Presence Of Symmetry Research Articles

Bootstrapping conformal defect operators on a line

We study a conformal field theory with cubic anisotropic symmetry in presence of a line defect. We compute the correlators of the low lying defect operators using Feynman diagrams and derive explicit expressions for the two, three and four point defect correlators at the cubic fixed point in 4 – ϵ dimensions to O(ϵ). We also compute the defect g-function for this setup and demonstrate that this is in agreement with the g-theorem, which states that the g-function is monotonic under the renormalisation group flow along the defect. Next, we focus on conformal bootstrap techniques to determine the CFT data associated with the defect operators, which is the main objective of the paper. We utilize the framework of crossing symmetric Polyakov bootstrap and compute the averaged CFT data to O(ϵ) up to a finite number of ambiguities. We comment on unmixing the CFT data for the double trace operators at O(ϵ) and use this to compute the O(ϵ2) data. Finally, we study these defect correlators non-perturbatively using numerical methods and isolate them near the free theory limit close to four dimensions.

The role of task on the human brain's responses to, and representation of, visual regularity defined by reflection and rotation

Identifying and segmenting objects in an image is generally achieved effortlessly and is facilitated by the presence of symmetry: a principle of perceptual organisation used to interpret sensory inputs from the retina into meaningful representations. However, while imaging studies show evidence of symmetry selective responses across extrastriate visual areas in the human brain, whether symmetry is processed automatically is still under debate. We used functional Magnetic Resonance Imaging (fMRI) to study the response to and representation of two types of symmetry: reflection and rotation. Dot pattern stimuli were presented to 15 human participants (10 female) under stimulus-relevant (symmetry) and stimulus-irrelevant (luminance) task conditions. Our results show that symmetry-selective responses emerge from area V3 and extend throughout extrastriate visual areas. This response is largely maintained when participants engage in the stimulus irrelevant task, suggesting an automaticity to processing visual symmetry. Our multi-voxel pattern analysis (MVPA) results extend these findings by suggesting that not only spatial organisation of responses to symmetrical patterns can be distinguished from that of non-symmetrical (random) patterns, but also that representation of reflection and rotation symmetry can be differentiated in extrastriate and object-selective visual areas. Moreover, task demands did not affect the neural representation of the symmetry information. Intriguingly, our MVPA results show an interesting dissociation: representation of luminance (stimulus irrelevant feature) is maintained in visual cortex only when task relevant, while information of the spatial configuration of the stimuli is available across task conditions. This speaks in favour of the automaticity for processing perceptual organisation: extrastriate visual areas compute and represent global, spatial properties irrespective of the task at hand.

Construction of Topological Bound States in the Continuum Via Subsymmetry.

Topological bound states in the continuum (BICs) are localized topological boundary modes coexisting with a continuous spectrum of extended modes. They have been realized in systems with symmetry-protected topological phases, where their immunity to defects and perturbations depends on the presence of symmetries. Here we propose a method that transforms an in-gap topological boundary state into a BIC by using the concept of subsymmetry. We design the coupling between a system possessing in-gap topological modes and a system possessing a continuum of states that results in topological BICs. We define the criteria for the coupling that yields the desired results. To implement this scheme, we construct representative topological BICs based on one-dimensional Su-Schrieffer-Heeger models and implement them in photonic lattices. Our results not only reveal novel physical phenomena but may also provide methods for designing a new generation of topological devices.

On the long-time behaviour of solutions to unforced evolution Navier–Stokes equations under Navier boundary conditions

We study the asymptotic behaviour of the solutions to Navier–Stokes unforced equations under Navier boundary conditions in a wide class of merely Lipschitz domains of physical interest. The paper draws its main motivation from celebrated results by Foias and Saut (1984) under Dirichlet conditions; here the choice of the boundary conditions requires carefully considering the geometry of the domain Ω, due to the possible lack of the Poincaré inequality in presence of symmetries. In non-axially symmetric domains we show the validity of the Foias–Saut result about the limit at infinity of the Dirichlet quotient, in axially symmetric domains we provide two invariants of the flow which completely characterize the motion and we prove that the Foias–Saut result holds for initial data belonging to one of the invariants.

Efficient Propagation Techniques for Handling Cyclic Symmetries in Binary Programs

The presence of symmetries in binary programs typically degrades the performance of branch-and-bound solvers. In this article, we derive efficient variable fixing algorithms to discard symmetric solutions from the search space based on propagation techniques for cyclic groups. Our algorithms come with the guarantee to find all possible variable fixings that can be derived from symmetry arguments; that is, one cannot find more variable fixings than those found by our algorithms. Because every permutation symmetry group of a binary program has cyclic subgroups, the derived algorithms can be used to handle symmetries in any symmetric binary program. In experiments, we also provide numerical evidence that our algorithms handle symmetries more efficiently than other variable fixing algorithms for cyclic symmetries. History: Accepted by Andrea Lodi, Area Editor for Design and Analysis of Algorithms—Discrete. Supplemental Material: The online appendix is available at https://doi.org/10.1287/ijoc.2022.0060 .

Attractiveness of Facial Symmetry in the Context of the Dominant Visual Field

One of the key features of an attractive face is symmetry. The presence of symmetry in living organisms reflects their ability to cope with various adverse environmental or genetic factors, thus a symmetrical face signals the hidden qualities of the organism. Despite the evolutionary basis for the attractiveness of facial symmetry, studies that have examined it have yielded diverse results. One reason may lie in the fact that the symmetrical stimulus faces are often composites that are created by using the mirror image of one, which can lead to contradictory outcomes. When evaluating human faces, the dominance of the left visual field (as a reflection of brain lateralisation functions) comes into play, which may modify the attractiveness of the composite depending on whether it was created as a left-sided mirror image (using the left half of the face) or a right-sided mirror image (using the right half of the face). The study aims to evaluate the attractiveness of left-sided and right-sided symmetrical facial composites and how the evaluator's visual field dominance affects the assessed attractiveness. The research was conducted on a sample of 1,921 participants aged from 15 to 77 (M = 23.57; SD = 9.52); 60.7% women using computerised facial composites in quasi-experimental research design. The results show that left-sided facial composites are significantly (p<0.001) more attractive than right-sided, for both female and male faces. Furthermore, it is noted that visual field dominance is not related to the type (left-sided vs. right-sided) of symmetry or the evaluation of its attractiveness – individuals with dominant left visual fields as well as those with dominant right visual fields universally rate the left-sided composite as significantly more attractive than the right-sided composite.

Experimental simulation of symmetry-protected higher-order exceptional points with single photons.

Exceptional points (EPs) of non-Hermitian (NH) systems have recently attracted increasing attention due to their rich phenomenology and intriguing applications. Compared to the predominantly studied second-order EPs, higher-order EPs have been assumed to play a much less prominent role because they generically require the tuning of more parameters. Here, we experimentally simulate two-dimensional topological NH band structures using single-photon interferometry, and observe topologically stable third-order EPs obtained by tuning only two real parameters in the presence of symmetry. In particular, we explore how different symmetries stabilize qualitatively different third-order EPs: the parity-time symmetry leads to a generic cube-root dispersion, while a generalized chiral symmetry implies a square-root dispersion coexisting with a flat band. Additionally, we simulate fourfold degeneracies, composed of the non-defective twofold degeneracies and second-order EPs. Our work reveals the abundant and conceptually richer higher-order EPs protected by symmetries and offers a versatile platform for further research on topological NH systems.

Heteroclinic cycles and chaos in a system of four identical phase oscillators with global biharmonic coupling.

We study a system of four identical globally coupled phase oscillators with a biharmonic coupling function. Its dimension and the type of coupling make it the minimal system of Kuramoto-type (both in the sense of the phase space's dimension and the number of harmonics) that supports chaotic dynamics. However, to the best of our knowledge, there is still no numerical evidence for the existence of chaos in this system. The dynamics of such systems is tightly connected with the action of the symmetry group on its phase space. The presence of symmetries might lead to an emergence of chaos due to scenarios involving specific heteroclinic cycles. We suggest an approach for searching such heteroclinic cycles and showcase first examples of chaos in this system found by using this approach.

Symmetry-protected topological exceptional chains in non-Hermitian crystals

In non-Hermitian systems, defective band degeneracies called exceptional points can form exceptional lines (ELs) in 3D momentum space in the absence of any symmetries. However, whether the presence of symmetries can affect the EL configurations had rarely been discussed. Here we show that a natural orientation can be assigned to every EL according to the eigenenergy braiding around it, and we establish the source-free principle of ELs stating that the number of ELs ingoing and outgoing from the junction must be conserved. Based on this principle, we discover that three crystalline-symmetry-based mechanisms can stabilize the junction of ELs, resulting in the formation of various types of exceptional chains (ECs). We further demonstrate that ECs can be observed in prototypical non-Hermitian photonic crystals. Our results combine the effect of non-Hermitian spatiotemporal symmetry and topology to pave the way for understanding and manipulating the morphology of ELs in non-Hermitian crystalline systems.

Deformation of d = 4, mathcal{N} ≥ 5 supergravities breaks nonlinear local supersymmetry

We study d = 4, mathcal{N} ≥ 5 supergravities and their deformation via candidate counterterms, with the purpose to absorb UV divergences. We generalize the earlier studies of deformation and twisted self-duality constraint to the case with unbroken local mathcal{H} -symmetry in presence of fermions. We find that the deformed action breaks nonlinear local supersymmetry. We show that all known cases of enhanced UV divergence cancellations are explained by nonlinear local supersymmetry.This result implies, in particular, that if mathcal{N} = 5 supergravity at five loop will turn out to be UV divergent, the deformed theory will be BRST inconsistent. If it will be finite, it will be a consequence of nonlinear local supersymmetry and E7-type duality.

Best constant and Mountain-Pass solutions for a supercritical Hardy-Sobolev problem in the presence of symmetries

Given a Riemannian manifold (M,g) and a group G of isometries of (M,g), we investigate the existence G-invariant positive solutions u:M→R to the nonlinear equation Δgu+au=u2⋆(k,s)−1dg(x,Gx0)s+huq−1 where Δg=−divg(∇). The singularity and the nonlinearity are such that the problem is critical for the Hardy-Sobolev embeddings. We prove existence by using the Aubin minimization and the Mountain-Pass lemma of Ambrosetti-Rabinowitz. As a by product of our analysis, we find the value of the best-constant in the associated Hardy-Sobolev inequality.

Analysis of model predictive control in numbered-up modular facilities

Modular production units are a key enabling technology for distributed manufacturing, an important emerging paradigm which helps promote sustainability, resource independence, and robustness in critical chemical production and distribution infrastructure. In modular systems, desired material throughput is achieved by “numbering up” rather than “scaling up”. Previous studies have quantified the benefits of introducing modular units when making decisions at a supply chain or process design level. However, modular units provide additional potential benefits at the level of operation and control which heretofore has not been as thoroughly studied. In this paper, we analyze the structure of the optimal modular system control problem and identify three qualities unique to problems with numbered-up units: the ability to control outputs locally or globally, the presence of symmetry in the underlying problem, and the possibility of reconfiguring the connectivity of modular units. We provide analysis and insights on ways to mitigate challenges and exploit beneficial properties resulting from the above qualities through a benchmark modular reactor case study.

Solutions of the Allen–Cahn equation on closed manifolds in the presence of symmetry

Solutions of the Allen–Cahn equation on closed manifolds in the presence of symmetry

Features of the problem on synchronization of two van der Pol-Duffing oscillators in the case of a direct connection and the presence of symmetry

Features of the problem on synchronization of two van der Pol-Duffing oscillators in the case of a direct connection and the presence of symmetry

On the relationships between covariance and the decoherence-free subalgebra of a quantum Markov semigroup

In this paper, we investigate if the presence of symmetries in the evolution of an open quantum system gives information about the invariant subspaces. Unfortunately, the answer is, in general, negative, but under suitable conditions we can observe that the representation through which we describe the symmetry determines a privileged family of orthogonal projections strongly correlated with the structure of the decoherence-free sub-algebra and, as a consequence, with harmonic projections.

Efficient computation of N-point correlation functions in D dimensions

We present efficient algorithms for computing the N-point correlation functions (NPCFs) of random fields in arbitrary D-dimensional homogeneous and isotropic spaces. Such statistics appear throughout the physical sciences and provide a natural tool to describe stochastic processes. Typically, algorithms for computing the NPCF components have [Formula: see text] complexity (for a dataset containing n particles); their application is thus computationally infeasible unless N is small. By projecting the statistic onto a suitably defined angular basis, we show that the estimators can be written in a separable form, with complexity [Formula: see text] or [Formula: see text] if evaluated using a Fast Fourier Transform on a grid of size [Formula: see text]. Our decomposition is built upon the D-dimensional hyperspherical harmonics; these form a complete basis on the [Formula: see text] sphere and are intrinsically related to angular momentum operators. Concatenation of [Formula: see text] such harmonics gives states of definite combined angular momentum, forming a natural separable basis for the NPCF. As N and D grow, the number of basis components quickly becomes large, providing a practical limitation to this (and all other) approaches: However, the dimensionality is greatly reduced in the presence of symmetries; for example, isotropic correlation functions require only states of zero combined angular momentum. We provide a Julia package implementing our estimators and show how they can be applied to a variety of scenarios within cosmology and fluid dynamics. The efficiency of such estimators will allow higher-order correlators to become a standard tool in the analysis of random fields.

Symmetry and spatial ability enhance change detection in visuospatial structures

Science, Technology, Engineering, and Mathematics (STEM) domains require people to recognize and transform complex visuospatial displays that appear to vastly exceed the limits of visuospatial working memory. Here, we consider possible domain-general mechanisms that may explain this advantage: capitalizing on symmetry, a structural regularity that can produce more efficient representations. Participants briefly viewed a structure made up of three-dimensional connected cubes of different colors, which was either asymmetrical or symmetrical. After a short delay, they were asked to detect a change (colors swapping positions) within a rotated second view. In change trials, the second display always had an asymmetrical structure. The presence of symmetry in the initial view improved change detection, and performance also declined with angular disparity of the encoding and test displays. People with higher spatial ability performed better on the change-detection task, but there was no evidence that they were better at leveraging symmetry than low-spatial individuals. The results suggest that leveraging symmetrical structures can help people of all ability levels exceed typical working memory limits by constructing more efficient representations and substituting resource-demanding mental rotation operations with alternative orientation-independent strategies.

Realizing exceptional points of any order in the presence of symmetry

Exceptional points~(EPs) appear as degeneracies in the spectrum of non-Hermitian matrices at which the eigenvectors coalesce. In general, an EP of order $n$ may find room to emerge if $2(n-1)$ real constraints are imposed. Our results show that these constraints can be expressed in terms of the determinant and traces of the non-Hermitian matrix. Our findings further reveal that the total number of constraints may reduce in the presence of unitary and antiunitary symmetries. Additionally, we draw generic conclusions for the low-energy dispersion of the EPs. Based on our calculations, we show that in odd dimensions the presence of sublattice or pseudo-chiral symmetry enforces $n$th order EPs to disperse with the $(n-1)$th root. For two-, three- and four-band systems, we explicitly present the constraints needed for the occurrence of EPs in terms of system parameters and classify EPs based on their low-energy dispersion relations.

Symmetry Reduction in AM/GM-Based Optimization

The arithmetic mean/geometric mean-inequality (AM/GM-inequality) facilitates classes of non-negativity certificates and of relaxation techniques for polynomials and, more generally, for exponential sums. Here, we present a first systematic study of the AM/GM-based techniques in the presence of symmetries under the linear action of a finite group. We prove a symmetry-adapted representation theorem and develop techniques to reduce the size of the resulting relative entropy programs. We study in more detail the complexity gain in the case of the symmetric group. In this setup, we can show in particular certain stabilization results. We exhibit several sequences of examples in growing dimensions where the size of the problem stabilizes. Finally, we provide some numerical results, emphasizing the computational speed-up.

Evaluation of root and canal morphologies of permanent canines in a Saudi Arabian sub population using cone-beam computed tomography

Background/purposeFailure to identify and treat the root canal system in its entirety has been known to be one of the leading causes of unsuccessful root canal treatment (RCT). This study aims to retrospectively assess the permanent canines in a Saudi Arabian sub population for the number of roots, root canal morphologies and the presence of symmetry among them using cone-beam computed tomography (CBCT). Materials and methodsCBCT scans belonging to 945 patients were screened. A total of 1880 permanent canines, 928 pertaining to maxilla and 952 pertaining to mandible were analyzed for the number of roots, root canal morphologies and the presence of symmetry among them. Comparative evaluation between genders was done using Fisher's exact test, since majority of the groups had expected count of less than 5. A calculated P-value of less than 0.05 was considered significant. Chi square test was used for statistical analysis of the data. Intra operator variability was observed using Cohen's Kappa test. ResultsSingle root was observed in 100% and 98.7% of the maxillary and mandibular canines respectively. Two roots were identified in 1.3% of the MnC's. Type I (97.48%), Type II (0.21%), Type III (1.05%) and Type V (1.26%) Vertucci canal configurations (VC) were observed in MnC's. Statistical significant difference was observed concerning the number of roots and canal morphology according to Vertucci in the mandibular canines. No difference was observed according to Ahmed et al. classification system. Moreover, there was no gender based difference seen among them. ConclusionMore variable root and canal morphologies are observed in MnC's, although single root with Type I VC is the most common.