General Class Research Articles

Correlator webs of massive multiparton amplitudes at four loops: A study of boomerang webs

The logarithm of the soft function can be organised into sets of Feynman diagrams known as correlator webs(cwebs). We introduced a new formalism in Agarwal [] that allows one to determine several of the building blocks of cweb mixing matrices without explicit computations. In Agarwal [], we used this formalism to obtain the diagonal blocks of four general classes of cwebs to all orders in perturbation theory which also covered all the four-loop boomerang cwebs connecting four Wilson lines. In this work, we present complete mixing matrices and exponentiated color factors for boomerang cwebs at four loops that connect three and four Wilson lines. Also, we present a more efficient version of the algorithm of generating cwebs that was presented in Agarwal []. This new algorithm has been used to generate the cwebs in the present work. Published by the American Physical Society 2024

How Close to the Mark Might Published Heritability Estimates Be?

The behavioural scientist who requires an estimate of narrow heritability, h2, will conduct a twin study, and input the resulting estimated covariance matrices into a particular mode of estimation, the latter derived under supposition of the standard biometric model (SBM). It is known that the standard biometric model can be expected to misrepresent the phenotypic (genetic) architecture of human traits. The impact of this misrepresentation on the accuracy of h2 estimation is unknown. We aimed to shed some light on this general issue, by undertaking three simulation studies. In each, we investigated the parameter recovery performance of five modes- Falconer’s coefficient and the SEM models, ACDE, ADE, ACE, and AE- when they encountered a constructed, non-SBM, architecture, under a particular informational input. In study 1, the architecture was single-locus with dominance effects and genetic-environment covariance, and the input was a set of population covariance matrices yielded under the four twin designs, monozygotic-reared together, monozygotic-reared apart, dizygotic-reared together, and dizygotic-reared apart; in study 2, the architecture was identical to that of study 1, but the informational input was monozygotic-reared together and dizygotic-reared together; and in study 3, the architecture was multi-locus with dominance effects, genetic-environment covariance, and epistatic interactions. The informational input was the same as in study 1. The results suggest that conclusions regarding the coverage of h2 must be drawn conditional on a) the general class of generating architecture in play; b) specifics of the architecture’s parametric instantiations; c) the informational input into a mode of estimation; and d) the particular mode of estimationemployed. The results showed that the more complicated the generating architecture, the poorer a mode’s h2 recovery performance. Random forest analyses furthermore revealed that, depending on the genetic architecture, h2, the dominance and locus additive parameter, and proportions of alleles were involved in complex interaction effects impacting on h2 parameter recovery performance of a mode of estimation. Data and materials: https://osf.io/aq9sx/

Quasi‐majority functional voting on expander graphs

AbstractConsider an ‐vertex graph where each vertex holds one of two distinct opinions. We are interested in the consensus time of synchronous voting processes, where each vertex is allowed to update its opinion according to a predefined commonly local updating rule. This article proposes a general class of voting processes called quasi‐majority functional voting and gives upper and lower bounds of the consensus time. Our results cover many previous results on specific processes, for example, best‐of‐two (a.k.a. 2Choices) and best‐of‐three (a.k.a. 3Majority), as special cases. Our key ingredient is a nonlinear extension of the expander mixing lemma, which enables us to estimate expected and variance changes in opinions of quasi‐majority functional voting on expander graphs.

Exactly solvable Hamiltonian fragments obtained from a direct sum of Lie algebras.

Exactly solvable Hamiltonians are useful in the study of quantum many-body systems using quantum computers. In the variational quantum eigensolver, a decomposition of the target Hamiltonian into exactly solvable fragments can be used for the evaluation of the energies via repeated quantum measurements. In this work, we apply more general classes of exactly solvable qubit Hamiltonians than previously considered to address the Hamiltonian measurement problem. The most general exactly solvable Hamiltonians we use are defined by the condition that within each simultaneous eigenspace of a set of Pauli symmetries, the Hamiltonian acts effectively as an element of a direct sum of so(N) Lie algebras and can, therefore, be measured using a combination of unitaries in the associated Lie group, Clifford unitaries, and mid-circuit measurements. The application of such Hamiltonians to decomposing molecular electronic Hamiltonians via graph partitioning techniques shows a reduction in the total number of measurements required to estimate the expectation value compared to previously used exactly solvable qubit Hamiltonians.

Supporting Knowledge and Language Acquisition of Secondary Emergent Bilinguals through Social Studies Instruction

AbstractThis study examined the initial efficacy of World Generation (WorldGen), a Tier I social studies instructional approach for emergent bilingual (EB) students and their native English‐speaking (non‐EB) peers in Grades 6 and 7. WorldGen builds on prior research on instructional practices that have been associated with improved content knowledge and literacy outcomes for EBs in classes of students with varying English proficiency. Using a within‐teacher design, middle grades world history teachers' classes were randomly assigned to WorldGen treatment (17) or comparison conditions (16) for three to four approximately two‐week units. The student sample included 42% EBs. Students in the treatment condition (n = 373) scored higher, on average, on world history content (Hedges' g = 0.47) and vocabulary knowledge (Hedges' g = 0.41) than students in the comparison condition (n = 343) but no statistically significant findings were yielded regarding disciplinary literacy skills at the end of WorldGen instruction. Of primary interest, the statistically significant main effects indicated that world history content knowledge and vocabulary learning was similar for both current EB and non‐EB students in the treatment condition. The findings provide initial support for the use of the WorldGen instructional practices for improving content acquisition and vocabulary in general education social studies classes with students with a range of English proficiency. Furthermore, teachers perceived the WorldGen instructional practices and materials as providing the information and learning experiences necessary to support students in meeting grade‐level expectations.

The Knapsack Problem with Conflict Pair Constraints on Bipartite Graphs and Extensions

In this paper, we study the knapsack problem with conflict pair constraints. After a thorough literature survey on the topic, our study focuses on the special case of bipartite conflict graphs. For complete bipartite (multipartite) conflict graphs, the problem is shown to be NP-hard but solvable in pseudo-polynomial time, and it admits an FPTAS. Extensions of these results to more general classes of graphs are also presented. Further, a class of integer programming models for the general knapsack problem with conflict pair constraints is presented, which generalizes and unifies the existing formulations. The strength of the LP relaxations of these formulations is analyzed, and we discuss different ways to tighten them. Experimental comparisons of these models are also presented to assess their relative strengths. This analysis disclosed various strong and weak points of different formulations of the problem and their relationships to different types of problem data. This information can be used in designing special purpose algorithms for KPCC involving a learning component.

Bayesian Lookahead Perturbation Policy for Inference of Regulatory Networks.

The complexity, scale, and uncertainty in regulatory networks (e.g., gene regulatory networks and microbial networks) regularly pose a huge uncertainty in their models. These uncertainties often cannot be entirely reduced using limited and costly data acquired from the normal condition of systems. Meanwhile, regulatory networks often suffer from the non-identifiability issue, which refers to scenarios where the true underlying network model cannot be clearly distinguished from other possible models. Perturbation or excitation is a well-known process in systems biology for acquiring targeted data to reveal the complex underlying mechanisms of regulatory networks and overcome the non-identifiability issue. We consider a general class of Boolean network models for capturing the activation and inactivation of components and their complex interactions. Assuming partial available knowledge about the interactions between components of the networks, this paper formulates the inference process through the maximum aposteriori (MAP) criterion. We develop a Bayesian lookahead policy that systematically perturbs regulatory networks to maximize the performance of MAP inference under the perturbed data. This is achieved by optimally formulating the perturbation process in a reinforcement learning context and deriving a scalable deep reinforcement learning perturbation policy to compute near-optimal Bayesian policy. The proposed method learns the perturbation policy through planning without the need for any real data. The high performance of the proposed approach is demonstrated by comprehensive numerical experiments using the well-known mammalian cell cycle and gut microbial community networks.

Study of ecosystem service functions in typical receiving areas of the South-to-North Water Diversion Central Route based on a set of long time series.

Hebi is located in the northern part of China's Henan Province and is a typical receiving area for China's South-to-North Water Diversion Project. The assessment of habitat quality and water yield over a long time series is important for evaluating the stability of ecosystem services in Hebi and other receiving areas and for maintaining ecological security and promoting sustainable development. This paper aims to evaluate and dynamically analyse habitat quality and water yield in Hebi, and analyses the characteristics of changes in spatial and temporal patterns of land cover types, habitat quality and water yield in Hebi over the past 20 years, using 2000, 2005, 2010, 2015 and 2020 as horizontal years. The results indicate that: (1) During the study period, the overall land use type in Hebi City has been constantly changing, with the most significant conversion from arable land to other land types; combined with its landscape pattern index, Hebi City has a general characteristic of significant landscape fragmentation and complexity in land use. (2) Habitat quality in Hebi shows an overall trend towards better development, with water availability decreasing and then increasing; the zoning of ecosystem services in Hebi is divided into three classes: superior, good and general, with the area covered by the superior and general classes expanding year by year. (3) Correlation analysis by SPSS software shows that the correlation between habitat quality and landscape pattern index is greater than the correlation between habitat quality and climate change. Additionally, the correlation between water availability and climate change is greater than the correlation between water availability and landscape pattern index.

Inhomogeneous long-range percolation in the weak decay regime

AbstractWe study a general class of percolation models in Euclidean space including long-range percolation, scale-free percolation, the weight-dependent random connection model and several other previously investigated models. Our focus is on the weak decay regime, in which inter-cluster long-range connection probabilities fall off polynomially with small exponent, and for which we establish several structural properties. Chief among them are the continuity of the bond percolation function and the transience of infinite clusters.

Evolutionary equations are G-compact

We prove a compactness result related to G-convergence for autonomous evolutionary equations in the sense of Picard. Compared to previous work related to applications, we do not require any boundedness or regularity of the underlying spatial domain; nor do we assume any periodicity or ergodicity assumption on the potentially oscillatory part. In terms of abstract evolutionary equations, we remove any compactness assumptions of the resolvent modulo kernel of the spatial operator. To achieve the results, we introduced a slightly more general class of material laws. As a by-product, we also provide a criterion for G-convergence for time-dependent equations solely in terms of static equations.

Key Factors Influencing Inclusive Placement Decisions of Students With Extensive Support Needs

This qualitative study examined educational professionals’ experiences including students with extensive support needs (ESN) in general education settings. Data were collected from 18 education professionals, including 5 special education teachers, 5 paraeducators, 4 administrators, and 4 general education teachers. The researcher used semi-structured interviews and analyzed them using thematic coding. The findings showed that the significant factors influencing successful inclusion were the belief systems of educational professionals, the number of general education classes available for inclusion, selective data collection by educators, superficial inclusion of students, the critical role of paraeducators, and interpersonal relationships among parents and educators. Recommendations included using multiple data collection methods, documenting student work in inclusive settings, revamping the paraeducator hiring and training process, increasing collaboration between general and special education teachers, expanding the number of classrooms available for ESN students, training general education teachers to teach all students, and challenging deficit thinking in teacher education programs.

Strange higher-spin topological systems in 3D

Motivated by the generation of action principles from off-shell dualisation, we present a general class of free, topological theories in three dimensional Minkowski spacetime that exhibit higher-spin gauge invariance. In the spin-two case, we recover a dual reformulation of the triplet system already known, while the higher-spin systems that we obtain seem to be new. They are associated with wild quivers. We study in which situations these exotic (or strange) higher-spin models can be extended to dS3 and AdS3 backgrounds, revealing that the flat limit of such models, when they exist, admits a one-parameter freedom. Interactions are studied in the simplest higher-spin case featuring spin-2 and spin-3 fields. We then give several higher-spin generalizations of these strange systems.

Extension of Exactly-Solvable Hamiltonians Using Symmetries of Lie Algebras.

Exactly solvable Hamiltonians that can be diagonalized by using relatively simple unitary transformations are of great use in quantum computing. They can be employed for the decomposition of interacting Hamiltonians either in Trotter-Suzuki approximations of the evolution operator for the quantum phase estimation algorithm or in the quantum measurement problem for the variational quantum eigensolver. One of the typical forms of exactly solvable Hamiltonians is a linear combination of operators forming a modestly sized Lie algebra. Very frequently, such linear combinations represent noninteracting Hamiltonians and thus are of limited interest for describing interacting cases. Here, we propose an extension in which the coefficients in these combinations are substituted by polynomials of the Lie algebra symmetries. This substitution results in a more general class of solvable Hamiltonians, and for qubit algebras, it is related to the recently proposed noncontextual Pauli Hamiltonians. In fermionic problems, this substitution leads to Hamiltonians with eigenstates that are single Slater determinants but with different sets of single-particle states for different eigenstates. The new class of solvable Hamiltonians can be measured efficiently using quantum circuits with gates that depend on the result of a midcircuit measurement of the symmetries.

Algebraic classification of 2+1 geometries: a new approach

We present a convenient method of algebraic classification of 2+1 spacetimes into the types I, II, D, III, N and O, without using any field equations. It is based on the 2+1 analogue of the Newman–Penrose curvature scalars ΨA of distinct boost weights, which are specific projections of the Cotton tensor onto a suitable null triad. The algebraic types are then simply determined by the gradual vanishing of such Cotton scalars, starting with those of the highest boost weight. This classification is directly related to the specific multiplicity of the Cotton-aligned null directions and to the corresponding Bel–Debever criteria. Using a bivector (that is 2-form) decomposition, we demonstrate that our method is fully equivalent to the usual Petrov-type classification of 2+1 spacetimes based on the eigenvalue problem and determining the respective canonical Jordan form of the Cotton–York tensor. We also derive a simple synoptic algorithm of algebraic classification based on the key polynomial curvature invariants. To show the practical usefulness of our approach, we perform the classification of several explicit examples, namely the general class of Robinson–Trautman spacetimes with an aligned electromagnetic field and a cosmological constant, and other metrics of various algebraic types.

Universal predictions of Siegel modular invariant theories near the fixed points

We analyze a general class of locally supersymmetric, CP and modular invariant models of lepton masses depending on two complex moduli taking values in the vicinity of a fixed point, where the theory enjoys a residual symmetry under a finite group. Like in models that depend on a single modulus, we find that all physical quantities exhibit a universal scaling with the distance from the fixed point. There is no dependence on the level of the construction, the weights of matter multiplets and their representations, with the only restriction that electroweak lepton doublets transform as irreducible triplets of the finite modular group. Also the form of the kinetic terms, which here are assumed to be neither minimal nor flavor blind, is irrelevant to the outcome. The result is remarkably simple and the whole class of examined theories gives rise to five independent patterns of neutrino mass matrices. Only in one of them, the predicted scaling agrees with the observed neutrino mass ratios and lepton mixing angles, exactly as in single modulus theories living close to τ = i.

Extrapolation of Compactness on Banach Function Spaces

We prove an extrapolation of compactness theorem for operators on Banach function spaces satisfying certain convexity and concavity conditions. In particular, we show that the boundedness of an operator T in the weighted Lebesgue scale and the compactness of T in the unweighted Lebesgue scale yields compactness of T on a very general class of Banach function spaces. As our main new tool, we prove various characterizations of the boundedness of the Hardy-Littlewood maximal operator on such spaces and their associate spaces, using a novel sparse self-improvement technique. We apply our main results to prove compactness of the commutators of singular integral operators and pointwise multiplication by functions of vanishing mean oscillation on, for example, weighted variable Lebesgue spaces.

Visualizing Genomic Medicine

The emerging field of genomic medicine offers an opportunity for biology and anatomy teachers to bring the topics of DNA, genetics, molecular processes, and evolution together into one experience. Through the genomic medicine paradigm, students see the unbroken connection between small biological topics such as mutations and their potential connection to disease phenotypes. In this paper, we present as a main example cystic fibrosis, which is an often-studied genetic disease in general biology class, for examination through the genomic medicine lens. Concepts such as genes, the plasma membrane, variation, mutations, the nucleus, and chromosomes can be used in a narrative and visual approach to genetics through the genomic medicine standpoint to engage and connect students with next-generation genomics and with the fundamental unit of life—the cell. It is through the genomic medicine lens that the cell’s context and relationship to the evolving world takes place.

Adaptive directional estimator of the density in [formula omitted] for independent and mixing sequences

A new multivariate density estimator for stationary sequences is obtained by Fourier inversion of the thresholded empirical characteristic function. This estimator does not depend on the choice of parameters related to the smoothness of the density; it is directly adaptive. We establish oracle inequalities valid for independent, α-mixing and τ-mixing sequences, which allows us to derive optimal convergence rates, up to a logarithmic loss. On general anisotropic Sobolev classes, the estimator adapts to the regularity of the unknown density but also achieves directional adaptivity. More precisely, the estimator is able to reach the convergence rate induced by the best Sobolev regularity of the density of AX, where A belongs to a class of invertible matrices describing all the possible directions. The estimator is easy to implement and numerically efficient. It depends on the calibration of a parameter for which we propose an innovative numerical selection procedure, using the Euler characteristic of the thresholded areas.

Numerics with coordinate transforms for efficient Brownian dynamics simulations

Many stochastic processes in the physical and biological sciences can be modelled as Brownian dynamics with multiplicative noise. However, numerical integrators for these processes can lose accuracy or even fail to converge when the diffusion term is configuration-dependent. One remedy is to construct a transform to a constant-diffusion process and sample the transformed process instead. In this work, we explain how coordinate-based and time-rescaling-based transforms can be used either individually or in combination to map a general class of variable-diffusion Brownian motion processes into constant-diffusion ones. The transforms are invertible, thus allowing recovery of the original dynamics. We motivate our methodology using examples in one dimension before then considering multivariate diffusion processes. We illustrate the benefits of the transforms through numerical simulations, demonstrating how the right combination of integrator and transform can improve computational efficiency and the order of convergence to the invariant distribution. Notably, the transforms that we derive are applicable to a class of multibody, anisotropic Stokes-Einstein diffusion that has applications in biophysical modelling.

Parameter inference for degenerate diffusion processes

We study parametric inference for ergodic diffusion processes with a degenerate diffusion matrix. Existing research focuses on a particular class of hypo-elliptic Stochastic Differential Equations (SDEs), with components split into ‘rough’/‘smooth’ and noise from rough components propagating directly onto smooth ones, but some critical model classes arising in applications have yet to be explored. We aim to cover this gap, thus analyse the highly degenerate class of SDEs, where components split into further sub-groups. Such models include e.g. the notable case of generalised Langevin equations. We propose a tailored time-discretisation scheme and provide asymptotic results supporting our scheme in the context of high-frequency, full observations. The proposed discretisation scheme is applicable in much more general data regimes and is shown to overcome biases via simulation studies also in the practical case when only a smooth component is observed. Joint consideration of our study for highly degenerate SDEs and existing research provides a general ‘recipe’ for the development of time-discretisation schemes to be used within statistical methods for general classes of hypo-elliptic SDEs.