Moment Expansion Research Articles

“I Get So Mad Cause We Ain’t Got No Freedom”: Black Women, Rage, and the Harlem Uprising of 1943

In the early evening of August 1, 1943, a New York City police officer arrested Marjorie Polite at the Braddock Hotel. Polite’s arrest created an expansive political moment for shortly after her arrest, some 3,000 New Yorkers deployed upon 125th Street. Over the course of the next two days and in their shared rage, a group of Black Harlemites targeted white-owned businesses which culminated in 500 physical injuries, at least six deaths, a reported 5 million dollars in property damages, and 623 arrests at the height of World War II. What do the stories of five ordinary women, each with different relationships to Harlem and the uprising, tell us about Black women’s experience in mid-twentieth century urban America? Using the biographical vignettes of Black women arrested in connection with the Harlem uprising, this article examines popular protest and property destruction as a feminine form of rage.

Dynamics of change in the polytropic exponent in the expansion stroke of diesel

In the article is considered the problem of achieving the optimal duration of the working stroke of a diesel engine piston during the expansion process and obtaining the maximum efficiency coefficient (EC). For this purpose, a hypothesis was put forward about the pumping action of the piston on the flow of expanding gases during the power stroke of an diesel internal combustion engine (ICE) as the piston moves from upper dead point (UDP) to bottom dead point (BDP).At a certain moment of expansion, the rate of the flow of expanding gases turns out to be equal to the rate with which the same flow is slowed down by the moving piston.The equality of these rates leads to the formation of a flow break line and has a significant impact on the nature of the change in the polytropic exponent; the value of the exponent becomes equal to one: n = 1. This indicates that the optimum duration of the engine’s working stroke has been achieved and corresponds to the maximum power that can be removed during the diesel engine’s operating cycle. An experimental relation was obtained between the initial p1 and final p2 pressures in the cylinder during gas expansion with the gas flow rate and the rate of deceleration of this flow due to the pumping action of the piston. An equation for the continuity of gas flow has been compiled for the process of gas expansion in the cylinder of an ICE with closed gas exchange organs. Based on this equation, the numericalvalue of the acceleration of gravity in the cylinder of ICE is obtained: gф ≈ 8,7 м/с2 < g, which confirms the pumping action of the piston. A theoretical (and graphical) dependence of the polytropic process exponent on the flow rate of expanding gases is obtained. The dependence allows to calculate the polytropic exponent and establish the gas relaxation period, indicating the achievement of the optimal duration of the piston stroke.

The Explosion of the Non-contemporary: Conversing about the Far Right, Contemporary Fascism, Ernst Bloch, and the Need for a Decolonizing Marxism

In this conversation, Beat Dietschy—Swiss philosopher, theologian, and collaborator of philosopher Ernst Bloch at Tübingen University—and Ana Cecilia Dinerstein, UK-based Argentinean scholar-activist, open Marxist, and critical feminist theorist—reflect on the potential of Bloch’s analyses of fascism and Nazism to comprehend the present daring political moment of authoritarian expansion by the Far Right in different contexts and degrees, on one hand, and the strengthening of territorial, social, rural, urban, feminist, and indigenous movements to stop the worsening ecological crisis by creating new practices moved by hope, on the other hand. Their dialogue explores Bloch’s notions of non-contemporaneity, non-simultaneity, multiversum, and multiple dialectics, elaborating on the plural contradictions of present social relations and class struggles (in a broad sense) against and beyond global capitalism. Finally, they enquire what kind of Marxism is required to decolonize current critical praxis and theory while navigating the pessimism of the present.

Systematic moment expansion for electroweak baryogenesis

We present a systematic moment expansion for solving the semiclassical Boltzmann equations for electroweak baryogenesis. The expansion is developed in powers of adiabatic coordinate velocity, and it is used for computing the CP-violating seed asymmetry at the front of the phase transition wall, that sources the eventual baryon asymmetry of the universe (BAU). We implement the method in a benchmark model, with a CP-violating mass arising from a dimension-5 operator coupling the fermion to a singlet scalar field. We find that the higher moment calculations yield a BAU that can significantly differ from the commonly used two-moment approximation. We discuss in detail the underlying approximations in the moment method and propose a new truncation scheme for the expansion, that appears to give more numerically robust results than the previous schemes.

CLASS-OneLoop: accurate and unbiased inference from spectroscopic galaxy surveys

The power spectrum is the most commonly applied summary statistics to extract cosmological information from the observed three-dimensional distribution of galaxies in spectroscopic surveys. We present CLASS-OneLoop, a new numerical tool, fully integrated into the Boltzmann code CLASS, enabling the calculation of the one-loop power spectrum of biased tracers in spectroscopic surveys. Built upon the Eulerian moment expansion framework for redshift-space distortions, the implemented model incorporates a complete set of nonlinear biases, counterterms, and stochastic contributions, and includes the infrared resummation and the Alcock-Paczynski effect. The code features an evaluation of the loops by either direct numerical integration or Fast Fourier Transform, and employs a fast-slow parameter decomposition, which is essential for accelerating MCMC runs. After presenting performance and validation tests, as an illustration of the capabilities of the code, we apply it to fit the measured redshift-space halo power spectrum wedges on a ΛCDM subset of the AbacusSummit simulation suite and considering scales up to kmax = 0.3 h/Mpc. We find that the one-loop model adeptly recovers the fiducial cosmology of the simulation, while a simplified model commonly used in the literature for sensitivity forecasts yields significantly biased results. Furthermore, we conduct Monte Carlo Markov Chain (MCMC) forecasts for a DESI-like survey, considering a model with a dynamical dark energy component. Our results demonstrate the ability to independently constrain cosmological and nuisance parameters, even in the presence of a large parameter space with twenty-nine variables.

Spherical bispectrum expansion and quadratic estimators

We describe a general expansion of spherical (full-sky) bispectra into a set of orthogonal modes. For squeezed shapes, the basis separates physically-distinct signals and is dominated by the lowest moments. In terms of reduced bispectra, we identify a set of discrete polynomials that are pairwise orthogonal with respect to the relevant Wigner 3j symbol, and reduce to Chebyshev polynomials in the flat-sky (high-momentum) limit for both parity-even and parity-odd cases. For squeezed shapes, the flat-sky limit is equivalent to previous moment expansions used for CMB bispectra and quadratic estimators, but in general reduces to a distinct expansion in the angular dependence of triangles at fixed total side length (momentum).We use the full-sky expansion to construct a tower of orthogonal CMB lensing quadratic estimators and construct estimators that are immune to foregrounds like point sources or noise inhomogeneities. In parity-even combinations (such as the lensing gradient mode from TT, or the lensing curl mode from EB) the leading two modes can be identified with information from the magnification and shear respectively, whereas the parity-odd combinations are shear-only. Although not directly separable, we show that these estimators can nonetheless be evaluated numerically sufficiently easily.

Moment expansion method for composite open quantum systems including a damped oscillator mode

Moment expansion method for composite open quantum systems including a damped oscillator mode

Asymptotic Expansions for the Stationary Moments of a Modified Renewal-Reward Process with Dependent Components

Asymptotic Expansions for the Stationary Moments of a Modified Renewal-Reward Process with Dependent Components

Wari across the Andes: Modeling the radiocarbon evidence

The expansion and impact of the Wari polity across the Andes has been heavily debated by scholars over the past two decades. We use radiocarbon dates, Bayesian statistics, and contextual data from several Andean regions to review the chronology for Wari expansion, political reorganization, and impact on local settlements. We recognize that Wari political and economic influence will vary in space and time and present a model that addresses how influential moments (expansion, reorganization, collapse) in Wari's trajectory may or may not have had broader impacts across the landscapes of its peer polities. Our model, while not completely comprehensive, draws on both Wari's presence in the north highlands and in the south, where scholars have argued for distinct trajectories and character of Wari influence. It also examines data from local communities in these same regions contemporary with identified Wari settlements, but perhaps without outward indicators of Wari hegemony, to evaluate broader patterns in Middle Horizon settlement through the latter half of the first millennium CE.

Democratization and inclusion: what women’s enfranchisement tells us about the second wave of democracy

ABSTRACT Most Latin American countries enfranchised women during the second wave of democracy. But how did this expansion of participation relate to other dimensions of democracy? In this essay, I use Robert Dahl’s two dimensions of democracy and evaluate what women’s inclusion tells us about democratization during this period. Using 14 countries as base for this analysis, I make three central claims: First, I present data on moments of expansion of inclusion and increased competitiveness and whether they coincided, confirming the late 1940s as the most significant period of democratization as both dimensions often advanced together. Second, I identify sequences of democratization based on whether contestation came before, at the same time, or after the expansion of participation to women and the characteristics of each of these sequences. Based on these sequences, I identify a revolutionary path, a democratic path, and an authoritarian path to women’s suffrage. Finally, using methodological notions of the trivialness and importance of necessary conditions, I conceptualize the dimensions of democratization and argue that the relative importance of inclusiveness has varied over time.

Comparative study on compact quantum circuits of hybrid quantum-classical algorithms for quantum impurity models

Predicting the properties of strongly correlated materials is a significant challenge in condensed matter theory. The widely used dynamical mean-field theory faces difficulty in solving quantum impurity models numerically. Hybrid quantum-classical algorithms such as variational quantum eigensolvers emerge as a potential solution for quantum impurity models. A common challenge in these algorithms is the rapid growth of the number of variational parameters with the number of spin-orbitals in the impurity. In our approach to this problem, we develop compact using a combination of two different strategies. First, we employ a compact physics-inspired , k-unitary cluster Jastrow , developed in the field of quantum chemistry. Second, we eliminate largely redundant variational parameters of physics-inspired associated with bath sites based on physical intuition. This is based on the fact that a quantum impurity model with a star-like geometry has no direct hopping between bath sites. We benchmark the accuracy of these for both ground-state energy and dynamic quantities by solving typical quantum impurity models with and without shot noise. The results suggest that we can maintain the accuracy of ground-state energy while we drop the number of variational parameters associated with bath sites. Furthermore, we demonstrate that a moment expansion, when combined with the proposed , can calculate the imaginary-time Green's functions under the influence of shot noise. This study demonstrates the potential for addressing complex impurity models in large-scale quantum simulations with fewer variational parameters without sacrificing accuracy. Published by the American Physical Society 2024

Performance analysis of a collision channel with abandonments

We consider a Markovian retrial queueing system with customer collisions and abandonment in the context of carrier-sense multiple access systems. Using z-transform techniques, we find a set of first-order differential equations for the probability generating functions of the orbit size when the server is empty, busy, or in the collision phase. We then rely on series expansion techniques to extract approximations for relevant performance measures from this set of differential equations. More precisely, we construct a numerical algorithm to calculate the terms in the series expansions of various factorial moments of the orbit size. To improve the accuracy of our series expansion approach, we apply Wynn’s epsilon algorithm which not only speeds up convergence, but also extends the region of convergence. We illustrate the accuracy of our approach by means of some numerical examples, and find that the method is both fast and accurate for a wide range of the parameter values.

VIX option pricing through nonaffine GARCH dynamics and semianalytical formula

AbstractThis paper develops analytical approximations for volatility index (VIX) option pricing under nonaffine generalized autoregressive conditional heteroskedasticity (GARCH) models as advocated by Christoffersen et al. We obtain the approximation formulae for pricing VIX options and then evaluate their performance with three expansions under four empirically well‐tested models. Our numerical experiments find that the weighted expansion generated by the fat‐tailed weighting kernel can significantly reduce approximation error over the Gram‐Charlier expansion; the Taylor expansion of conditional moments can lead to divergence for parameters with certain high persistence in the affine GARCH, nonlinear asymmetric GARCH, and Glosten‐Jagannathan‐Runkle GARCH models, while surviving during high persistence in the exponential GARCH.

Applications of moments of Dirichlet coefficients in elliptic curve families

The moments of the coefficients of elliptic curve [Formula: see text]-functions are related to numerous important arithmetic problems. Rosen and Silverman proved a conjecture of Nagao relating the first moment of one-parameter families satisfying Tate’s conjecture to the rank of the corresponding elliptic surface over [Formula: see text]; one can also construct families of moderate rank by finding families with large first moments. Michel proved that if [Formula: see text] is not constant, then the second moment of the family is of size [Formula: see text]; these two moments show that for suitably small support the behavior of zeros near the central point agree with that of eigenvalues from random matrix ensembles, with the higher moments impacting the rate of convergence. In his thesis, Miller noticed a negative bias in the second moment of every one-parameter family of elliptic curves over [Formula: see text] whose second moment had a (by him) calculable closed-form expression, specifically the first lower-order term which does not average to zero is on average negative. This Bias Conjecture has now been confirmed for many families; however, these are highly non-generic families as they are specially chosen so that the resulting Legendre sums can be determined. For cohomological reasons, each subsequent term in the second moment expansion is smaller than the previous by a factor on the order of [Formula: see text], and thus numerically, it is hard to see a term of size [Formula: see text] with a small negative average as it can be masked by a term of size [Formula: see text] which averages to zero. Inspired by the recent successes by Yang-Hui He, Kyu-Hwan Lee, Thomas Oliver, Alexey Pozdnyakov and others in investigations of murmurations of elliptic curve coefficients with machine learning techniques, we pose a similar problem for trying to understand the Bias Conjecture. As a start to this program, we numerically investigate the bias conjecture and provide a visual representation of the bias for the second moment. We find a one-parameter family of elliptic curves whose bias is positive for half the primes. However, the numerics do not offer conclusive evidence that negative bias for the other half is enough to overwhelm the positive bias. Without an explicit expansion for the second moment, we are not able to extract potential negative bias of the order [Formula: see text] term.

Theory and practice of second-order expansions for moments of 100ρ% accelerated sequential stopping times in parametric and nonparametric estimation with arbitrary fractional ρ

Sampling strategies with fractional acceleration 0 < ρ < 1 achieve substantial operational savings compared with purely sequential counterparts. But, acceleration customarily yielded second-order (s.o.) lower and upper bounds for requisite characteristics when ρ − 1 was not an integer. First time in the literature, we have recently designed acceleration with asymptotic s.o. expansions in normal mean problems with ρ − 1 arbitrary. In this article, a general unified theory is now developed leading to asymptotic s.o. expansions for customarily studied characteristics with arbitrary ρ − 1 . That is, the previously known s.o. lower/upper bounds can be replaced with appropriate s.o. expansions in a variety of inference problems with prescribed accuracy. We emphasize the theoretical foundation and ensuing analyses with a series of interesting inference problems from (a) a number of non-normal distributions as well as (b) one- and two-sample distribution-free scenarios. These prove a desirable breadth of coverage under our proposed big tent.

Robust network of globally coupled heterogeneous limit cycle oscillators due to inertia

We investigate the phase transition from macroscopic oscillatory state to stable homogeneous steady state in a heterogeneous network of globally coupled Stuart–Landau limit cycle oscillators in the presence of the inertial effect. The phase transition, known as aging transition, onsets above a critical fraction of inactive constituents in the mixed population of active and inactive units. We show that even a feeble increase in the inertial strength increases the critical fraction of inactive units significantly for the onset of the phase transition to the macroscopic steady state thereby resulting in a more robust network, in general. In contrast, a large coupling strength, in the case of a homogeneous network, facilitates the manifestation of the phase transition even for a small fraction of inactive oscillators leading to a more fragile network. Nevertheless, a large coupling strength, in the case of a heterogeneous network, increases the resilience of the network by facilitating the phase transition at a large fraction of inactive oscillators. Furthermore, a larger standard deviation of the natural frequencies always leads to a more fragile network. We derive the macroscopic evolution equations for the order parameters and the stability curve using the first-order moment expansion around the mean-field. In addition, we also deduce the critical fraction of inactive units and the critical inertial strength analytically that matches with the simulation results. Interestingly, we find that the critical inertial strength is reciprocally related to the square of the mean frequency of the network.

The Type II Exponentiated Half Logistic-Gompertz-G Power Series Class of Distributions: Properties and Applications

We propose and study a new generalized class of distributions called the Type II Exponentiated Half Logistic-Gompertz-G Power Series (TIIEHL-Gom-GPS) distribution. Some structural properties including expansion of density,ordinary and conditional moments, generating function, order statistics and entropy are derived. We present some specialcases of the proposed distribution. The maximum likelihood method is used for estimating the model parameters. Theimportance of the new class of distributions are illustrated by means of two applications to real data sets.

Streamwise dispersion of soluble matter in solvent flowing through a tube

For the dispersion of soluble matter in solvent flowing through a tube as investigated originally by G.I. Taylor, a streamwise dispersion theory is developed from a Lagrangian perspective for the whole process with multi-scale effects. By means of a convected coordinate system to decouple convection from diffusion, a diffusion-type governing equation is presented to reflect superposable diffusion processes with a multi-scale time-dependent anisotropic diffusivity tensor. A short-time benchmark, complementing the existing Taylor–Aris solution, is obtained to reveal novel statistical and physical features of mean concentration for an initial phase with isotropic molecular diffusion. For long times, effective streamwise diffusion prevails asymptotically corresponding to the overall enhanced diffusion in Taylor's classical theory. By inverse integral expansions of local concentration moments, a general streamwise dispersion model is devised to match the short- and long-time asymptotic solutions. Analytical solutions are provided for most typical cases of point and area sources in a Poiseuille tube flow, predicting persistent long tails and skewed platforms. The theoretical findings are substantiated through Monte Carlo simulations, from the initial release to the Taylor dispersion regime. Asymmetries of concentration distribution in a circular tube are certified as originated from (a) initial non-uniformity, (b) unidirectional flow convection, and (c) non-penetration boundary effect. Peculiar peaks in the concentration cloud, enhanced streamwise dispersivity and asymmetric collective phenomena of concentration distributions are illustrated heuristically and characterised to depict the non-equilibrium dispersion. The streamwise perspective could advance our understanding of macro-transport processes of both passive solutes and active suspensions.

One- and two-photon absorption spectra of organoboron complexes: vibronic and environmental effects.

We synthesized a series of four parent aza-β-ketoiminate organoboron complexes and performed spectroscopic studies using both experimental and computational techniques. We studied how benzannulation influences the vibronic structure of the UV/Vis absorption bands with a focus on the bright lowest-energy π → π* electronic excitation. Theoretical simulations, accounting for inhomogeneous broadening effects using different embedding schemes, allowed gaining in-depth insights into the observed differences in band shapes induced by structural modifications. We observed huge variations in the distributions of vibronic transitions depending on the position of benzannulation. By and large, the harmonic approximation combined with the adiabatic hessian model delivers qualitatively correct band shapes for the one-photon absorption spectra, except in one case. We also assessed the importance of non-Condon effects (accounted for by the linear term in Herzberg-Teller expansion of the dipole moment) for S0 → S1 band shapes. It turned out that non-Condon contributions have no effect on the band shape in one-photon absorption spectra. In contrast, these effects significantly change the Franck-Condon band shapes of the two-photon absorption spectra. For one of the studied organoboron complexes we also performed a preliminary exploration of mechanical anharmonicity, resulting in an increase of the intensity of the 0-0 transition, which improves the agreement with the experimental data compared to the harmonic model.

Sensitivity Analysis of Electromagnetic Scattering from Dielectric Targets with Polynomial Chaos Expansion and Method of Moments

Sensitivity Analysis of Electromagnetic Scattering from Dielectric Targets with Polynomial Chaos Expansion and Method of Moments