Program extraction from coinductive proofs and its application to exact real arithmetic

Program extraction has been initiated in the field of constructive mathematics, and it attracts interest not only from mathematicians but also from computer scientists nowadays. From a mathematical viewpoint its aim is to figure out computational meaning of proofs, while from a computer-scientific viewpoint its aim is the study of a method to obtain correct programs. Therefore, it is natural to have both theoretical results and a practical computer system to develop executable programs via program extraction. In this Thesis we study the computational interpretation of constructive proofs involving inductive and coinductive reasoning. We interpret proofs by translating the computational content of proofs into executable program code. This translation is the procedure we call program extraction and it is given through Kreisel's modified realizability. Here we study a proof-theoretic foundation for program extraction, enriching the proof assistant system Minlog based on this theoretical improvement. Once a proof of a formula is written in Minlog, a program can be extracted from the proof by the system itself, and the extracted program can be executed in Minlog. Moreover, extracted programs are provably correct with respect to the proven formula due to a soundness theorem which we prove. We practice program extraction by elaborating some case studies from exact real arithmetic within our formal theory. Although these case studies have been studied elsewhere, here we offer a formalization of them in Minlog, and also machine-extraction of the corresponding programs.Die Methode der Programmextraktion hat ihren Ursprung im Bereich der konstruktiven Mathematik, und stößt in letzter Zeit auf viel Interesse nicht nur bei Mathematikern sondern auch bei Informatikern. Vom Standpunkt der Mathematik ist ihr Ziel, aus Beweisen ihre rechnerische Bedeutung abzulesen, während vom Standpunkt der Informatik ihr Ziel die Untersuchung einer Methode ist, beweisbar korrekte Programme zu erhalten. Es ist deshalb naheliegend, neben theoretischen Ergebnissen auch ein praktisches Computersystem zur Verfügung zu haben, mit dessen Hilfe durch Programmextraktion lauffähige Programme entwickelt werden können. In dieser Doktorarbeit wird eine rechnerische Interpretation konstruktiver Beweise mit induktiven und koinduktiven Definitionen angegeben und untersucht. Die Interpretation geschieht dadurch, daß der rechnerische Gehalt von Beweisen in eine Programmiersprache übersetzt wird. Diese übersetzung wird Programmextraktion genannt; sie basiert auf Kreisels modifizierter Realisierbarkeit. Wir untersuchen die beweistheoretischen Grundlagen der Programmextraktion und erweitern den Beweisassistenten Minlog auf der Basis der erhaltenen theoretischen Resultate. Wenn eine Formel in Minlog formal bewiesen ist, läßt sich ein Programm aus dem Beweis extrahieren, und dieses extrahierte Programm kann in Minlog ausgeführt werden. Ferner sind extrahierte Programme beweisbar korrekt bezüglich der entsprechenden Formel aufgrund eines Korrektheitsatzes, den wir beweisen werden. Innerhalb unserer formalen Theorie bearbeiten wir einige aus der Literatur bekannte Fallstudien im Bereich der exakten reellen Arithmetik. Wir entwickeln eine vollständige Formalisierung der entsprechenden Beweise und diskutieren die in Minlog automatisch extrahierten Programme

I=2I=2 ππ\pi\pi potential in the HAL QCD method with all-to-all propagators

In this paper, we perform the first application of the hybrid method (exact low modes plus stochastically estimated high modes) for all-to-all propagators to the HAL QCD method. We calculate the HAL QCD potentials in the $I=2$ $\pi\pi$ scattering in order to see how statistical fluctuations of the potential behave under the hybrid method. All of the calculations are performed with the 2+1 flavor gauge configurations on $16^3 \times 32$ lattice at the lattice spacing $a \approx 0.12$ fm and $m_{\pi} \approx 870$ MeV. It is revealed that statistical errors for the potential are enhanced by stochastic noises introduced by the hybrid method, which, however, are shown to be reduced by increasing the level of dilutions, in particular, that of space dilutions. From systematic studies, we obtain a guiding principle for a choice of dilution types/levels and a number of eigenvectors to reduce noise contaminations to the potential while keeping numerical costs reasonable. We also confirm that we can obtain the scattering phase shifts for the $I=2$ $\pi\pi$ system by the hybrid method within a reasonable numerical cost, which are consistent with the result obtained with the conventional method. The knowledge we obtain in this study will become useful to investigate hadron resonances which require quark annihilation diagrams such as the $\rho$ meson by the HAL QCD potential with the hybrid method.Comment: 20 pages, 10 figures, published version in PTE

Passive spiral formation from halo gas starvation: Gradual transformation into S0s

Recent spectroscopic and high resolution $HST$-imaging observations have revealed significant numbers of ``passive'' spiral galaxies in distant clusters, with all the morphological hallmarks of a spiral galaxy (in particular, spiral arm structure), but with weak or absent star formation. Exactly how such spiral galaxies formed and whether they are the progenitors of present-day S0 galaxies is unclear. Based on analytic arguments and numerical simulations of the hydrodynamical evolution of a spiral galaxy's halo gas (which is a likely candidate for the source of gas replenishment for star formation in spirals), we show that the origin of passive spirals may well be associated with halo gas stripping. Such stripping results mainly from the hydrodynamical interaction between the halo gas and the hot intracluster gas. Our numerical simulations demonstrate that even if a spiral orbits a cluster with a pericenter distance $\sim$ 3 times larger than the cluster core radius, $\sim$ 80 % of the halo gas is stripped within a few Gyr and, accordingly, cannot be accreted by the spiral. Furthermore, our study demonstrates that this dramatic decline in the gaseous infall rate leads to a steady increase in the $Q$ parameter for the disk, with the spiral arm structure, although persisting, becoming less pronounced as the star formation rate gradually decreases. These results suggest that passive spirals formed in this way, gradually evolve into red cluster S0s.Comment: 13 pages 4 figures (fig.1 = jpg format), accepted by Ap

Program extraction from coinductive proofs and its application to exact real arithmetic

Program extraction has been initiated in the field of constructive mathematics, and it attracts interest not only from mathematicians but also from computer scientists nowadays. From a mathematical viewpoint its aim is to figure out computational meaning of proofs, while from a computer-scientific viewpoint its aim is the study of a method to obtain correct programs. Therefore, it is natural to have both theoretical results and a practical computer system to develop executable programs via program extraction. In this Thesis we study the computational interpretation of constructive proofs involving inductive and coinductive reasoning. We interpret proofs by translating the computational content of proofs into executable program code. This translation is the procedure we call program extraction and it is given through Kreisel's modified realizability. Here we study a proof-theoretic foundation for program extraction, enriching the proof assistant system Minlog based on this theoretical improvement. Once a proof of a formula is written in Minlog, a program can be extracted from the proof by the system itself, and the extracted program can be executed in Minlog. Moreover, extracted programs are provably correct with respect to the proven formula due to a soundness theorem which we prove. We practice program extraction by elaborating some case studies from exact real arithmetic within our formal theory. Although these case studies have been studied elsewhere, here we offer a formalization of them in Minlog, and also machine-extraction of the corresponding programs.Die Methode der Programmextraktion hat ihren Ursprung im Bereich der konstruktiven Mathematik, und stößt in letzter Zeit auf viel Interesse nicht nur bei Mathematikern sondern auch bei Informatikern. Vom Standpunkt der Mathematik ist ihr Ziel, aus Beweisen ihre rechnerische Bedeutung abzulesen, während vom Standpunkt der Informatik ihr Ziel die Untersuchung einer Methode ist, beweisbar korrekte Programme zu erhalten. Es ist deshalb naheliegend, neben theoretischen Ergebnissen auch ein praktisches Computersystem zur Verfügung zu haben, mit dessen Hilfe durch Programmextraktion lauffähige Programme entwickelt werden können. In dieser Doktorarbeit wird eine rechnerische Interpretation konstruktiver Beweise mit induktiven und koinduktiven Definitionen angegeben und untersucht. Die Interpretation geschieht dadurch, daß der rechnerische Gehalt von Beweisen in eine Programmiersprache übersetzt wird. Diese übersetzung wird Programmextraktion genannt; sie basiert auf Kreisels modifizierter Realisierbarkeit. Wir untersuchen die beweistheoretischen Grundlagen der Programmextraktion und erweitern den Beweisassistenten Minlog auf der Basis der erhaltenen theoretischen Resultate. Wenn eine Formel in Minlog formal bewiesen ist, läßt sich ein Programm aus dem Beweis extrahieren, und dieses extrahierte Programm kann in Minlog ausgeführt werden. Ferner sind extrahierte Programme beweisbar korrekt bezüglich der entsprechenden Formel aufgrund eines Korrektheitsatzes, den wir beweisen werden. Innerhalb unserer formalen Theorie bearbeiten wir einige aus der Literatur bekannte Fallstudien im Bereich der exakten reellen Arithmetik. Wir entwickeln eine vollständige Formalisierung der entsprechenden Beweise und diskutieren die in Minlog automatisch extrahierten Programme

Role of Temporal Processing Stages by Inferior Temporal Neurons in Facial Recognition

In this review, we focus on the role of temporal stages of encoded facial information in the visual system, which might enable the efficient determination of species, identity, and expression. Facial recognition is an important function of our brain and is known to be processed in the ventral visual pathway, where visual signals are processed through areas V1, V2, V4, and the inferior temporal (IT) cortex. In the IT cortex, neurons show selective responses to complex visual images such as faces, and at each stage along the pathway the stimulus selectivity of the neural responses becomes sharper, particularly in the later portion of the responses. In the IT cortex of the monkey, facial information is represented by different temporal stages of neural responses, as shown in our previous study: the initial transient response of face-responsive neurons represents information about global categories, i.e., human vs. monkey vs. simple shapes, whilst the later portion of these responses represents information about detailed facial categories, i.e., expression and/or identity. This suggests that the temporal stages of the neuronal firing pattern play an important role in the coding of visual stimuli, including faces. This type of coding may be a plausible mechanism underlying the temporal dynamics of recognition, including the process of detection/categorization followed by the identification of objects. Recent single-unit studies in monkeys have also provided evidence consistent with the important role of the temporal stages of encoded facial information. For example, view-invariant facial identity information is represented in the response at a later period within a region of face-selective neurons. Consistent with these findings, temporally modulated neural activity has also been observed in human studies. These results suggest a close correlation between the temporal processing stages of facial information by IT neurons and the temporal dynamics of face recognition

Non-Canonical Notch Signaling During Early Heart Development

The canonical Notch signaling pathway has been studied extensively and plays a key role during embryonic development. Recent evidence points to the existence of a non-canonical function of the Notch protein. Elucidation of a non-canonical Notch signaling pathway would significantly alter how the Notch protein is viewed in biological systems. Perhaps more importantly, the identification of downstream effectors could lead to discovery of novel gene networks functioning throughout development. One potential downstream effector of non-canonical Notch is Numb, which interacts with Notch during development. We provide evidence of the existence of a non-canonical pathway in both the embryonic stem cell and during early heart development. By developing two models that alter either the Notch protein or the canonical Notch signaling pathway, we studied non-canonical Notch signaling in vitro and in vivo. Upon overexpression of a tethered form of Notch, which cannot initiate canonical Notch signaling, we observed remarkable apoptosis in embryonic stem cells. Furthermore, Notch overexpression during early heart development led to decreased heart size due to decreased myocyte proliferation when the essential transcription factor to canonical Notch signaling, RBP-j, was knocked out. Similar phenotypes observed in a Numb knockout setting led us to hypothesize that an interaction between Numb and Notch is involved in heart development. Elucidation of a non-canonical Notch signaling pathway may lead to not only a better understanding of congenital heart disease, but also development of other organ systems, as well

Fracture behavior of single crystal silicon with thermal oxide layer

This paper reports on the effect of oxidation on fracture behavior of single crystal silicon (SCS). SCS specimens were fabricated from (1. 0. 0) silicon-on-insulator wafer with 5-μm-thick device layer and oxide layer were thermally grown. Quasi-static tensile testing of as-fabricated, oxidized and oxidized layer removed specimens was performed. The fracture origin location transited from the surface to silicon/oxide interface and inside of silicon. The transition may be caused by surface smoothing, thickening oxide layer and formation of oxide precipitation defects in silicon during oxidation. The radius of the oxide precipitation defects was estimated, which is well agreed with the fracture-initiating crack sizes

Bazedoxifene, a selective estrogen receptor modulator, reduces cerebral aneurysm rupture in Ovariectomized rats.

BackgroundEstrogen deficiency is thought to be responsible for the higher frequency of aneurysmal subarachnoid hemorrhage in post- than premenopausal women. Estrogen replacement therapy appears to reduce this risk but is associated with significant side effects. We tested our hypothesis that bazedoxifene, a clinically used selective estrogen receptor (ER) modulator with fewer estrogenic side effects, reduces cerebral aneurysm rupture in a new model of ovariectomized rats.MethodsTen-week-old female Sprague-Dawley rats were subjected to ovariectomy, hemodynamic changes, and hypertension to induce aneurysms (ovariectomized aneurysm rats) and treated with vehicle or with 0.3 or 1.0 mg/kg/day bazedoxifene. They were compared with sham-ovariectomized rats subjected to hypertension and hemodynamic changes (HT rats). The vasoprotective effects of bazedoxifene and the mechanisms underlying its efficacy were analyzed.ResultsDuring 12 weeks of observation, the incidence of aneurysm rupture was 52% in ovariectomized rats. With no effect on the blood pressure, treatment with 0.3 or 1.0 mg/kg/day bazedoxifene lowered this rate to 11 and 17%, almost the same as in HT rats (17%). In ovariectomized rats, the mRNA level of ERα, ERβ, and the tissue inhibitor of metalloproteinase-2 was downregulated in the cerebral artery prone to rupture at 5 weeks after aneurysm induction; the mRNA level of interleukin-1β and the matrix metalloproteinase-9 was upregulated. In HT rats, bazedoxifene restored the mRNA level of ERα and ERβ and decreased the level of interleukin-1β and matrix metalloproteinase-9. These findings suggest that bazedoxifene was protective against aneurysmal rupture by alleviating the vascular inflammation and degradation exacerbated by the decrease in ERα and ERβ.ConclusionsOur observation that bazedoxifene decreased the incidence of aneurysmal rupture in ovariectomized rats warrants further studies to validate this response in humans