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Chapman University

2013

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Articles 1 - 30 of 46

Full-Text Articles in Physical Sciences and Mathematics

Poly (N-Isopropylacrylamide) Microgel-Based Etalons And Etalon Arrays For Determining The Molecular Weight Of Polymers In Solution, Molla R. Islam, Michael J. Serpe Nov 2013

Poly (N-Isopropylacrylamide) Microgel-Based Etalons And Etalon Arrays For Determining The Molecular Weight Of Polymers In Solution, Molla R. Islam, Michael J. Serpe

Biology, Chemistry, and Environmental Sciences Faculty Articles and Research

Positively and/or negatively charged poly (N-isopropylacrylamide)-based microgels were deposited on a single substrate and isolated regions of Au overlayers were deposited on top of the microgels. Each spatially isolated Au overlayer region had a different thickness to make an etalon array.We found that areas with a thin Au overlayer (5 nm) responded to a range of polymer molecular weights (MW), while areas with a thick overlayer (35 nm) can only respond to low molecular weight polyelectrolytes. By comparing the optical responses of the device’s individual array elements, a good approximation of the polyelectrolyteMWin solution can be made.

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Directed Ratchet Transport In Granular Crystals, Vincent Berardi, J. Lydon, P. G. Kevrekidis, C. Daraio, R. Carretero-González Nov 2013

Directed Ratchet Transport In Granular Crystals, Vincent Berardi, J. Lydon, P. G. Kevrekidis, C. Daraio, R. Carretero-González

Psychology Faculty Articles and Research

Directed-ratchet transport (DRT) in a one-dimensional lattice of spherical beads, which serves as a prototype for granular chains, is investigated. We consider a system where the trajectory of the central bead is prescribed by a biharmonic forcing function with broken time-reversal symmetry. By comparing the mean integrated force of beads equidistant from the forcing bead, two distinct types of directed transport can be observed—spatial and temporal DRT. Based on the value of the frequency of the forcing function relative to the cutoff frequency, the system can be categorized by the presence and magnitude of each type of DRT. Furthermore, we …

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Action Principle For Continuous Quantum Measurement, A. Chantasri, Justin Dressel, Andrew N. Jordan Oct 2013

Action Principle For Continuous Quantum Measurement, A. Chantasri, Justin Dressel, Andrew N. Jordan

Mathematics, Physics, and Computer Science Faculty Articles and Research

We present a stochastic path integral formalism for continuous quantum measurement that enables the analysis of rare events using action methods. By doubling the quantum state space to a canonical phase space, we can write the joint probability density function of measurement outcomes and quantum state trajectories as a phase space path integral. Extremizing this action produces the most likely paths with boundary conditions defined by preselected and postselected states as solutions to a set of ordinary differential equations. As an application, we analyze continuous qubit measurement in detail and examine the structure of a quantum jump in the Zeno …

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Photon Counting Compressive Depth Mapping, Gregory A. Howland, Daniel J. Lum, Matthew R. Ware, John C. Howell Sep 2013

Photon Counting Compressive Depth Mapping, Gregory A. Howland, Daniel J. Lum, Matthew R. Ware, John C. Howell

Mathematics, Physics, and Computer Science Faculty Articles and Research

We demonstrate a compressed sensing, photon counting lidar system based on the single-pixel camera. Our technique recovers both depth and intensity maps from a single under-sampled set of incoherent, linear projections of a scene of interest at ultra-low light levels around 0.5 picowatts. Only two-dimensional reconstructions are required to image a three-dimensional scene. We demonstrate intensity imaging and depth mapping at 256 × 256 pixel transverse resolution with acquisition times as short as 3 seconds. We also show novelty filtering, reconstructing only the difference between two instances of a scene. Finally, we acquire 32 × 32 pixel real-time video for …

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Technical Advantages For Weak-Value Amplification: When Less Is More, Andrew N. Jordan, Julián Martínez-Rincón, John C. Howell Sep 2013

Technical Advantages For Weak-Value Amplification: When Less Is More, Andrew N. Jordan, Julián Martínez-Rincón, John C. Howell

Mathematics, Physics, and Computer Science Faculty Articles and Research

The technical merits of weak-value-amplification techniques are analyzed. We consider models of several different types of technical noise in an optical context and show that weak-value-amplification techniques (which only use a small fraction of the photons) compare favorably with standard techniques (which use all of them). Using the Fisher-information metric, we demonstrate that weak-value techniques can put all of the Fisher information about the detected parameter into a small portion of the events and show how this fact alone gives technical advantages. We go on to consider a time-correlated noise model and find that a Fisher-information analysis indicates that the …

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Strengthening Weak-Value Amplification With Recycled Photons, Justin Dressel, Kevin Lyons, Andrew N. Jordan, Trent M. Graham, Paul G. Kwiat Aug 2013

Strengthening Weak-Value Amplification With Recycled Photons, Justin Dressel, Kevin Lyons, Andrew N. Jordan, Trent M. Graham, Paul G. Kwiat

Mathematics, Physics, and Computer Science Faculty Articles and Research

We consider the use of cyclic weak measurements to improve the sensitivity of weak-value amplification precision measurement schemes. Previous weak-value experiments have used only a small fraction of events, while discarding the rest through the process of “postselection.” We extend this idea by considering recycling of events which are typically unused in a weak measurement. Here we treat a sequence of polarized laser pulses effectively trapped inside an interferometer using a Pockels cell and polarization optics. In principle, all photons can be postselected, which will improve the measurement sensitivity. We first provide a qualitative argument for the expected improvements from …

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Quantum Instruments As A Foundation For Both States And Observables, Justin Dressel, Andrew N. Jordan Aug 2013

Quantum Instruments As A Foundation For Both States And Observables, Justin Dressel, Andrew N. Jordan

Mathematics, Physics, and Computer Science Faculty Articles and Research

We demonstrate that quantum instruments can provide a unified operational foundation for quantum theory. Since these instruments directly correspond to laboratory devices, this foundation provides an alternate, more experimentally grounded, perspective from which to understand the elements of the traditional approach.We first show that in principle all measurable probabilities and correlations can be expressed entirely in terms of quantum instruments without the need for conventional quantum states or observables. We then show how these states and observables reappear as derived quantities by conditioning joint detection probabilities on the first or last measurement in a sequence as a preparation or a …

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Weak-Values Technique For Velocity Measurements, Gerardo I. Viza, Julián Martínez-Rincón, Gregory A. Howland, Hadas Frostig, Itay Shomroni, Barak Dayan, John C. Howell Aug 2013

Weak-Values Technique For Velocity Measurements, Gerardo I. Viza, Julián Martínez-Rincón, Gregory A. Howland, Hadas Frostig, Itay Shomroni, Barak Dayan, John C. Howell

Mathematics, Physics, and Computer Science Faculty Articles and Research

In a recent Letter, Brunner and Simon proposed an interferometric scheme using imaginary weak values with a frequency-domain analysis to outperform standard interferometry in longitudinal phase shifts [Phys. Rev. Lett 105, 010405 (2010)]. Here we demonstrate an interferometric scheme combined with a time-domain analysis to measure longitudinal velocities. The technique employs the near-destructive interference of non-Fourier limited pulses, one Doppler shifted due to a moving mirror in a Michelson interferometer. We achieve a velocity measurement of 400  fm/s and show our estimator to be efficient by reaching its Cramér–Rao bound.

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Spatiotemporal Fluorescent Detection Measurements Using Embedded Waveguide Sensors, Mark C. Harrison, Andrea M. Armani Jun 2013

Spatiotemporal Fluorescent Detection Measurements Using Embedded Waveguide Sensors, Mark C. Harrison, Andrea M. Armani

Engineering Faculty Articles and Research

Integrated waveguide biosensors, when combined with fluorescent labeling, have significantly impacted the field of biodetection. While there are numerous types of waveguide sensors, the fundamental excitation method is fairly consistent: the evanescent field of the waveguide excites a fluorophore whose emission is detected, either directly via imaging or indirectly via a decrease in power transfer. Recently, a sensor device was demonstrated which is able to back-couple the emitted light into the waveguide, allowing the signal to be detected directly. However, this previous work focused on the development of an empirical model, leaving many theoretical questions unanswered. Additionally, the results from …

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Einstein-Podolsky-Rosen Steering Inequalities From Entropic Uncertainty Relations, James Schneeloch, Curtis J. Broadbent, Stephen P. Walborn, Eric G. Cavalcanti, John C. Howell Jun 2013

Einstein-Podolsky-Rosen Steering Inequalities From Entropic Uncertainty Relations, James Schneeloch, Curtis J. Broadbent, Stephen P. Walborn, Eric G. Cavalcanti, John C. Howell

Mathematics, Physics, and Computer Science Faculty Articles and Research

We use entropic uncertainty relations to formulate inequalities that witness Einstein-Podolsky-Rosen (EPR)-steering correlations in diverse quantum systems. We then use these inequalities to formulate symmetric EPR-steering inequalities using the mutual information. We explore the differing natures of the correlations captured by one-way and symmetric steering inequalities and examine the possibility of exclusive one-way steerability in two-qubit states. Furthermore, we show that steering inequalities can be extended to generalized positive operator-valued measures, and we also derive hybrid steering inequalities between alternate degrees of freedom.

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Label-Free Detection Of Low Protein Concentration In Solution Using A Novel Colorimetric Assay, Molla R. Islam, Michael J. Serpe May 2013

Label-Free Detection Of Low Protein Concentration In Solution Using A Novel Colorimetric Assay, Molla R. Islam, Michael J. Serpe

Biology, Chemistry, and Environmental Sciences Faculty Articles and Research

Dual pH and temperature sensitive microgel-based etalons were fabricated by sandwiching a “monolithic” microgel layer between two semitransparent, Au layers. The devices exhibit visual color and multipeak reflectance spectra, both of which primarily depend on the distance between the Au surfaces mediated by the microgel diameter. We found that a polycationic polyelectrolyte can penetrate through the Au overlayer to interact with negatively charged microgel confined between Au overlayers. In this submission we report that biotinylated polycationic polymer can penetrate through the Au overlayer of a poly (N-isopropylacrylamide)-co-acrylic acid (pNIPAm-co-AAc) microgel-based etalon and cause the microgel layer to collapse. The collapse …

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Null Values And Quantum State Discrimination, Oded Zilberberg, Alessandro Romito, David J. Starling, Gregory A. Howland, Curtis J. Broadbent, John C. Howell, Yuval Gefen Apr 2013

Null Values And Quantum State Discrimination, Oded Zilberberg, Alessandro Romito, David J. Starling, Gregory A. Howland, Curtis J. Broadbent, John C. Howell, Yuval Gefen

Mathematics, Physics, and Computer Science Faculty Articles and Research

We present a measurement protocol for discriminating between two different quantum states of a qubit with high fidelity. The protocol, called null value, is comprised of a projective measurement performed on the system with a small probability (also known as partial collapse), followed by a tuned postselection. We report on an optical experimental implementation of the scheme. We show that our protocol leads to an amplified signal-to-noise ratio (as compared with a straightforward strong measurement) when discerning between the two quantum states.

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Rapidly Reconfigurable Optically Induced Photonic Crystals In Hot Rubidium Vapor, Bethany Little, David J. Starling, John C. Howell, Raphael D. Cohen, David Shwa, Nadav Katz Apr 2013

Rapidly Reconfigurable Optically Induced Photonic Crystals In Hot Rubidium Vapor, Bethany Little, David J. Starling, John C. Howell, Raphael D. Cohen, David Shwa, Nadav Katz

Mathematics, Physics, and Computer Science Faculty Articles and Research

Through periodic index modulation, we create two different types of photonic structures in a heated rubidium vapor for controlled reflection, transmission, and diffraction of light. The modulation is achieved through the use of the ac Stark effect resulting from a standing-wave control field. The periodic intensity structures create translationally invariant index profiles analogous to photonic crystals in spectral regions of steep dispersion. Experimental results are consistent with modeling.

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Violation Of Continuous-Variable Einstein-Podolsky-Rosen Steering With Discrete Measurements, James Schneeloch, P. Ben Dixon, Gregory A. Howland, Curtis J. Broadbent, John C. Howell Mar 2013

Violation Of Continuous-Variable Einstein-Podolsky-Rosen Steering With Discrete Measurements, James Schneeloch, P. Ben Dixon, Gregory A. Howland, Curtis J. Broadbent, John C. Howell

Mathematics, Physics, and Computer Science Faculty Articles and Research

In this Letter, we derive an entropic Einstein-Podolsky-Rosen (EPR) steering inequality for continuous-variable systems using only experimentally measured discrete probability distributions and details of the measurement apparatus. We use this inequality to witness EPR steering between the positions and momenta of photon pairs generated in spontaneous parametric down-conversion. We examine the asymmetry between parties in this inequality, and show that this asymmetry can be used to reduce the technical requirements of experimental setups intended to demonstrate the EPR paradox. Furthermore, we develop a more stringent steering inequality that is symmetric between parties, and use it to show that the down-converted …

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Plastic Deformation, Wrinkling, And Recovery In Microgel Multilayers, Jeffrey C. Gaulding, Mark W. Spears Jr., L. Andrew Lyon Jan 2013

Plastic Deformation, Wrinkling, And Recovery In Microgel Multilayers, Jeffrey C. Gaulding, Mark W. Spears Jr., L. Andrew Lyon

Biology, Chemistry, and Environmental Sciences Faculty Articles and Research

Microgel multi-layer films assembled from anionic particles and linear polycation were prepared on elastomeric substrates and their self-healing properties studied. Dried films were imaged in situ during mechanical deformation and were determined to undergo plastic deformation in response to linear strain, leading to film buckling upon strain relaxation. Hydration leads to rapid reorganization of the film building blocks, permitting recovery of the film to the undamaged state. Additionally, films were determined to heal in the presence of high relative humidity environments, suggesting that film swelling and hydration is a major factor in the restoration of film integrity, and that full …

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Using Mapreduce Streaming For Distributed Life Simulation On The Cloud, Atanas Radenski Jan 2013

Using Mapreduce Streaming For Distributed Life Simulation On The Cloud, Atanas Radenski

Mathematics, Physics, and Computer Science Faculty Books and Book Chapters

Distributed software simulations are indispensable in the study of large-scale life models but often require the use of technically complex lower-level distributed computing frameworks, such as MPI. We propose to overcome the complexity challenge by applying the emerging MapReduce (MR) model to distributed life simulations and by running such simulations on the cloud. Technically, we design optimized MR streaming algorithms for discrete and continuous versions of Conway’s life according to a general MR streaming pattern. We chose life because it is simple enough as a testbed for MR’s applicability to a-life simulations and general enough to make our results applicable …

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Dynamic Sequent Calculus For The Logic Of Epistemic Actions And Knowledge, Giuseppe Greco, Alexander Kurz, Alessandra Palmigiano Jan 2013

Dynamic Sequent Calculus For The Logic Of Epistemic Actions And Knowledge, Giuseppe Greco, Alexander Kurz, Alessandra Palmigiano

Engineering Faculty Articles and Research

"Dynamic Logics (DLs) form a large family of nonclassical logics, and perhaps the one enjoying the widest range of applications. Indeed, they are designed to formalize change caused by actions of diverse nature: updates on the memory state of a computer, displacements of moving robots in an environment, measurements in models of quantum physics, belief revisions, knowledge updates, etc. In each of these areas, DL-formulas express properties of the model encoding the present state of affairs, as well as the pre- and post-conditions of a given action. Actions are semantically represented as transformations of one model into another, encoding the …

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Revisiting The Fundamentals In The Design And Control Of Nanoparticulate Colloids In The Frame Of Soft Chemistry, Vuk Uskoković Jan 2013

Revisiting The Fundamentals In The Design And Control Of Nanoparticulate Colloids In The Frame Of Soft Chemistry, Vuk Uskoković

Pharmacy Faculty Articles and Research

This review presents thoughts on some of the fundamental features of conceptual models applied in the design of fine particles in the frames of colloid and soft chemistry. A special emphasis is placed on the limitations of these models, an acknowledgment of which is vital in improving their intricacy and effectiveness in predicting the outcomes of the corresponding experimental settings. Thermodynamics of self-assembly phenomena illustrated on the examples of protein assembly and micellization is analyzed in relation to the previously elaborated thesis that each self-assembly in reality presents a co-assembly, since it implies a mutual reorganization of the assembling system …

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Air-Sea Dimethylsulfide (Dms) Gas Transfer In The North Atlantic: Evidence For Limited Interfacial Gas Exchange At High Wind Speed, T. G. Bell, Warren J. De Bruyn, S. D. Miller, B. Ward, K. Christensen, E. S. Saltzman Jan 2013

Air-Sea Dimethylsulfide (Dms) Gas Transfer In The North Atlantic: Evidence For Limited Interfacial Gas Exchange At High Wind Speed, T. G. Bell, Warren J. De Bruyn, S. D. Miller, B. Ward, K. Christensen, E. S. Saltzman

Biology, Chemistry, and Environmental Sciences Faculty Articles and Research

Shipboard measurements of eddy covariance dimethylsulfide (DMS) air-sea fluxes and seawater concentration were carried out in the North Atlantic bloom region in June/July 2011. Gas transfer coefficients (k(660)) show a linear dependence on mean horizontal wind speed at wind speeds up to 11 m s(-1). At higher wind speeds the relationship between k(660) and wind speed weakens. At high winds, measured DMS fluxes were lower than predicted based on the linear relationship between wind speed and interfacial stress extrapolated from low to intermediate wind speeds. In contrast, the transfer coefficient for sensible heat did not exhibit this effect. The apparent …

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Development Of Self-Assembling Mixed Protein Micelles With Temperature-Modulated Avidities, Allyson S.C. Soon, Michael H. Smith, Emily S. Herman, L. Andrew Lyon, Thomas H. Barker Jan 2013

Development Of Self-Assembling Mixed Protein Micelles With Temperature-Modulated Avidities, Allyson S.C. Soon, Michael H. Smith, Emily S. Herman, L. Andrew Lyon, Thomas H. Barker

Biology, Chemistry, and Environmental Sciences Faculty Articles and Research

Elastin-like polypeptides (ELPs) are polypentapeptides that undergo hydrophobic collapse and aggregation above a specific transition temperature, Tt. ELP diblocks sharing a common “core” block (I60) but varying “outer” blocks (A80, P40) were designed, where Tt,I < Tt,A < Tt,P. The formation of ~55 nm diameter mixed micelles from these ELP diblocks was verified using dynamic light scattering (DLS), multiangle light scattering (MALS) and fluorescence resonance energy transfer (FRET). To confer affinity to the blood circulating protein fibrinogen, a fibrinogen-binding tetrapeptide sequence (GPRP) was fused to A80-I60, while P40-I60 was fused to a non-binding control (GPSP). The …

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Non-Commutative Stochastic Distributions And Applications To Linear Systems Theory, Daniel Alpay, Guy Salomon Jan 2013

Non-Commutative Stochastic Distributions And Applications To Linear Systems Theory, Daniel Alpay, Guy Salomon

Mathematics, Physics, and Computer Science Faculty Articles and Research

In this paper, we introduce a non-commutative space of stochastic distributions, which contains the non-commutative white noise space, and forms, together with a natural multiplication, a topological algebra. Special inequalities which hold in this space allow to characterize its invertible elements and to develop an appropriate framework of non-commutative stochastic linear systems.

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Residuated Frames With Applications To Decidability, Nikolaos Galatos, Peter Jipsen Jan 2013

Residuated Frames With Applications To Decidability, Nikolaos Galatos, Peter Jipsen

Mathematics, Physics, and Computer Science Faculty Articles and Research

Residuated frames provide relational semantics for substructural logics and are a natural generalization of Kripke frames in intuitionistic and modal logic, and of phase spaces in linear logic. We explore the connection between Gentzen systems and residuated frames and illustrate how frames provide a uniform treatment for semantic proofs of cut-elimination, the finite model property and the finite embeddability property, which imply the decidability of the equational/universal theories of the associated residuated lattice-ordered groupoids. In particular these techniques allow us to prove that the variety of involutive FL-algebras and several related varieties have the finite model property.

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Long-Term (1951-2007) Rainfall Trends Around Six Indian Cities: Current State, Meteorological, And Urban Dynamics, Shailesh Kumar Kharol, D. G. Kaskaoutis, Anu Rani Sharma, Ramesh P. Singh Jan 2013

Long-Term (1951-2007) Rainfall Trends Around Six Indian Cities: Current State, Meteorological, And Urban Dynamics, Shailesh Kumar Kharol, D. G. Kaskaoutis, Anu Rani Sharma, Ramesh P. Singh

Mathematics, Physics, and Computer Science Faculty Articles and Research

The present study focuses on analyzing the precipitation trends over six Indian cities during the summer monsoon (June-September) covering the period 1951-2007 and also attempting to investigate possible urban forcing and dynamics by examining the variation in precipitation in the upwind and downwind directions. The analysis shows negative trends in the total number of rainy days over Hyderabad (-10.4%), Kanpur (-7.1%), Jaipur (-10.5%), and Nagpur (-4.8%) and positive trends over Delhi (7.4%) and Bangalore (22.9%). On the other hand, decreases of -21.3%, -5.9%, -14.2%, and -14.6% in seasonal rainfall are found over Delhi, Hyderabad, Jaipur, and Kanpur, respectively, whereas Bangalore …

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Multi Geophysical Parameters For Earthquake Forecasting, Ramesh P. Singh Jan 2013

Multi Geophysical Parameters For Earthquake Forecasting, Ramesh P. Singh

Mathematics, Physics, and Computer Science Faculty Articles and Research

This article focuses on the importance of keeping the public aware of earthquake forecasting. This article also encourages proper seismic codes to design buildings in the seismic-prone regions because such practice can save lives and property associated with an earthquake.

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Practical Approach To Cosmological Perturbations In Modified Gravity, Alessandra Silvestri, Levon Pogosian, Roman V. Buniy Jan 2013

Practical Approach To Cosmological Perturbations In Modified Gravity, Alessandra Silvestri, Levon Pogosian, Roman V. Buniy

Mathematics, Physics, and Computer Science Faculty Articles and Research

The next generation of large scale surveys will not only measure cosmological parameters within the framework of general relativity, but will also allow for precision tests of the framework itself. At the order of linear perturbations, departures from the growth in the standard cosmological model can be quantified in terms of two functions of time and Fourier number k. We argue that in local theories of gravity, in the quasistatic approximation, these functions must be ratios of polynomials in k, with the numerator of one function being equal to the denominator of the other. Moreover, the polynomials are even and …

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The Classical Limit Of Quantum Optics: Not What It Seems At First Sight, Yakir Aharonov, Alonso Botero, Shmuel Nussinov, Sandu Popescu, Jeff Tollaksen, Lev Vaidman Jan 2013

The Classical Limit Of Quantum Optics: Not What It Seems At First Sight, Yakir Aharonov, Alonso Botero, Shmuel Nussinov, Sandu Popescu, Jeff Tollaksen, Lev Vaidman

Mathematics, Physics, and Computer Science Faculty Articles and Research

What light is and how to describe it has always been a central subject in physics. As our understanding has increased, so have our theories changed: geometrical optics, wave optics and quantum optics are increasingly sophisticated descriptions, each referring to a larger class of phenomena than its predecessor. But how exactly are these theories related? How and when wave optics reduces to geometric optics is a rather simple problem. Similarly, how quantum optics reduces to wave optics has also been considered to be a very simple business. It is not so. As we show here the classical limit of quantum …

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Quantum Cheshire Cats, Yakir Aharonov, Sandu Popescu, Daniel Rohrlich, Paul Skrzypczyk Jan 2013

Quantum Cheshire Cats, Yakir Aharonov, Sandu Popescu, Daniel Rohrlich, Paul Skrzypczyk

Mathematics, Physics, and Computer Science Faculty Articles and Research

In this paper we present a quantum Cheshire Cat. In a pre- and post-selected experiment we find the Cat in one place, and its grin in another. The Cat is a photon, while the grin is its circular polarization.

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Inter- And Intra-Annual Variability Of Vegetation In The Northern Hemisphere And Its Association With Precursory Meteorological Factors, Boksoon Myoung, Yong-Sang Choi, Seungbum Hong, Seon Ki Park Jan 2013

Inter- And Intra-Annual Variability Of Vegetation In The Northern Hemisphere And Its Association With Precursory Meteorological Factors, Boksoon Myoung, Yong-Sang Choi, Seungbum Hong, Seon Ki Park

Mathematics, Physics, and Computer Science Faculty Articles and Research

Determination of phenological variation is one of the most critical challenges in dynamic vegetation modeling, given the lack of a strong theoretical framework. Previous studies generally focused on the timing of a phenological event (e.g., bud-burst or onset of growing season) and its atmospheric prompts, but not on the interactive variations across phenological stages. This study, therefore, investigated the inter- and intra-annual variability existing in all the phenological stages and the relations of the variability with four meteorological variables (surface temperature (Ts), shortwave radiation (SW ), vapor pressure deficit (VPD), and precipitation (PRCP)) using a 25-year (1982-2006) dataset of leaf …

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Relation Algebras As Expanded Fl-Algebras, Nikolaos Galatos, Peter Jipsen Jan 2013

Relation Algebras As Expanded Fl-Algebras, Nikolaos Galatos, Peter Jipsen

Mathematics, Physics, and Computer Science Faculty Articles and Research

This paper studies generalizations of relation algebras to residuated lattices with a unary De Morgan operation. Several new examples of such algebras are presented, and it is shown that many basic results on relation algebras hold in this wider setting. The variety qRA of quasi relation algebras is defined and shown to be a conservative expansion of involutive FL-algebras. Our main result is that equations in qRA and several of its subvarieties can be decided by a Gentzen system, and that these varieties are generated by their finite members.

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Convex Cones Of Generalized Positive Rational Functions And Nevanlinna-Pick Interpolation, Daniel Alpay, Izchak Lewkowicz Jan 2013

Convex Cones Of Generalized Positive Rational Functions And Nevanlinna-Pick Interpolation, Daniel Alpay, Izchak Lewkowicz

Mathematics, Physics, and Computer Science Faculty Articles and Research

Scalar rational functions with a non-negative real part on the right half plane, called positive, are classical in the study of electrical networks, dissipative systems, Nevanlinna-Pick interpolation and other areas. We here study generalized positive functions, i.e with a non-negative real part on the imaginary axis. These functions form a Convex Invertible Cone, cic in short, and we explore two partitionings of this set: (i) into (infinitely many non-invertible) convex cones of functions with prescribed poles and zeroes in the right half plane and (ii) each generalized positive function can be written as a sum of even and odd parts. …

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