Straightforward Formalism Research Articles

Quantum Contextuality and Indeterminacy.

The circumstances of measurement have more direct significance in quantum than in classical physics, where they can be neglected for well-performed measurements. In quantum mechanics, the dispositions of the measuring apparatus-plus-environment of the system measured for a property are a non-trivial part of its formalization as the quantum observable. A straightforward formalization of context, via equivalence classes of measurements corresponding to sets of sharp target observables, was recently given for sharp quantum observables. Here, we show that quantum contextuality, the dependence of measurement outcomes on circumstances external to the measured quantum system, can be manifested not only as the strict exclusivity of different measurements of sharp observables or valuations but via quantitative differences in the property statistics across simultaneous measurements of generalized quantum observables, by formalizing quantum context via coexistent generalized observables rather than only its subset of compatible sharp observables. Here, the question of whether such quantum contextuality follows from basic quantum principles is then addressed, and it is shown that the Principle of Indeterminacy is sufficient for at least one form of non-trivial contextuality. Contextuality is thus seen to be a natural feature of quantum mechanics rather than something arising only from the consideration of impossible measurements, abstract philosophical issues, hidden-variables theories, or other alternative, classical models of quantum behavior.

Effect of dark counts on single-photon heralding with quasi-number-resolving detection schemes.

We consider photon heralding with quasi-number-resolving detection schemes and account for detection efficiencies and dark count probabilities. With a straightforward formalism, we develop closed-form expressions for the heralding probability, photon number distribution of the resulting heralded state, and fidelity of this heralded state to a single-photon state. We calculate that this fidelity has a maximum as a function of the number of multiplexed detection modes and that, for experimental configurations in which the maximum is reached for quite a large number of detection modes, it can still be highly beneficial to multiplex fewer modes.

A comparison of protocols for external beam radiotherapy beam calibrations

A number of codes of practice (CoP) for electron and photon radiotherapy beam dosimetry are currently in use. Comparison is made of the more widely used of these, specifically those of the International Atomic Energy Agency (IAEA TRS-398), the American Association of Physicists in Medicine (AAPM TG-51) and the Institute of Physics and Engineering in Medicine (IPEM 2003). All are based on calibration of ionization chambers in terms of absorbed dose to water, each seeking to reduce uncertainty in delivered dose, providing an even stronger system of primary standards than previous air-kerma based approaches. They also provide a firm, traceable and straight-forward formalism (Radiology, 1996). Included in making dose assessments for the three CoP are calibration coefficients for a range of beam quality indices. Measurements have been performed using clinical photon and electron beams, the absorbed dose to water being obtained following the recommendations given by each code. Electron beam comparisons have been carried out using measurements for electron beams of nominal energies 6, 9, 12, 16 and 20MeV. Comparisons were also carried out for photon beams of nominal energies 6 and 18MV. For photon beams use was made of NE2571 cylindrical graphite walled ionization chambers, cross-calibrated against an NE2611 Secondary Standard; for electron beams, PTW Markus and NACP-02 plane-parallel chambers were used. Irradiations were made using Varian 600C/2100C linacs, supported by water tanks and Virtual Water™ phantoms. The absorbed doses for photon and electron beams obtained following these CoP are all in good agreement, with deviations of less than 2%.A number of studies have been carried out by different groups in different countries to examine the consistency of dosimetry codes of practice or protocols. The aim of these studies is to confirm that the goal of those codes is met, namely uniformity in establishment of dosimetry of all radiation beam types used in cancer therapy in the world, and this is one of the studies.

Stieltjes–Calogero–Gil’ relations associated to entire functions of finite order

The classical Stieltjes–Calogero relations involving the zeros of the Hermite polynomials found over the years counterpart associated with virtually all the important polynomials appearing in mathematical physics. The standard method of deriving them typically rests on two different ways of looking at the Laurent expansion of the logarithmic derivative of a polynomial about a singular point, that is, a zero of the polynomial. While the first way is a straightforward formalism, the second proves to be cumbersome and is usually handled on a case by case basis, often based on Painlevé transcendent techniques, if the logarithmic derivative of the polynomial in question is solution to a suitable nonlinear differential equation. In this note we settle the problem completely and in full generality via an analysis based on Gil’s remarkable relations involving the zeros of an entire function of finite order. In addition to being elegant and efficient, the new method has wider applicability, addressing not just polynomials but also entire functions of finite order.

Modeling diffusion and phase transitions by a uniform-acceptance force-bias Monte Carlo method

The uniform-acceptance force-bias Monte Carlo (UFMC) method [G. Dereli, Mol. Simul. 8, 351 (1992)] is a little-used atomistic simulation method that has strong potential as alternative or complementary technique to molecular dynamics (MD). We have applied UFMC to surface diffusion, amorphization, melting, glass transition, and crystallization, mainly of silicon. The purpose is to study the potential and the limitations of the method: to investigate its applicability, determine safe and effective values of the two UFMC parameters---a temperature and a maximum allowed atomic displacement per iteration step---that lead to reliable results for different types of simulations, assess the computational speed increase relative to MD, discover the microscopic mechanisms that make UFMC work, and show in what kind of simulations it can be useful and preferable over MD. It is found that in many simulations, UFMC can be a very efficient alternative to MD: it leads to analogous results in much fewer iteration steps. Due to the straightforward formalism of UFMC, it can be easily implemented in any MD code. Thus both methods can be combined and applied in turn, using UFMC for the acceleration of certain processes and MD for keeping precision and monitoring individual atom trajectories.

Klivaj predika, or predicate clefts in Haitian

Haitian’s well studied predicate cleft and its unstudied predicate reduplication are closely related: the former derives from the latter by A-bar movement of one reduplicant. This claim solves two long standing problems of the construction (why, apparently, this A-bar movement targets a head and leaves no gap). Moreover, it predicts novel restrictions on when predicate clefts are possible and makes possible a straightforward formalization of their semantics.

Wherefore Psychosemiotics?

Immediately subsuming any cognitive relation as a sign reference, the Peircean view is able to explain any act of semiosis in theory, and thus unable to explain preferences and omissions in practice. To include these phenomena, we may combine semiotics and psychoanalysis, introducing objective opacity into semiotics, and straightforward formalization into psychoanalysis. To showcase the explanatory power of the resultant psychosemiotics, an outline on comics’ central sign type, the cartoon, is presented.

A Unified Theory and Test of Extended Immediate Deterrence

We present a unified theory and test of extended immediate deterrence—unified in the sense that we employ our theoretical deterrence model as our statistical model in the empirical analysis. The theoretical model is a straightforward formalization of the deterrence logic in Huth (1988) and Huth and Russett (1984), coupled with private information concerning utilities. Our statistical analysis suggests that the attacker and defender's decisions are influenced by the balance of forces, nuclear weapons, defender‐protege military alliances, arms transfers, and trade, as well as the regime types of those involved. Many of these findings contradict previous research by Huth (1988) and Huth and Russett (1988). We find that many of the variables involved in the deterrence calculus are nonmonotonically linked to the probability of deterrence success or war. We illustrate the results with case studies of the Soviet‐Japanese dispute over Manchukuo (1937–1938) and the Berlin Blockade (1948).

Minimality of a solution update in conflict resolution: An application of revision programming to the von Neumann-Morgenstern approach

In a 1944 book that started game theory (and the mathematical approach to conflict resolution), von Neumann and Morgenstern proposed the notion of a solution. When the situation changes, the old solution is often no longer a solution, so it needs to be updated. In practical applications, it is usually desirable to keep the solution change “minimal” in some reasonable sense. We show that for a seemingly straightforward formalization of this minimality, checking whether a change is minimal is NP-hard. We also show that by representing the notion of a solution as a collection of revision rules, we can produce a reasonable notion of minimality for which there exists a feasible algorithm for checking the minimality of the update. © 2005 Wiley Periodicals, Inc. Int J Int Syst 20: 939–956, 2005.

A formal model of real-time program compilation

Program compilation can be formally defined as a sequence of equivalence-preserving transformations, or refinements, from high-level language programs to assembler code. Recent models also incorporate timing properties, but the resulting formalisms are intimidatingly complex. Here we take advantage of a new, simple model of real-time refinement, based on predicate transformer semantics, to present a straightforward compilation formalism that incorporates real-time constraints.

Translational Dynamics of Diblock Copolymers

A study of the translational diffusion of a symmetric A-B diblock copolymer into homopolymer, A and B, host is reported. The segmental mobilities of homopolymer A into homopolymer B, A into A, B into A, and B into homopolymer B hosts were independently determined. These segmental mobilities were observed to differ by orders of magnitude. Using a straightforward formalism based entirely on reptation, reliable predictions of the magnitude of the diffusivity of the diblock were made using these independently determined mobilities. Current theories which address the diffusion of diblock copolymer chains all assume, in the absence of any experiments in this area, that a single, constant, friction factor characterizes the diffusion of diblock chains. It is anticipated that the incorporation of such differences in the relative magnitudes of the segmental mobilities might alter quantitative conclusions of such theories.

Scanning tunneling microscopy on rough surfaces: Deconvolution of constant current images

This letter critically discusses the topographical information obtained by scanning tunneling microscopy (STM) on surfaces with a mesoscopic roughness, i.e., in the range of some nm’s. In a foregoing publication [J. Appl. Phys. 67, 1156 (1990)], we already treated the evaluation of constant current images based on the knowledge of the real surface and the shape of the tunneling tip (‘‘tip shape limited resolution’’). Now we deal with the invers problem: the reconstruction of the real surface topography based on the corresponding STM image and the tip shape, using a simple, straightforward formalism.

Relaxation processes in chaotic states of one dimensional maps

Relaxation of probability distributions towards their stationary state is studied in one dimensional fully developed chaotic maps. Exponential relaxation is described by solving the eigenvalue problem of the Frobenius-Perron operator for families of maps. This happens via perturbation theory, for which a straightforward formalism is presented. Critical maps with power law decay are also considered.

Adiabatic theory of symmetry breaking and dipole moments of isotopic molecules. Correct dissociation of their electronic and muonic ions.

To calculate the nonzero dipole moment of isotopic molecules such as HD or the correct dissociation limit of ions such as ${\mathrm{HD}}^{+}$ via the usual approach requires cumbersome, expansive nonadiabatic corrections to the Born-Oppenheimer approximation. Such a complication is herein shown unnecessary; the ``best adiabatic'' approximation of Pack and Hirschfelder [J. Chem. Phys. 52, 521 (1970)] provides a single straightforward formalism which gives such effects correctly and yet retains the potential energy curve concept. Simple example calculations show the size of these symmetry-breaking effects to be at the level of high-resolution spectroscopy for ${\mathrm{HD}}^{+}$ but very large in ions such as dt\ensuremath{\mu}, which contains a deuteron, a triton, and a negative muon.

A straightforward formalization of the relational model

There has been a lot of recent interest in the formalization of the relational data model (RDM). Many approaches may be characterized as ones oriented mainly towards declaring the components of the RDM and their interrelationships. Other approaches provide also a tool for manipulating the components of RDM so that research topics on the model can be specified exactly. Usually the latter approaches are based on formal specification methods such as denotational semantics or abstract data types. However some in the data base community find them quite complex and cumbersome. The goal of the approach of this paper is of the latter kind. However, special attention is being paid to avoid the complexity of the formal specification methods because our notations and definitions are based on set theory. We attempt to provide an exact, convenient and general tool for specifications and proofs concerning various topics like relational query languages, query optimization, relational data base restructuring, data base design, etc.

A straightforward formalization of the relational model

There has been a lot of recent interest in the formalization of the relational data model (RDM). Many approaches may be characterized as ones oriented mainly towards declaring the components of the RDM and their interrelationships. Other approaches provide a tool for manipulating the components of RDM so that research topics on the model can be specified exactly. The latter approaches are based on formal specification methods such as denotational semantics or abstract data types. Some in the data base community experience them quite complex and cumbersome.The goal of the approach of this paper is of the latter kind. However, special attention is being paid to avoid the complexity of the formal specification methods because our notations and definitions are based on set theory. We attempt to provide an exact, convenient and general tool for specifications and proofs concerning various topics like relational query languages, query optimization, relational data base restructuring, data base design, etc.

Lorentz andCPTInvariances and the Einstein-Podolsky-Rosen Correlations

The $S$-matrix scheme allows a straightforward formalization of the Einstein-Podolsky-Rosen nonseparability either of distant measurements issuing from a common preparation, or of distant preparations converging into a common measurement. This implies Lorentz and $\mathrm{CPT}$ invariance of the causality concept at the elementary level, which is a quantal and relativistic extension of the 1876 Loschmidt reversibility statement.

Statistical Thermodynamics of Ionic Systems

AbstractA statistical thermodynamical method is presented for calculation of thermodynamic properties of ionic systems. The method has a straightforward formalism for taking into account a variety of physical factors, e.g., making allowance for different finite volumes of different ionic species, treatment of neutral species as thermodynamic components (rather than merely regarding them as a dielectric medium), consideration of dependences of the dielectric constant on solvent composition (in the case of a mixed solvent) and on electric field strength, nonionic interactions, etc. The method is based on an approach of J. L. Jackson [1] whereby a fluctuation state of the system is characterized in terms of a set of functions for the spatial variations of concentrations of the various species. For such a state an appropriate Boltzmann factor is defined and a calculation of a thermodynamic property of the system requires integrations of this factor over function spaces. Two simple applications of the method are worked out by way of illustration and other, more refined, applications are pointed out.

On the non-separable baroclinic parallel flow instability problem

Perturbation series are developed and mathematically justified, using a straightforward perturbation formalism (that is more widely applicable than those given in standard textbooks), for the case of the two-dimensional inviscid Orr-Sommerfeld-like eigenvalue problem describing quasi-geostrophic wave instabilities of parallel flows in rotating stratified fluids.The results are first used to examine the instability properties of the perturbed Eady problem, in which the zonal velocity profile has the formu=z+ μu1(y,z) where, formally, μ [Lt ] 1. The connexion between baroclinic instability theories with and without short wave cutoffs is clarified. In particular, it is established rigorously that there is instability at short wavelengths in all cases for which such instability would be expected from the ‘critical layer’ argument of Bretherton. (Therefore the apparently conflicting results obtained earlier by Pedlosky are in error.)For the class of profiles of formu=z+ μu1(y) it is then shown from an examination of theO(μ) eigenfunction correction why, under certain conditions, growing baroclinic waves will always produce a counter-gradient horizontal eddy flux of zonal momentum tending to reinforce the horizontal shear of such profiles. Finally, by computing a sufficient number of the higher corrections, this first-order result is shown to remain true, and its relationship to the actual rate of change of the mean flow is also displayed, for a particular jet-like form of profile withfinitehorizontal shear. The latter detailed results may help to explain at least one interesting feature of the mean flow found in a recent numerical solution for the wave régime in a heated rotating annulus.