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A method is presented for the improved calculation of super-shell partition functions which include the repulsive electron-electron interaction energy terms in the Boltzmann factor. Heretofore these interaction terms were approximately treated via the use of Feynman-Jensen inequalities. Such investigations are of particular interest for the super-transition-array approach of hot-plasma radiative opacity.
In this paper the finite-difference time-domain general vector auxiliary differential equation method [Greene, J. H. and A. Taflove, Opt. Express 14, 8305 (2006)], nonlinear polarization vector, the nonlinear electric dipole moment per unit volume, is extended to include anisotropy, in nonlinear isotropic media at optical frequencies. The theory is presented for extending the numerical method in 3D Cartesian coordinates, and then example simulation results are presented for two isotropic media. First, the simplified 2D transverse magnetic case is revisited for the fused silica example introduced in the 2006 paper, including the anisotropic part of the nonlinear polarization vector in the simulation; the simulation results including the anisotropic part of the polarization vector were compared with the purely isotropic polarization vector simulation results. Second, a simplified 2D transverse magnetic example was simulated in carbon disulfide, with its strong molecular re-orientation induced polarization anisotropy.
We briefly review the correspondence principle proposed in our previous paper, which claims that if we regard a matrix element defined in terms of the future state at time $T_B$ and the past state at time $T_A$ as an expectation value in the complex action theory whose path runs over not only past but also future, the expectation value at the present time $t$ of a future-included theory for large $T_B-t$ and large $t-T_A$ corresponds to that of a future-not-included theory with a proper inner product for large $t-T_A$. This correspondence principle suggests that the future-included theory is not excluded phenomenologically.
The Airy integral is a well-known contour integral solution of Airy's equation which has several applications and which has been used for mathematical illustrations due to its interesting properties. We present and derive properties of two families of contour integral solutions of linear differential equations, where one family includes the Airy integral and Airy's equation, such that the family generalizes known properties of the Airy integral which include exponential decay growth in a certain sector. The second family includes a known example and contains a subfamily with interesting properties where a separate analysis of three pairwise linearly independent contour integral solutions of a particular equation is given.
Third party tracking is the practice by which third parties recognize users accross different websites as they browse the web. Recent studies show that 90% of websites contain third party content that is tracking its users across the web. Website developers often need to include third party content in order to provide basic functionality. However, when a developer includes a third party content, she cannot know whether the third party contains tracking mechanisms. If a website developer wants to protect her users from being tracked, the only solution is to exclude any third-party content, thus trading functionality for privacy. We describe and implement a privacy-preserving web architecture that gives website developers a control over third party tracking: developers are able to include functionally useful third party content, the same time ensuring that the end users are not tracked by the third parties.
Selected results from the following topics are presented: Measurements of several top quark properties are obtained from the CMS data collected in 2011 at a center-of-mass energy of 7 TeV. The results include measurements of the top quark mass, the W helicity in top decays, the top quark charge, and of the $t\bar{t}$ spin correlation and the search for anomalous couplings.
We show that it is possible to equate the intensity reduction of a light wave caused by weak absorption with a geometrical reduction in intensity caused by a "transverse" conformal transformation of the spacetime metric in which the wave travels. We are consequently able to modify Gordon's optical metric to account for electromagnetic properties of ponderable material whose properties include both refraction and absorption. Unlike refraction alone however, including absorption requires a modification of the optical metric that depends on the eikonal of the wave itself. We derive the distance-redshift relation from the modified optical metric for Friedman-Lemaître-Robertson-Walker spacetimes whose cosmic fluid has associated refraction and absorption coefficients. We then fit the current supernovae data and provide an alternate explanation (other than dark energy) of the apparent acceleration of the universe.
A new, more efficient approach to include a three nucleon force into three-nucleon continuum calculations is presented. Results obtained in the new and our old approach are compared both for elastic nucleon-deuteron scattering as well as for the breakup process. The advantages of the new scheme are discussed.
Much work has been done taking into account the possibility that the gravitational {\it constant} $G$ may vary with cosmological time $t$ (or with the cosmological scale factor $a(t)$). The same may be said about the speed of light $c$. We present here two important remarks on these subject. These remarks include $G(t)$ and $c(t)$ varying with time with the restriction $8 πG / c^4 = \hbox{constant}$
One approach to defining Intention is to use the counterfactual tools developed to define Causality. Direct Intention is considered the highest level of intent in the common law, and is a sufficient component for the most serious crimes to be committed. Loosely defined it is the commission of actions to bring about a desired or targeted outcome. Direct Intention is not always necessary for the most serious category of crimes because society has also found it necessary to develop a theory of intention around side-effects, known as oblique intent or indirect intent. This is to prevent moral harms from going unpunished which were not the aim of the actor, but were natural consequences nevertheless. This paper uses a canonical example of a plane owner, planting a bomb on their own plane in order to collect insurance, to illustrate how two accounts of counterfactual intent do not conclude that murder of the plane's passengers and crew were directly intended. We extend both frameworks to include a definition of oblique intent developed in Ashton (2021)
A straightforward algebraic derivation is carried out of light quark propagator and effective action in the instanton-anti-instanton molecule. Exact expressions are obtained which contain contributions of all quark modes. Possible implications of the results include chiral phase transition and correlation functions of mesons and baryons.
In this paper, we introduce new classes of divergences by extending the definitions of the Bregman divergence and the skew Jensen divergence. These new divergence classes (g-Bregman divergence and skew g-Jensen divergence) satisfy some properties similar to the Bregman or skew Jensen divergence. We show these g-divergences include divergences which belong to a class of f-divergence (the Hellinger distance, the chi-square divergence and the alpha-divergence in addition to the Kullback-Leibler divergence). Moreover, we derive an inequality between the g-Bregman divergence and the skew g-Jensen divergence and show this inequality is a generalization of Lin's inequality.
Transport theory for the Nambu--Jona-Lasinio (NJL) model is examined. The collision term is investigated in a first approach in a coupling strength expansion. It can be demonstrated that this leads to a form easily recognized from the Boltzmann equation if the quasiparticle approximation is used. It is seen that enforcing a quasiparticle approximation suppresses the three body creation and annihilation processes that would otherwise be present. Including mesons and hadronization consistently in a $1/N_c$ expansion is discussed briefly. Some comments on the numerical simulation of the Vlasov equation and the relaxation time approximation to the collision term are made.
The Newtonian simulations describing the formation of large-scale structures do not include relativistic effects. A new approach to this problem is proposed, which consists of splitting the Hawking-Hayward quasi-local energy of a closed spacelike 2-surface into a "Newtonian" part due to local perturbations and a "relativistic" part due to the cosmology. It is found that the Newtonian part dominates over the relativistic one as time evolves, lending support to the validity of Newtonian simulations.
Early identification of college dropouts can provide tremendous value for improving student success and institutional effectiveness, and predictive analytics are increasingly used for this purpose. However, ethical concerns have emerged about whether including protected attributes in the prediction models discriminates against underrepresented student groups and exacerbates existing inequities. We examine this issue in the context of a large U.S. research university with both residential and fully online degree-seeking students. Based on comprehensive institutional records for this entire student population across multiple years, we build machine learning models to predict student dropout after one academic year of study, and compare the overall performance and fairness of model predictions with or without four protected attributes (gender, URM, first-generation student, and high financial need). We find that including protected attributes does not impact the overall prediction performance and it only marginally improves algorithmic fairness of predictions. While these findings suggest that including protected attributes is preferred, our analysis also offers guidance on how to eva
Interstellar dust has been detected in situ flowing through the heliosphere. However, our ability to derive the density and size distribution of the interstellar dust in the local interstellar medium from this directly detected dust requires modeling the transport of the grains as they interact with the solar wind magnetic field. The magnetic field in the sector region that contains the heliospheric current sheet has rapid polarity flips which can present an effectively very low averaged field strength to dust grains that have gyroradii tens of au in size. We present new calculations of dust transport through the heliosphere using models that include the sector region to assess the effects on dust transport. We show that the sector region can act as a window allowing even relatively small grains to penetrate deep into the heliosphere. We find the sector region reduces the variation in dust density with the solar cycle (as compared to models without the sector region), with very little concentration or dilution of the dust for grains larger than \sim 0.1$ $μ$m for most of the solar cycle. We still find a substantial concentration of the dust in the ecliptic plane for a focusing over
We derive a topological decoupling of the equations of modified nodal analysis (MNA) to a semi-explicit index one differential-algebraic equation. The decoupling explicitly allows for controlled sources, which play a crucial role in engineering design workflows. Furthermore, the proof is constructive and provides a graph-based algorithmic framework for the computation of the decoupling, enabling its application to a variety of industry problems. These include the generation of consistent initial conditions, model order reduction, (scientific) machine learning, as well as speeding up conventional circuit simulation. In addition, the decoupling preserves the structure of MNA, i.e. the resulting systems remain sparse and key parts remain positive definite. We illustrate the decoupling using multiple examples, including some of the most common subcircuits containing controlled sources. Lastly, we also provide a first software implementation of the decoupling.
Over the last decades, theoretical photochemistry has produced multiple techniques to simulate the nonadiabatic dynamics of molecules. Surprisingly, much less effort has been devoted to adequately describing the first step of a photochemical or photophysical process: photoexcitation. Here, we propose a formalism to include the effect of a laser pulse in trajectory-based nonadiabatic dynamics at the level of the initial conditions, with no additional cost. The promoted density approach (PDA) decouples the excitation from the nonadiabatic dynamics by defining a new set of initial conditions, which include an excitation time. PDA with surface hopping leads to nonadiabatic dynamics simulations in excellent agreement with quantum dynamics using an explicit laser pulse and highlights the strong impact of a laser pulse on the resulting photodynamics and the limits of the (sudden) vertical excitation. Combining PDA with trajectory-based nonadiabatic methods is possible for any arbitrary-sized molecules using a code provided in this work.
Missing data is a common challenge when analyzing epidemiological data, and imputation is often used to address this issue. Here, we investigate the scenario where a covariate used in an analysis has missingness and will be imputed. There are recommendations to include the outcome from the analysis model in the imputation model for missing covariates, but it is not necessarily clear if this recommendation always holds and why this is sometimes true. We examine deterministic imputation (i.e., single imputation with fixed values) and stochastic imputation (i.e., single or multiple imputation with random values) methods and their implications for estimating the relationship between the imputed covariate and the outcome. We mathematically demonstrate that including the outcome variable in imputation models is not just a recommendation but a requirement to achieve unbiased results when using stochastic imputation methods. Moreover, we dispel common misconceptions about deterministic imputation models and demonstrate why the outcome should not be included in these models. This paper aims to bridge the gap between imputation in theory and in practice, providing mathematical derivations to