number of aberrations in tumors with aggressive phenotypes and current tobacco exposure was identified. According to array CGH data, 23 candidate genes were selected for quantitative PCR (qPCR) analysis. The concordance observed between the genomic and expression changes in most of the genes suggested that they could be candidate cancer-related genes that contributed to the development of lung AD.published_or_final_versio

The Asteroseismological Richness of RCB and dLHdC Stars

RCB stars are $L\approx10^4\,L_{\odot}$ solar-mass objects that can exhibit large periods of extinction from dust ejection episodes. Many exhibit semiregular pulsations in the range of $30-50$ days with semi-amplitudes of $0.05-0.3$ magnitude. Space-based photometry has discovered that solar-like oscillations are ubiquitous in hydrogen-dominated stars that have substantial outer convective envelopes, so we explore the hypothesis that the pulsations in RCB stars and the closely related dustless hydrogen-deficient carbon (dLHdC) stars, which have large convective outer envelopes of nearly pure helium, have a similar origin. Through stellar modeling and pulsation calculations, we find that the observed periods and amplitudes of these pulsations follows the well-measured phenomenology of their H-rich brethren. In particular, we show that the observed modes are likely of angular orders $l=0,1$ and $2$ and predominantly of an acoustic nature (i.e. $p$-modes with low radial order). The modes with largest amplitude are near the acoustic cut-off frequency appropriately rescaled to the helium-dominated envelope, and the observed amplitudes are consistent with that seen in high luminosity ($L>10^3\,L_{\odot}$) H-rich giants. We also find that for $T_{\mathrm{eff}}\gtrsim5400\,\mathrm{K}$, an HdC stellar model exhibits a radiative layer between two outer convective zones, creating a $g$-mode cavity that supports much longer period ($\approx 100$ days) oscillations. Our initial work was focused primarily on the adiabatic modes, but we expect that subsequent space-based observations of these targets (e.g. with TESS or Plato) are likely to lead to a larger set of detected frequencies that would allow for a deeper study of the interiors of these rare stars.Comment: 12 pages, 4 figures; Accepted to Ap