Gaussian Map Research Articles

Diagnosis of cerebral microbleed via VGG and extreme learning machine trained by Gaussian map bat algorithm

Cerebral microbleed (CMB) is a serious public health concern. It is associated with dementia, which can be detected with brain magnetic resonance image (MRI). CMBs often appear as tiny round dots on MRIs, and they can be spotted anywhere over brain. Therefore, manual inspection is tedious and lengthy, and the results are often short in reproducible. In this paper, a novel automatic CMB diagnosis method was proposed based on deep learning and optimization algorithms, which used the brain MRI as the input and output the diagnosis results as CMB and non-CMB. Firstly, sliding window processing was employed to generate the dataset from brain MRIs. Then, a pre-trained VGG was employed to obtain the image features from the dataset. Finally, an ELM was trained by Gaussian-map bat algorithm (GBA) for identification. Results showed that the proposed method VGG-ELM-GBA provided better generalization performance than several state-of-the-art approaches.

On the Bielliptic and Bihyperelliptic Loci

We study some particular loci inside the moduli space $\mathcal{M}_g$, namely the bielliptic locus (i.e. the locus of curves admitting a $2:1$ cover over an elliptic curve $E$) and the bihyperelliptic locus (i.e. the locus of curves admitting a $2:1$ cover over a hyperelliptic curve $C'$, $g(C') \geq 2$). We show that the bielliptic locus is not a totally geodesic subvariety of $\mathcal{A}_g$ if $g \geq 4$ (while it is for $g=3$, see [16]) and that the bihyperelliptic locus is not totally geodesic in $\mathcal{A}_g$ if $g \geq 3g'$. We also give a lower bound for the rank of the second gaussian map on the generic point of the bielliptic locus and an upper bound for this rank for every bielliptic curve.

Audio Encryption Scheme Using Self-Adaptive Bit Scrambling and Two Multi Chaotic-Based Dynamic DNA Computations

In this paper, a novel scheme for secure audio transmission is introduced. The novelty of this scheme is that it combines four different techniques for audio encryption in the same scheme which makes it more secure: self-adaptive scrambling, multi chaotic maps, dynamic DNA encoding and cipher feedback encryption. Also, it introduces two new designed multi chaotic maps as pseudo random generators that combine five different chaotic maps with eight control parameters. The scheme consists of three phases with three secret keys. The first phase is a self-adaptive bit scrambling where SHA512 of the input audio is computed to be used as a first secret key for cyclic shifting the input audio binary stream which efficiently reduces the strong correlation between neighboring audio samples. The second phase is a dynamic DNA encoding of the scrambled audio by using a second secret key obtained from a pseudo random generator (LCS) using a novel design of multi chaotic maps including Sine, Chebyshev and Logistic map with three control parameters. As DNA encoding provides fast computations and large capacity for data transmission, the third phase consists of two DNA algebraic operations “AND” and “XOR” using a pseudorandom DNA sequence as a third secret key generated by another new designed multi chaotic HLG map which combines Henon, Logistic and Gaussian chaotic maps and has five control parameters. The third phase is structured in a cipher feedback mode and so it achieves strong diffusion and confusion in the encrypted audio. Also combining five different chaotic maps in the proposed scheme increases the number of secret control parameters which achieves a huge key space and so robust strength against brute force attacks. The scheme is evaluated by using different measurements including signal to noise ratio (SNR), peak signal to noise ratio (PSNR), number of samples change rate (NSCR), unified average changing intensity (UACI), root mean square (RMS), crest factor (CF), correlation coefficient, histogram, key sensitivity and key space. From results, it is clear that the scheme is highly secure and stronger than many recent similar audio encryption schemes against different types of attacks.

PSD – probabilistic algorithm for mobile robot 6D localization without natural and artificial landmarks based on 2.5D map and a new type of laser scanner in GPS-denied scenarios

This paper presents an approach to mobile robot 6D localization based on a 3D laser scanner in GPS-denied scenarios. Commonly, 6D localization using laser scanners is performed with the use of extraction and association of the features or by comparison of the whole scans (very often off-line) using the ICP algorithm or its modifications. However, in some unstructured non-urbanized rough terrain environments, feature extraction does not seem to be reliable enough. For such kind of environment, we present a new method to mobile robot localization in GPS-denied applications, called PSD (Point-to-Surfel Distance). Unlike state of the art localization methods using laser scanners, we consider every single laser scanner measurement as an observation and use Point-to-Surfel Distance for correction of position and orientation of the robot. Mobile robot localization is based on a specific representation of the terrain in the 2.5D surfel map (terrain height and inclination). The simulation tests compared our method using extended Kalman filter (EKF) and single laser scanner measurements with an up-to-date method using particle filter (PF) and comparing the scan lines with the reference map and with another method using Gaussian mixture maps. The tests confirmed that the proposed method provides satisfying results for GPS-denied scenarios in rough terrain without extractable landmarks and our method is thirty times faster than the PF method (serial implementation). KITTI benchmark tests and real terrain experiments confirmed its usefulness and advantages as well.

Complexity of Spatiotemporal Synchronization Activity of GaussianMap through Random Link

In this paper, we study spatiotemporal synchronization activity (STSA) of coupled Gaussian maps in a complex network. Our complex networks are changed stochastically with time. A coupled map lattice (CML) is adopted in Gaussian map as a prototype of a spatiotemporal chaotic systems with variation of parameters. A key motivation is that to determine (i) the effects of variation of randomness, (ii) the effects of variation of coupling strength e , (iii) the effects of variation of parameter α when β is fixed and (iv) the effects of variation of β when parameter α is fixed on the synchronization behaviour. The variation of the basin size with respect to rewiring probability for different coupling strength and basin size with respect to coupling strength e for different randomness, different parameters α and β are also plotted.

Recovery map for fermionic Gaussian channels

A recovery map effectively cancels the action of a quantum operation to a partial or full extent. We study the Petz recovery map in the case where the quantum channel and input states are fermionic and Gaussian. Gaussian states are convenient because they are totally determined by their covariance matrix and because they form a closed set under so-called Gaussian channels. Using a Grassmann representation of fermionic Gaussian maps, we show that the Petz recovery map is also Gaussian and determine it explicitly in terms of the covariance matrix of the reference state and the data of the channel. As a by-product, we obtain a formula for the fidelity between two fermionic Gaussian states. We also discuss subtleties arising from the singularities of the involved matrices.

Optimum design of large steel skeletal structures using chaotic firefly optimization algorithm based on the Gaussian map

In this paper, a new chaotic firefly algorithm based on Gaussian map (CGFA) is proposed for structural optimization problems. Different chaotic maps have different behaviors, and it is acknowledged by researchers that these maps improve the convergence and prevent algorithms to get stuck on local solutions. The objective function in this paper is considered as the weight of the structure, which is minimized subjected to serviceability and strength requirements. Three steel structures are designed by the LRFD-AISC specification to illustrate the performance of the presented algorithm. Comparison of the results of CGFA with some other well-known metaheuristic algorithms shows the robustness of the algorithm.

Chaos-based firefly algorithms for optimization of cyclically large-size braced steel domes with multiple frequency constraints

The success of the search in the firefly algorithm is highly dependent on a good balance between exploration and exploitation. Although, the basic firefly algorithm is relatively efficient; two chaotic firefly algorithms based on Logistic map (CLFA) and Gaussian map (CGFA) have been presented to improve basic FA. As numerical examples, some large-scale domes are designed for multiple frequency constraints optimization. Despite the fact that these problems are highly nonlinear, results illustrate a desirable performance of the algorithms in both obtaining lower weight and having a higher convergence rate.

Bifurcation Analysis of Reduced Network Model of Coupled Gaussian Maps for Associative Memory

This paper proposes an associative memory model based on a coupled system of Gaussian maps. A one-dimensional Gaussian map describes a discrete-time dynamical system, and the coupled system of Gaussian maps can generate various phenomena including asymmetric fixed and periodic points. The Gaussian associative memory can effectively recall one of the stored patterns, which were triggered by an input pattern by associating the asymmetric two-periodic points observed in the coupled system with the binary values of output patterns. To investigate the Gaussian associative memory model, we formed its reduced model and analyzed the bifurcation structure. Pseudo-patterns were observed for the proposed model along with other conventional associative memory models, and the obtained patterns were related to the high-order or quasi-periodic points and the chaotic trajectories. In this paper, the structure of the Gaussian associative memory and its reduced models are introduced as well as the results of the bifurcation analysis are presented. Furthermore, the output sequences obtained from simulation of the recalling process are presented. We discuss the mechanism and the characteristics of the Gaussian associative memory based on the results of the analysis and the simulations conducted.

一种基于高斯映射的三维点云特征线提取方法

一种基于高斯映射的三维点云特征线提取方法

Image Compression and Encryption Using DCT and Gaussian Map

The use of the image in daily life keeps increasing as information technology is constantly developing. Consequently, the demand for a form of security in sending images through the internet is unavoidable. The encryption algorithm is one of the solutions. Encryption will make any image become only readable by those authorized to access. A chaos-based encryption algorithm is the most commonly used image encryption method because of its sensitivity to the parameter value. In addition to security, image transmission speed is also on demand. Images with bigger size than texts require longer transmission time. For this issue, image compression is the answer. There are many kinds of algorithm that can be used for image size compression. One of which is DCT. DCT algorithm is known to transform spatial domain to frequency. Image encryption and compression are two different processes. Nevertheless, this study combined both processes into one scheme so that they become inseparable. This study has two findings. First, in the area of compression, the scheme produced cipher image with considerable compression ratio. Second, in the area of encryption, the produced cipher image’s histogram became completely different from the original histogram, indicating that the encryption algorithm used was immune to histogram analysis.

Self-Organizing Gaussian Mixture Map Based on Adaptive Recursive Bayesian Estimation

Self-Organizing Gaussian Mixture Map Based on Adaptive Recursive Bayesian Estimation

Qubit entanglement generation by Gaussian non-Markovian dynamics

We consider two qubits interacting with a common bosonic bath, but not directly between themselves. We derive the (bipartite) entanglement generation conditions for Gaussian non-Markovian dynamical maps and show that they are similar as in the Markovian regime. However, they depend on different physical coefficients and hold on different time scales. Indeed, for small times, in the non-Markovian regime entanglement is possibly generated on a shorter time scale () than in the Markovian regime (). Moreover, although the singular coupling limit of non-Markovian dynamics yields Markovian ones, we show that the same limit does not lead from non-Markovian entanglement generation conditions to Markovian ones. Also, entanglement generation conditions do not depend on the initial time for non-Markovian open dynamics resulting from couplings to bosonic Gaussian baths, while they may depend on time for open dynamics originated by couplings to classical, stochastic Gaussian environments.

Infrared LSS-Target Detection Via Adaptive TCAIE-LGM Smoothing and Pixel-Based Background Subtraction

Infrared small target detection is a significant and challenging topic for daily security. This paper proposes a novel model to detect LSS-target (low altitude, slow speed, and small target) under the complicated background. Firstly, the fundamental constituents of an infrared image including the complexity and entropy are calculated, which are invoked as adaptive control parameters of smoothness. Secondly, the adaptive L0 gradient minimization smoothing based on texture complexity and information entropy (TCAIE-LGM) is proposed in order to remove noises and suppress low-amplitude details in infrared image abstraction. Finally, difference of Gaussian (DoG) map is incorporated into the pixel-based adaptive segmentation (PBAS) background modeling algorithm, which can differ LSS-target from the sophisticated background. Experimental results demonstrate that the proposed novel model has a high detection rate and produces fewer false alarms, which outperforms most state-of-the-art methods.

Kac–Rice fixed point analysis for single- and multi-layered complex systems

We present a null model for single- and multi-layered complex systems constructed using homogeneous and isotropic random Gaussian maps. By means of a Kac–Rice formalism, we show that the mean number of fixed points can be calculated as the expectation of the absolute value of the characteristic polynomial for a product of independent Gaussian (Ginibre) matrices. Furthermore, using techniques from random matrix theory, we show that the high-dimensional limit of our system has a third-order phase transition between a phase with a single fixed point and a phase with exponentially many fixed points. This result is universal in the sense that it does not depend on finer details of the correlations for the random maps.

Monte Carlo Localization on Gaussian Process Occupancy Maps for Urban Environments

Map-aided localization methods have been employed for vehicle localization to overcome the limitations of global navigation satellite system (GNSS) devices. In this solution, sensor information is matched to the environment map to determine the vehicle position. Occupancy grid maps (OGMs) have been adapted for map-aided localization. However, there are known drawbacks of OGM, such as the environment discretization, the assumption of independence between grid cells, and the need for dense measurements. In recent years, Gaussian process occupancy map (GPOM) was developed to suppress some of the OGM limitations. GPOM enables the computation of the likelihood of occupancy at any location, even if not directly observed by the sensor, thus representing the environment in a continuous manner. Taking into account the superiority of GPOM over OGM, we devise a novel vehicle localization technique for urban environments. This solution enables more accurate localization due to the use of a representation that better models the real environment. The development of the proposed method is based on Monte Carlo localization, which is a popular map-aided localization method. Two road features commonly found in urban cities were chosen to build the maps: road curbs and road markings. Specifically, the proposed localization method relies on a GPOM constructed with curb data and an OGM built with road marking data. Experiments were performed in real urban environments. Maps were intentionally generated using sparse light detection and ranging (LIDAR) data to verify the localization in non-observed areas. The localization system was evaluated by comparing the results with a high precision GNSS device.

Reynolds and dispersive shear stress contributions above highly skewed roughness

The roughness functions induced by irregular peak- and/or pit-dominated surfaces in a fully developed turbulent channel flow are studied by direct numerical simulation. A surface generation algorithm is used to synthesise an irregular Gaussian height map with periodic boundaries. The Gaussian height map is decomposed into ‘pits-only’ and ‘peaks-only’ components, which produces two additional surfaces with similar statistical properties, with the exception of skewness, which are equal and opposite $({\mathcal{S}}=\pm 1.6)$. While the peaks-only surface yields a roughness function comparable to that of the Gaussian surface, the pits-only surface exhibits a far weaker roughness effect. Analysis of results is aided by deriving an equation for the roughness function that quantitatively identifies the mechanisms of momentum loss and/or gain. The statistical contributions of ‘form-induced’ and stochastic fluid motions to the roughness function are examined in further detail using quadrant analyses. Above the Gaussian and peaks-only surfaces, the contributions of dispersive and Reynolds shear stresses show a compensating effect, whereas above the pits-only surface, an additive effect is observed. Overall, the results emphasise the sensitivity of the near-wall flow with respect to higher-order topographical parameters, which can, in turn, induce significant differences in the roughness function above a peak- and/or pit-dominated surface.

Non-surjective Gaussian maps for singular curves on K3 surfaces

Let (S, L) be a polarized K3 surface with Pic(?)=ℤ[?] and ?⋅?=2?−2 , let C be a nonsingular curve of genus ?−1 and let ?:?→? be such that ?(?)∈|?| . We prove that the Gaussian map Φ??(−?) is non-surjective, where T is the degree two divisor over the singular point x of f(C). This generalizes a result of Kemeny with an entirely different proof. It uses the very ampleness of C on the blown-up surface ?˜ of S at x and a theorem of L’vovski.

Chaotic Itinerancy Observed in Mutually Coupled Gaussian Maps

A one-dimensional Gaussian map defined by a Gaussian function describes a discrete-time dynamical system. Chaotic behavior can be observed in both Gaussian and logistic maps. This study analyzes the bifurcation structure corresponding to the fixed and periodic points of a coupled system comprising two Gaussian maps. The bifurcation structure of a mutually coupled Gaussian map is more complex than that of a mutually coupled logistic map. In a coupled Gaussian map, it was confirmed that after a stable fixed point or stable periodic points became unstable through the bifurcation, the points were able to recover their stability while the system parameters were changing. Moreover, we investigated a parameter region in which symmetric and asymmetric stable fixed points coexisted. Asymmetric unstable fixed point was generated by the [Formula: see text]-type branching of a symmetric stable fixed point. The stability of the unstable fixed point could be recovered through period-doubling and tangent bifurcations. Furthermore, a homoclinic structure related to the occurrence of chaotic behavior and invariant closed curves caused by two-periodic points was observed. The mutually coupled Gaussian map was merely a two-dimensional dynamical system; however, chaotic itinerancy, known to be a characteristic property associated with high-dimensional dynamical systems, was observed. The bifurcation structure of the mutually coupled Gaussian map clearly elucidates the mechanism of chaotic itinerancy generation in the two-dimensional coupled map. We discussed this mechanism by comparing the bifurcation structures of the Gaussian and logistic maps.

DCT Maps: Compact Differentiable Lidar Maps Based on the Cosine Transform

Most robot mapping techniques for lidar sensors tessellate the environment into pixels or voxels and assume uniformity of the environment within them. Although intuitive, this representation entails disadvantages: The resulting grid maps exhibit aliasing effects and are not differentiable. In the present paper, we address these drawbacks by introducing a novel mapping technique that does neither rely on tessellation nor on the assumption of piecewise uniformity of the space, without increasing memory requirements. Instead of representing the map in the position domain, we store the map parameters in the discrete frequency domain and leverage the continuous extension of the inverse discrete cosine transform to convert them to a continuously differentiable scalar field in the position domain, which we call DCT map. A DCT map assigns to each point in space a lidar decay rate, which models the local permeability of the space for laser rays. In this way, the map can describe objects of different laser permeabilities, from completely opaque to completely transparent. DCT maps represent lidar measurements significantly more accurate than grid maps, Gaussian process occupancy maps, and Hilbert maps, all with the same memory requirements, as demonstrated in our real-world experiments.