Formal Analysis of Quantum Optics

At the beginning of the last century, the theory of quantum optics arose and led to a revolution in physics, since it allowed the interpretation of many unknown phenomena and the development of numerous powerful, cutting edge engineering applications, such as high precision laser technology. The analysis and verification of such applications and systems, however, are very complicated. Moreover, traditional analysis tools, e.g., simulation, numerical methods, computer algebra systems, and paper-and-pencil approaches are not well suited for quantum systems. In the last decade, a new emerging verification technique, called formal methods, became common among engineering domains, and has proven to be effective as an analysis tool. Formal methods consist in the development of mathematical models of the system subject for analysis, and deriving computer-aided mathematical proofs. In this thesis, we propose a framework for the analysis of quantum optics based on formal methods, in particular theorem proving. The framework aims at implementing necessary quantum mechanics and optics concepts and theorems that facilitate the modelling of quantum optical devices and circuits, and then reason about them formally. To this end, the framework consists of three major libraries: 1) Mathematical foundations, which mainly contain the theory of complex-valued-function linear spaces, 2) Quantum mechanics, which develops the general rules of quantum physics, and 3) Quantum Optics, which specializes these rules for light beams and implements all related concepts, e.g., light coherence which is typically emitted by laser sources. On top of these theoretical foundations, we build a library of formal models of a number of optical devices commonly used in quantum circuits, including, beam splitters, light displacers, and light phase shifters. Using the proposed framework, we have been able to formally verify common quantum optical computing circuits, namely the Flip gate, CNOT gate, and Mach-Zehnder interferometer

Endovascular management of iliac artery aneurysms

Purpose:  The  aim  is  to  evaluate  the  role  of  endovascular  interventions  in treatment of  iliac artery aneurysms with one year follow up. Patients and methods: our study included 20 patients with iliac artery aneurysms defined as (iliac artery with a diameter >3cm) with adequate proximal and distal landing zone. Patients with anastomotic aneurysms, infected aneurysms or with severe renal impairment (GFR <30ml/min/1.73m2) were excluded. FOR ISOLATED ILIAC ANEURYSM: access used through either: 1) Retrograde ipsilateral common femoral artery puncture. 2) Contralateral femoral puncture and performing a crossover technique. Under fluoroscopy, the stent graft devices were advanced into the iliac axis up to the planned graft deployment site, Embolization of the IIA was performed in cases where backflow from the IIA was expected to result in a type II endoleak. For Aorto-Iliac Aneurysms: Bilateral femoral access is needed to place endografts and can be performed via surgical femoral cut down. Once vascular access is established and landmarks for positioning the device are obtained with aortography, the main device is positioned with particular attention paid to the location of the opening for the contralateral iliac limb ("contralateral gate")

Fronto-temporal connectivity in never-medicated patients with first-episode schizophrenia: A DTI study

Purpose: To assess fronto-temporal connectivity in never-medicated patients with first episode schizophrenia (FES). Material and methods: Twelve never-medicated patients (median age = 25.5 y) with first episode schizophrenia (according to DSM-IV system) and sixteen demographically matched controls were enrolled in the study. Conventional MRI sequences were obtained. Single shot echo-planar DTI was acquired in 32 non-collinear directions. Tractography of the direct pathway of the superior longitudinal fasciculus (SLFd) and uncinate fasciculus of both hemispheres was performed, and ROIs at the anterior cingulum and external capsule of both hemispheres were drawn. Fractional anisotropy (FA), radial diffusivity (RD), axial diffusivity (AD) and Trace of the ROIs and reconstructed tracts were calculated. Group comparison was performed using independent sample t-test and Fisher’s exact test. Results: Compared to healthy participants, there was significant reduction of FA of the left external capsule (p = 0.001) with increase in RD and Trace (p = .004, .048 respectively). However, the right SLFd showed significant reduction of AD (p = 0.005) and the left SLFd showed significant reduction of its volume (p = 0.02). Conclusion: In patients with FES, impaired white matter connectivity was recognized in the right SLFd and left external capsule associated with reduction in the volume of the left SLFd

Islamic economics: a survey of the literature

A central thesis of this paper is that social science is the study of human experience, and hence is strongly conditioned by history. Modern Western political, economic and social structures have emerged as a consequence of the repudiation of religion associated with the Enlightenment and are based on secular principles. Many of these are inimical to Islamic principles, and cannot be adapted to an Islamic society. Muslim societies achieved freedom from colonial rule in the first half of the twentieth century and have sought to construct institutions in conformity with Islam. The development of Islamic economics is part of this process of transition away from Western colonial institutions. This paper is a survey of the literature on Islamic economics, which focuses on the contrasts between Western economic theories and Islamic approaches to the organization of economic affairs