Explore the vast range of titles available.

We consider the commutative limit of matrix geometry described by a large-N sequence of some Hermitian matrices. Under some assumptions, we show that the commutative geometry possesses a Kaehler structure. We find an explicit relation between the Kaehler structure and the matrix configurations which define the matrix geometry. We also discuss a relation between the matrix configurations and those obtained from the geometric quantization.

We provide a brief invitation to the novel understanding [1, 2, 3, 4] of anyonic topological order in fractional quantum (anomalous) Hall systems, via “extraordinary” quantization of effective magnetic flux in Cohomotopy — following our presentation at ISQS29 [5].

We formulate a string field theory for open$$\\mathcal{N}=2$$strings with an A ∞ algebra structure. Starting from the BRST cohomology relative to the U(1) anti-ghost zero-mode, we generalize [arXiv:1312.2948] and constructed all interacting vertices recursively and without singularity. We also show that our string field theory reproduces the correct perturbative S-matrix.

K-Means is a simple clustering algorithm that has the ability to throw large amounts of data, partition datasets into several clusters k. The algorithm is quite easy to implement and run, relatively fast and efficient. Another division of K-Means still has several weaknesses, namely in determining the number of clusters, determining the cluster center. The results of the cluster formed from the K-means method is very dependent on the initiation of the initial cluster center value provided. This causes the results of the cluster to be a solution that is locally optimal. This research was conducted to overcome the weaknesses in the K-Means algorithm, namely: improvements to the K-Means algorithm produce better clusters, namely the application of Sum Of Squared Error (SSE) to help K-Means Clustering in determining the optimum number of clusters, From this modification process, it is expected that the cluster center obtained will produce clusters, where the cluster members have a high level of similarity. Improving the performance of the K-Means cluster will be applied to determining the number of clusters using the elbow method.

The Wasserstein distance between two probability measures on a metric space is a measure of closeness with applications in statistics, probability, and machine learning. In this work, we consider the fundamental question of how quickly the empirical measure obtained from n independent samples from µ approaches µ in the Wasserstein distance of any order. We prove sharp asymptotic and finite-sample results for this rate of convergence for general measures on general compact metric spaces. Our finite-sample results show the existence of multi-scale behavior, where measures can exhibit radically different rates of convergence as n grows.

Quantization, which involves bit-width reduction, is considered as one of the most effective approaches to rapidly and energy-efficiently deploy deep convolutional neural networks (DCNNs) on resource-constrained embedded hardware. However, bit-width reduction on the weights and activations of DCNNs seriously degrades accuracy. To solve this problem, in this paper we propose a mixed hardware-friendly quantization (MXQN) method that applies fixed-point quantization and logarithmic quantization for DCNNs without the necessity to retrain and fine-tune the DCNN. Our MXQN algorithm is a multi-staged process where, first, we employ a signal-to-quantization-noise ratio (SQNR) process as the metric to estimate the interplay between the parameter quantization errors of each layer and the overall model prediction accuracy. Then, we utilize a fixed-point quantization process to quantize weights, and depending on the SQNR metric we empirically select either a logarithmic or a fixed-point quantization process to quantize activations. For improved accuracy, we propose an optimized logarithmic quantization scheme that affords a fine-grained step size. We evaluate the performance of MXQN utilizing the VGG16 network on the MNIST, CIFAR-10, CIFAR-100, and the ImageNet datasets, as well as VGG19 and ResNet (ResNet18, ResNet34, ResNet50) networks on the ImageNet, and demonstrate that the MXQN-quantized DCNN despite not being retrained and fine-tuned, it still achieves high accuracy close to the original DCNN.

Every clock is a physical system and thereby ultimately quantum. A naturally arising question is thus how to describe time evolution relative to quantum clocks and, specifically, how the dynamics relative to different quantum clocks are related. This is a particularly pressing issue in view of the multiple choice facet of the problem of time in quantum gravity, which posits that there is no distinguished choice of internal clock in generic general relativistic systems and that different choices lead to inequivalent quantum theories. Exploiting a recent unifying approach to switching quantum reference systems [Vanrietvelde et al 2020 Quantum 4 225; Vanrietvelde et al 2018 arXiv:1809.05093[quant-ph])], we exhibit a systematic method for switching between different clock choices in the quantum theory. We illustrate it by means of the parametrized particle, which, like gravity, features a Hamiltonian constraint. We explicitly switch between the quantum evolution relative to the non-relativistic time variable and that relative to the particle's position, which requires carefully regularizing the zero-modes in the so-called time-of-arrival observable. While this toy model is simple, our approach is general and, in particular, directly amenable to quantum cosmology. It proceeds by systematically linking the reduced quantum theories relative to different clock choices via the clock-choice-neutral Dirac quantized theory, in analogy to coordinate changes on a manifold. This method suggests a new perspective on the multiple choice problem, indicating that it is rather a multiple choice feature of the complete relational quantum theory, taken as the conjunction of Dirac quantized and quantum deparametrized theories. Precisely this conjunction permits one to consistently switch between different temporal reference systems, which is a prerequisite for a quantum notion of general covariance. Finally, we show that quantum uncertainties generically lead to a discontinuity in the relational dynamics when switching clocks, in contrast to the classical case.

Abstract We apply the BMHV scheme for non-anticommuting γ 5 to an abelian chiral gauge theory at the two-loop level. As our main result, we determine the full structure of symmetry-restoring counterterms up to the two-loop level. These counterterms turn out to have the same structure as at the one-loop level and a simple interpretation in terms of restoration of well-known Ward identities. In addition, we show that the ultraviolet divergences cannot be canceled completely by counterterms generated by field and parameter renormalization, and we determine needed UV divergent evanescent counterterms. The paper establishes the two-loop methodology based on the quantum action principle and direct computations of Slavnov-Taylor identity breakings. The same method will be applicable to nonabelian gauge theories.

Abstract We study the application of the Breitenlohner-Maison-’t Hooft-Veltman (BMHV) scheme of Dimensional Regularization to the renormalization of chiral gauge theories, focusing on the specific counterterm structure required by the non-anticommuting Dirac γ 5 matrix and the breaking of the BRST invariance. Calculations are performed at the one-loop level in a massless chiral Yang-Mills theory with chiral fermions and real scalar fields. We discuss the setup and properties of the regularized theory in detail. Our central results are the full counterterm structures needed for the correct renormalization: the singular UV-divergent counterterms, including evanescent counterterms that have to be kept for consistency of higher-loop calculations. We find that the required singular, evanescent counterterms associated with vector and scalar fields are uniquely determined but are not gauge invariant. Furthermore, using the framework of algebraic renormalization, we determine the symmetry-restoring finite counterterms, that are required to restore the BRST invariance, central to the consistency of the theory. These are the necessary building blocks in one-loop and higher-order calculations. Finally, renormalization group equations are derived within this framework, and the derivation is compared with the more customary calculation in the context of symmetry-invariant regularizations. We explain why, at one-loop level, the extra BMHV-specific counterterms do not change the results for the RGE. The results we find complete those that have been obtained previously in the literature in the absence of scalar fields.