We introduce some algebraic structures such as singularity, commutators and central extension in modified categories of interest. Additionally, we introduce the cat$^{1}$-objects with their connection to crossed modules in these categories which gives rise to unify many notions about (pre)crossed modules in various algebras of categories.

Ahmet Faruk Aslan Selim Çetin Enver Önder Uslu

We study the coarse geometry of the moduli space of dilation tori with two singularities and the dynamical properties of the action of the Teichmuller flow on this moduli space. This leads to a proof that the vertical foliation of a dilation torus is almost always Morse-Smale. As a corollary, we get that the generic piecewise affine circle homeomorphism with two break points -with respect to the Lebesgue measure- is Morse-Smale.

Selim Ghazouani

We show that the spectral flow of a one-parameter family of Schr\"odinger operators on a metric graph is equal to the Maslov index of a path of Lagrangian subspaces describing the vertex conditions. In addition, we derive an Hadamard-type formula for the derivatives of the eigenvalue curves via the Maslov crossing form.

Yuri Latushkin Selim Sukhtaiev

We study the $\mathrm{SL}_2(\mathbb{R})$-action on the moduli space of (triangulable) dilation tori with one boundary component. We prove that every orbit is either closed or dense, and that every orbit of the Teichmuller flow escapes to infinity.

Adrien Boulanger Selim Ghazouani

A peeling theorem for the Weyl tensor in higher dimensional Lorentzian manifolds is presented. We obtain it by generalizing a proof from the four dimensional case. We derive a generic behavior, discuss interesting subcases and retrieve the four dimensional result.

Selim Amar

The UA8 experiment previously reported the observation of jets in diffractive events containing leading protons (``hard diffraction''), which was interpreted as evidence for the partonic structure of an exchanged Reggeon, believed to be the Pomeron . In the present Letter, we report the final UA8 hard-diffractive (jet) cross section results and their interpretation. After corrections, the fraction of single diffractive events with mass from 118 to 189 GeV that have two scattered partons, each with Et_jet > 8 GeV, is in the range 0.002 to 0.003 (depending on x_p). We determine the product, fK, of the fraction by which the Pomeron's momentum sum rule is violated and the normalization constant of the Pomeron-Flux-Factor of the proton. For a pure gluonic- or a pure qqbar-Pomeron , respectively: fK = 0.30 +- 0.05 +- 0.09) and (0.56 +- 0.09 +- 0.17) GeV^-2.

UA8 Collaboration A. Brandt J. B. Cheze S. Erhan A. Kuzucu M. Medinnis N. Ozdes P. E. Schlein M. T. Zeyrek J. Zsembery J. G. Zweizig

It is shown that the copropagating three-wave-mixing parametric process, with appropriate type-II extended phase matching and pumped with a short second-harmonic pulse, can perform spectral phase conjugation and parametric amplification, which shows a threshold behavior analogous to backward wave oscillation. The process is also analyzed in the Heisenberg picture, which predicts a spontaneous parametric down conversion rate in agreement with the experimental result reported by Kuzucu et al. [Phys. Rev. Lett. 94, 083601 (2005)]. Applications in optical communications, signal processing, and quantum information processing can be envisaged.

Mankei Tsang

We demonstrate a new technique for characterizing two-photon quantum states based on joint temporal correlation measurements using time resolved single photon detection by femtosecond upconversion. We measure for the first time the joint temporal density of a two-photon entangled state, showing clearly the time anti-correlation of the coincident-frequency entangled photon pair generated by ultrafast spontaneous parametric down-conversion under extended phase-matching conditions. The new technique enables us to manipulate the frequency entanglement by varying the down-conversion pump bandwidth to produce a nearly unentangled two-photon state that is expected to yield a heralded single-photon state with a purity of 0.88. The time-domain correlation technique complements existing frequency-domain measurement methods for a more complete characterization of photonic entanglement in quantum information processing.

Onur Kuzucu Franco N. C. Wong Sunao Kurimura Sergey Tovstonog

Recently developed techniques for generating precisely equidistant optical frequencies over broad wavelength ranges are revolutionizing precision physical measurement [1-3]. These frequency "combs" are produced primarily using relatively large, ultrafast laser systems. However, recent research has shown that broad-bandwidth combs can be produced using highly-nonlinear interactions in microresonator optical parametric oscillators [4-11]. Such devices not only offer the potential for developing extremely compact optical atomic clocks but are also promising for astronomical spectroscopy [12-14], ultrashort pulse shaping [15], and ultrahigh-speed communications systems. Here we demonstrate the generation of broad-bandwidth optical frequency combs from a CMOS-compatible integrated microresonator [16,17], which is a fully-monolithic and sealed chip-scale device making it insensitive to the surrounding environment. We characterize the comb quality using a novel self-referencing method and verify that the comb line frequencies are equidistant over a bandwidth that is nearly an order of magnitude larger than previous measurements. In addition, we investigate the ultrafast temporal properties of the comb and demonstrate its potential to serve as a chip-scale source of ultrafast (sub-ps) pulses.

Mark A. Foster Jacob S. Levy Onur Kuzucu Kasturi Saha Michal Lipson Alexander L. Gaeta

Reversible logic has become immensely popular research area and its applications have spread in various technologies for their low power consumption. In this paper we proposed an efficient design of random access memory using reversible logic. In the way of designing the reversible random access memory we proposed a reversible decoder and a write enable reversible master slave D flip-flop. All the reversible designs are superior in terms of quantum cost, delay and garbage outputs compared to the designs existing in literature.

Md. Selim Al Mamun Syed Monowar Hossain