Search results for "Diagrammatic reasoning"
showing 10 items of 17 documents
Diagrammatic Expansion for Positive Spectral Functions in the Steady-State Limit
2019
Recently, a method was presented for constructing self-energies within many-body perturbation theory that are guaranteed to produce a positive spectral function for equilibrium systems, by representing the self-energy as a product of half-diagrams on the forward and backward branches of the Keldysh contour. We derive an alternative half-diagram representation that is based on products of retarded diagrams. Our approach extends the method to systems out of equilibrium. When a steady-state limit exists, we show that our approach yields a positive definite spectral function in the frequency domain.
Towards Diagrammatic Patterns
2008
This article presents the idea that the graphical representation (concrete syntax) of a visual language can be specified based on some pre-defined diagrammatic patterns. A diagram from the Specification and Description Language (SDL) is used as illustration.
Analytic gradients for the coupled-cluster singles, doubles, and triples (CCSDT) model
2002
The first implementation of analytic gradients for the coupled-cluster singles, doubles, triples (CCSDT) model is described. The relevant theoretical expressions are given in a diagrammatic form together with the corresponding algebraic formulas. The computational requirements of CCSDT gradient calculations are discussed and their applicability demonstrated by performing benchmark calculations for molecular geometries with large correlation-consistent basis sets. A statistical analysis of the data reveals that CCSDT and CCSD(T) in most cases perform equally well. The CCSDT calculations thus provide further evidence for the high accuracy of the CCSD(T) approach.
Analytic first and second derivatives for the CCSDT-n (n = 1–3) models: a first step towards the efficient calculation of CCSDT properties
2000
Analytic first and second derivatives of the energy are implemented for closed-shell systems described by the CCSDT-n (n=1, 1b, 2 and 3) and CC3 electron correlation models. A detailed discussion of the computational requirements of these calculations is given, along with diagrammatic formulas for all relevant quantities. The method is applied to calculate the nuclear magnetic shielding of H2O, CO and N2O and the structure and properties of propadienylidene.
Indispensability and Effectiveness of Diagrams in Molecular Biology
2019
Abstract: In this paper I aim to defend a twofold thesis. On one hand, I will support, against Perini (2005), the indispensability of diagrams when structurally complex biomolecules are concerned, since it is not possible to satisfactorily use linguistic-sentential representations at that domain. On the other hand, even when diagrams are dispensable I will defend than they will generally be more effective than other representations in encoding biomolecular knowledge, relying on Kulvicki-Shimojima’s diagrammatic effectiveness thesis. Finally, I will ground many epistemic virtues of biomolecular diagrams (understandability, explanatory power, prediction and hypothesis evaluation) on their cog…
Conceptual Spaces for Cognitive Architectures: A lingua franca for different levels of representation
2017
During the last decades, many cognitive architectures (CAs) have been realized adopting different assumptions about the organization and the representation of their knowledge level. Some of them (e.g. SOAR [Laird (2012)]) adopt a classical symbolic approach, some (e.g. LEABRA [O'Reilly and Munakata (2000)]) are based on a purely connectionist model, while others (e.g. CLARION [Sun (2006)] adopt a hybrid approach combining connectionist and symbolic representational levels. Additionally, some attempts (e.g. biSOAR) trying to extend the representational capacities of CAs by integrating diagrammatical representations and reasoning are also available [Kurup and Chandrasekaran (2007)]. In this p…
Diagrammatic expansion for positive density-response spectra: Application to the electron gas
2015
In a recent paper [Phys. Rev. B 90, 115134 (2014)] we put forward a diagrammatic expansion for the self-energy which guarantees the positivity of the spectral function. In this work we extend the theory to the density response function. We write the generic diagram for the density-response spectrum as the sum of partitions. In a partition the original diagram is evaluated using time-ordered Green's functions (GF) on the left-half of the diagram, antitime-ordered GF on the right-half of the diagram and lesser or greater GF gluing the two halves. As there exist more than one way to cut a diagram in two halves, to every diagram corresponds more than one partition. We recognize that the most co…
Theories relating baryon asymmetry and dark matter
2014
The nature of dark matter and the origin of the baryon asymmetry are two of the deepest mysteries of modern particle physics. In the absence of hints regarding a possible solution to these mysteries, many approaches have been developed to tackle them simultaneously leading to very diverse and rich models. We give a short review where we describe the general features of some of these models and an overview on the general problem. We also propose a diagrammatic notation to label the different models.
Diagrammatic expansion for positive spectral functions beyond GW : Application to vertex corrections in the electron gas
2014
We present a diagrammatic approach to construct self-energy approximations within many-body perturbation theory with positive spectral properties. The method cures the problem of negative spectral functions which arises from a straightforward inclusion of vertex diagrams beyond the GW approximation. Our approach consists of a two-steps procedure: we first express the approximate many-body self-energy as a product of half-diagrams and then identify the minimal number of half-diagrams to add in order to form a perfect square. The resulting self-energy is an unconventional sum of self-energy diagrams in which the internal lines of half a diagram are time-ordered Green's functions whereas those…
Diagrammatic approach to quantum search
2014
We introduce a simple diagrammatic approach for estimating how a randomly walking quantum particle searches on a graph in continuous-time, which involves sketching small weighted graphs with self-loops and considering degenerate perturbation theory's effects on them. Using this method, we give the first example of degenerate perturbation theory solving search on a graph whose evolution occurs in a subspace whose dimension grows with $N$.