Towards the Formalization of Fractional Calculus in Higher-Order Logic

Fractional calculus is a generalization of classical theories of integration and differentiation to arbitrary order (i.e., real or complex numbers). In the last two decades, this new mathematical modeling approach has been widely used to analyze a wide class of physical systems in various fields of science and engineering. In this paper, we describe an ongoing project which aims at formalizing the basic theories of fractional calculus in the HOL Light theorem prover. Mainly, we present the motivation and application of such formalization efforts, a roadmap to achieve our goals, current status of the project and future milestones.Comment: 9 page

3-Form Flux Compactification of Salam-Sezgin Supergravity

The compactification of 6 dimensional Salam-Sezgin model in the presence of 3-form flux H is investigated. We find a torus topology for this compactification with two cusps which are the places of branes, while at the limit of large size L of the compact direction we also obtain sphere topology. This resembles the Randall-Sundrum I,II model. The branes at one of the cusps can be chosen to be 3- and 4-branes which fill our 4-dimensional space together with the fact that H=0 at this position restores the Lorentz symmetry. This compactification also provides an example for the so-called `time warp' solution, [0812.5107 [hep-th]]. According to a no-go theorem in $d\ne 6$, the time warp compactification violates the null energy condition. While the theorem is quiet for d=6, our model gives a time warp compactification which satisfies the null energy condition. We also derive the four dimensional effective Planck mass which is not obvious due to the time warp nature of the solution.Comment: 19 pages, 5 fig

The GRA Beam-Splitter Experiments and Particle-Wave Duality of Light

Grangier, Roger and Aspect (GRA) performed a beam-splitter experiment to demonstrate the particle behaviour of light and a Mach-Zehnder interferometer experiment to demonstrate the wave behaviour of light. The distinguishing feature of these experiments is the use of a gating system to produce near ideal single photon states. With the demonstration of both wave and particle behaviour (in two mutually exclusive experiments) they claim to have demonstrated the dual particle-wave behaviour of light and hence to have confirmed Bohr's principle of complementarity. The demonstration of the wave behaviour of light is not in dispute. But we want to demonstrate, contrary to the claims of GRA, that their beam-splitter experiment does not conclusively confirm the particle behaviour of light, and hence does not confirm particle-wave duality, nor, more generally, does it confirm complementarity. Our demonstration consists of providing a detailed model based on the Causal Interpretation of Quantum Fields (CIEM), which does not involve the particle concept, of GRA's which-path experiment. We will also give a brief outline of a CIEM model for the second, interference, GRA experiment.Comment: 24 pages, 4 figure

Gravity duals for logarithmic conformal field theories

Logarithmic conformal field theories with vanishing central charge describe systems with quenched disorder, percolation or dilute self-avoiding polymers. In these theories the energy momentum tensor acquires a logarithmic partner. In this talk we address the construction of possible gravity duals for these logarithmic conformal field theories and present two viable candidates for such duals, namely theories of massive gravity in three dimensions at a chiral point.Comment: 15 pages, 1 figure, invited plenary talk at the First Mediterranean Conference on Classical and Quantum Gravity, v2: published version, corrected typo in left eq. (5

Enhanced terahertz magnetic dipole response by subwavelength fiber

Dielectric sub-wavelength particles have opened up a new platform for realization of magnetic light. Recently, we have demonstrated that a dipole emitter by a sub-wavelength fiber leads to an enhanced magnetic response. Here, we experimentally demonstrate an enhanced magnetic dipole source in the terahertz frequency range. By placing the fiber next to the hole in a metal screen, we find that the radiation power can be enhanced more than one order of magnitude. The enhancement is due to the excitation of the Mie-type resonances in the fiber. We demonstrate that such a system is equivalent to a double-fiber system excited by a magnetic source. This coupled magnetic dipole and optical fiber system can be considered a unit cell of metasurfaces for manipulation of terahertz radiation and is a proof-of-concept of a possibility to achieve enhanced radiation of a dipole source in proximity of a sub-wavelength fiber. It can also be scaled down to optical frequencies opening up promising avenues for developing integrated nanophotonic devices such as nanoantennas or lasers on fibers.Shaghik Atakaramians, Ilya V. Shadrivov, Andrey E. Miroshnichenko, Alessio Stefani, Heike Ebendorff-Heidepriem, Tanya M. Monro and Shahraam Afshar V

Testing foundations of quantum mechanics with photons

The foundational ideas of quantum mechanics continue to give rise to counterintuitive theories and physical effects that are in conflict with a classical description of Nature. Experiments with light at the single photon level have historically been at the forefront of tests of fundamental quantum theory and new developments in photonics engineering continue to enable new experiments. Here we review recent photonic experiments to test two foundational themes in quantum mechanics: wave-particle duality, central to recent complementarity and delayed-choice experiments; and Bell nonlocality where recent theoretical and technological advances have allowed all controversial loopholes to be separately addressed in different photonics experiments.Comment: 10 pages, 5 figures, published as a Nature Physics Insight review articl

Autophagy modulators : mechanistic aspects and drug delivery systems

Funding: this work was supported by a grant from NMRC-CIRG to CTY. APK was supported by grants from National Medical Research Council of Singapore, NCIS Yong Siew Yoon Research Grant through donations from the Yong Loo Lin Trust and by the National Research Foundation Singapore and the Singapore Ministry of Education under its Research Centers of Excellence initiative to Cancer Science Institute of Singapore, National University of Singapore. R.M. acknowledges financial supports of Kerman University of Medical Sciences.Autophagy modulation is considered to be a promising programmed cell death mechanism to prevent and cure a great number of disorders and diseases. The crucial step in designing an effective therapeutic approach is to understand the correct and accurate causes of diseases and to understand whether autophagy plays a cytoprotective or cytotoxic/cytostatic role in the progression and prevention of disease. This knowledge will help scientists find approaches to manipulate tumor and pathologic cells in order to enhance cellular sensitivity to therapeutics and treat them. Although some conventional therapeutics suffer from poor solubility, bioavailability and controlled release mechanisms, it appears that novel nanoplatforms overcome these obstacles and have led to the design of a theranostic-controlled drug release system with high solubility and active targeting and stimuli-responsive potentials. In this review, we discuss autophagy modulators-related signaling pathways and some of the drug delivery strategies that have been applied to the field of therapeutic application of autophagy modulators. Moreover, we describe how therapeutics will target various steps of the autophagic machinery. Furthermore, nano drug delivery platforms for autophagy targeting and co-delivery of autophagy modulators with chemotherapeutics/siRNA, are also discusse