Physical Sciences and Mathematics Commons^™

Entangled-Photon Compressive Ghost Imaging, Petros Zerom, Kam Wai Clifford Chan, John C. Howell, Robert W. Boyd

Mathematics, Physics, and Computer Science Faculty Articles and Research

We have experimentally demonstrated high-resolution compressive ghost imaging at the single-photon level using entangled photons produced by a spontaneous parametric down-conversion source and using single-pixel detectors. For a given mean-squared error, the number of photons needed to reconstruct a two-dimensional image is found to be much smaller than that in quantum ghost imaging experiments employing a raster scan. This procedure not only shortens the data acquisition time, but also suggests a more economical use of photons for low-light-level and quantum image formation.

Lagrange's Theory Of Analytical Functions And His Ideal Of Purity Of Method, Giovanni Ferraro, Marco Panza

MPP Published Research

We reconstruct essential features of Lagrange’s theory of analytical functions by exhibiting its structure and basic assumptions, as well as its main shortcomings. We explain Lagrange’s notions of function and algebraic quantity, and we concentrate on power-series expansions, on the algorithm for derivative functions, and the remainder theorem—especially on the role this theorem has in solving geometric and mechanical problems. We thus aim to provide a better understanding of Enlightenment mathematics and to show that the foundations of mathematics did not, for Lagrange, concern the solidity of its ultimate bases, but rather purity of method—the generality and internal organization of …

Sufficient Conditions For Uniqueness Of The Weak Value, Justin Dressel, Andrew N. Jordan

Mathematics, Physics, and Computer Science Faculty Articles and Research

We review and clarify the sufficient conditions for uniquely defining the generalized weak value as the weak limit of a conditioned average using the contextual values formalism introduced in Dressel, Agarwal and Jordan (2010 Phys. Rev. Lett. 104 240401). We also respond to criticism of our work by Parrott (arXiv:1105.4188v1) concerning a proposed counter-example to the uniqueness of the definition of the generalized weak value. The counter-example does not satisfy our prescription in the case of an underspecified measurement context. We show that when the contextual values formalism is properly applied to this example, a natural interpretation of the …

Identifying Social Influence In Networks Using Randomized Experiments, Sinan Aral, Dylan Walker

Business Faculty Articles and Research

The recent availability of massive amounts of networked data generated by email, instant messaging, mobile phone communications, micro blogs, and online social networks is enabling studies of population-level human interaction on scales orders of magnitude greater than what was previously possible.1'2 One important goal of applying statistical inference techniques to large networked datasets is to understand how behavioral contagions spread in human social networks. More precisely, understanding how people influence or are influenced by their peers can help us understand the ebb and flow of market trends, product adoption and diffusion, the spread of health behaviors such as smoking and …

Theoretical Analysis Of Quantum Ghost Imaging Through Turbulence, Kam Wai Clifford Chan, D. S. Simon, A. V. Sergienko, Nicholas D. Hardy, Jeffrey H. Shapiro, P. Ben Dixon, Gregory A. Howland, John C. Howell, Joseph H. Eberly, Malcolm N. O'Sullivan, Brandon Rodenburg, Robert W. Boyd

Mathematics, Physics, and Computer Science Faculty Articles and Research

Atmospheric turbulence generally affects the resolution and visibility of an image in long-distance imaging. In a recent quantum ghost imaging experiment [P. B. Dixon et al., Phys. Rev. A 83, 051803 (2011)], it was found that the effect of the turbulence can nevertheless be mitigated under certain conditions. This paper gives a detailed theoretical analysis to the setup and results reported in the experiment. Entangled photons with a finite correlation area and a turbulence model beyond the phase screen approximation are considered.

Extracting An Entanglement Signature From Only Classical Mutual Information, David J. Starling, Curtis J. Broadbent, John C. Howell

Mathematics, Physics, and Computer Science Faculty Articles and Research

We introduce a quantity which is formed using classical notions of mutual information and which is computed using the results of projective measurements. This quantity constitutes a sufficient condition for entanglement and represents the amount of information that can be extracted from a bipartite system for spacelike separated observers. In addition to discussion, we provide simulations as well as experimental results for the singlet and maximally correlated mixed states.

Quantum Ghost Imaging Through Turbulence, John C. Howell

Mathematics, Physics, and Computer Science Faculty Articles and Research

We investigate the effect of turbulence on quantum ghost imaging. We use entangled photons and demonstrate that for a specific experimental configuration the effect of turbulence can be greatly diminished. By decoupling the entangled photon source from the ghost-imaging central image plane, we are able to dramatically increase the ghost-image quality. When imaging a test pattern through turbulence, this method increases the imaged pattern visibility from V=0.15±0.04 to 0.42±0.04.

Communication: Bubbles, Crystals, And Laser-Induced Nucleation, Brandon C. Knott, Jerry L. Larue, Alec M. Wodtke, Michael F. Doherty, Baron Peters

Biology, Chemistry, and Environmental Sciences Faculty Articles and Research

Short intense laser pulses of visible and infrared light can dramatically accelerate crystal nucleation from transparent solutions; previous studies invoke mechanisms that are only applicable for nucleation of ordered phases or high dielectric phases. However, we show that similar laser pulses induce CO₂bubblenucleation in carbonated water. Additionally, in water that is cosupersaturated with argon and glycine, argon bubbles escaping from the water can induce crystal nucleation without a laser. Our findings suggest a possible link between laser-induced nucleation of bubbles and crystals.

Convolution Equations In Spaces Of Distributions Supported By Cones, Alex Meril, Daniele C. Struppa

Mathematics, Physics, and Computer Science Faculty Articles and Research

We describe some examples of surjective convolutors on D'(T), for T a closed convex cone in Rn. We also give necessary and suffficient conditions on Si,..., Sm in S'(T) to be generators of the whole convolution algebra S'(F).

Sbs-Based Radar True Time Delay, Mark Bashkansky, David Walker, Armen Gulian, Michael Steiner

Mathematics, Physics, and Computer Science Faculty Articles and Research

Stimulated Brillouin scattering (SBS) based slow light is considered for application to squint-free (true time delay) steering of phased array radar antennae. Results are presented on true time delay radar requirements, including delay precision and bandwidth. We experimentally investigated the level of delay precision that exists in actual slow-light systems (based on Brillouin scattering). The practical use of SBS to meet the necessary requirements for radar use is discussed.

Experimental Violation Of Two-Party Leggett-Garg Inequalities With Semiweak Measurements, Justin Dressel, Curtis J. Broadbent, John C. Howell, Andrew N. Jordan

Mathematics, Physics, and Computer Science Faculty Articles and Research

We generalize the derivation of Leggett-Garg inequalities to systematically treat a larger class of experimental situations by allowing multiparticle correlations, invasive detection, and ambiguous detector results. Furthermore, we show how many such inequalities may be tested simultaneously with a single setup. As a proof of principle, we violate several such two-particle inequalities with data obtained from a polarization-entangled biphoton state and a semiweak polarization measurement based on Fresnel reflection. We also point out a nontrivial connection between specific two-party Leggett-Garg inequality violations and convex sums of strange weak values.

Experimental Violation Of Two-Party Leggett-Garg Inequalities With Semiweak Measurements, Justin Dressel, C. J. Broadbent, J. C. Howell, Andrew N. Jordan

Mathematics, Physics, and Computer Science Faculty Articles and Research

We generalize the derivation of Leggett-Garg inequalities to systematically treat a larger class of experimental situations by allowing multiparticle correlations, invasive detection, and ambiguous detector results. Furthermore, we show how many such inequalities may be tested simultaneously with a single setup. As a proof of principle, we violate several such two-particle inequalities with data obtained from a polarization-entangled biphoton state and a semiweak polarization measurement based on Fresnel reflection. We also point out a nontrivial connection between specific two-party Leggett-Garg inequality violations and convex sums of strange weak values.

Synthesis And Physicochemical Properties Of Cationic Microgels Based On Poly(N-Isopropylmethacrylamide), Xiaobo Hu, Zhen Tong, L. Andrew Lyon

Biology, Chemistry, and Environmental Sciences Faculty Articles and Research

Surfactant-free, radical precipitation copolymerization of N-isopropylmethacrylamide and the cationic co-monomer N-(3-aminopropyl) methacrylamide hydrochloride (APMH) was carried out to prepare microgels functionalized with primary amines. The morphology and hydrodynamic diameter of the microgels were characterized by atomic force microscopy and photon correlation spectroscopy, with the effect of NaCl concentration and initiator type on the microgel size and yield being investigated. When a 2,2'-azobis (2-amidinopropane) dihydrochloride (V50)-initiated reaction was carried out in pure water, relatively small microgels (similar to 160 nm in diameter) were obtained in low yield (similar to 20%). However, both the yield and size increased if the reaction was …

Evaluation Of Satellite-Retrieved Extreme Precipitation Rates Across The Central United States, A. Aghakoucak, A. Behrangi, S. Sorooshian, K. Hsu, Eyal Amitai

Biology, Chemistry, and Environmental Sciences Faculty Articles and Research

Water resources management, forecasting, and decision making require reliable estimates of precipitation. Extreme precipitation events are of particular importance because of their severe impact on the economy, the environment, and the society. In recent years, the emergence of various satellite-retrieved precipitation products with high spatial resolutions and global coverage have resulted in new sources of uninterrupted precipitation estimates. However, satellite-based estimates are not well integrated into operational and decision-making applications because of a lack of information regarding the associated uncertainties and reliability of these products. In this study, four satellite-derived precipitation products (CMORPH, PERSIANN, TMPA-RT, and TMPA-V6) are evaluated with …

Relation Liftings On Preorders And Posets, Marta Bílková, Alexander Kurz, Daniela Petrişan, Jiří Velebil

Engineering Faculty Articles and Research

The category Rel(Set) of sets and relations can be described as a category of spans and as the Kleisli category for the powerset monad. A set-functor can be lifted to a functor on Rel(Set) iff it preserves weak pullbacks. We show that these results extend to the enriched setting, if we replace sets by posets or preorders. Preservation of weak pullbacks becomes preservation of exact lax squares. As an application we present Moss’s coalgebraic over posets.

Towards Nominal Formal Languages, Alexander Kurz, Tomoyuki Suzuki, Emilio Tuosto

Engineering Faculty Articles and Research

We introduce formal languages over infinite alphabets where words may contain binders.We define the notions of nominal language, nominal monoid, and nominal regular expressions. Moreover, we extend history-dependent automata (HD-automata) by adding stack, and study the recognisability of nominal languages.

Bulk Modulus Of Poly(N-Isopropylacrylamide) Microgels Through The Swelling Transition, B. Sierra-Martin, Y. Laporte, A. B. South, L. Andrew Lyon, A. Fernandez-Nieves

Biology, Chemistry, and Environmental Sciences Faculty Articles and Research

We report measurements of the bulk modulus of individual poly(N-isopropylacrylamide) microgels along their swelling transition. The modulus is determined by measuring the volume deformation of the microgel as a function of osmotic pressure using dextran solutions. We find that the modulus softens through the transition, displaying a nonmonotonous behavior with temperature. This feature is correctly reproduced by the theory of Flory for polymer gels, once the concentration dependence of the solvency parameter is properly incorporated.

An Upper Limit For Macromolecular Crowding Effects, Andrew C. Miklos, Congang Li, Courtney D. Sorell, L. Andrew Lyon, Gary J. Pielak

Biology, Chemistry, and Environmental Sciences Faculty Articles and Research

Background: Solutions containing high macromolecule concentrations are predicted to affect a number of protein properties compared to those properties in dilute solution. In cells, these macromolecular crowders have a large range of sizes and can occupy 30% or more of the available volume. We chose to study the stability and ps-ns internal dynamics of a globular protein whose radius is similar to 2 nm when crowded by a synthetic microgel composed of poly(N-isopropylacrylamide-co-acrylic acid) with particle radii of similar to 300 nm.

Results: Our studies revealed no change in protein rotational or ps-ns backbone dynamics and only mild …

Generic Trace Logics, Christian Kissig, Alexander Kurz

Engineering Faculty Articles and Research

We combine previous work on coalgebraic logic with the coalgebraic traces semantics of Hasuo, Jacobs, and Sokolova.

Aerosol Climatology Over Nile Delta Based On Modis, Misr And Omi Satellite Data, H. S. Marey, J. C. Gille, Hesham El-Askary, E. A. Shalaby, Mohamed El Raey

Mathematics, Physics, and Computer Science Faculty Articles and Research

Since 1999 Cairo and the Nile delta region have suffered from air pollution episodes called the “black cloud” during the fall season. These have been attributed to either burning of agriculture waste or long-range transport of desert dust. Here we present a detailed analysis of the optical and microphysical aerosol properties, based on satellite data. Monthly mean values of Moderate Resolution Imaging Spectroradiometer (MODIS) aerosol optical depth (AOD) at 550 nm were examined for the 10 yr period from 2000–2009. Significant monthly variability is observed in the AOD with maxima in April or May (_0.5) and October (_0.45), and a …

Contrasting Aerosol Trends Over South Asia During The Last Decade Based On Modis Observations, Dimitris G. Kaskaoutis, Shailesh Kumar Kharol, P. R. Sinha, Ramesh P. Singh, K. V. S. Badarinath, Waseem Mehdi, Manish Sharma

Mathematics, Physics, and Computer Science Faculty Articles and Research

Atmospheric aerosols over south Asia constitute a major environmental and climate issue. Thus, extensive land and cruise campaigns have been conducted over the area focusing on investigating the aerosol properties and climate implications. Except from the ground-based instrumentation, several studies dealt with analyzing the aerosol properties from space, focusing mainly on the spatial distribution of the aerosol optical depth (AOD) and possible feedbacks of aerosols on the monsoon system. However, except from some works using ground-based instrumentation or satellite observations over a specific region, there is lack of studies dealing with monitoring of the aerosol trend over south Asia. The …

Superluminal Neutrinos At Opera Confront Pion Decay Kinematics, Ramanath Cowsick, Shmuel Nussinov, Utpal Sarkar

Mathematics, Physics, and Computer Science Faculty Articles and Research

Violation of Lorentz invariance (VLI) has been suggested as an explanation of the superluminal velocities of muon neutrinos reported by OPERA. In this Letter, we show that the amount of VLI required to explain this result poses severe difficulties with the kinematics of the pion decay, extending its lifetime and reducing the momentum carried away by the neutrinos. We show that the OPERA experiment limits alpha = (upsilon(v) - c)/c < 4 x 10(-6). We then take recourse to cosmic-ray data on the spectrum of muons and neutrinos generated in Earth's atmosphere to provide a stronger bound on VLI: (upsilon - c)/c < 10(-12).

Dynamic Light Scattering And Zeta Potential Of Colloidal Mixtures Of Amelogenin And Hydroxyapatite In Calcium And Phosphate Rich Ionic Milieus, Vuk Uskoković, Roselyn Odsinada, Sonia Djordjevic, Stefan Habelitz

Pharmacy Faculty Articles and Research

The concept of zeta-potential has been used for more than a century as a basic parameter in controlling the stability of colloidal suspensions, irrespective of the nature of their particulate ingredients – organic or inorganic. There are prospects that self-assembly of peptide species and the protein-mineral interactions related to biomineralization may be controlled using this fundamental physicochemical parameter. In this study, we have analyzed the particle size and zeta-potential of the full-length recombinant human amelogenin (rH174), the main protein of the developing enamel matrix, in the presence of calcium and phosphate ions and hydroxyapatite (HAP) particles. As calcium and phosphate …

Two-Language, Two-Paradigm Introductory Computing Curriculum Model And Its Implementation, Vladimir Zanev, Atanas Radenski

Mathematics, Physics, and Computer Science Faculty Articles and Research

This paper analyzes difficulties with the introduction of object-oriented concepts in introductory computing education and then proposes a two-language, two-paradigm curriculum model that alleviates such difficulties. Our two-language, two-paradigm curriculum model begins with teaching imperative programming using Python programming language, continues with teaching object-oriented computing using Java, and concludes with teaching object-oriented data structures with Java.

Aerosol Properties Over The Indo‐Gangetic Plain: A Mesoscale Perspective From The Tigerz Experiment, D. M. Giles, B. N. Holben, Sachchida N. Tripathi, Thomas F. Eck, W. Wayne Newcomb, Ilya Slutsker, Russell R. Dickerson, Anne M. Thompson, Shana Mattoo, Sheng-Hsiang Wang, Ramesh P. Singh, Aliaksandyr Sinyuk, Joel S. Schafer

Mathematics, Physics, and Computer Science Faculty Articles and Research

High aerosol loading over the northern Indian subcontinent can result in poor air quality leading to human health consequences and climate perturbations. The international 2008 TIGERZ experiment intensive operational period (IOP) was conducted in the Indo-Gangetic Plain (IGP) around the industrial city of Kanpur (26.51 degrees N, 80.23 degrees E), India, during the premonsoon (April-June). Aerosol Robotic Network (AERONET) Sun photometers performed frequent measurements of aerosol properties at temporary sites distributed within an area covering similar to 50 km(2) around Kanpur to characterize pollution and dust in a region where complex aerosol mixtures and semi-bright surface effects complicate satellite retrieval …

Extremely Large Anthropogenic-Aerosol Contribution To Total Aerosol Load Over The Bay Of Bengal During Winter Season, Dimitris G. Kaskaoutis, Shailesh Kumar Kharol, P. R. Sinha, Ramesh P. Singh, H. D. Kambezidis, Anu Rani Sharma, K. V. S. Bardarinath

Mathematics, Physics, and Computer Science Faculty Articles and Research

Ship-borne observations of spectral aerosol optical depth (AOD) have been carried out over the entire Bay of Bengal (BoB) as part of the W-ICARB cruise campaign during the period 27 December 2008-30 January 2009. The results reveal a pronounced temporal and spatial variability in the optical characteristics of aerosols mainly due to anthropogenic emissions and their dispersion controlled by local meteorology. The highest aerosol amount, with mean AOD(500)> 0.4, being even above 1.0 on specific days, is found close to the coastal regions in the western and northern parts of BoB. In these regions the Angstrom exponent is also found …

Estimation Of Nox Emissions From Delhi Using Car Max-Doas Observations And Comparison With Omi Satellite Data, R. Shaiganfar, S. Beirle, Manish Sharma, A. Chauhan, Ramesh P. Singh, T. Wagner

Mathematics, Physics, and Computer Science Faculty Articles and Research

We present the first Multi-Axis-(MAX-) DOAS observations in India performed during April 2010 and January 2011 in Delhi and nearby regions. The MAX-DOAS instrument was mounted on a car roof, which allowed us to perform measurements along individual driving routes. From car MAX-DOAS observations along closed circles around Delhi, together with information on wind speed and direction, the NOx emissions from the greater Delhi area were determined: our estimate of 4.4 x 10(25) molecules s(-1) is found to be slightly lower than the corresponding emission estimates using the EDGAR emission inventory and substantially smaller compared to a recent study by …

Quaternionic Hermitian Spinor Systems And Compatibility Conditions, Alberto Damiano, David Eelbode, Irene Sabadini

Mathematics, Physics, and Computer Science Faculty Articles and Research

In this paper we show that the systems introduced in [12] and [22] are equivalent, both giving the notion of quaternionic Hermitian monogenic functions. This makes it possible to prove that the free resolution associated to the system is linear in any dimension, and that the first cohomology module is nontrivial, thus generalizing the results in [22]. Furthermore, exploiting the decomposition of the spinor space into sp(m)-irreducibles, we find a certain number of "algebraic" compatibility conditions for the system, suggesting that the usual spinor reduction is not applicable.

Dynamical Features Of Interference Phenomena In The Presence Of Entanglement, Tirzah Kaufherr, Yakir Aharonov, Shmuel Nussinov, Sandu Popescu, Jeff Tollaksen

Mathematics, Physics, and Computer Science Faculty Articles and Research

A strongly interacting, and entangling, heavy nonrecoiling external particle effects a significant change of the environment. Described locally, the corresponding entanglement event is a generalized electric Aharonov-Bohm effect, which differs from the original one in a crucial way. We propose a gedanken interference experiment. The predicted shift of the interference pattern is due to a self-induced or "private" potential difference experienced while the particle is in vacuum. We show that all nontrivial Born-Oppenheimer potentials are "private" potentials. We apply the Born-Oppenheimer approximation to interference states. Using our approach, we calculate the relative phase of the external heavy particle as well …

A Class Of Gaussian Processes With Fractional Spectral Measures, Daniel Alpay, Palle Jorgensen, David Levanony

Mathematics, Physics, and Computer Science Faculty Articles and Research

We study a family of stationary increment Gaussian processes, indexed by time. These processes are determined by certain measures σ (generalized spectral measures), and our focus here is on the case when the measure σ is a singular measure. We characterize the processes arising from when σ is in one of the classes of affine self-similar measures. Our analysis makes use of Kondratiev-white noise spaces. With the use of a priori estimates and the Wick calculus, we extend and sharpen (see Theorem 7.1) earlier computations of Ito stochastic integration developed for the special case of stationary increment processes having absolutely …