Group Modulo Research Articles

Randomized Key-based GMO-BCS Image Encryption for Securing Medical Image

An essential security requirement while transmitting and receiving medical images is to maintain confidentiality and authorization of these medical images. This paper contains a proposal of an enhanced lossless image encryption algorithm that provides security to Digital Imaging and Communications in Medicine (DICOM) images by producing a random key with using enhanced group modulo based bit circular shift (GMO-BCS) technique. Random key production is the backbone of this technique to provide robust security of medical images that transfer over a network. In the encryption process, we randomly generate a key for each and every pixel of the DICOM image. Group theory is used in this process to create circular shifting in 8-bit pixel values while the security enhancement employs the random key for encryption. This technique is more suitable for medical image encryption either by direct transmission or multimedia app-based transmission under telemedicine and others.

Fundamental groups, 3-braids, and effective estimates of invariants

We define invariants of braids rather than invariants of conjugacy classes of braids. For any pure 3-braid we give effective upper and lower bounds for these invariants. This is done in terms of a natural syllable decomposition of the word representing the image of the braid in the braid group modulo its center. The bounds differ by a multiplicative constant not depending on the word. Respective bounds are given for all 3-braids. We also obtain effective upper and lower bounds for the entropy of pure 3-braids in these terms. The proof leads to the study of the extremal length (in the sense of Ahlfors) of classes of curves representing elements of the fundamental group of the twice punctured complex plane.

Mechanical study of polyurethane elastomer and Medpor as the material of artificial auricular scaffold

By comparing the mechanics of human auricular cartilage, polyurethane elastic material, and high density polyethylene material (Medpor), to produce theoretical proof on choosing optimal artificial auricular scaffold materials. The experimental materials were divided into 3 groups with 6 samples in each: the auricular cartilage group (group A), the polyurethane elastic material group (group B), and the Medpor group (group C). With an Instron5967 mechanical testing machine, compression and tensile testing were performed to respectively measure values of compression parameters (including yield stress, yield load, elastic modulus, yield compressibility, compressibility within 2 MPa, and compression stress within 10% strain) and values of tensile parameters (including yield stress, yield load, elastic modulus, yield elongation, elongation within 2 MPa, tensile stress within 1% strain) for comparison. Compression testing: no obvious yield points were observed in the whole process in samples of group B, while obvious yield points were observed in samples of groups A and C. There was no significant difference between groups A and C with respect to yield stress and yield load ( P>0.05); while the yield compressibility in group C was significantly lower than that in group A ( P<0.05) and the elastic modulus in group C was significantly higher than that in group A ( P<0.05). There was a significant difference with respect to compressibility within 2 MPa of materials among the 3 groups ( P<0.05), the high, medium, and low values go to groups B, A, and C respectively. The compression stress within 10% strain in group C was significantly higher than that in groups A and B ( P<0.05), and there was no significant difference between that in groups A and B ( P>0.05). Tensile testing: the materials in group B had extremely high tensile strength. The yield stress in groups A and B was significantly higher than that in group C ( P<0.05), and the elastic modulus and tensile stress within 1% strain were significantly lower than those in group C ( P<0.05); but no significant difference was found between those in groups A and B ( P>0.05). There was no significant difference with respect to yield load among the 3 groups ( P>0.05); but there was significant difference with respect to yield elongation among the 3 groups ( P<0.05), and the high, medium, and low values go to groups B, A, and C respectively. The elongation within 2 MPa in group B was significantly higher than that in groups A and C ( P<0.05), and there was no significant difference between that in groups A and C ( P>0.05). Compared with the Medpor, the polyurethane elastic material is a more ideal artificial auricular scaffold material.

On properties of output sequence of multi-cyclic generator over direct sum of residue groups modulo 2

Abstract The formula for the frequencies of symbols in the output sequence of multi-cyclic generator over the direct sum of residue groups modulo 2 is obtained. In the case when cells of registers contain independent random values with the uniform distribution the limit joint distribution of the frequencies (as lengths of the registers tend to infinity) is obtained.

On the Nil R-mod Abelian Groups

Let M be an abelian group and N be a subgroup of M. Given a ring R, the notion of a left nil R-mod group modulo N is introduced as a generalization of a left nil R-mod group. Moreover, we define \(\text {Nil}^{l}_{R}(M)\) as a subgroup of M which is defined to be the intersection of all subgroups N of M such that M is a left nil R-mod group modulo N. In this paper, we investigate some properties of the \(\text {Nil}^{l}_{R}(M)\). Moreover, we describe it in some torsion-free abelian groups of rank two.

Goldie Rings Graded by a Group with Periodic Quotient Group Modulo the Center

In this paper, we study gr-prime and gr-semiprime Goldie rings graded by a group with periodic quotient group modulo the center. We enhance the theorem of Goodearl and Stafford (2000) about gr-prime rings graded by Abelian groups; we extend the Abelian group class to the class of groups with periodic quotient group modulo the center. We also decompose the orthogonal graded completion Ogr(R) of a gr-semiprime Goldie ring R (graded by a group satisfying the same condition) into a direct sum of gr-prime Goldie rings R1, . . . , Rn and prove that the maximal graded quotient ring Qgr(R) equals the direct sum of classical graded quotients rings of R1, . . . , Rn.

Topological Methods in One Numerical Scheme of Solving Three-Dimensional Continuum Mechanics Problems

We discuss numerical schemes of finite element method for solving the continuum mechanics problems. Previously a method of acceleration of calculations was developed which uses the simplicial mesh inscribed in the original cubic cell partition of a three-dimensional body. In this paper we show that the obstacle to the construction of this design may be described in terms of homology groups modulo 2. The main goal of the paper is to develop a method of removing this obstacle. The reaching of the goal is based on efficient algorithms for computing bases of the homology groups which are dual with respect to the intersection form.

Continuous-light versus pulsed-light accelerated corneal crosslinking with ultraviolet-A and riboflavin

To determine whether the pulsed-light ultraviolet-A (UVA) accelerated corneal crosslinking (CXL) procedure is more efficacious and selective than its continuous-light counterpart in rabbits. School of Ophthalmology and Optometry, Wenzhou Medical University, Wenzhou, Zhejiang, China. Experimental study. Fifty-four rabbits were divided into 2 groups. Group 1 had continuous-light accelerated CXL using 9mW/cm2 UVA for 10minutes (5.4J/cm2). Group 2 had pulsed-light accelerated CXL by exposing them to 9mW/cm2 UVA for 20minutes (1second on/1second off). Corneal stromal demarcation line depth, invivo confocal microscopic analysis, biomechanical stiffness, endothelial cell density, and keratocyte apoptosis were measured after performing these CXL procedures. The mean stromal demarcation line depth was 254.7μm±47.4 (SD) in Group 1 and 341.1±36.1μm in Group 2 (P<.01). One day after CXL, confocal analysis and histological staining identified keratocyte apoptotic fragments in the anterior stroma in the Group 2 corneas whereas all cells were obliterated in Group1. Seven days after treatment, the thicknesses in Group 1 were significantly greater than those in Group 2 (P<.05). Endothelial cell losses were reversible; however, in Group 1, some losses were still evident on day 7. Increases in both the stress-strain relationship and tangent modulus in Group 2 were greater than those in Group1. The pulsed-light accelerated CXL protocol was less injurious and more efficacious at inducing CXL than the continuous-light accelerated CXL protocol in rabbit corneas.

A new public key cryptosystem over ℤn2*

At Eurocrypt ’99, Paillier showed a cryptographic application of the group [Formula: see text], the multiplicative group modulo [Formula: see text] where [Formula: see text] is some RSA modulus. In this paper, we have present a new public key cryptosystem over [Formula: see text] where [Formula: see text] is a product of two safe primes, which is based on two intractable problems namely, integer factorization and partial discrete logarithm problem over [Formula: see text], the group of quadratic residues modulo [Formula: see text]. This scheme is a combination of BCP (Bresson–Catalano–Pointcheval) cryptosystem, proposed by Bresson et al. at Asiacrypt ’03 and the Rabin–Paillier scheme proposed by Galindo et al. at PKC 2003. We will show that the one-wayness of this new scheme equally depends on the Computational Diffie–Hellman assumption and factoring assumption. We will also prove that the proposed scheme is more secure than the BCP cryptosystem and the Rabin–Paillier cryptosystem.

Effects of Astragalus Polysaccharide on Mechanical Characterization of Liver Sinusoidal Endothelial Cells by Atomic Force Microscopy at Nanoscale

To study the effects of Astragalus polysaccharide (APS), the primary effective component of the Chinese herb medicine Astragalus membranaceus (frequently used for its anti-hepatic fibrosis effects), on nanoscale mechanical properties of liver sinusoidal endothelial cells (SECs). Using endothelial cell medium as the control, 5 experimental groups were established utilizing different concentrations of APS, i.e. 12.5, 25, 50, 100, and 200 μg/mL. By using atomic force microscopy along with a microcantilever modified with a silicon dioxide microsphere as powerful tools, the value of Young's modulus in each group was calculated. SAS 9.1 software was applied to analyze the values of Young's modulus at the pressed depth of 300 nm. Environmental scanning electron microscopy was performed to observe the surface microtopography of the SECs. The value of Young's modulus in each APS experimental group was significantly greater than that of the control group: as APS concentration increased, the value of Young's modulus presented as an increasing trend. The difference between the low-concentration (12.5 and 25 μg/mL) and high-concentration (200 μg/mL) groups was statistically significant (P<0.05), but no significant differences were observed between moderateconcentration (50 and 100 μg/mL) groups versus low- or high-concentration groups (P>0.05). Surface topography demonstrated that APS was capable of increasing the total area of fenestrae. The values of Young's modulus increased along with increasing concentrations of APS, suggesting that the stiffness of SECs increases gradually as a function of APS concentration. The observed changes in SEC mechanical properties may provide a new avenue for mechanistic research of anti-hepatic fibrosis treatments in Chinese medicine.

Iwasawa theory of quadratic twists of X 0(49)

The field \(K = \mathbb{Q}\left( {\sqrt { - 7} } \right)\) is the only imaginary quadratic field with class number 1, in which the prime 2 splits, and we fix one of the primes p of K lying above 2. The modular elliptic curve X0(49) has complex multiplication by the maximal order O of K, and we let E be the twist of X0(49) by the quadratic extension \(KK(\sqrt M )/K\), where M is any square free element of O with M ≡ 1 mod 4 and (M,7) = 1. In the present note, we use surprisingly simple algebraic arguments to prove a sharp estimate for the rank of the Mordell-Weil group modulo torsion of E over the field F∞ = K(Ep∞), where Ep∞ denotes the group of p∞-division points on E. Moreover, writing B for the twist of X0(49) by \(K(\sqrt[4]{{ - 7}})/K\), our Iwasawa-theoretic arguments also show that the weak form of the conjecture of Birch and Swinnerton-Dyer implies the non-vanishing at s = 1 of the complex L-series of B over every finite layer of the unique Z2-extension of K unramified outside p. We hope to give a proof of this last non-vanishing assertion in a subsequent paper.

ABELIAN -DIVISION FIELDS OF ELLIPTIC CURVES AND BRAUER GROUPS OF PRODUCT KUMMER &amp; ABELIAN SURFACES

Let$Y$be a principal homogeneous space of an abelian surface, or a K3 surface, over a finitely generated extension of$\mathbb{Q}$. In 2008, Skorobogatov and Zarhin showed that the Brauer group modulo algebraic classes$\text{Br}\,Y/\text{Br}_{1}\,Y$is finite. We study this quotient for the family of surfaces that are geometrically isomorphic to a product of isogenous non-CM elliptic curves, as well as the related family of geometrically Kummer surfaces; both families can be characterized by their geometric Néron–Severi lattices. Over a field of characteristic$0$, we prove that the existence of a strong uniform bound on the size of the odd torsion of$\text{Br}Y/\text{Br}_{1}Y$is equivalent to the existence of a strong uniform bound on integers$n$for which there exist non-CM elliptic curves with abelian$n$-division fields. Using the same methods we show that, for a fixed prime$\ell$, a number field$k$of fixed degree$r$, and a fixed discriminant of the geometric Néron–Severi lattice,$\#(\text{Br}Y/\text{Br}_{1}Y)[\ell ^{\infty }]$is bounded by a constant that depends only on$\ell$,$r$, and the discriminant.

A new public key scheme based on DRSA and generalized GDLP

In this paper, we propose a new public key scheme, which is a combination of RSA variant namely the DRSA and the generalization of generalized discrete logarithm problem (generalized GDLP). The security of this scheme depends equally on the integer factorization of [Formula: see text] and the discrete logarithm problem (DLP) on [Formula: see text], where [Formula: see text] is the product of two large primes and [Formula: see text] is the multiplicative group modulo [Formula: see text]. The scheme is a randomized algorithm. It is at least as secure as the DRSA and ElGamal schemes. We also compare the encryption–decryption performance of the proposed scheme with the RSA and DRSA schemes.

Complex varieties with infinite Chow groups modulo 2

For a very general principally polarized complex abelian 3-fold, the Chow group of algebraic cycles is innite modulo every prime number. In particular, this gives the

Explicit estimates for the zeros of Hecke L-functions

Let K be a number field and, for an integral ideal q of K, let χ be a character of the narrow ray class group modulo q. We establish various new and improved explicit results, with effective dependence on K,q and χ, regarding the zeros of the Hecke L-function L(s,χ), such as zero-free regions, Deuring–Heilbronn phenomenon, and zero density estimates.

On numerical equivalence for algebraic cobordism

We define and study the notion of numerical equivalence on algebraic cobordism cycles. We prove that algebraic cobordism modulo numerical equivalence is a finitely generated module over the Lazard ring, and it reproduces the Chow group modulo numerical equivalence. We show this theory defines an oriented Borel–Moore homology theory on schemes and oriented cohomology theory on smooth varieties.We compare it with homological equivalence and smash-equivalence for cobordism cycles. For the former, we show that homological equivalence on algebraic cobordism is strictly finer than numerical equivalence, answering negatively the integral cobordism analogue of the standard conjecture (D). For the latter, using Kimura finiteness on cobordism motives, we partially resolve the cobordism analogue of a conjecture by Voevodsky on rational smash-equivalence and numerical equivalence.

High-irradiance CXL combined with myopic LASIK: flap and residual stroma biomechanical properties studied ex-vivo

Background/aimsTo evaluate ex vivo biomechanical and enzymatic digestion resistance differences between standard myopic laser in-situ keratomileusis (LASIK) compared with LASIK+CXL, in which high-irradiance cross-linking (CXL) is added.MethodsEight human donor corneas...

Experimental study of glyceraldehyde cross-linking of posterior scleral on FDM in guinea pigs

The purpose of this study is to observe the effects of glyceraldehyde cross-linking on sclera biomechanical strength and experimental myopia. 50 three weeks aged guinea pigs were randomly divided into 5 groups: A, B, C, D, E. Each group had 10 guinea pigs. The right eye was set as the experimental eye, the left eye was used as control. Group A: 7 days mask; Group B: 21 days mask, plus physiological saline retrobulbar injection at mask day 1, 8, 15; Group C: 21 days mask, plus 0.05 mol/L glyceraldehyde retrobulbar injection at mask day 1, 8, 15; Group D: 21 days mask, plus 0.5 mol/L glyceraldehyde retrobulbar injection at mask day 1, 8, 15; Group E: normal control group. Several parameters of 7 guinea pigs of each group were measured before and after deprivation (mask day 7, 14, 21), including ocular axial length, refractive error, ultimate stress (σmax) (MPa), ultimate strain(εmax) (%) and 6% elastic modulus (MPa). The effects of glyceraldehyde on adjacent tissues of the rest 3 guinea pigs were detected by histopathological and immunohistochemical studies. Differences between experiment eyes and contralateral, eyes were compared with paired t test and correlative analysis. The experimental eyes appeared the increase of the the vitreous cavity length, the axial length and myopia after deprivation. In group A, group B and group C, the differences of the length of the vitreous cavity (group A (2.991 ± 0.078) mm, group B (2.961 ± 0.038) mm and group C (2.936 ± 0.021) mm), the axial length(group A (7.263 ± 0.133) mm, group B (7.732 ± 0.099) mm and group C (7.665 ± 0.055) mm) and refractive error (group A (-2.214 ± 2.881) D, group B (-4.525 ± 2.415) D and group C (-1.607 ± 0.866) D) between the experimental eye and the fellow eye was statistically significant (vitreous cavity = 3.234, 4.758, 7.608; Pvitreous cavity = 0.018, 0.002, 0.001; axial = 3.198,, 4.758, 7.608; Paxial = 0.019, 0.002, 0.000; refraction = -7.120, -4.020, -6.334; Prefraction = 0.000, 0.005, 0.001). In group D and group E, there is no difference between deprived eye and control eye about the length of the vitreous chamber as well as axial length (vitreous = 0.542, -0.646; Pvitreous cavity = 0.607, 0.539; axial = 0.542, -0.646; Paxial = 0.607, 0.539). The experimental eye ((-3.921 ± 0.874)D) and the fellow eye ((-3.321 ± 1.205)D) of group D, the difference of diopter was statistically significant (refraction = -3.154, Prefraction = 0.020). At the end of the experiment, the change of diopter of experimental eye of group B, C, D, E was significantly different (F = 61.249, P = 0.000). The difference of diopter change between group B ((8.800 ± 0.616) D), group C ( (7.236 ± 2.198) D), group D ( (6.271 ± 1.112) D) and the normal control group ((0.934 ± 0.158) D) was statistically significant (PB = 0.000, PC = 0.000, PD = 0.000). At the end of the experiment, the ultimate stress and 6% elastic modulus of group B experimental eye was (7.988 ± 3.677) MPa (P = 0.002) and (19.938 ± 4.871) MPa (P = 0.001), decreased 10.06% and 34.17% respectively. On the other hand the ultimate strain was (28.6 ± 3.6) % (P = 0.034), increased 19.17%. After the cross-linking treatment, the ultimate stress and 6% elastic modulus of group C experimental eye was (9.244 ± 0.806) MPa (P = 0.001) and (26.180 ± 4.388) MPa (P = 0.031) , decreased 23.13% and 13.34%, the ultimate strain was (26.2 ± 1.0) % (P = 0.016) , increased 12.93% separately. The ultimate stress of group D experimental eye was (12.476 ± 2.507) MPa (P = 0.580), decreased 5.50%, 6% elastic modulus was (30.446 ± 3.410) MPa (P = 0.314), increased 6.53%, ultimate strain was (23.8 ± 1.8) % (P = 0.253), decreased 4.42% respectively. Ultrastructure examination showed that, decreased scleral thickness with fibers lined up in order, without inflammatory cells Infiltration. Expressions of matrix metalloproteinases-2(MMP-2) mainly decrease in the episcleral tissue. The stroma of choroid, and the outer plexiform layer. Glyceraldehyde is a safe and effective cross-linking agent that could significantly enhance the sclera biomechanical strength. Glyceraldehyde cross-linking method could effectively control the development of myopia in animal model.

On the range of Carmichael's universal-exponent function

Let $\lambda $ denote Carmichael's function, so $\lambda (n)$ is the universal exponent for the multiplicative group modulo $n$. It is closely related to Euler's $\varphi $-function, but we show here that the image of $\lambda $ is much denser than the im

Effect of solid freeform fabrication-based polycaprolactone/poly(lactic-co-glycolic acid)/collagen scaffolds on cellular activities of human adipose-derived stem cells and rat primary hepatocytes

Highly biocompatible polycaprolactone (PCL)/poly(lactic-co-glycolic acid) (PLGA)/collagen scaffolds in which the PCL/PLGA collagen solution was selectively dispensed into every other space between the struts were fabricated using solid freeform fabrication (SFF) technology, as we described previously. The objective of this study was to evaluate and compare the PCL/PLGA/collagen scaffolds (group 3) with PCL/PLGA-only scaffolds (group 1) and PCL/PLGA scaffolds with collagen by the dip-coating method (group 2) using human adipose-derived stem cells (hASCs) and rat primary hepatocytes. The selectively dispensed collagen formed a three-dimensional (3D) network of nanofibers in group 3, as observed by scanning electron microscopy. The compressive strength and modulus of group 3 were approximately 140 and 510 times higher, respectively, than those of a sponge-type collagen scaffold whose weak mechanical properties were regarded as a critical drawback. Proliferation and osteogenic differentiation of hASCs were promoted significantly in group 3 compared to groups 1 and 2. In addition, we found that the viability and albumin secretion ability of rat primary hepatocytes were highly retained for 10 days in group 3 but not group 1. Interestingly, hepatocyte aggregation, which enhances hepatic function through cell-cell interactions, was observed particularly in group 3. In conclusion, group 3, in which the collagen was selectively dispensed in the 3D space of the porous PCL/PLGA framework, will be a promising 3D scaffold for culturing various cell types.