Gray Map Research Articles

Analysis of Cyber Security Threats of the Printing Enterprise

The topic of scientific works on the implementation of modern technologies and systems of automated management of the enterprise, its resources and technical means is analyzed, and the insufficient completeness of research on the features of the integrated approach to the design and deployment of innovative means of production order support. Based on the determined factors of the operation of the enterprise in the latest conditions of the fourth industrial revolution, directions for the formation of strategies for the introduction of the elements of Industry 4.0 in modern printing enterprises, as well as information protection systems, are determined with electronic document circulation. The mechanisms of decision of tasks of management informative risks considered in complex control system by printeries in the conditions of vagueness and at co-operation of elements of control system between itself. The necessity of using a web portal for the formation of printing orders is substantiate, the main components are define and the levels of access to them described. The paper examines the use of classic and gray fuzzy cognitive maps to solve the problem of cyber security risk assessment of the intelligent management system of a printing enterprise. It is demonstrate that the average estimate of local risk, which is formed using an ensemble of two heterogeneous fuzzy cognitive maps, decreases compared to the use of individual cognitive maps. In order tî better, highlight the results of the research, an example of the application of the proposed methodology for assessing the risks of ensuring the integrity of telemetric information in the industrial network of the intelligent technological process management system of a printing enterprise given, with the continuity of the technological process of manufacturing printing products. In addition to the classic FCM, the paradigms of two variants of the FCM extension were also use in the study, namely, the gray FCM, which used to solve the problem of assessing cyber security risks of intelligent management systems of printing enterprises. An analysis of the possibility of building FCM ensembles to increase the effectiveness of risk assessment using several options for formalizing the expert’s knowledge and experience performed. A fragment of the enterprise management system was consider and an analysis of possible directions of attacks on the printing enterprise by malicious software was perform. These are attacks such as replacing the executable files of server and ARM software, overwriting PLC projects during system operation, and refusing to service the equipment. Based on the formed list of attack vectors and the consequences of their implementation, the task of analyzing the risks of cyber security of a printing enterprise, taking into account the impact on the system of possible internal threats, was considered, using the cognitive modeling apparatus as a modeling tool. The scenario of cognitive modeling of the influence of an internal criminal who exploits the vulnerabilities of the software and hardware components of the control system using the given variants of FCM construction is considered. The average assessment of local risks, which formed using an ensemble of cognitive maps, is better from the point of view of dispersion of assessments of the state of target concepts than the use of individual FCMs. The spread of estimates of the state of ensemble concepts is smaller than the spread of estimates of their gray values using the GFCM, on average by 1.4–1.8 times, which indicates a decrease in the influence of the subjectivity factor on the results of risk assessment. The performed scenario modeling showed that the use of the specified means of protection and organizational measures allows reducing the assessment of local risks by 12–18%, which is a significant indicator. This technique allows obtaining a qualitative and quantitative assessment of risk indicators, taking into account the entire set of objective and subjective factors of uncertainty.

Skew Cyclic Codes over $\mathbb{Z}_{8}+u\mathbb{Z}_{8}+v\mathbb{Z}_{8}$

In this paper, we study the skew cyclic codes over the ring $S=\mathbb{Z}_{8}+u\mathbb{Z}_{8}+v\mathbb{Z}_{8}$, where $u^{2}=u$, $v^{2}=v$, $uv=vu=0$. We consider these codes as left $S[x,\theta]$-submodules and use the Gray map on $S$ to obtain the $\mathbb{Z}_{8}$-images. The generator and parity-check matrices of a free $\theta$-cyclic
 code of even length over $S$ are determined. Also, these codes are generalized to double skew-cyclic codes. We give some examples using Magma computational algebra system.

One Weight Codes Over the Ring $F_q[v]/(v^s-1)$

In this study, we obtain one-Lee weight codes over a class of nonchain rings and study their structures.
 We give an explicit construction for one-Lee weight codes. A method to derive more one-Lee weight codes from given a one-Lee weight code is also represented. By defining and making use of a distance-preserving Gray map, we get a family of optimal one-Hamming weight codes over finite fields.

Two families of few-weight codes over a finite chain ring

Linear codes over finite chain rings meeting the Griesmer bound are particularly interesting since they are closely related to minihyper in projective Hjelmslev spaces. In this paper, motivated by the nice article (Li et al., 2018 [23]), two classes of linear codes with few non-zero Hamming weights over the finite chain ring R=Fq+uFq are constructed, and one of them meets the Griesmer bound over finite commutative local rings. By a Gray map, we obtain that the Gray images of the constructed codes over the ring R are linear codes with two weights over the finite field Fq with q elements, and these codes are optimal with respect to the well-known Griesmer bound under certain conditions. Our results give an affirmative answer to two (related) open questions raised in the article mentioned above. Remarkably, some of the constructed linear codes over R presented in this paper correspond to minihypers in projective Hjelmslev spaces over finite chain rings. Besides, their Gray images can be used to construct secret sharing schemes with nice access structures and other applications thanks to the minimality property that possesses our constructed codes.

Quantum Codes Obtained from Skew ϱ - λ -Constacyclic Codes over R k

Let R k = F q u 1 , u 2 , ⋯ , u k / < u i 2 = α i u i , u i u j = u j u i = 0 > , where q = p m , p is an odd prime, α i is a unit over F q , and i , j = 1,2 , ⋯ , k . In this article, we define a Gray map from R k n to F q k + 1 n , we study the structure of skew ϱ - λ -constacyclic codes over R k , and then we give the necessary and sufficient conditions for skew ϱ - λ -constacyclic codes over R k to satisfy dual containing. Further, we have obtained some new nonbinary quantum codes from skew ϱ - λ -constacyclic over R k by using the CSS construction.

QUANTUM CODES OBTAINED THROUGH -CONSTACYCLIC CODES OVER

The structural properties and construction of quantum codes over using Constacyclic codes over the finite commutative non-chain ring = where are the focus of htis paperand is field having elements with characteristic p where p is an prime such that . A Gray map is defined between and . Decomposing constacyclic codes into cyclic and negacyclic codes over yields the parameters of quantum codes over . Some examples of quantum codes of arbitrary length are also obtained as an application.

Quantum codes from constacyclic codes over S_{k}

Let S_{k}={mathbb{F}}_{q}[u_{1},u_{2},ldots ,u_{k}]/langle u^{3}_{i}=u_{i},u_{i}u_{j}=u_{j}u_{i}=0 rangle , where 1leq i,jleq k, q=p^{m}, p is an odd prime. First, we define two new Gray maps phi _{k} and varphi _{k}, and study their Gray images. Further, we determine the structure of constacyclic codes and their dual codes, and give a necessary and sufficient conditions of constacyclic codes to contain their duals. Finally, we obtain some new quantum codes over mathbb{F}_{q} by using CSS construction, and compare the constructed codes better than the existing literature.

An Adjusted Gray Map Technique for Constructing Large Four-Level Uniform Designs

An Adjusted Gray Map Technique for Constructing Large Four-Level Uniform Designs

DNA Code from Cyclic and Skew Cyclic Codes over F4[v]/⟨v3⟩

The main motivation of this work is to study and obtain some reversible and DNA codes of length n with better parameters. Here, we first investigate the structure of cyclic and skew cyclic codes over the chain ring R:=F4[v]/⟨v3⟩. We show an association between the codons and the elements of R using a Gray map. Under this Gray map, we study reversible and DNA codes of length n. Finally, several new DNA codes are obtained that have improved parameters than previously known codes. We also determine the Hamming and the Edit distances of these codes.

Constacyclic Codes Over 𝑭𝒒[𝒖] /〈𝒖𝟑 = 𝟎〉 and Their Application of Constructing Quantum Codes

Let 𝑅 = 𝐹𝑞+u𝐹𝑞+𝑢^2𝐹𝑞, 𝑢^3=0 be a finite chain ring. In this paper, we give the structure of constacyclic codes over 𝑅 and obtain self-orthogonal codes over 𝐹𝑞 by using the Gray map from 𝑅𝑛 to 𝐹𝑞^(3𝑛). As an application, we present a construction of quantum codes from the codes obtained from this class.

Duadic codes over <inline-formula><tex-math id="M1">$ \mathbb{Z}_4+u\mathbb{Z}_4 $</tex-math></inline-formula>

In this paper, we study the structure of duadic codes of an odd length $ n $ over $ \mathbb{Z}_4+u\mathbb{Z}_4 $, $ u^2 = 0 $, (more generally over $ \mathbb{Z}_{q}+u\mathbb{Z}_{q} $, $ u^2 = 0 $, where $ q = p^r $, $ p $ a prime and $ (n, p) = 1 $) using the discrete Fourier transform approach. We study these codes by considering them as a class of abelian codes. Some results related to self-duality and self-orthogonality of duadic codes are presented. Some conditions on the existence of self-dual augmented and extended duadic codes over $ \mathbb{Z}_4+u\mathbb{Z}_4 $ are determined. We present a sufficient condition for abelian codes of the same length over $ \mathbb{Z}_4+u\mathbb{Z}_4 $ to have the same minimum Hamming distance. A new Gray map over $ \mathbb{Z}_4+u\mathbb{Z}_4 $ is defined, and it is shown that the Gray image of an abelian code over $ \mathbb{Z}_4+u\mathbb{Z}_4 $ is an abelian code over $ \mathbb{Z}_4 $. We have obtained five new linear codes of length $ 18 $ over $ \mathbb{Z}_4 $ from duadic codes of length $ 9 $ over $ \mathbb{Z}_4+u\mathbb{Z}_4 $ through the Gray map and a new map from $ \mathbb{Z}_4+u\mathbb{Z}_4 $ to $ \mathbb{Z}_4^2 $.

On codes over product of finite chain rings

In this paper, codes over the direct product of two finite commutative chain rings are studied. The standard form of the parity-check matrix is determined. The structure of self-dual codes is described. A distance preserving Gray map from the direct product of chain rings to a finite field is defined. Two upper bounds on minimum distance are obtained.

Linearity and classification of [formula omitted]-linear generalized Hadamard codes

The ZpZp2-additive codes are subgroups of Zpα1×Zp2α2, and can be seen as linear codes over Zp when α2=0, Zp2-additive codes when α1=0, or Z2Z4-additive codes when p=2. A ZpZp2-linear generalized Hadamard (GH) code is a GH code over Zp which is the Gray map image of a ZpZp2-additive code. Recursive constructions of ZpZp2-additive GH codes of type (α1,α2;t1,t2) with t1,t2≥1 are known. In this paper, we generalize some known results for ZpZp2-linear GH codes with p=2 to any p≥3 prime when α1≠0, and then we compare them with the ones obtained when α1=0. First, we show for which types the corresponding ZpZp2-linear GH codes are nonlinear over Zp. Then, for these codes, we compute the kernel and its dimension, which allow us to classify them completely. Moreover, by computing the rank of some of these codes, we show that, unlike Z4-linear Hadamard codes, the Zp2-linear GH codes are not included in the family of ZpZp2-linear GH codes with α1≠0 when p≥3 prime. Indeed, there are some families with infinite nonlinear ZpZp2-linear GH codes, where the codes are not equivalent to any Zps-linear GH code with s≥2.

Using Whole Slide Gray Value Map to Predict HER2 Expression and FISH Status in Breast Cancer.

Accurate detection of HER2 expression through immunohistochemistry (IHC) is of great clinical significance in the treatment of breast cancer. However, manual interpretation of HER2 is challenging, due to the interobserver variability among pathologists. We sought to explore a deep learning method to predict HER2 expression level and gene status based on a Whole Slide Image (WSI) of the HER2 IHC section. When applied to 228 invasive breast carcinoma of no special type (IBC-NST) DAB-stained slides, our GrayMap+ convolutional neural network (CNN) model accurately classified HER2 IHC level with mean accuracy 0.952 ± 0.029 and predicted HER2 FISH status with mean accuracy 0.921 ± 0.029. Our result also demonstrated strong consistency in HER2 expression score between our system and experienced pathologists (intraclass correlation coefficient (ICC) = 0.903, Cohen's κ = 0.875). The discordant cases were found to be largely caused by high intra-tumor staining heterogeneity in the HER2 IHC group and low copy number in the HER2 FISH group.

Diagnosing Parkinson's disease by combining neuromelanin and iron imaging features using an automated midbrain template approach

Background and purposeEarly diagnosis of Parkinson's disease (PD) is still a clinical challenge. Most previous studies using manual or semi-automated methods for segmenting the substantia nigra (SN) are time-consuming and, despite raters being well-trained, individual variation can be significant. In this study, we used a template-based, automatic, SN subregion segmentation pipeline to detect the neuromelanin (NM) and iron features in the SN and SN pars compacta (SNpc) derived from a single 3D magnetization transfer contrast (MTC) gradient echo (GRE) sequence in an attempt to develop a comprehensive imaging biomarker that could be used to diagnose PD. Materials and methodsA total of 100 PD patients and 100 age- and sex-matched healthy controls (HCs) were imaged on a 3T scanner. NM-based SN (SNNM) boundaries and iron-based SN (SNQSM) boundaries and their overlap region (representing the SNpc) were delineated automatically using a template-based SN subregion segmentation approach based on quantitative susceptibility mapping (QSM) and NM images derived from the same MTC-GRE sequence. All PD and HC subjects were evaluated for the nigrosome-1 (N1) sign by two raters independently. Receiver Operating Characteristic (ROC) analyses were performed to evaluate the utility of SNNM volume, SNQSM volume, SNpc volume and iron content with a variety of thresholds as well as the N1 sign in diagnosing PD. Correlation analyses were performed to study the relationship between these imaging measures and the clinical scales in PD. ResultsIn this study, we verified the value of the fully automatic template based midbrain deep gray matter mapping approach in differentiating PD patients from HCs. The automatic segmentation of the SN in PD patients led to satisfactory DICE similarity coefficients and volume ratio (VR) values of 0.81 and 1.17 for the SNNM, and 0.87 and 1.05 for the SNQSM, respectively. For the HC group, the average DICE similarity coefficients and VR values were 0.85 and 0.94 for the SNNM, and 0.87 and 0.96 for the SNQSM, respectively. The SNQSM volume tended to decrease with age for both the PD and HC groups but was more severe for the PD group. For diagnosing PD, the N1 sign performed reasonably well by itself (Area Under the Curve (AUC) = 0.783). However, combining the N1 sign with the other quantitative measures (SNNM volume, SNQSM volume, SNpc volume and iron content) resulted in an improved diagnosis of PD with an AUC as high as 0.947 (using an SN threshold of 50ppb and an NM threshold of 0.15). Finally, the SNQSM volume showed a negative correlation with the MDS-UPDRS III (R2 = 0.1, p = 0.036) and the Hoehn and Yahr scale (R2 = 0.04, p = 0.013) in PD patients. ConclusionIn summary, this fully automatic template based deep gray matter mapping approach performs well in the segmentation of the SN and its subregions for not only HCs but also PD patients with SN degeneration. The combination of the N1 sign with other quantitative measures (SNNM volume, SNQSM volume, SNpc volume and iron content) resulted in an AUC of 0.947 and provided a comprehensive set of imaging biomarkers that, potentially, could be used to diagnose PD clinically.

Longitudinal evolution of neuropathological substrates of Alzheimer’s disease in obese patients

AbstractBackgroundObesity is a metabolic condition with increasing prevalence all over the world. Patients with a body mass index (BMI) higher than 30 are considered obese. Obesity is also a risk factor for chronic morbidities such as type 2 diabetes and may increase the risk of developing Alzheimer's disease (AD). Not much is known about longitudinal changes in Alzheimer’s pathology in these patients. We hypothesised that BMI would predict longitudinal pathological alterations derived from imaging parameters.Method252 participants (n=107 obese non‐diabetic patients with BMI>30) cognitively normal (n=80) and with mild cognitive impairment (n=172) were evaluated from the Alzheimer’s Disease Neuroimaging Initiative (Mean age = 73.6 years, SD = 8.0). All participants had two T1‐weighted MPRAGE MRI scans within two‐years (Mean gap=718 days, SD=107). Regional cortical thickness was measured on T1‐MPRAGE using FreeSurfer v.6.0. Individual gray matter density maps were computed using voxel‐based morphometry (VBM) and regional values were sampled in various cortical regions. Regional cortical thickness and gray matter density are expressed as delta values between baseline and followup (Value followup ‐ Value Baseline). Spearman’s correlation coefficients were calculated to assess the relationship between BMI and imaging biomarkers.ResultIn the whole cohort, we found that BMI is significantly negatively correlated with longitudinal changes in cortical thickness in anterior cingulate (ACC, p=0.0073, r=‐0.17) and posterior cingulate (PCC, p=0.0147, r=‐0.15) cortical thickness. We also found that BMI is significantly negatively correlated with longitudinal changes in frontal (p=0.0184, r=‐0.15), parietal (p=0.0057, r=‐0.18) and temporal (p=0.0141, r=‐0.16) gray matter density. When looking only at MCI participants, we found similar results with even stronger correlations. BMI is significantly negatively correlated with delta anterior cingulate (ACC, p=0.0008, r=‐0.25) and posterior cingulate (PCC, p=0.004, r=‐0.22) cortical thickness.ConclusionIn this cohort of obese and non‐obese participants cognitively normal and with MCI, we found that obesity was associated with a longitudinal 2‐years worsening of macrostructural changes. Higher BMI was associated with a higher reduction of cortical thickness and with a decreased gray matter density in several brain regions.

On quantum codes from codes over Rm

Let Rm = Fq [y] = /〈ym - 1〉, where m|q - 1. In this paper, we obtain the structure of linear and cyclic codes over Rm. Also, we introduce a preserving-orthogonality Gray map from Rm to Fmq. Among the main results, we obtain the exact structure of self-orthogonal cyclic codes over Rm to introduce parameters of quantum codes from cyclic codes over Rm.

Reversible complement cyclic codes over ℤ4 + uℤ4 + vℤ4 for DNA computing

In this paper, we develop a theory for constructing cyclic codes of odd length over the ring [Formula: see text], where [Formula: see text], which plays an important role in DNA computing. A direct link between the elements of [Formula: see text] and the [Formula: see text] codons used in the amino acids of the living organisms is established. Then, we investigate reversible cyclic codes and reversible complement cyclic codes of odd length over [Formula: see text]. Moreover, we give some properties of binary images of the codons under the Gray map. Finally, two examples of cyclic codes over [Formula: see text] with their minimum Hamming distance will be studied as well.

Quantum codes from constacyclic codes over a semi-local ring

Let R r = F q + v 1 F F q + ··· + v r F q , where q is the power of prime, v i 2 = v i , v i v j = v j v i = 0 for 1 ≤ i, j ≤ r and r ≥ 1. In this paper, the structure of λ-constacyclic codes over the ring R r is studied and a Gray map ϕ from R r n to F q ( r +1) n is given. The necessary and sufficient conditions for these codes to contain their Euclidean duals are determined. As an application, we obtain many new better quantum codes from dual-containing λ-constacyclic codes over R r , for r = 1, 2, 3, that improve the known existing quantum codes.

Butson full propelinear codes

In this paper we study Butson Hadamard matrices, and codes over finite rings coming from these matrices in logarithmic form, called BH-codes. We introduce a new morphism of Butson Hadamard matrices through a generalized Gray map on the matrices in logarithmic form, which is comparable to the morphism given in a recent note of Ó Catháin and Swartz. That is, we show how, if given a Butson Hadamard matrix over the k{mathrm{th}} roots of unity, we can construct a larger Butson matrix over the ell mathrm{th} roots of unity for any ell dividing k, provided that any prime p dividing k also divides ell . We prove that a {mathbb {Z}}_{p^s}-additive code with p a prime number is isomorphic as a group to a BH-code over {mathbb {Z}}_{p^s} and the image of this BH-code under the Gray map is a BH-code over {mathbb {Z}}_p (binary Hadamard code for p=2). Further, we investigate the inherent propelinear structure of these codes (and their images) when the Butson matrix is cocyclic. Some structural properties of these codes are studied and examples are provided.