Gray Map Research Articles

TOGA-Based Fuzzy Grey Cognitive Map for Spacecraft Debris Avoidance

TOGA-Based Fuzzy Grey Cognitive Map for Spacecraft Debris Avoidance

Low complexity joint optimization of QAM gray mapping and non-binary LDPC Coefficients

Low complexity joint optimization of QAM gray mapping and non-binary LDPC Coefficients

A multimodal vision transformer for interpretable fusion of functional and structural neuroimaging data.

Multimodal neuroimaging is an emerging field that leverages multiple sources of information to diagnose specific brain disorders, especially when deep learning-based AI algorithms are applied. The successful combination of different brain imaging modalities using deep learning remains a challenging yet crucial research topic. The integration of structural and functional modalities is particularly important for the diagnosis of various brain disorders, where structural information plays a crucial role in diseases such as Alzheimer's, while functional imaging is more critical for disorders such as schizophrenia. However, the combination of functional and structural imaging modalities can provide a more comprehensive diagnosis. In this work, we present MultiViT, a novel diagnostic deep learning model that utilizes vision transformers and cross-attention mechanisms to effectively fuse information from 3D gray matter maps derived from structural MRI with functional network connectivity matrices obtained from functional MRI using the ICA algorithm. MultiViT achieves an AUC of 0.833, outperforming both our unimodal and multimodal baselines, enabling more accurate classification and diagnosis of schizophrenia. In addition, using vision transformer's unique attentional maps in combination with cross-attentional mechanisms and brain function information, we identify critical brain regions in 3D gray matter space associated with the characteristics of schizophrenia. Our research not only significantly improves the accuracy of AI-based automated imaging diagnostics for schizophrenia, but also pioneers a rational and advanced data fusion approach by replacing complex, high-dimensional fMRI information with functional network connectivity, integrating it with representative structural data from 3D gray matter images, and further providing interpretative biomarker localization in a 3D structural space.

Research on the Laser Scattering Characteristics of Three-Dimensional Imaging Based on Electro-Optical Crystal Modulation.

In this paper, we construct a laser 3D imaging simulation model based on the 3D imaging principle of electro-optical crystal modulation. Unlike the traditional 3D imaging simulation method, this paper focuses on the laser scattering characteristics of the target scene. To accurately analyze and simulate the scattering characteristic model of the target under laser irradiation, we propose a BRDF (Bidirectional Reflectance Distribution Function) model fitting algorithm based on the hybrid BBO-Firefly model, which can accurately simulate the laser scattering distribution of the target at different angles. Finally, according to the fitted scattering characteristic model, we inverted the target imaging gray map. We used the laser 3D imaging restoration principle to reconstruct the 3D point cloud of the target to realize the laser 3D imaging of the target.

Quantum Codes as an Application of Constacyclic Codes

The main focus of this paper is to analyze the algebraic structure of constacyclic codes over the ring R=Fp+w1Fp+w2Fp+w22Fp+w1w2Fp+w1w22Fp, where w12−α2=0, w1w2=w2w1, w23−β2w2=0, and α,β∈Fp∖{0}, for a prime p. We begin by introducing a Gray map defined over R, which is associated with an invertible matrix. We demonstrate its advantages over the canonical Gray map through some examples. Finally, we create new and improved quantum codes from constacyclic codes over R using Calderbank–Shore–Steane (CSS) construction.

Study of high-order non-equal probability QAM for visible light communication systems.

In this Letter, we propose and experimentally demonstrate a high-order non-equal probability quadrature amplitude modulation (NEP-QAM) scheme for visible light communication (VLC) systems, where NEP-72QAM is considered as an example. Nonlinear coding is introduced to generate the NEP-18QAM signal in the first quadrant, which is then jointly mapped with the other two bits to obtain the four-quadrant symmetric NEP-72QAM signal. Moreover, a bit-to-symbol labeling scheme is proposed to achieve thorough Gray mapping. The experimental results show that the NEP-72QAM scheme achieves better performance than the traditional 64QAM scheme regardless of whether the light-emitting diode (LED) operates in the linear or nonlinear range. Compared with the probabilistically shaped 72QAM scheme, the available range of the driving peak-to-peak voltage of the NEP-72QAM scheme is only reduced by 20 mV when 0.92 is used as the normalized generalized mutual information threshold, but the complexity is much lower.

Gray mapping method of QAM constellation for trellis shaping

Gray mapping method of QAM constellation for trellis shaping

ON QUANTUM CODES CONSTRUCTION FROM CONSTACYCLIC CODES OVER THE RING I_q[u,v] / <u^2-a^2, v^2-a^2, uv-vu>

This paper focuses on studying the properties of constacyclic codes, quantum error-correcting codes. The code is studied over a specific mathematical structure called the ring $\mathfrak{S}$, which is defined as $\mathfrak{S}=\mathfrak{I}_q[\mathfrak{u},\mathfrak{v}]/\langle \mathfrak{u}^2-\alpha^2,~ \mathfrak{v}^2-\alpha^2,~\mathfrak{u}\mathfrak{v}-\mathfrak{v}\mathfrak{u} \rangle$, where $\mathfrak{I}_q$ is a finite field of $q$ elements, $\alpha$ be the nonzero elements of the field $\mathfrak{I}_q$ and $q$ is a power of an odd prime $p$ such that $q=p^m, ~\textup{for}~ m \ge 1$. The paper also introduces a Gray map and use it to decompose constacyclic codes over the ring $\mathfrak{S}$ into a direct sum of constacyclic codes over $\mathfrak{I}_q$. We construct new and better quantum error-correcting codes over the ring $\mathfrak{S}$ (cf.; Table 1 and Table 2). Moreover, we also obtain best known linear codes as well as best dimension linear codes (cf.; Table 4).

On reversible DNA codes over the ring $${\mathbb {Z}}_4[u,v]/\langle u^2-2,uv-2,v^2,2u,2v\rangle$$ based on the deletion distance

AbstractLet$${\mathfrak {R}}= {\mathbb {Z}}_4[u,v]/\langle u^2-2,uv-2,v^2,2u,2v\rangle$$R=Z4[u,v]/⟨u2-2,uv-2,v2,2u,2v⟩be a ring, where$${\mathbb {Z}}_{4}$$Z4is a ring of integers modulo 4. This ring$${\mathfrak {R}}$$Ris a local non-chain ring of characteristic 4. The main objective of this article is to construct reversible cyclic codes of odd lengthnover the ring$${\mathfrak {R}}.$$R.Employing these reversible cyclic codes, we obtain reversible cyclic DNA codes of lengthn, based on the deletion distance over the ring$${\mathfrak {R}}.$$R.We also construct a bijection$$\Gamma$$Γbetween the elements of the ring$${\mathfrak {R}}$$Rand$$S_{D_{16}}.$$SD16.As an application of$$\Gamma ,$$Γ,the reversibility problem which occurs in DNAk-bases has been solved. Moreover, we introduce a Gray map$$\Psi _{\hom }:{\mathfrak {R}}^{n}\rightarrow {\mathbb {F}}_{2}^{8n}$$Ψhom:Rn→F28nwith respect to homogeneous weight$$w_{\hom }$$whomover the ring$${\mathfrak {R}}$$R. Further, we discuss theGC-content of DNA cyclic codes and their deletion distance. Moreover, we provide some examples of reversible DNA cyclic codes.

Application of (σ,δ)-cyclic codes in DNA codes over a non-chain ring

For a prime [Formula: see text] and a positive integer [Formula: see text], let [Formula: see text] be the finite field of characteristic [Formula: see text], and [Formula: see text] be a non-chain ring for a positive integer [Formula: see text]. In this paper, we study the [Formula: see text]-cyclic codes over [Formula: see text]. Further, we study the application of these codes in finding DNA codes. Toward this, we first define a Gray map to find classical codes over [Formula: see text] using codes over the ring [Formula: see text]. Later, we find the conditions for a [Formula: see text]-cyclic code to be reversible. Finally, we provide DNA codes using this algebraic method with some classical codes of better parameters.

Cyclic Codes over a Non-Commutative Non-Unital Ring

In this paper, we investigate cyclic codes over the ring E of order 4 and characteristic 2 defined by generators and relations as E=⟨a,b∣2a=2b=0,a2=a,b2=b,ab=a,ba=b⟩. This is the first time that cyclic codes over the ring E are studied. Each cyclic code of length n over E is identified uniquely by the data of an ordered pair of binary cyclic codes of length n. We characterize self-dual, left self-dual, right self-dual, and linear complementary dual (LCD) cyclic codes over E. We classify cyclic codes of length at most 7 up to equivalence. A Gray map between cyclic codes of length n over E and quasi-cyclic codes of length 2n over F2 is studied. Motivated by DNA computing, conditions for reversibility and invariance under complementation are derived.

Skew cyclic codes over 𝔻4 R and their applications to DNA codes construction

Abstract The fundamental aim of this research is to analyze the configuration of 𝔽4 R submodules, skew cyclic codes over 𝔽4 R and establish their connection with DNA codes, where 𝔽4 is a field of order 4 and R = 𝔽4 + u𝔽4 + v𝔽4 + w𝔽4 with u 2 = u, v 2 = v, w 2 = w, uv = vu = 0, vw = wv = 0, wu = uw = 0 is a finite ring. This is achieved by examining particular subclasses like reversible codes. Ultimately, this study aims to utilize Gray maps to derive codes that possess the characteristics of DNA structures. At the end of this paper, we have provided the necessary and sufficient condition for skew cyclic codes to be reversible complement.

On reversibility problem in DNA bases over a class of rings

Let R k = Z 4 [ u 1 , u 2 , … , u k ] / ⟨ u i 2 − u i , u i u j − u j u i ⟩ be a non-chain ring of characteristic 4, where 1 ≤ i , j ≤ k and k ≥ 1 . In this article, we discuss reversible cyclic codes of odd lengths over the ring R k . We construct bijections between the elements of the ring R k and DNA- 2 k bases for k = 1, 2 in such a manner that the reversibility problem is solved. Employing these bijections, reversible complement cyclic codes of odd lengths are generated. Furthermore, we construct a Gray map Φ : R k n → Z 4 2 k n and as an application of the Gray map Φ, we obtain the GC-content of cyclic codes of arbitrary odd length over the ring R k . Meanwhile, we provide some examples of reversible cyclic codes of odd lengths over the ring R k for different values of k, and also obtain the Lee distances of these codes.

Skew Cyclic and Skew Constacyclic Codes over a Mixed Alphabet

In this note, we study skew cyclic and skew constacyclic codes over the mixed alphabet R=FqR1R2, where q=pm, p is an odd prime with m odd and R1=Fq+uFq with u2=u, and R2=Fq+uFq+vFq with u2=u,v2=v,uv=vu=0. Such codes consist of the juxtaposition of three codes of the same size over Fq,R1, and R2, respectively. We investigate the generator polynomial for skew cyclic codes over R. Furthermore, we discuss the structural properties of the skew cyclic and skew constacyclic codes over R. We also study their q-ary images under suitable Gray maps.

Raw infrared image enhancement via an inverted framework based on infrared basic prior

Existing raw infrared image enhancement methods can effectively compress image and improve contrast. However, there still exist limitations. First, enhanced images are often over-exposed. Second, a high contrast but low noise enhanced image is difficult to be obtained due to the fact that the noise level increases with contrast. Third, the targets are not sufficiently salient in enhanced image. In this paper, we design an inverted enhancement framework to address the three limitations simultaneously. Specifically, we analyze the widely recognized features of raw infrared image and call them infrared image basic prior. That is, infrared detectors are often used to detect targets under special conditions and our attention mechanism is to focus on high radiation objects, but there are few targets in the scene. Then we modify the traditional image enhancement framework into an inverted framework based on infrared image basic prior and design an inverted nonlinear gray mapping curve, which avoids over-exposure and noise over-amplification. Furthermore, result is further improved by using layer decomposition model and gamma correction. Enhanced result yields the targets of our main interest. Finally, the extended applications are performed and show ability to stimulate the effectiveness of algorithms of related fields. Experiments show that our approach yields better results than state-of-the-art methods. A video of results is provided at https://github.com/wangyuro/Datashare1.

Functional connectivity changes in neurodegenerative biomarker-positive athletes with repeated concussions.

Multimodal biomarkers may identify former contact sports athletes with repeated concussions and at risk for dementia. Our study aims to investigate whether biomarker evidence of neurodegeneration in former professional athletes with repetitive concussions (ExPro) is associated with worse cognition and mood/behavior, brain atrophy, and altered functional connectivity. Forty-one contact sports athletes with repeated concussions were divided into neurodegenerative biomarker-positive (n = 16) and biomarker-negative (n = 25) groups based on positivity of serum neurofilament light-chain. Six healthy controls (negative for biomarkers) with no history of concussions were also analyzed. We calculated cognitive and mood/behavior composite scores from neuropsychological assessments. Gray matter volume maps and functional connectivity of the default mode, salience, and frontoparietal networks were compared between groups using ANCOVAs, controlling for age, and total intracranial volume. The association between the connectivity networks and sports characteristics was analyzed by multiple regression analysis in all ExPro. Participants presented normal-range mean performance in executive function, memory, and mood/behavior tests. The ExPro groups did not differ in professional years played, age at first participation in contact sports, and number of concussions. There were no differences in gray matter volume between groups. The neurodegenerative biomarker-positive group had lower connectivity in the default mode network (DMN) compared to the healthy controls and the neurodegenerative biomarker-negative group. DMN disconnection was associated with increased number of concussions in all ExPro. Biomarkers of neurodegeneration may be useful to detect athletes that are still cognitively normal, but with functional connectivity alterations after concussions and at risk of dementia.

Infrared Maritime Small-Target Detection Based on Fusion Gray Gradient Clutter Suppression

The long-distance ship target turns into a small spot in an infrared image, which has the characteristics of small size, weak intensity, limited texture information, and is easily affected by noise. Moreover, the presence of heavy sea clutter, including sun glints that exhibit local contrast similar to small targets, negatively impacts the performance of small-target detection methods. To address these challenges, we propose an effective detection scheme called fusion gray gradient clutter suppression (FGGCS), which leverages the disparities in grayscale and gradient between the target and its surrounding background. Firstly, we designed a harmonic contrast map (HCM) by using the two-dimensional difference of Gaussian (2D-DoG) filter and eigenvalue harmonic mean of the structure tensor to highlight high-contrast regions of interest. Secondly, a local gradient difference measure (LGDM) is designed to distinguish isotropic small targets from background edges with local gradients in a specific direction. Subsequently, by integrating the HCM and LGDM, we designed a fusion gray gradient clutter suppression map (FGGCSM) to effectively enhance the target and suppress clutter from the sea background. Finally, an adaptive constant false alarm threshold is adopted to extract the targets. Extensive experiments on five real infrared maritime image sequences full of sea glints, including a small target and sea–sky background, show that FGGCS effectively increases the signal-to-clutter ratio gain (SCRG) and the background suppression factor (BSF) by more than 22% and 82%, respectively. Furthermore, its receiver operating characteristic (ROC) curve has an obviously more rapid convergence rate than those of other typical detection algorithms and improves the accuracy of small-target detection in complex maritime backgrounds.

Pain Relief-Related Structural Brain Alterations in Trigeminal Neuralgia Induced by Noninvasive Stereotactic Radiosurgery: A Pilot Study

PurposeTrigeminal neuralgia (TN) is a devastating chronic pain disorder, defined by unilateral shock like pain in at least one division of the trigeminal nerve. Although several studies have investigated structural brain plasticity in TN patients, treatment-induced alterations remain largely uninvestigated. Materials/MethodsCombining T1-weighted magnetic resonance imaging (MRI) with voxel-based morphometry (VBM) and multiple-regression analyses, we assessed gray matter maps of TN patients to investigate changes in gray matter volume (GMV) from before to half a year after stereotactic radiosurgery (SRS). ResultsComparing pre- and post-GMV of 25 TN patients (16 females; mean age 67 years) did not yield any significant clusters, suggesting that the impact of SRS intervention itself on gray matter structure may be negligible. In relation to SRS-induced pain-relief, we found a significant GMV increase in the left superior frontal gyrus associated with greater degrees of pain relief (p=0.024), and a trend toward an increase in GMV in the left dorsolateral prefrontal cortex (p=0.097). ConclusionIn this pilot study, we observed significant increases of GMV in the left superior frontal gyrus with SRS-induced improvements in pain, and a trend for the dorsolateral prefrontal cortex. Future studies are indicated to validate these findings and determine whether SRS-induced decrease in distracting pain events and subsequent increases in GMV result in improved functionality, decreased dependence on "top-down" control, and improved cognitive/executive balance with amelioration of pain events.

Cyclic Codes over a Non-Local Non-Unital Ring

We study cyclic codes over the ring H of order 4 and characteristic 2 defined by generators and relations as H=⟨a,b∣2a=2b=0,a2=0,b2=b,ab=ba=0⟩. This is the first time that cyclic codes over a non-unitary ring are studied. Every cyclic code of length n over H is uniquely determined by the data of an ordered pair of binary cyclic codes of length n. We characterize self-dual, quasi-self-dual, and linear complementary dual cyclic codes H. We classify cyclic codes of length at most 7 up to equivalence. A Gray map between cyclic codes of length n over H and quasi-cyclic codes of length 2n over F2 is studied.

Gray Images of Constacyclic Codes over a Non-chain Extension of Z 4

Let [Formula: see text] be the ring of integers modulo 4. We study the [Formula: see text]-constacyclic and [Formula: see text]-cyclic codes over the non-chain ring [Formula: see text] for a unit [Formula: see text] in [Formula: see text]. We define several Gray maps and find that the respective Gray images of a quasi-cyclic code over [Formula: see text] are cyclic, quasi-cyclic or permutation equivalent to this code. For an odd positive integer [Formula: see text], we determine the generator polynomials of cyclic and [Formula: see text]-constacyclic codes of length [Formula: see text] over [Formula: see text]. Further, we prove that a [Formula: see text]-cyclic code of length [Formula: see text] is a [Formula: see text]-constacyclic code if [Formula: see text] is odd, and a [Formula: see text]-quasi-twisted code if [Formula: see text] is even. A few examples are also incorporated, in which two parameters are new and one is best known to date.