Auxiliary Metric Research Articles

Virtual multi-staining in a single-section view for renal pathology using generative adversarial networks

Sections stained in periodic acid-Schiff (PAS), periodic acid-methenamine silver (PAM), hematoxylin and eosin (H&E), and Masson's trichrome (MT) stain with minimal morphological discordance are helpful for pathological diagnosis in renal biopsy. Here, we propose an artificial intelligence-based re-stainer called PPHM-GAN (PAS, PAM, H&E, and MT-generative adversarial networks) with multi-stain to multi-stain transformation capability. We trained three GAN models on 512 × 512-pixel patches from 26 training cases. The model with the best transformation quality was selected for each pair of stain transformations by human evaluation. Frechet inception distances, peak signal-to-noise ratio, structural similarity index measure, contrast structural similarity, and newly introduced domain shift inception score were calculated as auxiliary quality metrics. We validated the diagnostic utility using 5120 × 5120 patches of ten validation cases for major glomerular and interstitial abnormalities. Transformed stains were sometimes superior to original stains for the recognition of crescent formation, mesangial hypercellularity, glomerular sclerosis, interstitial lesions, or arteriosclerosis. 23 of 24 glomeruli (95.83 %) from 9 additional validation cases transformed to PAM, PAS, or MT facilitated recognition of crescent formation. Stain transformations to PAM (p = 4.0E-11) and transformations from H&E (p = 4.8E-9) most improved crescent formation recognition. PPHM-GAN maximizes information from a given section by providing several stains in a virtual single-section view, and may change the staining and diagnostic strategy.

RICH: A rapid method for image-text cross-modal hash retrieval

Deep cross-modal hash retrieval (DCMHR) methods can effectively analyze the correlation of multimodal data while maintaining efficiency. However, to pursue better accuracy, most existing hash methods forget that the original purpose of introducing hash technology is to reduce training consumption, and overtraining also leads to overfitting. This paper proposes a rapid method for image-text cross-modal hash retrieval (RICH) based on DenseNet and multi-head attention (MHA) BOW (Bag of Words), which makes full use of unlabeled samples and uses EarlyStop in training. To fully extract image case features, we propose multiple dense feature sampling for cross-modal retrieval. It is worth noting that this method applies DenseNet and EarlyStop to unsupervised cross-modal retrieval for the first time and greatly reduces training costs while keeping good results. Then it is discussed that the MHA be carried in the TxtNet, which can extract neglected features. Furthermore, to alleviate the heterogeneous gap between different modalities, we also use the auxiliary similarity metrics. Experiments on three datasets show that the average performance of this method is higher than most of the DCMHR methods. In addition, compared to most of the SoTA unsupervised DCMHR methods, the training cost and stability of RICH are more excellent, which proves the effectiveness and superiority of this method.

Development of a classification model for Cynanchum wilfordii and Cynanchum auriculatum using convolutional neural network and local interpretable model-agnostic explanation technology.

Cynanchum wilfordii is a perennial tuberous root in the Asclepiadaceae family that has long been used medicinally. Although C. wilfordii is distinct in origin and content from Cynancum auriculatum, a genus of the same species, it is difficult for the public to recognize because the ripe fruit and root are remarkably similar. In this study, images were collected to categorize C. wilfordii and C. auriculatum, which were then processed and input into a deep-learning classification model to corroborate the results. By obtaining 200 photographs of each of the two cross sections of each medicinal material, approximately 800 images were employed, and approximately 3200 images were used to construct a deep-learning classification model via image augmentation. For the classification, the structures of Inception-ResNet and VGGnet-19 among convolutional neural network (CNN) models were used, with Inception-ResNet outperforming VGGnet-19 in terms of performance and learning speed. The validation set confirmed a strong classification performance of approximately 0.862. Furthermore, explanatory properties were added to the deep-learning model using local interpretable model-agnostic explanation (LIME), and the suitability of the LIME domain was assessed using cross-validation in both situations. Thus, artificial intelligence may be used as an auxiliary metric in the sensory evaluation of medicinal materials in future, owing to its explanatory ability.

Convergence and Riemannian bounds on Lagrangian submanifolds

We consider collections of Lagrangian submanifolds of a given symplectic manifold which respect uniform bounds of curvature type coming from an auxiliary Riemannian metric. We prove that, for a large class of metrics on these collections, convergence to an embedded Lagrangian submanifold implies convergence to it in the Hausdorff metric. This class of metrics includes well-known metrics such as the Lagrangian Hofer metric, the spectral metric and the shadow metrics introduced by Biran et al. [Lagrangian shadows and triangulated categories, Astérisque 426 (2021) 1–128]. The proof relies on a version of the monotonicity lemma, applied on a carefully-chosen metric ball.

Alleviating Data Sparsity Problems in Estimated Time of Arrival via Auxiliary Metric Learning

With millions of people using ride-hailing platforms for daily travel, estimated time of arrival (ETA) has become a significant problem in intelligent transportation systems and attracted considerable attention recently. Deep learning-based ETA methods have achieved promising results using massive spatial-temporal data. However, we find that the prediction accuracy is not satisfactory in practical applications due to the prevalent data sparsity problems. Instead of focusing on the average prediction performance as many other methods, this study aims to alleviate the data sparsity problems in ETA to enhance user experience. In general, the data sparsity problems arise from two aspects. The first is the road network, where many links are only traversed by few floating cars. The second aspect is drivers, where many drivers’ trajectories are too scarce (e.g., with only 3 trip records). To alleviate the sparsity in road network, we propose a Road Network Metric Learning framework for ETA (RNML-ETA), where an auxiliary metric learning task is used to improve the link-embedding, especially for links with insufficient data. A novel triangle loss is proposed to improve metric learning effectiveness for links. Experiments on massive real-world data show that RNML-ETA outperforms competing methods by promoting the cold links with limited data. Furthermore, we propose a novel unified framework to Alleviate Data Sparsity problems in ETA (ADS-ETA) by extending RNML-ETA with an additional auxiliary task for driver ID embedding. Results with extensive experiments demonstrate that ADS-ETA can effectively alleviate the data sparsity problems caused by road network and driver sparsity.

Null and timelike circular orbits from equivalent 2D metrics

The motion of particles on spherical dimensional spacetimes can, under some assumptions, be described by the curves on a two-dimensional manifold, the optical and Jacobi manifolds for null and timelike curves, respectively. In this paper we resort to auxiliary two-dimensional metrics to study circular geodesics of generic static, spherically symmetric, and asymptotically flat dimensional spacetimes, whose functions are at least C 2 smooth. This is done by studying the Gaussian curvature of the bidimensional equivalent manifold as well as the geodesic curvature of circular paths on these. This study considers both null and timelike circular geodesics. The study of null geodesics through the optical manifold retrieves the known result of the number of light rings on the spacetime outside a black hole and on spacetimes with horizonless compact objects. With an equivalent procedure we can formulate a similar theorem on the number of marginally stable timelike circular orbits of a given spacetime satisfying the previously mentioned assumptions.

Utilizing Grasp Monitoring to Predict Microsurgical Expertise

IntroductionMost microsurgical procedures require the surgeon to use tools to grasp and hold fragile objects in the surgical site. Prior research on grasping in surgery has mostly either been in other surgical techniques or used grasping as an auxiliary metric. We focus on microsurgery and investigate what grasping can tell about microsurgical skill and suturing performance. This study lays groundwork for using automatic detection of grasps to evaluate surgical skill. MethodsFive expert surgeons and six novices completed sutures on a microsurgical training board. Video recordings of the performance were annotated for the number of grasps, while an eye tracker recorded the participants’ pupil dilations for cognitive workload assessment. Performance was measured with suturing duration and the University of Western Ontario Microsurgical Skills Assessment instrument (UWOMSA). Differences in skill, suturing performance and cognitive workload were compared with grasping behavior. ResultsNovices needed significantly more grasps to complete sutures and failed to grasp more often than the experts. The number of grasps affected the suturing duration more in novices. Decreasing suturing efficiency as measured by UWOMSA instrument was associated with increase in grasps, even when we controlled for overall skill differences. Novices displayed larger pupil dilations when averaged over a sufficiently large sample, and the difference increased after the grasp. ConclusionsGrasping action during microsurgical procedures can be used as a conceptually simple yet objective proxy in microsurgical performance assessment. If the grasps could be detected automatically, they could be used to aid in computational evaluation of surgical trainees’ performance.

A heuristic for two-echelon urban distribution systems

The negative impacts of urban freight transport have fostered the design of new distribution systems for inner city deliveries. One of the proposed city logistics solutions is the establishment of two-echelon distribution systems, where freight originating from the periphery of the city is transferred at intermediate locations (satellites) from larger vehicles (urban freighters) to smaller more environmentally friendly vehicles (city freighters), deemed more suited to operate in the city centre. In this paper, we address a variant of the two-echelon (capacitated) vehicle routing problem (2E-CVRP) arising in the context of city logistics encompassing characteristics such as a heterogeneous fleet of city freighters, time windows, vehicles synchronisation at satellites, direct deliveries, the possibility of freight transfers at customers, and multiple trips by city freighters. We propose a heuristic solution method for this problem based on a Variable Neighbourhood Search (VNS) heuristic, as well as a set of auxiliary evaluation metrics designed to support the decision making process. Preliminary results show the flexibility of the proposed heuristic to account for different problem characteristics, as well as the impacts of considering different best insertion criteria for the initial solution construction. Additionally, the proposed evaluation metrics have allowed for an improved assessment of the trade-offs between different city logistic solutions, and may be considered when developing decision support systems.

Modelling Aboveground Biomass Carbon Stock of the Bohai Rim Coastal Wetlands by Integrating Remote Sensing, Terrain, and Climate Data

Remotely sensed vegetation indices (VIs) have been widely used to estimate the aboveground biomass (AGB) carbon stock of coastal wetlands by establishing Vis-related linear models. However, these models always have high uncertainties due to the large spatial variation and fragmentation of coastal wetlands. In this paper, an efficient coastal wetland AGB model for the Bohami Rim coastal wetlands was presented based on multiple data sets. The model was developed statistically with 7 independent variables from 23 metrics derived from remote sensing, topography, and climate data. Compared to previous models, it had better performance, with a root mean square error and r value of 188.32 g m−2 and 0.74, respectively. Using the model, we firstly generated a regional coastal wetland AGB map with a 10 m spatial resolution. Based on the AGB map, the AGB carbon stock of the Bohai Rim coastal wetland was 2.11 Tg C in 2019. The study demonstrated that integrating emerging high spatial resolution multi-remote sensing data and several auxiliary metrics can effectively improve VIs-based coastal wetland AGB models. Such models with emerging freely available data sets will allow for the rapid monitoring and better understanding of the special role that “blue carbon” plays in global carbon cycle.

Free data at spacelike {mathscr {I}} and characterization of Kerr-de Sitter in all dimensions

We study the free data in the Fefferman–Graham expansion of asymptotically Einstein (n+1)-dimensional metrics with non-zero cosmological constant. We analyze the relation between the electric part of the rescaled Weyl tensor at {mathscr {I}}, D, and the free data at {mathscr {I}}, namely a certain traceless and transverse part of the n-th order coefficient of the expansion mathring{g}_{(n)}. In the case Lambda <0 and Lorentzian signature, it was known [23] that conformal flatness at {mathscr {I}} is sufficient for D and mathring{g}_{(n)} to agree up to a universal constant. We recover and extend this result to general signature and any sign of non-zero Lambda . We then explore whether conformal flatness of {mathscr {I}} is also neceesary and link this to the validity of long-standing open conjecture that no non-trivial purely magnetic Lambda -vacuum spacetimes exist. In the case of {mathscr {I}} non-conformally flat we determine a quantity constructed from an auxiliary metric which can be used to retrieve mathring{g}_{(n)} from the (now singular) electric part of the Weyl tensor. We then concentrate in the Lambda >0 case where the Cauchy problem at {mathscr {I}} of the Einstein vacuum field equations is known to be well-posed when the data at {mathscr {I}} are analytic or when the spacetime has even dimension. We establish a necessary and sufficient condition for analytic data at {mathscr {I}} to generate spacetimes with symmetries in all dimensions. These results are used to find a geometric characterization of the Kerr-de Sitter metrics in all dimensions in terms of its geometric data at null infinity.

First-Order Formalism and Thick Branes in Mimetic Gravity

In this paper, we investigate thick branes generated by a scalar field in mimetic gravity theory, which is inspired by considering the conformal symmetry under the conformal transformation of an auxiliary metric. By introducing two auxiliary super-potentials, we transform the second-order field equations of the system into a set of first-order equations. With this first-order formalism, several types of analytical thick brane solutions are obtained. Then, tensor and scalar perturbations are analyzed. We find that both kinds of perturbations are stable. The effective potentials for the tensor and scalar perturbations are dual to each other. The tensor zero mode can be localized on the brane while the scalar zero mode cannot. Thus, the four-dimensional Newtonian potential can be recovered on the brane.

Positive Energy Functional for Massless Scalars in Rotating Black Hole Backgrounds of Maximal Ungauged Supergravity.

We outline a proof of the stability of a massless neutral scalar field ψ in the background of a wide class of four dimensional asymptotically flat rotating and "electrically charged" solutions of supergravity, and the low energy limit of string theory, known as STU metrics. Despite their complexity, we find it possible to circumvent the difficulties presented by the existence of ergo regions and the related phenomenon of superradiance in the original metrics by following a strategy due to Whiting, and passing to an auxiliary metric admitting an everywhere lightlike Killing field and constructing a scalar field ψ (related to a possible unstable mode ψ by a nonlocal transformation) which satisfies the massless wave equation with respect to the auxiliary metric. By contrast with the case for ψ, the associated energy density of ψ is not only conserved but is also non-negative.

Mimetic f(T) teleparallel gravity and cosmology

We formulate mimetic theory in f(T) teleparallel gravity where T is torsion scalar. It is shown that the construction of the mimetic theory in the teleparallel gravity requires the vierbeins to be left unchanged and the confomal transformation performed on the Minkowski metric of the tangent space. It is further argued that the conformal degree of freedom in this teleparallel mimetic theory becomes dynamical and mimics the behavior of cold dark matter. We also show that it is possible to employ the Lagrange multipliers method to formulate the mimetic theory in an f(T) theory without any auxiliary metric. The mimetic f(T) theory is examined by the method of dynamical system and it is found that there are five fixed points representing inflation, radiation, matter, mimetic dark matter and dark energy dominated eras in the theory if some conditions are satisfied. We examined the power-law model and its phase trajectories with these conditions.

Braneworld mimetic f(R) gravity

Following our recent work on braneworld mimetic gravity, in this paper, we study an extension of braneworld mimetic gravity to the case that the gravitational sector on the brane is modified in the spirit of [Formula: see text] theories. We assume the physical 5D bulk metric in the Randall–Sundrum II braneworld scenario consists of a 5D scalar field (which mimics the dark sectors on the brane) and an auxiliary 5D metric. We find the 5D Einstein’s field equations and the 5D equation of motion of the bulk scalar field in this setup. By using the Gauss–Codazzi equations, we obtain the induced Einstein’s field equations on the brane. Finally, by adopting the FRW background, we find the Friedmann equation on the brane in this [Formula: see text] mimetic braneworld setup.

Analysis of User Control Attainment in SMR-based Brain Computer Interfaces

ContextSensorimotor rhythms (SMR) have been the neuronal phenomena of choice in non-invasive EEG-based endogenous brain computer interfaces (BCIs) for more than two decades and SMR-based BCIs have achieved the highest degree of freedom control so far. Nevertheless, they are subject to long periods of training prior to attaining a satisfactory level of control requiring users to learn to modulate their rhythms. The goal of this work is to analyse this problem, discuss the causes of the slow rise in performance and provide recommendations on alternative solutions to quicken control attainment. MethodsThe study has been conducted by both theoretical and empirical analysis. A theoretical model has been developed that explains the principle operation of SMR-based BCIs focusing on major performance contributors respectively the user, periodic feature selection and the translation model thus contrasting user adaptation and machine learning. Five able-bodied subjects (age: 26±2.55) participated in six sessions of online computer cursor control experiments over three weeks to evaluate control attainment performances and gather data for statistical analysis (∼1152 trials per subject). Correlation (r2) between user control features and target position over sessions was assessed as an estimate of neural adaptation and the predictive power of the translation algorithm (10 × 10 fold cross-validation) was calculated over sessions as an estimate of machine adaptation. Auxiliary performance metrics were evaluated. ResultsFeatures-target correlation increased over sessions, while at the same time the predictive accuracy (R2) of the translation model remained averagely steady and very low (Rbest2=0.04) demonstrating continuous user adaptation and low model predictive accuracy. Periodic feature selection was theoretically discussed to be very instrumental and its relevance was empirically illustrated. ConclusionsThe study concludes that the slow control attainment in SMR-based BCIs is due to its reliance on user training (neural adaptation) which is adaptive but too slow in the context of SMR modulations and due to the weak decoding of the neuronal phenomenon utilised by the user. As a recommendation, the optimality of the feature selection algorithm could be looked at to guarantee the use of the most relevant features. However and most importantly the predictive power of the translation model should be significantly improved in order to quicken control attainment as thereafter the control attainment effort could be shifted from neural adaptation to machine learning.

Composite graviton self-interactions in a model of emergent gravity

We consider a theory of scalars minimally coupled to an auxiliary background metric. The theory is generally covariant and subject to the constraint of vanishing energy-momentum tensor. Eliminating the auxiliary metric leads to a reparametrization invariant, non-polynomial, metric-independent action for the scalar fields. Working in the limit of a large number of physical scalars, a composite massless spin-2 state, the graviton, was identified in previous work, in a two-into-two scalar scattering process. Here, we further explore the possibility that dynamical emergent gravity is a natural feature of generally covariant quantum field theories, by studying the self-interactions of the emergent composite graviton. We show that the fine-tuning previously imposed to ensure the vanishing of the cosmological constant, as well as the existence of the massless spin-2 state, also assures that the emergent graviton's cubic self-interactions are consistent with those of Einstein's general relativity, up to higher-derivative corrections. We also demonstrate in a theory with more than one type of scalar that the composite graviton coupling is universal.

The trivial role of torsion in projective invariant theories of gravity with non-minimally coupled matter fields

We study a large family of metric-affine theories with a projective symmetry, including non-minimally coupled matter fields which respect this invariance. The symmetry is straightforwardly realised by imposing that the connection only enters through the symmetric part of the Ricci tensor, even in the matter sector. We leave the connection completely free (including torsion), and obtain its general solution as the Levi-Civita connection of an auxiliary metric, showing that the torsion only appears as a projective mode. This result justifies the widely used condition of setting vanishing torsion in these theories as a simple gauge choice. We apply our results to some particular cases considered in the literature, including the so-called Eddington-inspired-Born–Infeld theories among others. We finally discuss the possibility of imposing a gauge fixing where the connection is metric compatible, and comment on the genuine character of the non-metricity in theories where the two metrics are not conformally related.

Primordial cosmology in mimetic born-infeld gravity

The Eddington-inspired-Born-Infeld (EiBI) model is reformulated within the mimetic approach. In the presence of a mimetic field, the model contains non-trivial vacuum solutions which could be free of spacetime singularity because of the Born-Infeld nature of the theory. We study a realistic primordial vacuum universe and prove the existence of regular solutions, such as primordial inflationary solutions of de Sitter type or bouncing solutions. Besides, the linear instabilities present in the EiBI model are found to be avoidable for some interesting bouncing solutions in which the physical metric as well as the auxiliary metric are regular at the background level.

Singular instantons in Eddington-inspired-Born-Infeld gravity

In this work, we investigate O(4)-symmetric instantons within the Eddington-inspired-Born-Infeld gravity theory (EiBI) . We discuss the regular Hawking-Moss instanton and find that the tunneling rate reduces to the General Relativity (GR) value, even though the action value is different by a constant. We give a thorough analysis of the singular Vilenkin instanton and the Hawking-Turok instanton with a quadratic scalar field potential in the EiBI theory. In both cases, we find that the singularity can be avoided in the sense that the physical metric, its scalar curvature and the scalar field are regular under some parameter restrictions, but there is a curvature singularity of the auxiliary metric compatible with the connection. We find that the on-shell action is finite and the probability does not reduce to its GR value. We also find that the Vilenkin instanton in the EiBI theory would still cause the instability of the Minkowski space, similar to that in GR, and this is observationally inconsistent. This result suggests that the singularity of the auxiliary metric may be problematic at the quantum level and that these instantons should be excluded from the path integral.

Ghost free massive gravity with singular reference metrics

An auxiliary metric (reference metric) is inevitable in massive gravity theory. In the scenario of gauge/gravity duality, a singular reference metric corresponds to momentum dissipations, which describes the electric and heat conductivity for normal conductors. We demonstrate in detail that the massive gravity with singular reference metric is ghost-free.