Order Interaction Terms Research Articles

On democratic string field theories

We reexamine democratic open string field theories, namely, theories in which string fields are not constrained to a single picture number and picture changing is obtained as a gauge transformation. We describe several possibilities for regular free theories and attempt to construct the lowest order interaction term and identify the lowest order gauge transformation for some of these theories. We also discuss projections over string field spaces that might be needed for a consistent off-shell implementation of picture changing.

Loop contributions to the scalar power spectrum due to quartic order action in ultra slow roll inflation

The investigation of the theory of inflation beyond the linearorder in perturbations is important both for theoretical consistency andpotential observables.In the contemporary literature, the calculation of modifications to theinflationary scalar power spectrum due to the loops from the higher orderinteraction terms in the Hamiltonian have led to an interesting discussionregarding the validity of perturbation theory and the robustness of itspredictions.Recently, there have been many efforts to examine the contributions to thescalar power spectrum due to the loops arising from the cubic order termsin the action describing the perturbations, specifically in inflationaryscenarios that permit an epoch of ultra slow roll (USR).A brief phase of USR during inflation is known to lead to interesting featuresin the scalar power spectrum which in turn has significant observationalconsequences, such as the copious production of primordial black holes.In this work, we consider the loop contributions to the scalar power spectrumin a scenario of USR inflation arising due to the quartic order termsin the action describing the scalar perturbations.We compute the loop contributions to the scalar power spectrum due to thedominant term in the action at the quartic order in a scenario wherein ashort phase of USR is sandwiched between two stages of slow roll (SR) inflation.We analyze the behaviour of the loop contributions in terms of the parametersthat characterize the non-trivial inflationary dynamics, viz. the onset andduration of USR, and the smoothness of transitions between the USR and SR phases.We examine three different cases of the scenario — the late, intermediate andearly epochs of USR during inflation, each of which affects the scalar powerspectrum over different ranges of wave numbers.In the inflationary scenario involving a late phase of USR, for reasonable choicesof the parameters, we show that the loop corrections are negligible for the entirerange of wave numbers.In the intermediate case, the contributions from the loops prove to be scaleinvariant over large scales and, we find that these contributions can amountto 30% of the leading order (i.e. the Gaussian) power spectrum.In the case wherein USR sets in early, we find that the loop contributions couldbe negative and can dominate the power spectrum at the leading order, whichindicates a breakdown of the validity of the perturbative expansion.We discuss the origin of the negative sign and the divergences that arise in theloop contributions to the power spectrum.We conclude with a brief summary and outlook.

Spatial dynamics of higher order rock-paper-scissors and generalisations

We introduce and study the spatial replicator equation with higher order interactions and both infinite (spatially homogeneous) populations and finite (spatially inhomogeneous) populations. We show that in the special case of three strategies (rock–paper–scissors) higher order interaction terms allow travelling waves to emerge in non-declining finite populations. We show that these travelling waves arise from diffusion stabilisation of an unstable interior equilibrium point that is present in the aspatial dynamics. Based on these observations and prior results, we offer two conjectures whose proofs would fully generalise our results to all odd cyclic games, both with and without higher order interactions, assuming a spatial replicator dynamic. Intriguingly, these generalisations for N⩾5 strategies seem to require declining populations, as we show in our discussion.

Universal signature of quantum entanglement across cosmological distances

Although the paradigm of inflation has been extensively studied to demonstrate how macroscopic inhomogeneities in our Universe originate from quantum fluctuations, most of the established literature ignores the crucial role that entanglement between the modes of the fluctuating field plays in its observable predictions. In this paper, we import techniques from quantum information theory to reveal hitherto undiscovered predictions for inflation which, in turn, signals how quantum entanglement across cosmological scales can affect large scale structure. Our key insight is that observable long-wavelength modes must be part of an open quantum system, so that the quantum fluctuations can decohere in the presence of an environment of short-wavelength modes. By assuming the simplest model of single-field inflation, and considering the leading order interaction term from the gravitational action, we derive a universal lower bound on the observable effect of such inescapable entanglement. Although this signal is too weak for direct detection in the foreseeable future, we discuss the importance of its theoretical implications.

Solvable model for a charge- 4e superconductor

A charge-$4e$ superconductor forms due to the condensation of quartets of electrons. While in previous works the mechanism for the formation of charge-$4e$ superconductivity has been analyzed in terms of the binding of Cooper pairs in unconventional superconductors, its properties in the fermionic sector have not been studied systematically due to its inherently interacting nature even at the mean-field level. Here we propose a solvable model for a charge-$4e$ superconductor -- a spinful version of the Sachdev-Ye-Kitaev model with an anomalous quartic term. We show that the ground state is gapless and resembles a heavy Fermi liquid. We analytically solve for the superfluid density and show that it is perturbative in the strength of the charge-$4e$ order parameter, in sharp contrast with a regular (charge-$2e$) superconductor. Upon lowering temperature, we show that the correlation between charge-$4e$ order and regular interaction terms can drive a first-order phase transition to a charge-$2e$ superconducting state.

The Mechanical Properties of Gangue Paste Material for Deep Mines: An Experimental and Model Study.

Gangue paste material is mainly composed of coal gangue with particle size, which is mixed with cement. Fly ash and additives can be added to change its performance. In this paper, the influence of each component on the mechanical properties of gangue paste material was studied by an orthogonal experiment. The conversion relationship among various indexes of mechanical properties of gangue paste material and the response surface prediction model were discussed. The results show that the mechanical properties of gangue paste materials are positively correlated with the content of cement, the content of fly ash and the mass concentration, which increase with the increase of the three factors, and show the primary and secondary relationship of the content of cement > the content of fly ash > the mass concentration. A response surface prediction model of mechanical property parameters is established, which includes the first order term of the influencing factors of gangue paste material and the first order interaction term between any two factors. In the response surface prediction model of uniaxial compressive strength, splitting tensile strength, cohesion and elastic modulus, the goodness of fit test coefficients are 0.998, 0.957, 0.970 and 0.997, respectively, which proves that the model has good goodness of fit. The research results provide basic parameters for paste filling mining practice, and also provide the basis for numerical simulation of filling body value.

Calibration of cloud and aerosol related parameters for solar irradiance forecasts in WRF-solar

Model parameters are one of the sources of uncertainties in numerical weather prediction. Recently, the Weather Research and Forecasting model with Solar extensions (WRF-Solar) has been upgraded by enhancing the treatment of sub-grid scale cloud and aerosols with augmentations of a sub-grid scale cloud scheme (CLD3) and an upgraded aerosol-aware Thompson-Eidhammer scheme (TE14). However, the value of model parameters associated with these parameterizations are assigned based on limited measurements or theoretical calculations. Calibrating the sensitive parameters has the potential to improve solar irradiance predictions. In this work, we adopted a multi-objective surrogate-based optimization (SBO) framework to calibrate nine parameters used in CLD3 and TE14 that lead to the largest sensitivity in simulated irradiance. The normalized mean-absolute-error (NMAE) of global horizontal irradiance (GHI) and direct normal irradiance (DNI) are minimized by calibrating WRF-Solar over two regions including the Southern Great Plains (SGP) and Central California. We selected two cloudy cases, one over less-polluted SGP and another over Central California with high aerosol loading associated with wildfire events. The results show that generalized linear model (GLM)-based surrogate models approximate physical models well, particularly when the third order and three-way interaction terms are considered. The SBO framework efficiently searches the parameter space for optimal solutions with less computational costs than directly calibrating the physical model. We first calibrate CLD3 parameters over the less-polluted SGP region. Optimized CLD3 parameters alone result in NMAE reduction by 14% for the site-mean and up to 33% for individual cases over the SGP region. With further calibration of TE14 parameters over the Central California during active fire periods, the optimized parameters lead to over 20% reductions of NMAE.

Multigroup SIS Epidemics With Simplicial and Higher Order Interactions

This article analyzes a susceptible–infected–susceptible (SIS) model of epidemic propagation over hypergraphs, and motivated by an important special case, we refer to the model as the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">simplicial SIS model</i> . Classically, the multigroup SIS model has assumed pairwise interactions of contagion across groups and, thus, has been vastly studied in the literature. It is only recently that renewed special attention has been drawn to the study of contagion dynamics over higher order interactions and over more general graph structures, such as simplexes. Previous work on mean-field approximation scalar models of the simplicial SIS model has indicated that a new dynamical behavior domain, compared to the classical SIS model, appears due to the newly introduced higher order interaction terms: both a disease-free equilibrium and an endemic equilibrium coexist and are both locally asymptotically stable. This article formally establishes that bistability (as a new epidemiological behavior) also appears in the multigroup simplicial SIS model. We give sufficient conditions over the model’s parameters for the appearance of this and the other behavioral domains present in the classical multigroup SIS model. We additionally provide an algorithm to compute the value of the endemic equilibrium and report numerical analysis of the transition from the disease-free domain to the bistable domain.

Principal component regression in GAMLSS applied to Greek–German government bond yield spreads

A solution to the problem of having to deal with a large number of interrelated explanatory variables within a generalized additive model for location, scale and shape (GAMLSS) is given here using as an example the Greek–German government bond yield spreads from 25 April 2005 to 31 March 2010. Those were turbulent financial years, and in order to capture the spreads behaviour, a model has to be able to deal with the complex nature of the financial indicators used to predict the spreads. Fitting a model, using principal components regression of both main and first order interaction terms, for all the parameters of the assumed distribution of the response variable seems to produce promising results.

A Quantum State Scenario for Biological Self-Replication

With the prevalent conception of self-replication (SR, a hallmark of living systems) as a non-equilibrium process subject to thermodynamic laws, a complementary approach derives the low energy quantum states arising from a Hamiltonian that appears to be specific for bio-systems by its containing some strongly binding terms. The bindings attract properties of the template (T) and the reactants to form a replicate (R). The criterion for SR that emerges from the theory is that second order (bi-linear) interaction terms between degrees of motion of T-R and the thermal bath dominate negatively over a linear self-energy term, and thereby provide a binding between the attributes of T and R. The formalism (reminiscent of the Kramers-Anderson mechanism for superexchange) is from first principles, but hinges on a drastic simplification by modelling the T, R and bath variables on interacting qubits and by congesting the attraction into a single (control) parameter. The development relies on further simplifying features, such as Random Phase Approximations and an Effective Hamiltonian formalism. The entropic balance to replication is considered and found to reside in the far surroundings.

An Effective Theory of Quarkonia in QCD Matter

The problem of quarkonium production in heavy ion collisions presents a set of unique theoretical challenges – from the relevant production mechanism of J/ψs and ϒs to the relative significance of distinct cold and hot nuclear matter effects in the observed attenuation of quarkonia. In these proceedings we summarize recent work on the generalization of non-relativistic Quantum Chromodynamics (NRQCD) to include Glauber gluon interactions in strongly interacting matter. This new effective theory provides for the first time a universal microscopic description of the in-medium interaction of heavy quarkonia, consistently applicable to a range of phases such as cold nuclear matter, dense hadron gas, and quark-gluon plasma. It is an important step forward in understanding the common trends in proton-nucleus and nucleus-nucleus data on quarkonium suppression. We derive explicitly the lowest order (LO) and next-to-leading order (NLO) interaction terms in the Lagrangian and show the connection of the LO result to existing phenomenology.

Soil-Based Vegetation Productivity Model for Coryell County, Texas

Managers, scientists, planners and designers of landscapes are interested in systematic investigations, to predict the reconstruction of disturbed soil resources for optimum vegetation productivity. In this study, a predictive equation for estimating neo-soil plant growth in Coryell County, Texas was developed. The equation predicts the vegetation growth for wheat (Triticum aestivum L.), oats [Avena sativa L. (1753)], sorghum [Sorghum bicolor (L.) Moench], cotton lint (Gossypium hirsutum L.), Bermuda grass [Cynodon dactylon (L.) Pers.], and rangeland production in general. The results suggest that an all-vegetation predictive model was highly significant (p ≤ 0.0001), explaining over 80% of the variance. The equation employed hydraulic conductivity as a main-effect variable; bulk density and hydraulic conductivity as squared terms; and percent clay times bulk density, bulk density times soil reaction, hydraulic conductivity times available water holding capacity, and hydraulic conductivity times soil reactions as first order interaction terms, with each predicting variable containing a p-value equal to or less than 0.05. The results suggest that an annual crop equation and a plant-specific cotton lint equation also have merit.

Multi- π+ systems in a finite volume

We present a formalism to describe two-$\pi^+$ and three-$\pi^+$ dynamics in finite volume, the formalism is based on combination of a variational approach and the Faddeev method. Both pair-wise and three-body interactions are included in the presentation. Impacts of finite lattice spacing and the cubic lattice symmetry are also discussed. To illustrate application of the formalism, the pair-wise contact interaction that resembles the leading order interaction terms in chiral effective theory is used to analyze recent lattice results.

An experimental and modeling study aiming to enhance the performance of OSR of a methane fuel processor via Box-Behnken design

OSR is the energy efficient hydrogen production route used in small scale fuel processors. The performance of the methane OSR catalyst is crucial for the overall performance of FPs. Current work proves the activity and hydrogen selectivity of OSR catalyst can exceed thermodynamic limits if the contact time is defined properly. It furtherly shows the intricate nature of OSR, comprising synchronous series and parallel reactions, can be modeled parsimoniously unveiling the effect of parameters. Results of total 27 experiments according to a Box-Behnken (BB) design revealed higher CH4 conversion values were experimentally obtained for higher temperature, higher S/C feed ratio and lower C/O2 feed ratio with certain exception(s) for S/C feed ratio; however, mostly lower CH4 conversion values were observed for higher catalyst weight, i.e. higher contact time. Contrary to the conventional practice of including up to quadratic terms in the BB models, statistical analysis shows the necessity of including 3rd order two-way interaction terms in the models. The most statically significant 3rd order interaction terms were those between W and S/C, which are required to explain the unexpected partial effects of W and S/C on response variables.

Increased long-term mortality in women with high left ventricular ejection fraction: data from the CONFIRM (COronary CT Angiography EvaluatioN For Clinical Outcomes: An InteRnational Multicenter) long-term registry.

There are significant sex-specific differences in left ventricular ejection fraction (LVEF), with a higher LVEF being observed in women. We sought to assess the clinical relevance of an increased LVEF in women and men. A total of 4632 patients from the CONFIRM (COronary CT Angiography EvaluatioN For Clinical Outcomes: An InteRnational Multicenter) registry (44.8% women; mean age 58.7 ± 13.2 years in men and 59.5 ± 13.3 years in women, P = 0.05), in whom LVEF was measured by cardiac computed tomography, were categorized according to LVEF (low <55%, normal 55-65%, and high >65%). The prevalence of high LVEF was similar in both sexes (33.5% in women and 32.5% in men, P = 0.46). After 6 years of follow-up, no difference in mortality was observed in patients with high LVEF in the overall cohort (P = 0.41). When data were stratified by sex, women with high LVEF died more often from any cause as compared to women with normal LVEF (8.6% vs. 7.1%, log rank P = 0.032), while an opposite trend was observed in men (5.8% vs. 6.8% in normal LVEF, log rank P = 0.89). Accordingly, a first order interaction term of male sex and high LVEF was significant (hazard ratios 0.63, 95% confidence intervals 0.41-0.98, P = 0.043) in a Cox regression model of all-cause mortality adjusted for age, cardiovascular risk factors, and severity of coronary artery disease (CAD). Increased LVEF is highly prevalent in patients referred for evaluation of CAD and is associated with an increased risk of death in women, but not in men. Differentiating between normal and hyperdynamic left ventricles might improve risk stratification in women with CAD. https://clinicaltrials.gov/ct2/show/NCT01443637.

Tests on a Subset of Regression Parameters for Factorial Experimental Data with Uncertain Higher Order Interactions

The data generated by many factorial experiments are analyzed by linear regression models. Often the higher order interaction terms of such models are negligible (e.g., R. Mead, The Design of Experiments, Cambridge University Press, Cambridge, 1988, p. 368) although there is uncertainty around it. This kind of nonsample prior information (NSPI) can be presented by null hypotheses (cf. T.A. Bancroft, Ann. Math. Stat. 15 (1944), 190–204), and its uncertainty removed through appropriate statistical test. Depending on the level of the NSPI the unrestricted, restricted, and pretest (PTT) tests are defined. The sampling distributions of test statistics and power functions of the three tests are derived. The graphical and analytical comparisons of powers reveal that the PTT dominates over the other tests.

Estimation of multidrug resistance variability in the National Antimicrobial Monitoring System

Multidrug resistance is a serious problem raising the specter of infections for which there is no treatment. One of the most important tools in combating multidrug resistance is large scale monitoring programs, because they track resistance over large geographic areas and time scales. This large scope, however, can also introduce variability into the data. The primary monitoring program in the United States is the National Antimicrobial Resistance Monitoring System (NARMS). This study examines the variability of a previously identified resistance pattern in Escherichia coli among ampicillin, gentamicin, sulfisoxazole, and tetracycline using samples isolated from chicken during the years 2004 to 2006 and 2008 to 2012. 2007 is excluded because sulfisozaxole resistance was not measured at slaughter that year. To assess variability in this resistance pattern susceptibility/resistance contingency tables were constructed for each of the 15 combinations of the 4 drugs for each of the years. For each table, variability across the years was assessed at the full table multinomial level as a measure of general variability of the resistance pattern and at the level of the highest order interaction term in a log-linear model of the table as a measure of variability in that particular component of the resistance pattern. A power analysis using the traditional asymptotic normal approximation and one using a Dirichlet-multinomial simulation were carried out to determine the effect of variation on ability to detect nonzero highest order loglinear model terms and the validity of the normal approximation in carrying out such tests. All tables exhibit overdispersion at the multinomial level and in their highest order model parameters. The normal approximation performs well for large sample sizes, low levels of dispersion, and small log-linear model parameters. The approximation breaks down as dispersion or the log linear model parameter grows or sample size shrinks. Taken together these analyses indicate that the level of variability in the NARMS dataset makes it difficult to detect multidrug resistance patterns at the current level of sample collection. In order to better control this dispersion NARMS could collect more variables on each of the samples.

Bayesian variable selection with strong heredity constraints

In this paper, we propose a Bayesian variable selection method for linear regression models with high-order interactions. Our method automatically enforces the heredity constraint, that is, a higher order interaction term can exist in the model only if both of its parent terms are in the model. Based on the stochastic search variable selection George and McCulloch (1993), we propose a novel hierarchical prior that fully considers the heredity constraint and controls the degree of sparsity simultaneously. We develop a Markov chain Monte Carlo (MCMC) algorithm to explore the model space efficiently while accounting for the heredity constraint by modifying the shotgun stochastic search algorithm Hans et al. (2007). The performance of the new model is demonstrated through comparisons with other methods. Numerical studies on both real data analysis and simulations show that our new method tends to find relevant variable more effectively when higher order interaction terms are considered.

Fast Hyperspectral Unmixing in Presence of Nonlinearity or Mismodeling Effects

This paper presents two novel hyperspectral mixture models and associated unmixing algorithms. The two models assume a linear mixing model corrupted by an additive term whose expression can be adapted to account for multiple scattering nonlinearities (NL), or mismodeling effects (ME). The NL model generalizes bilinear models by taking into account higher order interaction terms. The ME model accounts for different effects, such as endmember variability or the presence of outliers. The abundance and residual parameters of these models are estimated by considering a convex formulation suitable for fast estimation algorithms. This formulation accounts for constraints, such as the sum-to-one and nonnegativity of the abundances, the nonnegativity of the nonlinearity coefficients, the spectral smoothness of the ME terms and the spatial sparseness of the residuals. The resulting convex problem is solved using the alternating direction method of multipliers whose convergence is ensured theoretically. The proposed mixture models and their unmixing algorithms are validated on both synthetic and real images showing competitive results regarding the quality of the inference and the computational complexity when compared to the state-of-the-art algorithms.

High-temperature noncollinear magnetism in a classical bilinear-biquadratic Heisenberg model

Motivated by the magnetically-driven high-temperature ferroelectric behavior of CuO and the subsequent theoretical efforts to understand this intriguing phenomenon, we study a spin model on a two-dimensional square lattice which possesses some of the key features of the models proposed for CuO. The model consists of Heisenberg couplings between nearest and next-nearest neighbor spins, and biquadratic couplings between nearest neighbors. We use a combination of variational calculations and classical Monte Carlo simulations to study this model at zero and finite temperatures. We show that even an arbitrarily weak biquadratic coupling plays a crucial role in selecting the magnetic ground state. More importantly, a non-collinear magnetic state, characterized by a finite spin current, is stable at finite temperatures. The interesting aspect is that the present model neither includes an inversion-symmetry-breaking term nor the effects of lattice distortions in the Hamiltonian. We conclude that non-collinear magnetism at high temperatures, as observed in CuO, can be explained via pure spin Hamiltonians. We find that the spiral phase is inhomogeneous, and is stabilized by entropic effects. Our study demonstrates that higher order interaction terms are of crucial importance if the stronger interactions together with the lattice geometry contemplate to generate a near degeneracy of magnetic states. The conclusions presented in this work are of particular relevance to the non-collinear magnetism and ferroelectricity observed at high temperatures in cupric oxide.