Physical Sciences and Mathematics Commons^™

Weak Values Are Universal In Von Neumann Measurements, Justin Dressel, Andrew N. Jordan

Mathematics, Physics, and Computer Science Faculty Articles and Research

We refute the widely held belief that the quantum weak value necessarily pertains to weak measurements. To accomplish this, we use the transverse position of a beam as the detector for the conditioned von Neumann measurement of a system observable. For any coupling strength, any initial states, and any choice of conditioning, the averages of the detector position and momentum are completely described by the real parts of three generalized weak values in the joint Hilbert space. Higher-order detector moments also have similar weak value expansions. Using the Wigner distribution of the initial detector state, we find compact expressions for …

Efficient High-Dimensional Entanglement Imaging With A Compressive-Sensing Double-Pixel Camera, Gregory A. Howland, John C. Howell

Mathematics, Physics, and Computer Science Faculty Articles and Research

We implement a double-pixel compressive-sensing camera to efficiently characterize, at high resolution, the spatially entangled fields that are produced by spontaneous parametric down-conversion. This technique leverages sparsity in spatial correlations between entangled photons to improve acquisition times over raster scanning by a scaling factor up to n²/log(n) for n-dimensional images. We image at resolutions up to 1024 dimensions per detector and demonstrate a channel capacity of 8.4 bits per photon. By comparing the entangled photons’ classical mutual information in conjugate bases, we violate an entropic Einstein-Podolsky-Rosen separability criterion for all measured resolutions. More broadly, our result indicates that …

Building A Computer Program To Support Children, Parents, And Distraction During Healthcare Procedures, Kirsten Hanrahan, Ann Marie Mccarthy, Charmaine Kleiber, Kaan Ataman, W. Nick Street, M. Bridget Zimmerman, Annel L. Ersig

Business Faculty Articles and Research

This secondary data analysis used data mining methods to develop predictive models of child risk for distress during a healthcare procedure. Data used came from a study that predicted factors associated with children's responses to an intravenous catheter insertion while parents provided distraction coaching. From the 255 items used in the primary study, 44 predictive items were identified through automatic feature selection and used to build support vector machine regression models. Models were validated using multiple cross-validation tests and by comparing variables identified as explanatory in the traditional versus support vector machine regression. Rule-based approaches were applied to the model …

Serpentine Low Loss Trapezoidal Silica Waveguides On Silicon, Xiaomin Zhang, Mark Harrison, Audrey Harker, Andrea M. Armani

Engineering Faculty Articles and Research

We report the fabrication and characterization of straight and serpentine low loss trapezoidal silica waveguides integrated on a silicon substrate. The waveguide channel was defined using a dual photo-lithography and buffered HF etching and isolated from the silicon substrate using an isotropic silicon etchant. The waveguide is air-clad and thus has a core-cladding effective index contrast of approximately 25%. Measured at 658, 980 and 1550nm, the propagation loss was found to be 0.69, 0.59, and 0.41dB/cm respectively, with a critical bending radius less than 375μm. The waveguide’s polarization behavior was investigated both theoretically and experimentally. Additionally, the output power shows …

Double Lorentzian Atomic Prism, David J. Starling, Steven M. Bloch, Praveen K. Vudyasetu, Joseph S. Choi, Bethany Little, John C. Howell

Mathematics, Physics, and Computer Science Faculty Articles and Research

We present an atomic prism spectrometer that utilizes the steep linear dispersion between two strongly absorbing hyperfine resonances of rubidium. We resolve spectral lines 50 MHz apart and, utilizing a larger part of the available spectrum than only between the two resonances, we spatially separate collinear pump, signal, and idler beams resulting from a four-wave mixing process. Due to the high transparency possible between the resonances, these results have applications in the filtering of narrow-band entangled photons and interaction-free measurements.

Quantum Mutual Information Capacity For High-Dimensional Entangled States, P. Ben Dixon, Gregory A. Howland, James Schneeloch, John C. Howell

Mathematics, Physics, and Computer Science Faculty Articles and Research

High-dimensional Hilbert spaces used for quantum communication channels offer the possibility of large data transmission capabilities. We propose a method of characterizing the channel capacity of an entangled photonic state in high-dimensional position and momentum bases. We use this method to measure the channel capacity of a parametric down-conversion state by measuring in up to 576 dimensions per detector. We achieve a channel capacity over 7  bits/photon in either the position or momentum basis. Furthermore, we provide a correspondingly high-dimensional separability bound that suggests that the channel performance cannot be replicated classically.

Contextual-Value Approach To The Generalized Measurement Of Observables, Justin Dressel, Andrew N. Jordan

Mathematics, Physics, and Computer Science Faculty Articles and Research

We present a detailed motivation for and definition of the contextual values of an observable, which were introduced by Dressel et al. [Phys. Rev. Lett. 104, 240401 (2011)]. The theory of contextual values is a principled approach to the generalized measurement of observables. It extends the well-established theory of generalized statemeasurements by bridging the gap between partial state collapse and the observables that represent physically relevant information about the system. To emphasize the general utility of the concept, we first construct the full theory of contextual values within an operational formulation of classical probability theory, paying special attention to observable …

From Velocities To Fluxions, Marco Panza

MPP Published Research

"Though the De Methodis results, for its essential structure and content, from a re-elaboration of a previous unfinished treatise composed in the Fall of 1666—now known, after Whiteside, as The October 1666 tract on fluxions ([22], I, pp. 400-448)—, the introduction of the term ‘fluxion’ goes together with an important conceptual change concerned with Newton’s understanding of his own achievements. I shall argue that this change marks a crucial step in the origins of analysis, conceived as an autonomous mathematical theory."

Significance Of The Imaginary Part Of The Weak Value, Justin Dressel, Andrew N. Jordan

Mathematics, Physics, and Computer Science Faculty Articles and Research

Unlike the real part of the generalized weak value of an observable, which can in a restricted sense be operationally interpreted as an idealized conditioned average of that observable in the limit of zero measurement disturbance, the imaginary part of the generalized weak value does not provide information pertaining to the observable being measured.What it does provide is direct information about howthe initial statewould be unitarily disturbed by the observable operator. Specifically, we provide an operational interpretation for the imaginary part of the generalized weak value as the logarithmic directional derivative of the postselection probability along the unitary flow generated …

Measuring Which-Path Information With Coupled Electronic Mach-Zehnder Interferometers, Justin Dressel, Y. Choi, Andrew N. Jordan

Mathematics, Physics, and Computer Science Faculty Articles and Research

We theoretically investigate a generalized “which-path” measurement on an electronic Mach-Zehnder Interferometer (MZI) implemented via Coulomb coupling to a second electronic MZI acting as a detector. The use of contextual values, or generalized eigenvalues, enables the precise construction of which-path operator averages that are valid for any measurement strength from the available drain currents. The form of the contextual values provides direct physical insight about the measurement being performed, providing information about the correlation strength between system and detector, the measurement inefficiency, and the proper background removal. We find that the detector interferometer must display maximal wavelike behavior to optimally …

Assessing Satellite-Based Rainfall Estimates In Semiarid Watersheds Using The Usda-Ars Walnut Gulch Gauge Network And Trmm Pr, Eyal Amitai, Carl L. Unkrich, David C. Goodrich, Emad Habib, Bryson Thill

Biology, Chemistry, and Environmental Sciences Faculty Articles and Research

The rain gauge network associated with the Walnut Gulch Experimental Watershed (WGEW) in southeastern Arizona provides a unique opportunity for direct comparisons of in situ measurements and satellite-based instantaneous rain rate estimates like those from the Tropical Rainfall Measuring Mission (TRMM) precipitation radar (PR). The WGEW network is the densest rain gauge network in the PR coverage area for watersheds greater than 10 km(2). It consists of 88 weighing rain gauges within a 149-km(2) area. On average, approximately 10 gauges can be found in each PR field of view (similar to 5-km diameter). All gauges are very well synchronized with …

Quantitative Analysis Of Some Important Metals And Metalloids In Tobacco Products By Inductively Coupled Plasma-Mass Spectrometry (Icp-Ms), Syed Ghulam Musharraf, Muhammad Shoaib, Amna Jabbar Siddiqui, Muhammad Najam-Ul-Haq, Aftab Ahmed

Pharmacy Faculty Articles and Research

Background: Large scale usage of tobacco causes a lot of health troubles in human. Various formulations of tobacco are extensively used by the people particularly in developing world. Besides several toxic tobacco constituents some metals and metalloids are also believed to pose health risks. This paper describes inductively coupled plasma-mass spectrometric (ICP-MS) quantification of some important metals and metalloids in various brands of smoked, sniffed, dipped and chewed tobacco products.

Results: A microwave-assisted digestion method was used for sample preparation. The method was validated by analyzing a certified reference material. Percentage relative standard deviation (% R.S.D.) between recovered …

Pegylated Silicon Nanowire Coated Silica Microparticles For Drug Delivery Across Intestinal Epithelium, Vuk Uskoković, Phin-Peng Lee, Laura Walsh, Kathleen Fischer, Tejal Dasai

Pharmacy Faculty Articles and Research

Composite particles made by growing nanoscopic silicon wires from the surface of monodispersed, microsized silica beads were tested in this study for their ability to affect the integrity and permeability of an epithelial cell layer. Polyethylene glycol (PEG) is known to sterically stabilize particles and prevent protein binding; as such, it is a routine way to impart in vivo longevity to drug carriers. The effect of the silica beads, both with and without silicon nanowires and PEG, on the disruption of the tight junctions in Caco-2 cells was evaluated by means of: (a) analysis of the localization of zonula occludens-1 …

A New, Simple, Green And One-Pot Four-Component Synthesis Of Bare And Poly(Α, Γ, L-Glutamic Acid) Capped Silver Nanoparticles, Magdalena Stevanović, Igor Savanović, Vuk Uskoković, Srečo D. Škapin, Ines Bračko, Uroš Jovanović, Dragan Uskoković

Pharmacy Faculty Articles and Research

A simple and green chemical method has been developed to synthesize stable bare and capped silver nanoparticles based on the reduction of silver ions by glucose and capping by poly(α,γ,Lglutamic acid) (PGA). The use of ammonia during synthesis was avoided. PGA has had a dual role in the synthesis and was used as a capping agent to make the silver nanoparticle more biocompatible and to protect the nanoparticles from agglomerating in the liquid medium. The synthesized PGA-capped silver nanoparticles in the size range 5–45 nm were stable over long periods of time, without signs of precipitation. Morphological examination has shown …

Dynamic Light Scattering And Microelectrophoresis: Main Prospects And Limitations, Vuk Uskoković

Pharmacy Faculty Articles and Research

Microelectrophoresis based on the dynamic light scattering (DLS) effect has been a major tool for assessing and controlling the conditions for stability of colloidal systems. However, both the DLS methods for characterization of the hydrodynamic size of dispersed submicron particles and the theory behind the electrokinetic phenomena are associated with fundamental and practical approximations that limit their sensitivity and information output. Some of these fundamental limitations, including the spherical approximation of DLS measurements and an inability of microelectrophoretic analyses of colloidal systems to detect discrete charges and differ between differently charged particle surfaces due to rotational diffusion and particle orientation …

Structural Properties Of Thermoresponsive Poly(N-Isopropylacrylamide)-Poly(Ethyleneglycol) Microgels, J. Clara-Rahola, A. Fernandez-Nieves, B. Sierra-Martin, A. B. South, L. Andrew Lyon, J. Kohlbrecher, A. F. Barbero

Biology, Chemistry, and Environmental Sciences Faculty Articles and Research

The application of RNA interference to treat disease is an important yet challenging concept in modern medicine. In particular, small interfering RNA (siRNA) have shown tremendous promise in the treatment of cancer. However, siRNA show poor pharmacological properties, which presents a major hurdle for effective disease treatment especially through intravenous delivery routes. In response to these shortcomings, a variety of nanoparticle carriers have emerged, which are designed to encapsulate, protect, and transport siRNA into diseased cells. To be effective as carrier vehicles, nanoparticles must overcome a series of biological hurdles throughout the course of delivery. As a result, one promising …

Personality Type Differences Between Ph.D. Climate Researchers And The General Public: Implications For Effective Communication, C. Susan Weiler, Jason K. Keller, Christina Olex

Biology, Chemistry, and Environmental Sciences Faculty Articles and Research

Effectively communicating the complexity of climate change to the public is an important goal for the climate change research community, particularly for those of us who receive public funds. The challenge of communicating the science of climate change will be reduced if climate change researchers consider the links between personality types, communication tendencies and learning preferences. Jungian personality type is one of many factors related to an individual’s preferred style of taking in and processing information, i.e., preferred communication style. In this paper, we demonstrate that the Jungian personality type profile of interdisciplinary, early career climate researchers is significantly different …

Toward A Framework For Systematic Error Modeling Of Spaceborne Precipitation Radar With Noaa/Nssl Ground Radar Based National Mosaic Qpe, Pierre-Emmanuel Kirstetter, Y. Hong, J. J. Gourley, S. Chen, Z. Flamig, J. Zhang, M. Schwaller, W. Peterson, Eyal Amitai

Biology, Chemistry, and Environmental Sciences Faculty Articles and Research

Characterization of the error associated with satellite rainfall estimates is a necessary component of deterministic and probabilistic frameworks involving spaceborne passive and active microwave measurements for applications ranging from water budget studies to forecasting natural hazards related to extreme rainfall events. The authors focus here on the error structure of NASA's Tropical Rainfall Measurement Mission (TRMM) Precipitation Radar (PR) quantitative precipitation estimation (QPE) at ground. The problem is addressed by comparison of PR QPEs with reference values derived from ground-based measurements using NOAA/NSSL ground radar based National Mosaic and QPE system (NMQ/Q2). A preliminary investigation of this subject has been …

Pbr, Epr, And All That Jazz, Matthew S. Leifer

Mathematics, Physics, and Computer Science Faculty Articles and Research

"In the past couple of months, the quantum foundations world has been abuzz about a new preprint entitled "The Quantum State Cannot be Interpreted Statistically" by Matt Pusey, Jon Barrett and Terry Rudolph (henceforth known as PBR). Since I wrote a blog post explaining the result, I have been inundated with more correspondence from scientists and more requests for comment from science journalists than at any other point in my career. Reaction to the result amongst quantum researchers has been mixed, with many people reacting negatively to the title, which can be misinterpreted as an attack on the Born rule. …

Fog- And Cloud-Induced Aerosol Modification Observed By The Aerosol Robotic Network (Aeronet), T. F. Eck, B. N. Holben, J. S. Reid, D. M. Giles, M. A. Rivas, Ramesh P. Singh, S. N. Tripathi, C. J. Bruegge, S. Platnick, G. T. Arnold, N. A. Krotkov, S. A. Carn, A. Sinyuk, O. Dubovik, A. Arola, J. S. Schafer, P. Artaxo, A. Smirnov, H. Chen, P. Goloub

Mathematics, Physics, and Computer Science Faculty Articles and Research

Large fine mode-dominated aerosols (submicron radius) in size distributions retrieved from the Aerosol Robotic Network (AERONET) have been observed after fog or low-altitude cloud dissipation events. These column-integrated size distributions have been obtained at several sites in many regions of the world, typically after evaporation of low-altitude cloud such as stratocumulus or fog. Retrievals with cloud-processed aerosol are sometimes bimodal in the accumulation mode with the larger-size mode often similar to 0.4-0.5 mu m radius (volume distribution); the smaller mode, typically similar to 0.12 to similar to 0.20 mu m, may be interstitial aerosol that were not modified by incorporation …

Everything Is Entangled, Roman V. Buniy, Stephen D. H. Hsu

Mathematics, Physics, and Computer Science Faculty Articles and Research

We show that big bang cosmology implies a high degree of entanglement of particles in the universe. In fact, a typical particle is entangled with many particles far outside our horizon. However, the entanglement is spread nearly uniformly so that two randomly chosen particles are unlikely to be directly entangled with each other - the reduced density matrix describing any pair is likely to be separable.

An Algebraic Classification Of Entangled States, Roman V. Buniy, Thomas W. Kephart

Mathematics, Physics, and Computer Science Faculty Articles and Research

We provide a classification of entangled states that uses new discrete entanglement invariants. The invariants are defined by algebraic properties of linear maps associated with the states. We prove a theorem on a correspondence between the invariants and sets of equivalent classes of entangled states. The new method works for an arbitrary finite number of finite-dimensional state subspaces. As an application of the method, we considered a large selection of cases of three subspaces of various dimensions. We also obtain an entanglement classification of four qubits, where we find 27 fundamental sets of classes.

New Invariants For Entangled States, Roman V. Buniy, Thomas W. Kephart

Mathematics, Physics, and Computer Science Faculty Articles and Research

We propose new algebraic invariants that distinguish and classify entangled states. Considering qubits as well as higher spin systems, we obtained complete entanglement classifications for cases that were either unsolved or only conjectured in the literature.

Toward Solving The Cosmological Constant Problem By Embedding, Roman V. Buniy, Thomas W. Kephart

Mathematics, Physics, and Computer Science Faculty Articles and Research

The typical scalar field theory has a cosmological constant problem. We propose a generic mechanism by which this problem is avoided at tree level by embedding the theory into a larger theory. The metric and the scalar field coupling constants in the original theory do not need to be fine-tuned, while the extra scalar field parameters and the metric associated with the extended theory are fine-tuned dynamically. Hence, no fine-tuning of parameters in the full Lagrangian is needed for the vacuum energy in the new physical system to vanish at tree level. The cosmological constant problem can be solved if …

Impact Of Vegetation On Land-Atmosphere Coupling Strength And Its Implication For Desertification Mitigation Over East Asia, Boksoon Myoung, Yong-Sang Choi, Suk-Jin Choi, Seon Ki Park

Mathematics, Physics, and Computer Science Faculty Articles and Research

Desertification of the East Asian drylands and the consequent dust transport have been serious concerns for adjacent Asian countries as well as the western United States. Tree planting has been considered one applicable strategy to mitigate the desertification. However, the desired effect of the tree planting would not be brought to fruition unless the newly planted trees change the coupling characteristics between the land and the atmosphere. Based on this perception, we attempt to clarify the effects of vegetation on the coupling strength between the atmosphere and land surface, and we suggest the most efficient areas of tree planting for …

White Noise Based Stochastic Calculus Associated With A Class Of Gaussian Processes, Daniel Alpay, Haim Attia, David Levanony

Mathematics, Physics, and Computer Science Faculty Articles and Research

Using the white noise space setting, we define and study stochastic integrals with respect to a class of stationary increment Gaussian processes. We focus mainly on continuous functions with values in the Kondratiev space of stochastic distributions, where use is made of the topology of nuclear spaces. We also prove an associated Ito formula.

An Interpolation Problem For Functions With Values In A Commutative Ring, Daniel Alpay, Haim Attia

Mathematics, Physics, and Computer Science Faculty Articles and Research

It was recently shown that the theory of linear stochastic systems can be viewed as a particular case of the theory of linear systems on a certain commutative ring of power series in a countable number of variables. In the present work we study an interpolation problem in this setting. A key tool is the principle of permanence of algebraic identities.

Schur Functions And Their Realizations In The Slice Hyperholomorphic Setting, Daniel Alpay, Fabrizio Colombo, Irene Sabadini

Mathematics, Physics, and Computer Science Faculty Articles and Research

In this paper we start the study of Schur analysis in the quaternionic setting using the theory of slice hyperholomorphic functions. The novelty of our approach is that slice hyperholomorphic functions allows to write realizations in terms of a suitable resolvent, the so called S-resolvent operator and to extend several results that hold in the complex case to the quaternionic case. We discuss reproducing kernels, positive definite functions in this setting and we show how they can be obtained in our setting using the extension operator and the slice regular product. We define Schur multipliers, and find their co-isometric realization …

On The Class Rsi Of J-Contractive Functions Intertwining Solutions Of Linear Differential Equations, Daniel Alpay, Andrey Melnikov, Victor Vinnikov

Mathematics, Physics, and Computer Science Faculty Articles and Research

In this paper we extend and solve in the class of functions RSI mentioned in the title, a number of problems originally set for the class RS of rational functions contractive in the open right-half plane, and unitary on the imaginary line with respect to some preassigned self-adjoint matrix. The problems we consider include the Schur algorithm, the partial realization problem and the Nevanlinna-Pick interpolation problem. The arguments rely on the one-to-one correspondence between elements in a given subclass of RSI and elements in RS. Another important tool in the arguments is a new result pertaining to the classical tangential …

Stochastic Processes Induced By Singular Operators, Daniel Alpay, Palle Jorgensen

Mathematics, Physics, and Computer Science Faculty Articles and Research

In this paper we study a general family of multivariable Gaussian stochastic processes. Each process is prescribed by a fixed Borel measure σ on Rn. The case when σ is assumed absolutely continuous with respect to Lebesgue measure was stud- ied earlier in the literature, when n = 1. Our focus here is on showing how different equivalence classes (defined from relative absolute continuity for pairs of measures) translate into concrete spectral decompositions of the corresponding stochastic processes under study. The measures σ we consider are typically purely singular. Our proofs rely on the theory of (singular) unbounded operators in …