Physical Sciences and Mathematics Commons^™

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.

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 …

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 …

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 …

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 …

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 …

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 …

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.

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 …

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.

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 …

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.

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.

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 …

Cancer Quasispecies And Stem-Like Adaptive Aneuploidy, Domenico Napoletani, M. Signore, Daniele C. Struppa

Mathematics, Physics, and Computer Science Faculty Articles and Research

In this paper we develop a theoretical frame to understand self-regulation of aneuploidy rate in cancer and stem cells. This is accomplished building upon quasispecies theory, by leaving its formal mathematical structure intact, but by drastically changing the meaning of its objects. In particular, we propose a novel definition of chromosomal master sequence, as a sequence of physically distinct whole or fragmented chromosomes, whose length is taken to be the sum of the copy numbers of each whole or fragmented chromosome. This fundamental change in the functional objects of quasispecies theory allows us to show that previously measured aneuploidy rates …

Nominal Regular Expressions For Languages Over Infinite Alphabets, Alexander Kurz, Tomoyuki Suzuki, Emilio Tuosto

Engineering Faculty Articles and Research

We propose regular expressions to abstractly model and study properties of resource-aware computations. Inspired by nominal techniques – as those popular in process calculi – we extend classical regular expressions with names (to model computational resources) and suitable operators (for allocation, deallocation, scoping of, and freshness conditions on resources). We discuss classes of such nominal regular expressions, show how such expressions have natural interpretations in terms of languages over infinite alphabets, and give Kleene theorems to characterise their formal languages in terms of nominal automata.

Annual Patterns Of Atmospheric Pollutions And Episodes Over Cairo Egypt, Y. Aboel Fetouh, Hesham El-Askary, Mohamed El Raey, Mohamed Allali, W. A. Sprigg, Menas Kafatos

Mathematics, Physics, and Computer Science Faculty Articles and Research

The Nile Delta major cities, particularly Cairo, experienced stagnant air pollution episodes, known as Black Cloud, every year over the past decade during autumn. Low-elevated thermal inversion layers play a crucial role in intensifying pollution impacts. Carbon monoxide, ozone, atmospheric temperature, water vapor, and methane measurements from the tropospheric emission spectrometer (TES) on board the Aura have been used to assess the dominant component below the inversion layer. In this study, time series analysis, autocorrelations, and cross correlations are performed to gain a better understanding of the connections between those parameters and their local effect. Satellite-based data were obtained for …

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. …

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.

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 …

Topological Convolution Algebras, Daniel Alpay, Guy Salomon

Mathematics, Physics, and Computer Science Faculty Articles and Research

In this paper we introduce a new family of topological convolution algebras of the form ⋃p∈NL2(S,μp), where S is a Borel semi-group in a locally compact group G, which carries an inequality of the type ∥f∗g∥p≤Ap,q∥f∥q∥g∥p for p>q+d where d pre-assigned, and Ap,q is a constant. We give a sufficient condition on the measures μp for such an inequality to hold. We study the functional calculus and the spectrum of the elements of these algebras, and present two examples, one in the setting of non commutative stochastic distributions, and the other related to Dirichlet series.

Pontryagin De Branges-Rovnyak Spaces Of Slice Hyperholomorphic Functions, Daniel Alpay, Fabrizio Colombo, Irene Sabadini

Mathematics, Physics, and Computer Science Faculty Articles and Research

We study reproducing kernel Hilbert and Pontryagin spaces of slice hyperholomorphic functions which are analogs of the Hilbert spaces of analytic functions introduced by de Branges and Rovnyak. In the first part of the paper we focus on the case of Hilbert spaces, and introduce in particular a version of the Hardy space. Then we define Blaschke factors and Blaschke products and we consider an interpolation problem. In the second part of the paper we turn to the case of Pontryagin spaces. We first prove some results from the theory of Pontryagin spaces in the quaternionic setting and, in particular, …

Relation Lifting, With An Application To The Many-Valued Cover Modality, Marta Bílková, Alexander Kurz, Daniela Petrişan, Jirí Velebil

Engineering Faculty Articles and Research

We introduce basic notions and results about relation liftings on categories enriched in a commutative quantale. We derive two necessary and sufficient conditions for a 2-functor T to admit a functorial relation lifting: one is the existence of a distributive law of T over the “powerset monad” on categories, one is the preservation by T of “exactness” of certain squares. Both characterisations are generalisations of the “classical” results known for set functors: the first characterisation generalises the existence of a distributive law over the genuine powerset monad, the second generalises preservation of weak pullbacks.

The results presented in this paper …

Epistemic Updates On Algebras, Alexander Kurz, Alessandra Palmigiano

Engineering Faculty Articles and Research

We develop the mathematical theory of epistemic updates with the tools of duality theory. We focus on the Logic of Epistemic Actions and Knowledge (EAK), introduced by Baltag-Moss-Solecki, without the common knowledge operator. We dually characterize the product update construction of EAK as a certain construction transforming the complex algebras associated with the given model into the complex algebra associated with the updated model. This dual characterization naturally generalizes to much wider classes of algebras, which include, but are not limited to, arbitrary BAOs and arbitrary modal expansions of Heyting algebras (HAOs). As an application of this dual characterization, we …

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 …

Nominal Computation Theory (Dagstuhl Seminar 13422), Mikołaj Bojanczyk, Bartek Klin, Alexander Kurz, Andrew M. Pitts

Engineering Faculty Articles and Research

This report documents the program and the outcomes of Dagstuhl Seminar 13422 “Nominal Computation Theory”. The underlying theme of the seminar was nominal sets (also known as sets with atoms or Fraenkel-Mostowski sets) and they role and applications in three distinct research areas: automata over infinite alphabets, program semantics using nominal sets and nominal calculi of concurrent processes.

Nominal Coalgebraic Data Types With Applications To Lambda Calculus, Alexander Kurz, Daniela Petrişan, Paula Severi, Fer-Jan De Vries

Engineering Faculty Articles and Research

We investigate final coalgebras in nominal sets. This allows us to define types of infinite data with binding for which all constructions automatically respect alpha equivalence. We give applications to the infinitary lambda calculus.

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 …

On Discrete Analytic Functions: Products, Rational Functions, And Reproducing Kernels, Daniel Alpay, Palle Jorgensen, Ron Seager, Dan Volok

Mathematics, Physics, and Computer Science Faculty Articles and Research

We introduce a family of discrete analytic functions, called expandable discrete analytic functions, which includes discrete analytic polynomials, and define two products in this family. The first one is defined in a way similar to the Cauchy-Kovalevskaya product of hyperholomorphic functions, and allows us to define rational discrete analytic functions. To define the second product we need a new space of entire functions which is contractively included in the Fock space. We study in this space some counterparts of Schur analysis.

Point–Counterpoint: Can Anything Be Learned From Surveys On The Interpretations Of Quantum Mechanics?, Matthew S. Leifer, Nathan Harshman

Mathematics, Physics, and Computer Science Faculty Articles and Research

"In what follows, Matt Leifer and Nathan Harshman present opposing views on the value of surveys on foundational attitudes towards quantum mechanics. Three such surveys were recently published and their results are summarized in Table 1. Matt takes the `point,’ arguing that such surveys are not useful, while Nathan takes the `counterpoint.’ A complete set of references for both is given at the end."