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The Fréchet distance is a popular measure of dissimilarity for polygonal curves. It is defined as a min–max formulation that considers all orientation-preserving bijective mappings between the two curves. Because of its susceptibility to noise, Driemel and Har-Peled introduced the shortcut Fréchet distance in 2012, where one is allowed to take shortcuts along one of the curves, similar to the edit distance for sequences. We analyse the parameterised version of this problem, where the number of shortcuts is bounded by a parameter \(k\). The corresponding decision problem can be stated as follows: Given two polygonal curves \(T\) and \(B\) of at most \(n\) vertices, a parameter \(k\) and a distance threshold \(\delta\) , is it possible to introduce \(k\) shortcuts along \(B\) such that the Fréchet distance of the resulting curve and the curve \(T\) is at most \(\delta\) ? We study this problem for polygonal curves in the plane. We provide a complexity analysis for this problem with the following results: (1) there exists a decision algorithm with running time in \(\mathcal{O}(kn^{2k+2}\log n)\) ; (2) assuming the exponential-time hypothesis (ETH), there exists no algorithm with running time bounded by \(n^{o(k)}\). In contrast, we also show that efficient approximate decider algorithms are possible, even when \(k\) is large. We present a \((3+\varepsilon)\) -approximate decider algorithm with running time in \(\mathcal{O}(kn^{2}\log^{2}n)\) for fixed \(\varepsilon\). In addition, we can show that, if \(k\) is a constant and the two curves are \(c\) -packed for some constant \(c\) , then the approximate decider algorithm runs in near-linear time. [ABSTRACT FROM AUTHOR]

In Cz–Si growth, the shape of the solid–liquid interface and the v/G ratio significantly impact crystal quality. This study utilizes a data‐driven approach, employing multilayer perceptron (MLP) neural networks and Bayesian optimization, to investigate the scale‐up process of Cz–Si under conditions of partial similarity. The focus is on exploring the influence of various process and furnace geometry parameters, as well as radiation shield material properties, on the critical measures of crystal quality. Axisymmetric CFD modeling produces 340 sets of 18D raw data, from which 14‐dimensionless derived data tuples are generated for the design and training of the MLP. The best MLP obtained demonstrates the ability to accurately assess the complex nonlinear dependencies among dimensionless numbers derived from CFD data and, on the output side, interface deflection and v/G. These relationships, crucial for scale‐up, are successfully generalized across a wide range of parameters. [ABSTRACT FROM AUTHOR]

Imaging studies help us understand the important role of brainstem and midbrain regions in human trigeminal pain processing without solving the question of how these regions actually interact. In the current study, we describe this connectivity and its dynamics during nociception with a novel analytical approach called Partial Similarity (PS). We developed PS specifically to estimate the communication between individual hubs of the network in contrast to the overall communication within that network. Partial Similarity works on trial-to-trial variance of neuronal activity acquired with functional magnetic resonance imaging. It discovers direct communication between two hubs considering the remainder of the network as confounds. A similar method to PS is Representational Similarity, which works with ordinary correlations and does not consider any external influence on the communication between two hubs. Particularly the combination of Representational Similarity and Partial Similarity analysis unravels brainstem dynamics involved in trigeminal pain using the spinal trigeminal nucleus (STN)—the first relay station of peripheral trigeminal input—as a seed region. The combination of both methods can be valuable tools in discovering the network dynamics in fMRI and an important instrument for future insight into the nature of various neurological diseases like primary headaches.

The similarity measuring between 3D objects can be reduced to a distance between their descriptors. Therefore, the principal challenge is the mapping of objects into reduced and compact representations referred to as descriptors. Generally speaking, descriptors based on global features cannot be effective to describe incomplete 3D objects. This paper presents a novel partial 3D object retrieval approach called adaptive slices clustering (ASC). To ensure that similar objects will be decomposed similarly, normalization is applied to the objects as a preprocessing step. Then, we characterize each object by a set of 2D slices corresponding to its three principal axes, transforming the shape-matching problem between objects into similarity measuring between their slices. Next, we choose among the extracted 2D slices the most representative to reduce searching time without diminishing the performance of our approach. The results show that our approach provides better performance than the descriptors that characterize the whole object. [ABSTRACT FROM AUTHOR]

In this paper, we propose a method for computing partial functional correspondence between non-rigid shapes. We use perturbation analysis to show how removal of shape parts changes the Laplace-Beltrami eigenfunctions, and exploit it as a prior on the spectral representation of the correspondence. Corresponding parts are optimization variables in our problem and are used to weight the functional correspondence; we are looking for the largest and most regular (in the Mumford-Shah sense) parts that minimize correspondence distortion. We show that our approach can cope with very challenging correspondence settings. [ABSTRACT FROM AUTHOR]

Neighbor-based collaborative filtering is one of the most practical recommendation approaches that is renowned because of its simplicity and explanation. However, the big limitation is its high computational complexity. It is demonstrated that clustering-based algorithms, that restrict the neighborhood space, speed up the recommendation process at the price of lower accuracy. We propose a new algorithm, called TasteMiner that efficiently learns partial users taste to restrict the neighborhood space. We frame TasteMiner as a method for neighborhood collaborative filtering, and show its effectiveness compared to previous algorithms [ABSTRACT FROM AUTHOR]

This paper proposes a fast method for measuring the partial Similarity between 3D Model and 3D point Cloud (SimMC). It is crucial to measure SimMC for many point cloud-related applications such as 3D object retrieval and inverse procedural modelling. In our proposed method, the surface area of model and the Distance from Model to point Cloud (DistMC) are exploited as measurements to calculate SimMC. Here, DistMC is defined as the weighted distance of the distances between points sampled from model and point cloud. Similarly, Distance from point Cloud to Model (DistCM) is defined as the average distance of the distances between points in point cloud and model. In order to reduce huge computational burdens brought by calculation of DistCM in some traditional methods, we define SimMC as the ratio of weighted surface area of model to DistMC. Compared to those traditional SimMC measuring methods that are only able to measure global similarity, our method is capable of measuring partial similarity by employing distance-weighted strategy. Moreover, our method is able to be faster than other partial similarity assessment methods. We demonstrate the superiority of our method both on synthetic data and laser scanning data. [ABSTRACT FROM AUTHOR]

Highlights: [•] We propose a new method for analyzing time series data. [•] The method detects partial similar patterns in simultaneously occurring time series data at different locations. [•] A graphical representation helps us understand the similarity between the data and classify them into smaller subgroups. [•] Numerical measures evaluate the effectiveness of clusters and provide a means of testing their statistical significance. [Copyright &y& Elsevier]

This paper provides a defence of the account of partial resemblances between properties according to which such resemblances are due to partial identities of constituent properties. It is argued, first of all, that the account is not only required by realists about universals à la Armstrong, but also useful (of course, in an appropriately re-formulated form) for those who prefer a nominalistic ontology for material objects. For this reason, the paper only briefly considers the problem of how to conceive of the structural universals first posited by Armstrong in order to explain partial resemblances, and focuses instead on criticisms that have been levelled against the theory (by Pautz, Eddon, Denkel and Gibb) and that apply regardless of one's preferred ontological framework. The partial identity account is defended from these objections and, in doing so, a hitherto quite neglected connection-between the debate about partial similarity as partial identity and that concerning ontological finitism versus infinitism-is looked at in some detail. [ABSTRACT FROM AUTHOR]

Similarity is one of the most important abstract concepts in human perception of the world. In computer vision, numerous applications deal with comparing objects observed in a scene with some a priori known patterns. Often, it happens that while two objects are not similar, they have large similar parts, that is, they are partially similar. Here, we present a novel approach to quantify partial similarity using the notion of Pareto optimality. We exemplify our approach on the problems of recognizing non-rigid geometric objects, images, and analyzing text sequences. [ABSTRACT FROM AUTHOR]

Analysis of deformable two-dimensional shapes is an important problem, encountered in numerous pattern recognition, computer vision and computer graphics applications. In this paper, we address three major problems in the analysis of non-rigid shapes: similarity, partial similarity, and correspondence. We present an axiomatic construction of similarity criteria for deformation-invariant shape comparison, based on intrinsic geometric properties of the shapes, and show that such criteria are related to the Gromov-Hausdorff distance. Next, we extend the problem of similarity computation to shapes which have similar parts but are dissimilar when considered as a whole, and present a construction of set-valued distances, based on the notion of Pareto optimality. Finally, we show that the correspondence between non-rigid shapes can be obtained as a byproduct of the non-rigid similarity problem. As a numerical framework, we use the generalized multidimensional scaling (GMDS) method, which is the numerical core of the three problems addressed in this paper. [ABSTRACT FROM AUTHOR]

Imaging studies help us understand the important role of brainstem and midbrain regions in human trigeminal pain processing without solving the question of how these regions actually interact. In the current study, we describe this connectivity and its dynamics during nociception with a novel analytical approach called Partial Similarity (PS). We developed PS specifically to estimate the communication between individual hubs of the network in contrast to the overall communication within that network. Partial Similarity works on trial-to-trial variance of neuronal activity acquired with functional magnetic resonance imaging. It discovers direct communication between two hubs considering the remainder of the network as confounds. A similar method to PS is Representational Similarity, which works with ordinary correlations and does not consider any external influence on the communication between two hubs. Particularly the combination of Representational Similarity and Partial Similarity analysis unravels brainstem dynamics involved in trigeminal pain using the spinal trigeminal nucleus (STN)—the first relay station of peripheral trigeminal input—as a seed region. The combination of both methods can be valuable tools in discovering the network dynamics in fMRI and an important instrument for future insight into the nature of various neurological diseases like primary headaches. [ABSTRACT FROM AUTHOR]