Symmetric Maps Research Articles

Rotationally symmetric symphonic maps

Rotationally symmetric symphonic maps

Symmetrical, non-sovereign cartography as a means for conservation: insights from a participatory forest mapping exercise

Studies of participatory mapping consider it to be a grassroots activity that secures customary rights, the sovereignty of marginalized communities, and as a tool for conservation and sustainable resource management. Political ecology sees such grassroots struggles as sites where multiple (human) groups/actors articulate and contest their knowledge of, and control over, entities called 'resources.' However, 'resources' exclude the role of other-than-humans, thereby perpetuating asymmetrical and anthropocentric ways of knowing and conceptualizing place-based struggles. In the quest for distributive justice, the modern principle of sovereignty also goes unchallenged. Through an ethnographic observation of participatory mapping among the indigenous Gonds of Adilabad in South India, this Grassroots article shows that by incorporating other-than-human actors as equal agents of conservation, the Gonds have produced a non-sovereign, symmetrical map that challenges notions of human sovereignty over a seemingly inert 'nature.' Grassroots mapping can include other-than-humans, making it a potent exercise in revealing and articulating more-than-human ways of conservation.

Geographically and temporally weighted co-location quotient: an analysis of spatiotemporal crime patterns in greater Manchester

Incident data, a form of big data frequently used in urban studies, are characterized by point features with high spatial and temporal resolution and categorical values. In contrast to panel data, such spatial data pooled over time reflect multi-directional spatial effects but only unidirectional temporal effects, which are challenging to analyze. This paper presents an innovative approach to address this challenge – a geographically and temporally weighted co-location quotient which includes global and local computation, a method to calculate a spatiotemporal weight matrix and a significance test using Monte Carlo simulation. This new approach is used to identify spatio-temporal crime patterns across Greater Manchester in 2016 from open source recorded crime data. The results show that this approach is suitable for the analysis and visualization of spatio-temporal dependence and heterogeneity in categorical spatial data pooled over time. It is particularly useful for detecting symmetrical spatio-temporal co-location patterns and mapping local clusters. The method also addresses the unbalanced temporal scale problem caused by unidirectional temporal data representation and explores potential impacts. The empirical evidence of the spatiotemporal crime patterns might usefully be deployed to inform the development of criminological theory by helping to disentangle the relationships between crime and the urban environment.

A novel pseudo-random number generator for IoT based on a coupled map lattice system using the generalised symmetric map

Pseudo-random number generators (PRNGs) are one of the building blocks of cryptographic methods and therefore, new and improved PRNGs are continuously developed. In this study, a novel method to generate pseudo-random sequences using coupled map lattices is presented. Chaotic maps only show their chaotic behaviour for a specified range of control parameters, what can restrict their application in cryptography. In this work, generalised symmetric maps with adaptive control parameter are presented. This novel idea allows the user to choose any symmetric chaotic map, while ensuring that the output is a stream of independent and random sequences. Furthermore, to increase the complexity of the generated sequences, a lattice-based structure where every local map is linked to its neighbouring node via coupling factor has been used. The dynamic behaviour and randomness of the proposed system has been studied using Kolmogorov–Sinai entropy, bifurcation diagrams and the NIST statistical suite for randomness. Experimental results show that the proposed PRNG provides a large key space, generates pseudo-random sequences and is computationally suitable for IoT devices.

From modular decomposition trees to rooted median graphs

The modular decomposition of a symmetric map δ:X×X→Υ (or, equivalently, a set of pairwise-disjoint symmetric binary relations, a 2-structure, or an edge-colored undirected graph) is a natural construction to capture key features of δ in terms of a labeled tree. A map δ is explained by a vertex-labeled rooted tree (T,t) if the label δ(x,y) coincides with the label of the lowest common ancestor of x and y in T, i.e., if δ(x,y)=t(lca(x,y)). Only maps whose modular decomposition does not contain prime nodes, i.e., the symbolic ultrametrics, can be explained in this manner. Here we consider rooted median graphs as a generalization of (modular decomposition) trees to explain symmetric maps. We derive a linear-time algorithm that stepwisely resolves prime vertices in the modular decomposition tree to obtain a rooted and labeled median graph that explains a given symmetric map δ.

A Novel Sentiment Polarity Detection Framework for Chinese

Nowadays, mining opinions or sentiment from online user-generated text has become a research hot spot. Although a large amount of lexicon-based Chinese polarity detection works have been done, the existing methods have one common flaw: that even the same word can have opposite polarities among different seed lexicons. This is known as polarity fuzziness. To enhance the performance of Chinese sentiment polarity detection, we start from a two-aspect lexicon expansion so that the polarity fuzziness can be avoided. Specifically, we detect sentiment polarity for new words and revise sentiment polarity for words already defined in seed lexicons. Then, we formulate a novel sentiment polarity detection framework for Chinese (SPDFC) with more attention to fine-grained sentiment processing, which is involved in symmetrical mapping, sentiment feature pruning and text representation. In this way, words’ polarity can be directly taken as features, penetrating further in the polarity detection phase. According to our experimental results, the proposed SPDFC framework can achieve the best overall performance from the perspective of Chinese polarity detection, sentiment feature pruning, and text representation compared to other classical and state-of-the-art methods.

Improved Secure and Efficient Chebyshev Chaotic Map-Based User Authentication Scheme

A Chebyshev chaotic map is a method for implementing efficient authentication. Recently, Chatterjee <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i> proposed an authentication scheme for multi-server/multi-client environments using a Chebyshev chaotic map. However, we found four critical vulnerabilities in the proposed authentication method. To begin with, the method is open to user as well as server impersonation attacks. User revocation is also infeasible. Finally, there is a possibility of critical information leakage. We propose a new scheme that overcomes the four weaknesses listed previously using a symmetric Chebyshev chaotic map. We tested our proposed scheme using ProVerif and AVISPA, and compared its performance with that of the conventional authentication method. Results indicate that our scheme is 44.025 times more efficient than the conventional method.

The relaxed area of 𝕊1-valued singular maps in the strictBV-convergence

Given a bounded open set Ω ⊂ ℝ2, we study the relaxation of the nonparametric area functional in the strict topology inBV(Ω; ℝ2). and compute it for vortex-type maps, and more generally for maps inW1,1(Ω;S1) having a finite number of topological singularities. We also extend the analysis to some specific piecewise constant maps inBV(Ω;S1), including the symmetric triple junction map.

Fast synchronization of symmetric Hénon maps using adaptive symmetry control

The article discusses the possibility of synchronizing adaptive discrete chaotic maps through the control of the symmetry coefficient. Since a change in the symmetry coefficient in symmetric chaotic maps possesses a much less influence on the system oscillation mode than a change in nonlinearity parameters, we assume that the synchronization of such systems can be achieved in a small number of iterations. To experimentally examine this hypothesis, we studied three cases of adaptive synchronization feedback controllers for the conventional Hénon map and adaptive Hénon map. We found that synchronization occurs faster while the symmetry coefficient is controlled by comparing the synchronization times in all considered cases. Averagely, an accurate estimate of the adaptive coefficient is achieved after 3–5 iterations. Applying this approach to the communication systems based on modulation through switching parameters of chaotic systems can significantly reduce the transient processes inherent in this method. The numerical experiments show that it is possible to decrease the transmission time by more than 25%, even in the case of short messages.

Learning Deep Models: Critical Points and Local Openness

With the increasing popularity of nonconvex deep models, developing a unifying theory for studying the optimization problems that arise from training these models becomes very significant. Toward this end, we present in this paper a unifying landscape analysis framework that can be used when the training objective function is the composite of simple functions. Using the local openness property of the underlying training models, we provide simple sufficient conditions under which any local optimum of the resulting optimization problem is globally optimal. We first completely characterize the local openness of the symmetric and nonsymmetric matrix multiplication mapping. Then we use our characterization to (1) provide a simple proof for the classical result of Burer-Monteiro and extend it to noncontinuous loss functions; (2) show that every local optimum of two-layer linear networks is globally optimal. Unlike many existing results in the literature, our result requires no assumption on the target data matrix [Formula: see text], and input data matrix [Formula: see text]; (3) develop a complete characterization of the local/global optima equivalence of multilayer linear neural networks (we provide various counterexamples to show the necessity of each of our assumptions); and (4) show global/local optima equivalence of overparameterized nonlinear deep models having a certain pyramidal structure. In contrast to existing works, our result requires no assumption on the differentiability of the activation functions and can go beyond “full-rank” cases.

Forecasting nonadiabatic dynamics using hybrid convolutional neural network/long short-term memory network.

Modeling nonadiabatic dynamics in complex molecular or condensed-phase systems has been challenging, especially for the long-time dynamics. In this work, we propose a time series machine learning scheme based on the hybrid convolutional neural network/long short-term memory (CNN-LSTM) framework for predicting the long-time quantum behavior, given only the short-time dynamics. This scheme takes advantage of both the powerful local feature extraction ability of CNN and the long-term global sequential pattern recognition ability of LSTM. With feature fusion of individually trained CNN-LSTM models for the quantum population and coherence dynamics, the proposed scheme is shown to have high accuracy and robustness in predicting the linearized semiclassical and symmetrical quasiclassical mapping dynamics as well as the mixed quantum-classical Liouville dynamics of various spin-boson models with learning time up to 0.3ps. Furthermore, if the hybrid network has learned the dynamics of a system, this knowledge is transferable that could significantly enhance the accuracy in predicting the dynamics of a similar system. The hybrid CNN-LSTM network is thus believed to have high predictive power in forecasting the nonadiabatic dynamics in realistic charge and energy transfer processes in photoinduced energy conversion.

Higher-order tensor decomposition based scalp-to-intracranial EEG projection for detection of interictal epileptiform discharges

Objective. Interictal epileptiform discharges (IEDs) occur between two seizures onsets. IEDs are mainly captured by intracranial recordings and are often invisible over the scalp. This study proposes a model based on tensor factorization to map the time-frequency (TF) features of scalp EEG (sEEG) to the TF features of intracranial EEG (iEEG) in order to detect IEDs from over the scalp with high sensitivity. Approach. Continuous wavelet transform is employed to extract the TF features. Time, frequency, and channel modes of IED segments from iEEG recordings are concatenated into a four-way tensor. Tucker and CANDECOMP/PARAFAC decomposition techniques are employed to decompose the tensor into temporal, spectral, spatial, and segmental factors. Finally, TF features of both IED and non-IED segments from scalp recordings are projected onto the temporal components for classification. Main results. The model performance is obtained in two different approaches: within- and between-subject classification approaches. Our proposed method is compared with four other methods, namely a tensor-based spatial component analysis method, TF-based method, linear regression mapping model, and asymmetric–symmetric autoencoder mapping model followed by convolutional neural networks. Our proposed method outperforms all these methods in both within- and between-subject classification approaches by respectively achieving 84.2% and 72.6% accuracy values. Significance. The findings show that mapping sEEG to iEEG improves the performance of the scalp-based IED detection model. Furthermore, the tensor-based mapping model outperforms the autoencoder- and regression-based mapping models.

Resource efficient activation functions for neural network accelerators

Implementations of machine learning models in resource-limited embedded systems are becoming highly desired. This has led to a need for resource-efficient building blocks for computing the mathematical operations required for neural network training and inferencing. Efficient activation functions for low-end hardware devices with limited hardware capabilities are important. In this work, we present a method for generating symmetric and asymmetric activation functions for deep and convolution neural networks. Furthermore, we propose a solution that simultaneously computes a symmetric activation function with an integrated scaling functionality for Long Short Term Memory (LSTM) models. This effectively eliminates two of the three element-wise multipliers in an LSTM cell. Also, this built-in scaling requires no additional computation time because it is integrated within the computation of the symmetric non-linear mapping. This approach replaces the need to compute several Tanh activation functions and element-wise multipliers separately. A resource-efficient approximate multiplier is also proposed to eliminate the third element-wise multiplier and potentially replace all the resource-hungry multipliers. The digital implementation of the proposed method is highly amenable to parallelization and is extremely resource-efficient. We record an area-saving on field-programmable gate arrays with different precision. Our proposal’s formulaic equivalents are also computationally fast on CPU-based engines. On an embedded ARM processor, our method achieves a speedup of at least 4.37× for the proposed functions. We show that LSTMs with our method can achieve up to 3.5× resource footprint saving when compared to the hard activation implementation. We demonstrate that our method achieves competitive results with negligible loss of performance.

Response of the Cerebral Cortex to Resistance and Non-resistance Exercise Under Different Trajectories: A Functional Near-Infrared Spectroscopy Study.

Background: At present, the effects of upper limb movement are generally evaluated from the level of motor performance. The purpose of this study is to evaluate the response of the cerebral cortex to different upper limb movement patterns from the perspective of neurophysiology.Method: Thirty healthy adults (12 females, 18 males, mean age 23.9 ± 0.9 years) took resistance and non-resistance exercises under four trajectories (T1: left and right straight-line movement; T2: front and back straight-line movement; T3: clockwise and anticlockwise drawing circle movement; and T4: clockwise and anticlockwise character ⁕ movement). Each movement included a set of periodic motions composed of a 30-s task and a 30-s rest. Functional near-infrared spectroscopy (fNIRS) was used to measure cerebral blood flow dynamics. Primary somatosensory cortex (S1), supplementary motor area (SMA), pre-motor area (PMA), primary motor cortex (M1), and dorsolateral prefrontal cortex (DLPFC) were chosen as regions of interests (ROIs). Activation maps and symmetric heat maps were applied to assess the response of the cerebral cortex to different motion patterns.Result: The activation of the brain cortex was significantly increased during resistance movement for each participant. Specifically, S1, SMA, PMA, and M1 had higher participation during both non-resistance movement and resistance movement. Compared to non-resistance movement, the resistance movement caused an obvious response in the cerebral cortex. The task state and the resting state were distinguished more obviously in the resistance movement. Four trajectories can be distinguished under non-resistance movement.Conclusion: This study confirmed that the response of the cerebral motor cortex to different motion patterns was different from that of the neurophysiological level. It may provide a reference for the evaluation of resistance training effects in the future.

Solving a Fractional-Order Differential Equation Using Rational Symmetric Contraction Mappings

The intent of this manuscript is to present new rational symmetric ϖ−ξ-contractions and infer some fixed-points for such contractions in the setting of Θ-metric spaces. Furthermore, some related results such as Suzuki-type rational symmetric contractions, orbitally Υ-complete, and orbitally continuous mappings in Θ-metric spaces are introduced. Ultimately, the theoretical results are shared to study the existence of the solution to a fractional-order differential equation with one boundary stipulation.

Research on Pseudorandom Number Generator Based on Several New Types of Piecewise Chaotic Maps

This paper proposes three types of one-dimensional piecewise chaotic maps and two types of symmetrical piecewise chaotic maps and presents five theorems. Furthermore, some examples that satisfy the theorems are constructed, and an analysis and model of the dynamic properties are discussed. The construction methods proposed in this paper have a certain generality and provide a theoretical basis for constructing a new discrete chaotic system. In addition, this paper designs a pseudorandom number generator based on piecewise chaotic map and studies its application in cryptography. Performance evaluation shows that the generator can generate high quality random sequences efficiently.

Paramodular forms coming from elliptic curves

There is a lifting from a non-CM elliptic curve E/Q to a paramodular form f of degree 2 and weight 3 given by the symmetric cube map. We find the level of f in terms of the coefficients of the Weierstrass equation of E. In order to compute the paramodular level, we use the available description of the local representations of GL(2,Qp) attached to E for p≥5 and determine the local representation of GL(2,Q3) attached to E.

TMF: A GNSS Tropospheric Mapping Function for the Asymmetrical Neutral Atmosphere

Tropospheric mapping function plays a vital role in the high precision Global Navigation Satellites Systems (GNSS) data processing for positioning. However, most mapping functions are derived under the assumption that atmospheric refractivity is spherically symmetric. In this paper, the pressure, temperature, and humidity fields of ERA5 data with the highest spatio-temporal resolution available from the European Centre for Medium-range Weather Forecast (ECMWF) were utilized to compute ray-traced delays by the software WHURT. Results reveal the universal asymmetry of the hydrostatic and wet tropospheric delays. To accurately represent these highly variable delays, a new mapping function that depends on elevation and azimuth angles—Tilting Mapping Function (TMF)—was applied. The basic idea is to assume an angle between the tropospheric zenith direction and the geometric zenith direction. Ray-traced delays served as the reference values. TMF coefficients were fitted by Levenberg–Marquardt nonlinear least-squares method. Comparisons demonstrate that the TMF can improve the MF-derived slant delay’s accuracy by 73%, 54% and 29% at the 5° elevation angle, against mapping functions based on the VMF3 concept, without, with a total and separate estimation of gradients, respectively. If all coefficients of a symmetric mapping function are determined together with gradients by a least-square fit at sufficient elevation angles, the accuracy is only 6% lower than TMF. By adopting the b and c coefficients of VMF3, TMF can keep its high accuracy with less computational cost, which could be meaningful for large-scale computing.

A Computational Model Based on Symmetry for Generating Visually Pleasing Maps of Platform Games

In this paper we introduce a computational model based on the concept of symmetry to generate visually pleasing maps of platform games. We cast the problem of generating symmetrical maps as an optimization task and propose a heuristic search algorithm to solve it. A user study using a platform game shows the advantage of our method over other approaches in terms of visual aesthetics and enjoyment. Another user study shows that our method is able to generate maps as visually pleasing as maps created by professional designers.

Common Best Proximity Point Results for T-GKT Cyclic ϕ-Contraction Mappings in Partial Metric Spaces with Some Applications

The aim of this paper is to derive some common best proximity point results in partial metric spaces defining a new class of symmetric mappings, which is a generalization of cyclic ϕ-contraction mappings. With the help of these symmetric mappings, the characterization of completeness of metric spaces given by Cobzas (2016) is extended here for partial metric spaces. The existence of a solution to the Fredholm integral equation is also obtained here via a fixed-point formulation for such mappings.