Diagrammatic Method Research Articles

Testing for normality: a user's (cautionary) guide.

The normality assumption postulates that empirical data derives from a normal (Gaussian) population. It is a pillar of inferential statistics that enables the theorization of probability functions and the computation of p-values thereof. The breach of this assumption may not impose a formal mathematical constraint on the computation of inferential outputs (e.g., p-values) but may make them inoperable and possibly lead to unethical waste of laboratory animals. Various methods, including statistical tests and qualitative visual examination, can reveal incompatibility with normality and the choice of a procedure should not be trivialized. The following minireview will provide a brief overview of diagrammatical methods and statistical tests commonly employed to evaluate congruence with normality. Special attention will be given to the potential pitfalls associated with their application. Normality is an unachievable ideal that practically never accurately describes natural variables, and detrimental consequences of non-normality may be safeguarded by using large samples. Therefore, the very concept of preliminary normality testing is also, arguably provocatively, questioned.

Green/WeakCoupling: Implementation of fully self-consistent finite-temperature many-body perturbation theory for molecules and solids

The accurate ab-initio simulation of molecules and periodic solids with diagrammatic perturbation theory is an important task in quantum chemistry, condensed matter physics, and materials science. In this article, we present the WeakCoupling module of the open-source software package Green, which implements fully self-consistent diagrammatic weak coupling simulations, capable of dealing with real materials in the finite-temperature formalism. The code is licensed under the permissive MIT license. We provide self-consistent GW (scGW) and self-consistent second-order Green's function perturbation theory (GF2) solvers, analysis tools, and post-processing methods. This paper summarises the theoretical methods implemented and provides background, tutorials and practical instructions for running simulations. Program summaryProgram Title:Green/WeakCouplingCPC Library link to program files:https://doi.org/10.17632/2ysyhzww6t.1Developer's repository link:https://github.com/Green-Phys/green-mbptProgramming language:C++17, CUDA, PythonLicensing provisions: MIT LicenseExternal routines/libraries:MPI >= 3.0, BLAS, Eigen >= 3.4.0, cmake >= 3.18, cuBLAS.Nature of problem: The simulation of periodic solids and molecules using diagrammatic perturbation theorySolution method: We present an open-source implementation of the fully self-consistent finite-temperature many-body perturbation theory formalism at the GW and second-order perturbation theory level.

The typology of school mapping synergies: a diagrammatic morphological evaluation of middle schools in Iran

PurposeThis study introduces diagrammatic morphology as a novel method for analysing the synergistic interactions within school mapping. It seeks to reshape the evaluation of school mapping typologies, focusing on the interconnectedness of learning activities, social interactions, and spatial configurations. Aims: (1) To develop the morphological evaluation procedures for school mapping. (2) To evaluate the Iranian Middle Schools' Interior Architecture (IMSIA) using the diagrammatic morphological method.Design/methodology/approachThis qualitative study has been conducted in two steps: A review of the morphological method for school mapping evaluation. A case study analysis of fifty-five IMSIA samples.FindingsThe spatial typology of IMSIA were categorized into four distinct models. These models included ten distinct pattern categories within twenty-one different types. The case study evaluation identified three levels of synergistic complexity within the school mapping: primary, intermediate, and advanced. The advanced level displayed the strongest connection to pedagogies among the analysed models.Originality/valueThis research innovatively evaluates the synergistic context of schools based on the assemblage theory through an occupational analysis of the Iranian middle schools' interior architecture mapping diagrammatic morphological method.

Wave turbulence and the kinetic equationbeyond leading order.

We derive a scheme by which to solve the Liouville equationperturbatively in the nonlinearity, which we apply to weakly nonlinear classical field theories. Our solution is a variant of the Prigogine diagrammatic method and is based on an analogy between the Liouville equationin infinite volume and scattering in quantum mechanics, described by the Lippmann-Schwinger equation. The motivation for our work is wave turbulence: A broad class of nonlinear classical field theories are believed to have a stationary turbulent state-a far-from-equilibrium state, even at weak coupling. Our method provides an efficient way to derive properties of the weak wave turbulent state. A central object in these studies, which is a reduction of the Liouville equation, is the kinetic equation, which governs the occupation numbers of the modes. All properties of wave turbulence to date are based on the kinetic equationfound at leading order in the weak nonlinearity. We explicitly obtain the kinetic equationto next-to-leading order.

Spatialities between property and the commons: an interval of tolerance

This paper examines the relations of ‘space’ with ‘property’ and ‘commons’. Property is an exclusionary mechanism that regulates human relationships through space based on ownership, boundary, and control. Contrarily, the commons is a spatial practice of encounter, collaboration, and sharing, open to all kinds of participation of the multitude. With a research methodology grounded in the principle of ‘tolerance’, this study questions the spatialities between property and the commons, with or without coexistence and communication. To achieve this, a diagrammatical method for ‘a theoretical reading over an interval’ is generated, which enables a debate on the property and the commons over a conceptual graph of connections of ‘spatial tendencies’, ‘theoretical structures’, and ‘spatial activism’. The ‘interval of tolerance’ graph reveals the connections as a tolerance environment for encountering differences and ensuring spatial relations. Thus, the expansion of networks of connections means the expansion of tolerance. The study concludes that the interval of tolerance narrows towards property but broadens towards the commons, which means spatial toleration is high in the commons, but low in property.

The development of computational methods for Feynman diagrams

Over the last 70 years, Feynman diagrams have played an essential role in the development of many theoretical predictions derived from the standard model Lagrangian. In fact, today they have become an essential and seemingly irreplaceable tool in quantum field theory calculations. In this article, we propose to explore the development of computational methods for Feynman diagrams with a special focus on their automation, drawing insights from both theoretical physics and the history of science. From the latter perspective, the article particularly investigates the emergence of computer algebraic programs, such as the pioneering SCHOONSCHIP, REDUCE, and ASHMEDAI, designed to handle the intricate calculations associated with Feynman diagrams. This sheds light on the many challenges faced by physicists when working at higher orders in perturbation theory and reveal, as exemplified by the test of the validity of quantum electrodynamics at the turn of the 1960s and 1970s, the indispensable necessity of computer-assisted procedures. In the second part of the article, a comprehensive overview of the current state of the algorithmic evaluation of Feynman diagrams is presented from a theoretical point of view. It emphasizes the key algorithmic concepts employed in modern perturbative quantum field theory computations and discusses the achievements, ongoing challenges, and potential limitations encountered in the application of the Feynman diagrammatic method. Accordingly, we attribute the enduring significance of Feynman diagrams in contemporary physics to two main factors: the highly algorithmic framework developed by physicists to tackle these diagrams and the successful advancement of algebraic programs used to process the involved calculations associated with them.

Full one-loop radiative corrections to e+e−→H+H− in the inert doublet model

We compute the full one-loop radiative corrections for charged scalar pair production e+e−→H+H− in the inert doublet model. The on-shell renormalization scheme has been used. We take into account both the weak contributions as well as the soft and hard QED corrections. We compute both the real emission and the one-loop virtual corrections using the Feynman diagrammatic method. The resummed cross section is introduced to cure the Coulomb singularity which occurs in the QED corrections. We have analyzed the parameter space of the inert doublet model in three scenarios after taking into account theoretical constraints, the collider experimental bounds, and dark matter search bounds as well. It is found that the weak interaction dominates the radiative corrections, and its size is determined by the triple Higgs coupling λh0H+H−, which is further connected to the mass of the charged scalar. In the scenario where all the constraints are taken into account, we find that for s=250 GeV and s=500 GeV, the weak corrections are around −6%∼−5% and −10%∼−3%, respectively. While for s=1000 GeV, the weak corrections can reach −15%∼+25%. The new feature is that the weak corrections can be positive near the threshold when the charged scalar is heavier than 470 GeV. Six benchmark points for future collider searches have been proposed. Published by the American Physical Society 2024

РАСЧЕТ ПАРАМЕТРА ЖИВУЧЕСТИ ЖЕЛЕЗОБЕТОННЫХ РАМ СО СЛОЖНОНАПРЯЖЕННЫМИ ЭЛЕМЕНТАМИ

On the energy basis, using the diagrammatic method, the solution of the problem of determining the survivability parameter of the reinforced concrete frame structure of a multistory building with complex-stressed elements under static-dynamic deformation caused by a special impact is obtained. Determination of the parametric load value, at which in the most stressed spatial section at the considered loading mode one of the criteria of the special limit state comes from the system of canonical equations of the extraordinary version of the mixed method. Comparison of the experimental and design survivability parameters gives an assessment of the efficiency and reliability of the proposed design dependencies. It has been shown that with the adopted initial hypotheses, the proposed method for calculating the survivability of frames with complex stressed elements satisfactorily describes the process of their deformation and destruction under the considered impacts.

Illustration Design Strategies of Idioms Series Supporting Primary School Language Textbooks in the Context of Artificial Intelligence--Taking “Picture Idioms” as an Example

Abstract Idioms have various compositions and are part of the long history and culture of the Chinese nation, with their unique ways of expression. In this paper, taking “Pictures of Idioms” as an example, we propose a strategy for designing illustrations for a related series of books on idioms using artificial intelligence technology. Using the LSTM model, the description of the given idiom text is realized to generate images. The generated images are processed by a decoder and fed into a neural network model to generate illustrations that match the description of the idiom text. Further, a diffusion model is proposed to improve the quality of illustration generation and diversify the illustrations by continuously adding conditions to the generation process. Taking “Picture Talking Idioms” as an example, we propose a design strategy for the illustrations of the Idioms series accompanying elementary school language textbooks and quantify the effect of practical application in terms of the design effect of the final product, the reading satisfaction, and the effect of the use of “Picture Talking Idioms.” Students were more satisfied with the use of blue-gray and blue colors in the illustrations in “Diagrams to Tell Idioms,” with ratings of 4.9 and 4.6, respectively. 52% of the students used the diagrammatic method of reading “Diagrams to Tell Idioms” and rated the knowledge content of the books in terms of idioms at 9.458, which is a high satisfaction rate of 98%. The use of diagramming idioms has been very effective in assisting with language text.

Diagrammatic multiplet sum method (MSM) density functional theory (DFT): Investigation of the transferability of integrals in "simple" DFT-based approaches to multideterminantal problems.

Kohn-Sham density functional theory (DFT) typically works well for describing dynamic correlation. Two other types of correlation, arising in the cases of degenerate (static) or quasidegenerate (nondynamic) zero-order states, represent a difficult problem for DFT. When symmetry is present, multiplet sum method (MSM) DFT [Ziegler et al., Theor. Chim. Acta 4, 877 (1977)] provides one of the earliest and simplest ways to include static correlation in DFT. MSM-DFT assumes that DFT provides a good description of single-determinant energies and uses symmetry and simple ansätze to include the effects of static correlation. This is equivalent to determining the off-diagonal matrix elements in a small configuration interaction (CI) eigenvalue problem. Our ultimate goal, however, is nondynamic correlation in cases where symmetry is inadequate for fixing the dynamic-correlation limitation of DFT. To this end, we have developed a diagrammatic approach to MSM-DFT, which does not, by itself, solve the nondynamic correlation problem in DFT but which facilitates comparison with wave function CI and so allows educated guesses of off-diagonal CI matrix elements even in the absence of symmetry. In every case, an additional exchange-only ansatz (EXAN) allows the MSM-DFT formulas to be transformed into wave function formulas. This EXAN also works for transforming time-dependent DFT into time-dependent Hartree-Fock. Although not enough to uniquely guess DFT formulas from wave function formulas, the diagrammatic approach and the EXAN provide important constraints on any guesses that might be used. We illustrate how diagrammatic MSM-DFT may be used to guess a nondynamic correlation correction for the dissociation of H2 and how diagrammatic MSM-DFT may be used to guess a nonsymmetry-based coupling element in the O2 multiplet problem, which is reasonably close to a previous symmetry-derived result.

Real-Time Simulation of Open Quantum Spin Chains with the Inchworm Method.

We study the real-time simulation of open quantum systems, where the system is modeled by a spin chain with each spin associated with its own harmonic bath. Our method couples the inchworm method for the spin-boson model and the modular path integral methodology for spin systems. In particular, the introduction of the inchworm method can significantly suppress the numerical sign problem. Both methods are tweaked to make them work seamlessly with each other. We represent our approach in the language of diagrammatic methods and analyze the asymptotic behavior of the computational cost. Extensive numerical experiments are performed to validate our method.

Novel diagrammatical analyses of turnover of patients with cancer

Background/Aims The Inverted Nomogramma di Gandy is a diagrammatical method for evaluating staff turnover in large organisations. This exploratory research investigated whether it could be applied to cohorts of ‘active’ patients with cancer (those within the first 5 years of diagnosis) and provide additional insights into the underlying dynamics of cancer incidence and prevalence. Methods The Inverted Nomogramma di Gandy method was applied using relevant data for all clinical commissioning groups in England in 2017. This article details the data and results for breast and lung cancer. To evaluate the method's usefulness to healthcare practitioners, a report was circulated throughout the Cheshire and Merseyside Cancer Alliance, with readers asked to respond to a 15-item survey about their perceptions of the method and its usefulness. Results were analysed using descriptive statistics. Results There were wide variations in incidence and prevalence of breast and lung cancer across England. The diagram showed dispersed patterns for cancer alliances and identified the locations of individual outliers, revealing the underlying dynamics. The patterns for breast cancer and lung cancer were very different; even within the Cheshire and Merseyside Cancer Alliance there were some marked variations between locations. Survey respondents were generally neutral or positive about the method. Conclusions This diagrammatical method provided useful analyses that were complementary to incidence and prevalence data, and potentially useful for practitioners. Because the method uses existing available data, it could be rapidly introduced to services.

Theoretical Study of the Electronic Structure and Ionization Spectrum of γ-Pyrone

The electronic structure and ionization spectrum of γ-pyrone (4H-pyran-4-one) were calculated using the third-order algebraic diagrammatic construction method for the single-particle Green function [IP-ADC(3)] and some other high-level quantum chemical methods. The results of calculations were used to interpret its recently recorded photoelectron spectra. New assignments have been proposed for the nature of a series of photoelectron maxima of γ-pyrone located above 12 eV, where, according to calculations, the one-electron ionization pattern is disturbed due to electron correlation effects. The obtained results significantly change the interpretation of the spectrum available in the literature.

SMEFT goes dark: Dark Matter models for four-fermion operators

We study ultra-violet completions for d = 6 four-fermion operators in the standard model effective field theory (SMEFT), focusing on models that contain cold dark matter candidates. Via a diagrammatic method, we generate systematically lists of possible UV completions, with the aim of providing sets of models, which are complete under certain, well specified assumptions. Within these lists of models we rediscover many known DM models, as diverse as R-parity conserving supersymmetry or the scotogenic neutrino mass model. Our lists, however, also contain many new constructions, which have not been studied in the literature so far. We also briefly discuss how our DM models could be constrained by reinterpretations of LHC searches and the prospects for HL-LHC and future lepton colliders.

A comprehensive analysis of charge transfer effects on donor-pyrene (bridge)-acceptor systems using different substituents.

The alternant polycyclic aromatic hydrocarbon pyrene has photophysical properties that can be tuned with different donor and acceptor substituents. Recently, a D (donor)-Pyrene (bridge)-A (acceptor) system, DPA, with the electron donor N,N-dimethylaniline (DMA), and the electron acceptor trifluoromethylphenyl (TFM), was investigated by means of time-resolved spectroscopic measurements (J. Phys. Chem. Lett. 2021, 12, 2226-2231). DPA shows great promise for potential applications in organic electronic devices. In this work, we used the ab initio second-order algebraic diagrammatic construction method ADC(2) to investigate the excited-state properties of a series of analogous DPA systems, including the originally synthesized DPAs. The additionally investigated substituents were amino, fluorine, and methoxy as donors and nitrile and nitro groups as acceptors. The focus of this work was on characterizing the lowest excited singlet states regarding charge transfer (CT) and local excitation (LE) characters. For the DMA-pyrene-TFM system, the ADC(2) calculations show two initial electronic states relevant for interpreting the photodynamics. The bright S1 state is locally excited within the pyrene moiety, and an S2 state is localized ~0.5 eV above S1 and characterized as a donor to pyrene CT state. HOMO and LUMO energies were employed to assess the efficiency of the DPA compounds for organic photovoltaics (OPVs). HOMO-LUMO and optical gaps were used to estimate power conversion and light-harvesting efficiencies for practical applications in organic solar cells. Considering the systems using smaller D/A substituents, compounds with the strong acceptor NO2 substituent group show enhanced CT and promising properties for use in OPVs. Some of the other compounds with small substituents are also found to be competitive in this regard.

Normative Diagrams as a Tool for Representing Legal Systems

The paper at hand introduces and discusses a diagrammatic method to represent legal norms first developed by the second author. It is shown how this method can be used to represent not only norms and argument forms originating from classic legal methodology (legal subsumption, analogy, appeal to the contrary), but also more complex legal-theoretical phenomena, especially legal antinomies. Beyond its didactic virtues, the diagram is a useful theoretical tool for investigating how norms interact with each other and how singular actions can be considered as satisfying or violating a given norm.

Tree-level UV completions for NRSMEFT d = 6 and d = 7 operators

We study ultra-violet completions for operators in standard model effective field theory extended with right-handed neutrinos (NRSMEFT). Using a diagrammatic method, we generate systematically lists of possible tree-level completions involving scalars, fermions or vectors for all operators at d = 6 and d = 7, which contain at least one right-handed neutrino. We compare our lists of possible UV models to the ones found for pure SMEFT. We also discuss how the observation of LNV processes via NRSMEFT operators at the LHC can be related to Majorana neutrino masses of the standard model neutrinos.

Diagrammatic method for many-body non-Markovian dynamics: Memory effects and entanglement transitions

Diagrammatic method for many-body non-Markovian dynamics: Memory effects and entanglement transitions

Scaled opposite-spin atomic-orbital based algebraic diagrammatic construction scheme for the polarization propagator with asymptotic linear-scaling effort: Theory and implementation.

A novel local approach for the quantum-chemical computation of excited states is presented, where the concept of the atomic-orbital formulation of the second-order Møller-Plesset energy expression is extended to the second-order algebraic diagrammatic construction scheme by virtue of the Laplace transform. The scaled opposite-spin second-order algebraic diagrammatic construction method with Cholesky decomposed densities and density-fitting, or CDD-DF-SOS-ADC(2) for short, exploits the sparsity of the two-electron repulsion integrals, the atomic ground-state density matrix, and the atomic transition density matrix to drastically reduce the computational effort. By using a local density-fitting approximation, it is shown that asymptotically linear scaling can be achieved for linear carboxylic acids. For electron-dense systems, sub-cubic scaling can be achieved if the excitation is local, and hence the transition density is sparse. Furthermore, the memory footprint and accuracy of the CDD-DF-SOS-ADC(2) method are explored in detail.

Electronic structure, cationic, and excited states of nitrogen-containing spiroborates.

This paper presents the results of the study of the electronic structure and cationic and excited states of three spiroborate complexes (2-acetylacetonato-1,3,2-benzodioxaborol, its NH- and NMe-derivatives) and three corresponding ligands (acetylacetone, 4-aminopent-3-en-2-one, and 4-methylaminopent-3-en-2-one).Materials based on spiroborates are used in medicine, for example, as a drug carrier. In industry, spiroborate anions are used in ionic liquids and as alternative high performance lubricants. Analysis of experimental and calculated data allowed determining the influence of functional groups on the parameters of the electronic structure and energy of electronic transitions. Compared to acetylacetone and its NH- and NMe-derivatives, the upper filled molecular orbitals of the corresponding spiroborates are stabilized at 0.4-1.7eV, which is due to the positive charge of the ligand due to the acceptor properties of the dioxyphenylene fragment. Among the studied compounds, when replacing the oxygen atom in the α-position with the NH- or NMe-group, a bathochromic shift of intense bands in the absorption spectra is observed, since the energy intervals between the orbitals of the π3 and π4 ligand are reduced. In addition, in a number of spiroborates, the violation of C2v symmetry when replacing an oxygen atom leads to the appearance of a low-intensity maximum in the long-wave part of the absorption spectrum, due to the π2X → π4 transition. Complexeswere studied by photoelectron spectroscopy, absorption spectroscopy, and high-level ab initio quantum chemical computations, including the algebraic diagrammatic construction method for the polarization propagator of the second order (ADC(2)), the outer-valence Green's function (OVGF), the density functional theory(DFT), the time-dependent density functional theory(TDDFT) andthe domain-based local pair natural orbital (EOM-DLPNO) methods.X-ray photoelectronic spectra of two spiroborates in the condensed state were measured using a two-chamber high-vacuum system MXPS XP (Omicron, Germany).UV-visible absorption spectra were recorded using a spectrophotometer 2550 (Shimadzu-UV, Japan).The geometry ofallstudied compounds was optimized by the DFT/B3LYP/Def2-SVP method. The energy of electron levels in the S0 state and the distribution of electron density at each MO were obtained by the DFT/CAMB3LYP/cc-pVDZ method.The energies of excited states were obtained by the TDDFT/CAMB3LYP/cc-pVDZ, ADC(2)/cc-pVDZ and EOM-DLPNO/cc-pVDZmethods.All DFT and TDDFT calculations were carried out in the GAMESS (US)software computing package. ADC(2) calculations of excited states were performed using the Orca 4.0.1software package. EOM-DLPNO and OVGFcalculations were carried out in the Gaussian 16software package.