Linear Divergence Research Articles

3D surface defect map for assessing buccolingual profile of single tooth gaps following alveolar ridge preservation.

A new, non-invasive approach suggests using single intraoral optical scanning to analyze the ridge profile of single-tooth gaps following alveolar ridge preservation in the absence of a baseline scan. This method involves creating a three-dimensional (3D) surface map to identify and assess contour changes and ridge profiles based on the adjacent teeth. The present study was designed as a cross-sectional pilot analysis on a convenience sample of patients undergoing alveolar ridge preservation. Intraoral optical scans were taken on 23 patients, capturing data from 30 edentulous sites. The digital models were then imported into an image analysis software for a 3D surface defect map analysis performed by one examiner. This analysis characterized the buccolingual profile of the single tooth gap relative to the adjacent teeth. 10 linear divergence points, spaced 0.5 mm apart in a corona-apical direction, were identified at the midfacial aspect of the sites. Based on these points the sites were plotted and grouped in three different buccolingual profiles (linear, concave, and convex). Clinical parameters including Keratinized mucosa Width (KMW), and soft tissue phenotype with Colorvue biotype probes were also recorded. Three different buccolingual patterns (linear, convex, and concave) were identified. Seven sites exhibited a linear profile, 10 sites displayed a concave shape, and 13 showed a convex profile. The linear profile had surface discrepancies similar to the neighboring teeth. In contrast, the convex profile revealed mid-buccal discrepancy localized only at the crestal aspect, while the concave had an extended divergence ranging from 1 to 5 mm below the soft tissue margin. Univariate and multiple logistic regression analyses did not reveal any statistically significant variables influencing profilometric analysis; however, when combining phenotype and KMW, thick phenotypes demonstrated a higher proportion of concavity (OR = 4.83) compared to thin ones, suggesting a significant trend. With every 1 mm of increase in KMW, the probability of showing a concavity decreased (p = 0.057). A 3D surface defect map represents a useful tool for objectively quantifying ridge defects and profiles by assessing profilometric and surface differences compared to adjacent dentition using a single intraoral scan. This method also indicates that KMW may play a critical role in preventing concavity defects. The 3D defect map can guide decision-making during soft tissue augmentation procedures by emphasizing the specific location of the defect and providing more detailed insights into its localization. These parameters can enable the tailoring of flap management and soft tissue grafting strategies to address the patient's individual needs.

Entanglement of defect subregions in double holography

In the framework of double holography, we investigate the entanglement behavior of a subregion of the defect on the boundary of a CFT3. The entanglement entropy of this defect subregion is determined by the quantum extremal surface (QES) anchored at the two endpoints of the subregion from the brane perspective. We further analyze the entanglement entropy of the quantum matter within this QES, which can be extracted from the total entanglement entropy. We find there are two phases of the QES. To numerically distinguish these phases, we design a strategy for approaching the QES by progressively reducing the width of a semi-ellipse-like region within the CFT3, which is bounded by the defect. During this process, we discover an entanglement phase transition driven by the degree of freedom on the brane. In the shrinking phase, the entanglement wedge of the defect subregion sharply decreases to zero as the removal of the CFT3. In contrast, in the stable phase, the wedge almost remains constant. In this phase, the formulas of entanglement measures can be derived based on defect and CFT3 central charges in the semi-classical limit. For entanglement entropy, the classical geometry only contributes a subleading term with logarithmic divergence, but the matter entanglement exhibits a dominant linear divergence, even in the semi-classical limit. For the reflected entropy within the defect subregion, classical geometry contributes a leading term with logarithmic divergence, while the quantum matter within the entanglement wedge only contributes a finite term.

Parton distributions from boosted fields in the Coulomb gauge

We propose a new method to calculate parton distribution functions (PDFs) from lattice correlations of boosted quarks and gluons in the Coulomb gauge. Compared to the widely used gauge-invariant Wilson-line operators, these correlations greatly simplify the renormalization thanks to the absence of linear power divergence. Additionally, they enable access to larger off-axis momenta under preserved 3D rotational symmetry, as well as enhanced long-range precision that facilitates the Fourier transform. We verify the factorization formula that relates this new observable to the quark PDF at one-loop order in perturbation theory. Moreover, through a lattice calculation of the pion valence quark PDF, we demonstrate the aforementioned advantage and features of the Coulomb gauge correlation and show that it yields consistent results with the gauge-invariant method. This opens the door to a more efficient way to calculate parton physics on the lattice. Published by the American Physical Society 2024

Divergence Property of the Brown-Thompson Groups and Braided Thompson Groups

AbstractGolan and Sapir proved that Thompson’s groups F, T and V have linear divergence. In the current paper, we focus on the divergence property of several generalisations of the Thompson groups. We first consider the Brown-Thompson groups $$F_n$$ F n , $$T_n$$ T n and $$V_n$$ V n (also called Brown-Higman-Thompson group in some other context) and find that these groups also have linear divergence functions. We then focus on the braided Thompson groups BF, $$\widehat{BF}$$ BF ^ and $$\widehat{BV}$$ BV ^ and prove that these groups have linear divergence. The case of BV has also been done independently by Kodama.

Hybrid renormalization for quasi distribution amplitudes of a light baryon

We develop a hybrid scheme to renormalize quasi distribution amplitudes of a light baryon on the lattice, which combines the self-renormalization and ratio scheme. By employing self-renormalization, the UV divergences and linear divergence at large spatial separations in quasi distribution amplitudes are removed without introducing extra nonperturbative effects, while making a ratio with respect to the zero-momentum matrix element can properly remove the UV divergences in small spatial separations. As a specific application, distribution amplitudes of the Λ baryon made of uds are investigated, and the requisite equal-time correlators, which define quasi distribution amplitudes in coordinate space, are perturbatively calculated up to the next-to-leading order in strong coupling constant αs. These perturbative equal-time correlators are used to convert lattice QCD matrix elements to the continuum space during the renormalization process. Subsequently, quasi distribution amplitudes are matched onto lightcone distribution amplitudes by integrating out hard modes and the corresponding hard kernels are derived up to next-to-leading order in αs including the hybrid counterterms. These results are valuable in the lattice-based investigation of the lightcone distribution amplitudes of a light baryon from the first principles of QCD.

Complexity of warped conformal field theory

Warped conformal field theories in two dimensions are exotic nonlocal, Lorentz violating field theories characterized by Virasoro–Kac–Moody symmetries and have attracted a lot of attention as candidate boundary duals to warped AdS_3 spacetimes, thereby expanding the scope of holography beyond asymptotically AdS spacetimes. Here we investigate WCFT_2 s using circuit complexity as a tool. First we compute the holographic volume complexity (CV) which displays a linear UV divergence structure, more akin to that of a local CFT_2 and has a very complicated dependence on the Virasoro central charge c and the U(1) Kac–Moody level parameter k. Next we consider circuit complexity based on Virasoro–Kac–Moody symmetry gates where the complexity functional is the geometric (group) action on coadjoint orbits of the Virasoro–Kac–Moody group. We consider a special solution to extremization equations for which complexity scales linearly with “time”. In the semiclassical limit (large c, k, while c/k remains finite and small) both the holographic volume complexity and circuit complexity scales with k.

Global linear convergence of evolution strategies with recombination on scaling-invariant functions

Evolution Strategies (ESs) are stochastic derivative-free optimization algorithms whose most prominent representative, the CMA-ES algorithm, is widely used to solve difficult numerical optimization problems. We provide the first rigorous investigation of the linear convergence of step-size adaptive ESs involving a population and recombination, two ingredients crucially important in practice to be robust to local irregularities or multimodality. We investigate the convergence of step-size adaptive ESs with weighted recombination on composites of strictly increasing functions with continuously differentiable scaling-invariant functions with a global optimum. This function class includes functions with non-convex sublevel sets and discontinuous functions. We prove the existence of a constant r such that the logarithm of the distance to the optimum divided by the number of iterations converges to r. The constant is given as an expectation with respect to the stationary distribution of a Markov chain—its sign allows to infer linear convergence or divergence of the ES and is found numerically. Our main condition for convergence is the increase of the expected log step-size on linear functions. In contrast to previous results, our condition is equivalent to the almost sure geometric divergence of the step-size on linear functions.

Why KDAC? A general activation function for knowledge discovery

Deep learning oriented named entity recognition (DNER) has gradually become the paradigm of knowledge discovery, which greatly promotes domain intelligence. However, the activation function of DNER fails to treat gradient vanishing, no negative output or non-differentiable existence, which may impede the exploration of knowledge due to the omission and incomplete representation of the latent semantic. To break through the dilemma, we present a novel activation function termed KDAC. Detailly, KDAC is an aggregation function with multiple conversion modes. The backbone is the interaction between exponent and linearity, and the both ends are extended through adaptive linear divergence, which can surmount the gradient vanishing and no negative output. Crucially, the non-differentiable points can be alerted and eliminated by an approximate smoothing algorithm. KDAC has a series of brilliant properties, such as nonlinear, stable near-linear transformation and derivative, as well as dynamic style, etc. We perform experiments based on BERT-BiLSTM-CNN-CRF model on six benchmark datasets containing different domain knowledge, such as Weibo, Clinical, E-commerce, Resume, HAZOP and People's daily. The evaluation results show that KDAC is advanced and effective, and can provide more generalized activation to stimulate the performance of DNER. We hope that KDAC can be exploited as a promising activation function to devote itself to the construction of knowledge.

Transport of micro‐polar fluids in an exponentially diverging tube by means of peristaltic waves of dilating amplitude

AbstractThe paper models a peristaltically driven flow when the cross section of the tube changes exponentially. This may resemble the shape of the oesophagus when it suffers from sliding hiatus hernia, that is, when the abdomen protrudes through the hiatus. The fluid transported is considered micro‐polar while the peristaltic waves propagating along wall too dilate exponentially. Bulging, caused by herniation, in tube is examined considering two different cases: (i) tube diverging entirely from the first end to the other, and (ii) tube diverging partly limited to the other end only. Effects of dilating amplitude, the coupling number and the micro‐polar parameter are also investigated. Non‐linear governing equations are linearized by the method of low Reynolds number and long wavelength approximations and computer simulation is used to estimate the numerical results. It is observed that whether the tube diverges entirely or partly, pressure required for carrying the fluid is less, hence facilitating easier swallowing, which causes sliding hiatus hernia to go unnoticed. Exponential divergence in the tube geometry makes swallowing easier than linear divergence. While pressure increases with the coupling number, it declines with the micropolar parameter. Reflux region is further found to shrink once the wave amplitude dilates.

RI/MOM renormalization of the parton quasidistribution functions in lattice regularization

We analyze the lattice spacing dependence for the pion unpolarized matrix element of a quark bilinear operator with a Wilson link (parton quasidistribution functions operator, quasi-PDFs) in the rest frame, using 13 lattice spacings ranging from 0.032 to 0.121 fm. We compare results for three different fermion actions with or without good chiral symmetry on dynamical gauge ensembles from three collaborations. This investigation is motivated by the fact that the gauge link generates a $1/a$ divergence, the cancellation of which in many ratios can be numerically tricky. Indeed, our results show that this cancellation deteriorates with decreasing lattice spacing, and that the RI/MOM method leaves a linearly divergent residue for quasi-PDFs. We also show that in the Landau gauge the interaction between the Wilson link and the external state results in a linear divergence which depends on the discretized fermion action.

Genomic and acoustic differences separate Lilian’s Meadowlark (Sturnella magna lilianae) from Eastern (S. magna) and Western (S. neglecta) meadowlarks

AbstractExamining differences among recently diverged populations can provide insight into the traits and evolutionary mechanisms that drive or maintain divergence. The genus Sturnella includes 2 recently diverged species, Sturnella magna (Eastern Meadowlark) and S. neglecta (Western Meadowlark), the former of which has a complex of subspecies distributed across the Americas. Of the S. magna subspecies that occur in the United States, S. m. lilianae is the only one with a disjunct range, occurring in the southwestern United States and central Mexico. It also has markedly different song patterns than all other S. magna subspecies. In order to assess population differentiation, we performed whole-genome sequencing of 35 birds and analyzed song characteristics from 85 birds. Songs from each species and S. m. lilianae were diagnosable using linear discriminant function analysis and support divergence in song between all taxa. Phylogenetic analysis and admixture proportions support 3 distinct clades within North American meadowlarks, and tests of introgression failed to detect a significant signal. Overall, our results indicate that S. m. lilianae exhibits high levels of genetic and vocal differentiation from both S. magna and S. neglecta, with no evidence of introgression between any group, and forms a distinct evolutionary lineage. We thus recommend the elevation of S. m. lilianae to species status.

Divergence and quasi-isometry classes of random Gromov’s monsters

AbstractWe show that Gromov’s monsters arising from i.i.d. random labellings of expanders (that we call random Gromov’s monsters) have linear divergence along a subsequence, so that in particular they do not contain Morse quasigeodesics, and they are not quasi-isometric to Gromov’s monsters arising from graphical small cancellation labellings of expanders.Moreover, by further studying the divergence function, we show that there are uncountably many quasi-isometry classes of random Gromov’s monsters.

Black hole gluing in de Sitter space

We construct dynamical many-black-hole spacetimes with well-controlled asymptotic behavior as solutions of the Einstein vacuum equation with positive cosmological constant. We accomplish this by gluing Schwarzschild–de Sitter or Kerr–de Sitter black hole metrics into neighborhoods of points on the future conformal boundary of de Sitter space, under certain balance conditions on the black hole parameters. We give a self-contained treatment of solving the Einstein equation directly for the metric, given the scattering data we encounter at the future conformal boundary. The main step in the construction is the solution of a linear divergence equation for trace-free symmetric 2-tensors; this is closely related to Friedrich’s analysis of scattering problems for the Einstein equation on asymptotically simple spacetimes.

Dynamical quark mass generation in QCD3 within the Hamiltonian approach in Coulomb gauge

We investigate the equal-time (static) quark propagator in Coulomb gauge within the Hamiltonian approach to QCD in d = 2 spatial dimensions. Although the underlying Clifford algebra is very different from its counterpart in d = 3, the gap equation for the dynamical mass function has the same form. The additional vector kernel which was introduced in d = 3 to cancel the linear divergence of the gap equation and to preserve multiplicative renormalizability of the quark propagator makes the gap equation free of divergences also in d = 2.

Sleep Network Deterioration as a Function of Dim-Light-At-Night Exposure Duration in a Mouse Model.

Artificial light, despite its widespread and valuable use, has been associated with deterioration of health and well-being, including altered circadian timing and sleep disturbances, particularly in nocturnal exposure. Recent findings from our lab reveal significant sleep and sleep electroencephalogram (EEG) changes owing to three months exposure to dim-light-at-night (DLAN). Aiming to further explore the detrimental effects of DLAN exposure, in the present study, we continuously recorded sleep EEG and the electromyogram for baseline 24-h and following 6-h sleep deprivation in a varied DLAN duration scheme. C57BL/6J mice were exposed to a 12:12 h light:DLAN cycle (75lux:5lux) vs. a 12:12 h light:dark cycle (75lux:0lux) for one day, one week, and one month. Our results show that sleep was already affected by a mere day of DLAN exposure with additional complications emerging with increasing DLAN exposure duration, such as the gradual delay of the daily 24-h vigilance state rhythms. We conducted detrended fluctuation analysis (DFA) on the locomotor activity data following 1-month and 3-month DLAN exposure, and a significantly less healthy rest-activity pattern, based on the decreased alpha values, was found in both conditions compared to the control light-dark. Taking into account the behavioral, sleep and the sleep EEG parameters, our data suggest that DLAN exposure, even in the shortest duration, induces deleterious effects; nevertheless, potential compensatory mechanisms render the organism partly adjustable and able to cope. We think that, for this reason, our data do not always depict linear divergence among groups, as compared with control conditions. Chronic DLAN exposure impacts the sleep regulatory system, but also brain integrity, diminishing its adaptability and reactivity, especially apparent in the sleep EEG alterations and particular low alpha values following DFA.

Feature Extraction of Human Motion Video Based on Virtual Reality Technology

In virtual reality scenes, the premise of moving target recognition in video is accurate target segmentation and extraction of target low-level features. In order to distinguish moving targets, it is not enough to use the underlying features. Further extraction of structural features that reflect the target structure can improve the recognition and tracking of moving targets. In order to ensure the stability of the feature areas extracted from the three-channel most stable extremum region, this article proposes an improved algorithm of the three-channel most stable extremum region to improve the three-channel most stable extremum region. The algorithm can adaptively select the filters of each channel to filter the feature regions extracted from the three most stable extreme value regions. An action cycle is generally 30~50 frames, so it is faster and more advantageous to directly use the first 50 frames of video for processing. In this article, two feature representation methods of variance gait energy graph algorithm and image splitting algorithm are proposed. The variance energy graph algorithm significantly improves the recognition rate; image splitting enhances the robustness of behavior classification. This article proposes a feature representation algorithm of “distance from contour line to center line” to improve the recognition rate. By analyzing the feature extraction methods of principal component analysis, Fisher linear discriminant analysis and maximum divergence difference discriminant analysis, the main component discriminant analysis of row maximum divergence discriminant column and the two-dimensional two-dimensional maximum divergence discriminant analysis of row and column are proposed. This further enhances the ability to classify behaviors.

Fatty acid profile as a discriminatory tool for the origin of lamb muscle and adipose tissue from different pastoral grazing areas in North Macedonia – A short communication

The fatty acid (FA) profiles of lamb muscle and adipose tissue originating from ten different grazing areas in North Macedonia and an assessment of whether the meat origin could be distinguished on the basis of FA profile are presented. Muscle and adipose tissues of three-month-old male lambs (crossbreds of autochthonous Ovcepolian and Württemberg) reared on spring pastures were studied. Statistically significant differences in the individual FA contents, FA groups and FA ratios were observed between lamb tissues from the different geographic regions. Canonical discriminant analysis showed there was a significant linear divergence between tissues from almost all examined regions. The greatest weight in the differentiation of the different areas showed fatty acid ratios, C18:3n3, C18:1n9c and C20:5n3 for the muscle tissue, as well as C18:1n9c, C18:2n6c, C16:1 and C17:1 for the adipose tissue. This showed that the FA composition of muscle and adipose tissue obtained from lambs reared on pasture could serve as a useful indicator to aid differentiation of its geographic origin but it should be confirmed through further replicated studies.

Transverse momentum dependent parton quasidistributions

We investigate the transverse momentum dependent parton distributions (TMDs) in the quasi-parton-distribution framework. The long standing hurdle of the so-called pinch pole singularity from the space-like gauge links in the TMD definitions can be resolved by the finite length of the gauge link along the hadron moving direction. In addition, with the soft factor subtraction, the quasi-TMD is free of linear divergence. We further demonstrate that the energy evolution equation of the quasi-TMD a.k.a. the Collins-Soper evolution, only depends on the hadron momentum. This leads to a clear matching between the quasi-TMD and the standard TMDs.

Aeroelastic Stability Analysis of Damaged High-Aspect-Ratio Composite Wings

In this paper, linear and nonlinear divergence and flutter analyses for damaged high-aspect-ratio wings undergoing large deformations are presented. To exploit the computational efficiency of reduced dimensional beam models along with the accuracy of three-dimensional continuum models, a joined multidimensional finite element approach is proposed. To this end, the computational model of a high-aspect-ratio wing is divided into two parts: a one-dimensional geometrically exact beam model, which constitutes most of the wing structure, and a small three-dimensional region encompassing structural damages. The two parts are rigorously joined together at their intersection through a transformation derived using the variational asymptotic method. Aerodynamic forces and moments, acting upon the wing, are accounted for using a two-dimensional finite-state unsteady aerodynamic theory. The wing structure is made of layered composite materials with various layup arrangements. The preexisting structural damages are assumed to be in the form of crack and delamination. The intensity and locations of the structural damages are varying along the wing. Accordingly, linear and nonlinear aeroelastic stability analyses are carried out in order to study the effects of various structural damages on the divergence and flutter boundaries of the wing.

Convergence of surface energy calculations for various methods: (0 0 1) hematite as benchmark

Different methods for calculating the surface energy from ab initio simulations are applied to the relaxed (0 0 1) surface of the metal oxide hematite (-Fe2O3). The simulations are carried out with a rather moderate k-point grid with shrinking factors of (6 6 6) for all bulk and (6 6) for all slab simulations. Very good convergence is obtained if a linear fit of the slab energies with respect to the number of layers in the slab is performed. In comparison to the other methods employed, this procedure is ultimately the most accurate and reliable method for extracting convergent surface energies from (0 0 1) hematite slabs. Additionally, we propose a way to determine the least possible starting point for calculating the surface energy by the linear-fit method. Furthermore, we find the Boettger method to perform nearly equally well, if the bulk energy is extracted from the energy difference per layer between the slabs with 12 and 18 layers thickness. Both methods give a surface energy of 2.43 J m−2 with a deviation of less than 0.005 J m−2. The standard approach, which uses a separate bulk simulation, instead shows a significant linear divergence with increasing number of layers in the slab. We also carried out bulk simulations with a surface-oriented bulk unit cell, but found it in our case not to improve the convergence of the standard approach.