Monte Carlo construction of cubature on Wiener space

In this paper, we investigate application of mathematical optimization to construction of a cubature formula on Wiener space, which is a weak approximation method of stochastic differential equations introduced by Lyons and Victoir (Proc R Soc Lond A 460:169–198, 2004). After giving a brief review on the cubature theory on Wiener space, we show that a cubature formula of general dimension and degree can be obtained through a Monte Carlo sampling and linear programming. This paper also includes an extension of stochastic Tchakaloff’s theorem, which technically yields the proof of our primary result.

A basis of analytic functionals for CFTs in general dimension

We develop an analytic approach to the four-point crossing equation in CFT, for general spacetime dimension. In a unitary CFT, the crossing equation (for, say, the s- and t-channel expansions) can be thought of as a vector equation in an infinite-dimensional space of complex analytic functions in two variables, which satisfy a boundedness condition at infinity. We identify a useful basis for this space of functions, consisting of the set of s- and t-channel conformal blocks of double-twist operators in mean field theory. We describe two independent algorithms to construct the dual basis of linear functionals, and work out explicitly many examples. Our basis of functionals appears to be closely related to the CFT dispersion relation recently derived by Carmi and Caron-Huot.

Searching for gauge theories with the conformal bootstrap

Infrared fixed points of gauge theories provide intriguing targets for the modern conformal bootstrap program. In this work we provide some preliminary evidence that a family of gauged fermionic CFTs saturate bootstrap bounds and can potentially be solved with the conformal bootstrap. We start by considering the bootstrap for SO(N) vector 4-point functions in general dimension D. In the large N limit, upper bounds on the scaling dimensions of the lowest SO(N) singlet and traceless symmetric scalars interpolate between two solutions at ∆ = D/2 − 1 and ∆ = D − 1 via generalized free field theory. In 3D the critical O(N) vector models are known to saturate the bootstrap bounds and correspond to the kinks approaching ∆ = 1/2 at large N. We show that the bootstrap bounds also admit another infinite family of kinks $$ {\mathcal{T}}_D $$ T D , which at large N approach solutions containing free fermion bilinears at ∆ = D − 1 from below. The kinks $$ {\mathcal{T}}_D $$ T D appear in general dimensions with a D-dependent critical N* below which the kink disappears. We also study relations between the bounds obtained from the bootstrap with SO(N) vectors, SU(N) fundamentals, and SU(N) × SU(N) bi-fundamentals. We provide a proof for the coincidence between bootstrap bounds with different global symmetries. We show evidence that the proper symmetries of the underlying theories of $$ {\mathcal{T}}_D $$ T D are subgroups of SO(N), and we speculate that the kinks $$ {\mathcal{T}}_D $$ T D relate to the fixed points of gauge theories coupled to fermions.

Conformal correlators as simplex integrals in momentum space

We find the general solution of the conformal Ward identities for scalar n-point functions in momentum space and in general dimension. The solution is given in terms of integrals over (n − 1)-simplices in momentum space. The n operators are inserted at the n vertices of the simplex, and the momenta running between any two vertices of the simplex are the integration variables. The integrand involves an arbitrary function of momentum-space cross ratios constructed from the integration variables, while the external momenta enter only via momentum conservation at each vertex. Correlators where the function of cross ratios is a monomial exhibit a remarkable recursive structure where n-point functions are built in terms of (n − 1)-point functions. To illustrate our discussion, we derive the simplex representation of n-point contact Witten diagrams in a holographic conformal field theory. This can be achieved through both a recursive method, as well as an approach based on the star-mesh transformation of electrical circuit theory. The resulting expression for the function of cross ratios involves (n − 2) integrations, which is an improvement (when n > 4) relative to the Mellin representation that involves n(n − 3)/2 integrations.

More on heavy-light bootstrap up to double-stress-tensor

We investigate the heavy-light four-point function up to double-stress-tensor, supplementing 1910.06357. By using the OPE coefficients of lowest-twist double-stress- tensor in the literature, we find the Regge behavior for lowest-twist double-stress-tensor in general even dimension within the large impact parameter regime. In the next, we perform the Lorentzian inversion formula to obtain both the OPE coefficients and anomalous dimensions of double-twist operators [$$ \mathcal{O} $$ O H$$ \mathcal{O} $$ O L]n,J with finite spin J in d = 4. We also extract the anomalous dimensions of double-twist operators with finite spin in general dimension, which allows us to address the cases that ∆L is specified to the poles in lowest-twist double-stress-tensors where certain double-trace operators [$$ \mathcal{O} $$ O L$$ \mathcal{O} $$ O L]n,J mix with lowest-twist double-stress-tensors. In particular, we verify and discuss the Residue relation that deter- mines the product of the mixed anomalous dimension and the mixed OPE. We also present the double-trace and mixed OPE coefficients associated with ∆L poles in d = 6, 8. In the end, we turn to discuss CFT2, we verify the uniqueness of double-stress-tensor that is consistent with Virasoso symmetry.

Psychometric properties of the UWES-9S in Peruvian college students

The objective of this study was to evaluate the internal structure dimensionality of the Utrech Work Engagement Scale – Student (UWES–9S) and its association with the academic procrastination reported by 321 psychology students from a private university in Cajamarca (Peru) ranging between 17 and 41 years old (79% women; Mage = 22.50 years; 84% between 17 and 25 years old). The UWES-9S and the Academic Procrastination Scale (APS) were used and both a confirmatory and a bifactor analysis were conducted on the UWES–9S, as well as a structural regression analysis that specified the influence of the general and specific dimensions of engagement on the dimensions of academic procrastination. Regarding the results, the bifactor model is the one that best defines the construct, whereas the general dimension of engagement has a greater influence on the dimensions of academic procrastination than the specific ones. The theoretical and practical implications of the findings are discussed, as well as the need to focus on the students’ positive resources in order to achieve greater involvement in their academic work.

Psychometric properties of the UWES-9S in Peruvian college students

The objective of this study was to evaluate the internal structure dimensionality of the Utrech Work Engagement Scale – Student (UWES–9S) and its association with the academic procrastination reported by 321 psychology students from a private university in Cajamarca (Peru) ranging between 17 and 41 years old (79% women; Mage = 22.50 years; 84% between 17 and 25 years old). The UWES-9S and the Academic Procrastination Scale (APS) were used and both a confirmatory and a bifactor analysis were conducted on the UWES–9S, as well as a structural regression analysis that specified the influence of the general and specific dimensions of engagement on the dimensions of academic procrastination. Regarding the results, the bifactor model is the one that best defines the construct, whereas the general dimension of engagement has a greater influence on the dimensions of academic procrastination than the specific ones. The theoretical and practical implications of the findings are discussed, as well as the need to focus on the students’ positive resources in order to achieve greater involvement in their academic work.

On top or underneath: where does the general factor of psychopathology fit within a dimensional model of psychopathology?

Background Dimensional models of psychopathology are increasingly common and there is evidence for the existence of a general dimension of psychopathology (‘p’). The existing literature presents two ways to model p: as a bifactor or as a higher-order dimension. Bifactor models typically fit sample data better than higher-order models, and are often selected as better fitting alternatives but there are reasons to be cautious of such an approach to model selection. In this study the bifactor and higher-order models of p were compared in relation to associations with established risk variables for mental illness. Methods A trauma exposed community sample from the United Kingdom (N = 1051) completed self-report measures of 49 symptoms of psychopathology. Results A higher-order model with four first-order dimensions (Fear, Distress, Externalising and Thought Disorder) and a higher-order p dimension provided satisfactory model fit, and a bifactor representation provided superior model fit. Bifactor p and higher-order p were highly correlated (r = 0.97) indicating that both parametrisations produce near equivalent general dimensions of psychopathology. Latent variable models including predictor variables showed that the risk variables explained more variance in higher-order p than bifactor p. The higher-order model produced more interpretable associations for the first-order/specific dimensions compared to the bifactor model. Conclusions The higher-order representation of p, as described in the Hierarchical Taxonomy of Psychopathology, appears to be a more appropriate way to conceptualise the general dimension of psychopathology than the bifactor approach. The research and clinical implications of these discrepant ways of modelling p are discussed.