Multiplicative Inverse Research Articles

Nuevo enfoque para el calculo de la Caja-S para Rijndael-AES basado en una red neuronal artificial

The S-box is a basic important component in symmetric key encryption, used in block ciphers to confuse or hide the relationship between the plaintext and the ciphertext. In this paper a way to develop the transformation of an input of the S-box specified in AES encryption system through an artificial neural network and the multiplicative inverse in Galois Field is presented. With this implementation more security is achieved since the values of the S-box remain hidden and the inverse table serves as a distractor since it would appear to be the complete S-box. This is implemented on MATLAB and HSPICE using a network of perceptron neurons with a hidden layer and null error.

Improved Phase Corrections for Transoceanic Tsunami Data in Spatial and Temporal Source Estimation: Application to the 2011 Tohoku Earthquake

AbstractSystemic travel time delays of up to 15 min relative to the linear long waves for transoceanic tsunamis have been reported. A phase correction method, which converts the linear long waves into dispersive waves, was previously proposed to consider seawater compressibility, the elasticity of the Earth, and gravitational potential change associated with tsunami motion. In the present study, we improved this method by incorporating the effects of ocean density stratification, actual tsunami raypath, and actual bathymetry. The previously considered effects amounted to approximately 74% for correction of the travel time delay, while the ocean density stratification, actual raypath, and actual bathymetry, contributed to approximately 13%, 4%, and 9% on average, respectively. The improved phase correction method accounted for almost all the travel time delay at far‐field stations. We performed single and multiple time window inversions for the 2011 Tohoku tsunami using the far‐field data (>3 h travel time) to investigate the initial sea surface displacement. The inversion result from only far‐field data was similar to but smoother than that from near‐field data and all stations, including a large sea surface rise increasing toward the trench followed by a migration northward along the trench. For the forward simulation, our results showed good agreement between the observed and computed waveforms at both near‐field and far‐field tsunami gauges, as well as with satellite altimeter data. The present study demonstrates that the improved method provides a more accurate estimate for the waveform inversion and forward prediction of far‐field data.

Multiple level-set joint inversion of traveltime and gravity data with application to ore delineation: A synthetic study

We have developed a multiple level-set method for simultaneous inversion of gravity and seismic traveltime data. The method recovers the boundaries between regions with distinct physical properties assumed constant and known, creating structurally consistent models of two subsurface properties: P-wave velocity and density. In single level-set methods, only two rock units can be considered: background and inclusion. Such methods have been applied to examples representing various geophysical scenarios, including in the context of joint inversion. In multiple level-set methods, several units can be considered, which make them far more applicable to real earth scenarios. Recently, a multiple level-set method has been proposed for inversion of magnetic data. We extend the multiple level-set formulation to joint inversion of gravity and traveltime data, improving upon previous work, and we investigate applicability of such an inversion method in ore delineation. In mineral exploration environments, traditional seismic imaging and inversion methods are challenging because of the small target size and the specific physical property contrasts involved. First-arrival seismic traveltime and gravity data complement each other, and we found that joint multiple level-set inversion is more beneficial than separate inversions, especially with limited data and slow targets. Our method is more robust than the joint inversion method based on clustering of physical properties in recovery of piecewise homogeneous models not well-constrained by the data. To justify the known property assumption, we found the degree of robustness of the multiple level-set joint inversion to uncertainties arising from incomplete knowledge of small-scale subsurface physical property variations and target composition.

Search for Monic Irreducible Polynomials with Decimal Equivalents of Polynomials over Galois Field <I>GF</I>(<I>p<sup>q</sup></I>)

Substitution boxes or S-boxes play a significant role in encryption and de-cryption of bit level plaintext and cipher-text respectively. Irreducible Poly-nomials (IPs) have been used to construct 4-bit or 8-bit substitution boxes in many cryptographic block ciphers. In Advance Encryption Standard, the ele-ments of 8-bit S-box have been obtained from the Multiplicative Inverse (MI) of elemental polynomials (EPs) of the 1st IP over Galois field GF(28) by adding an additive element. In this paper, a mathematical method and the algorithm of the said method with the discussion of the execution time of the algorithm, to obtain monic IPs over Galois field GF(pq) have been illustrated with example. The method is very similar to polynomial multiplication of two polynomials over Galois field GF(pq) but has a difference in execution. The decimal equivalents of polynomials have been used to identify Basic Polynomials (BPs), EPs, IPs and Reducible polynomials (RPs). The monic RPs have been determined by this method and have been cancelled out to produce monic IPs. The non-monic IPs have been obtained with multiplication of α where α∈ GF(pq) and assume values from 2 to (p − 1) to monic IPs.

A multiple model adaptive inverse method for nonlinear heat transfer system with temperature-dependent thermophysical properties

A multiple model adaptive inverse (MMAI) method is proposed to estimate the boundary heat flux distribution of nonlinear heat transfer system with temperature-dependent thermophysical properties. In the temperature space of system, the nonlinear heat transfer system is divided into several linear subspaces, and for each subspace, the linear prediction submodel of the temperature at the measurement point is established. Furthermore, according to the instantaneous matching degree between each prediction submodel and the actual heat transfer system, the prediction submodels then are weighted and synthesized to gain the global prediction model of the nonlinear heat transfer system. Finally, based on the global prediction model, the boundary heat fluxes are simultaneously estimated through rolling optimization. Numerical experiments are performed to study the effects of system nonlinearity and measurement errors on the inversion results. Comparisons with the existing dynamic matrix control inverse method and the adaptive sequential function specification method are also conducted, and they all show the validity of the inverse method established in this paper.

The structure of the Kauffman bracket skein algebra at roots of unity

This paper examines the structure of the Kauffman bracket skein algebra of a punctured surface at roots of unity. A criterion that determines when a collection of skeins forms a basis of the skein algebra as a module over the $$SL(2,{{\mathbb {C}}})$$ characters of the fundamental group of the surface, with appropriate localization is given. This is used to prove that when the algebra is localized so that every nonzero element of the center has a multiplicative inverse, it is a division algebra. Finally, it is proved that the localized skein algebra can be split as a module over its center as a tensor product of two commutative subalgebras.

Contrasting Evolutionary Paths Among Indo-Pacific Pomacentrus Species Promoted by Extensive Pericentric Inversions and Genome Organization of Repetitive Sequences.

Pomacentrus (damselfishes) is one of the most characteristic groups of fishes in the Indo-Pacific coral reef. Its 77 described species exhibit a complex taxonomy with cryptic lineages across their extensive distribution. Periods of evolutionary divergences between them are very variable, and the cytogenetic events that followed their evolutionary diversification are largely unknown. In this respect, analyses of chromosomal divergence, within a phylogenetic perspective, are particularly informative regarding karyoevolutionary trends. As such, we conducted conventional cytogenetic and cytogenomic analyses in four Pomacentrus species (Pomacentrus similis, Pomacentrus auriventris, Pomacentrus moluccensis, and Pomacentrus cuneatus), through the mapping of repetitive DNA classes and transposable elements, including 18S rDNA, 5S rDNA, (CA)15, (GA)15, (CAA)10, Rex6, and U2 snDNA as markers. P. auriventris and P. similis, belonging to the Pomacentrus coelestis complex, have indistinguishable karyotypes (2n = 48; NF = 48), with a peculiar syntenic organization of ribosomal genes. On the other hand, P. moluccensis and P. cuneatus, belonging to another clade, exhibit very different karyotypes (2n = 48, NF = 86 and 92, respectively), with a large number of bi-armed chromosomes, where multiple pericentric inversions played a significant role in their karyotype organization. In this sense, different chromosomal pathways followed the phyletic diversification in the Pomacentrus genus, making possible the characterization of two well-contrasting species groups regarding their karyotype features. Despite this, pericentric inversions act as an effective postzygotic barrier in many organisms, which appear to be also the case for P. moluccensis and P. cuneatus; the extensive chromosomal similarities in the two species of P. coelestis complex suggest minor participation of chromosomal postzygotic barriers in the phyletic diversification of these species.

Stress regimes in the northwest of Iran from stress inversion of earthquake focal mechanisms

Northwestern Iran is one of the seismically active regions with a high seismic risk in the world. This area is a part of the complex tectonic system due to the interaction between Arabia, Anatolia and Eurasia. The purpose of this study is to deduce the stress regimes in the northwestern Iran and surrounding regions from stress inversion of earthquake focal mechanisms. We compile 92 focal mechanisms data from the Global CMT catalogue and other sources and also determine the focal mechanisms of 14 earthquakes applying the moment tensor inversion. We divide the studied region into 9 zones using similarity of the horizontal GPS velocities and existing focal mechanisms. We implement two stress inversion methods, Multiple Inverse Method and Iterative Joint Inversion Method, which provide comparable results in terms of orientations of maximum horizontal stress axes SHmax. The similar results of the two methods should make us more confident about the interpretations. We consider zones of exclusion surrounding all the earthquakes according to independent focal mechanisms hypothesis. The hypothesis says that the inversion should involve events that are far enough from each other in order that any previous event doesn't affect the stress field near the earthquake under consideration. Accordingly we deal with the matter by considering zones of exclusion around all the events. The result of exclusion is only significant for eastern Anatolia. The stress regime in this region changes from oblique to strike slip faulting because of the exclusion. In eastern Anatolia, the direction of maximum horizontal stress is nearly north-south. The direction alters to east-west in Talesh region. Errors of σ1 are lower in all zones comparing with errors of σ2 and σ3 and there is a trade-off between data resolution and covariance of the model. The results substantiate the strike-slip and thrust faulting stress regimes in the northwest of Iran.

Intrachromosomal Rearrangements in Rodents from the Perspective of Comparative Region-Specific Painting.

It has long been hypothesized that chromosomal rearrangements play a central role in different evolutionary processes, particularly in speciation and adaptation. Interchromosomal rearrangements have been extensively mapped using chromosome painting. However, intrachromosomal rearrangements have only been described using molecular cytogenetics in a limited number of mammals, including a few rodent species. This situation is unfortunate because intrachromosomal rearrangements are more abundant than interchromosomal rearrangements and probably contain essential phylogenomic information. Significant progress in the detection of intrachromosomal rearrangement is now possible, due to recent advances in molecular biology and bioinformatics. We investigated the level of intrachromosomal rearrangement in the Arvicolinae subfamily, a species-rich taxon characterized by very high rate of karyotype evolution. We made a set of region specific probes by microdissection for a single syntenic region represented by the p-arm of chromosome 1 of Alexandromys oeconomus, and hybridized the probes onto the chromosomes of four arvicolines (Microtus agrestis, Microtus arvalis, Myodes rutilus, and Dicrostonyx torquatus). These experiments allowed us to show the intrachromosomal rearrangements in the subfamily at a significantly higher level of resolution than previously described. We found a number of paracentric inversions in the karyotypes of M. agrestis and M. rutilus, as well as multiple inversions and a centromere shift in the karyotype of M. arvalis. We propose that during karyotype evolution, arvicolines underwent a significant number of complex intrachromosomal rearrangements that were not previously detected.

RANDOMIZED DES USING IRREDUCIBLE POLYNOMIAL OVER GALOIS FIELD GF(73)

Multiplicative inverses under an irreducible polynomial over Galois Field GF(p^m) play important role in cryptography. The substitution box of Advanced Encryption Standard is designed in 1999 with multiplicative inverses under the first irreducible polynomial over GF(2^8). In the present paper, a recently published pseudorandom number generator GF7 designed over GF(7^3) in 2016, is intuitively incorporated into the Data Encryption Standard algorithm to modify it by increasing its randomness as well as security. Following the method proposed by National Institute of Standards and Technology, the statistical randomness testing is done on a large number of output ciphers obtained by the algorithm. The statistical result shows tremendous improvement in randomness for the proposed modified algorithm.

Hardware Implementation of Single Iterated Multiplicative Inverse Square Root

Inverse square root has played an important role in Cholesky decomposition, which devoted to hardware efficient compressed sensing. However, the performance is usually limited by the trade-off between throughput and precision. This paper presents hardware implementation of fixed-point single iterated multiplicative inverse square root. Multiple piecewise linear approximation in softly nonlinear range is used to compute the initial value. Single iterated Newton-Raphson method is employed to obtain high precision. Multiple constants multiplication technique is proposed to achieve high throughput. The combination of these techniques yields high performance in terms of throughput and precision. It obtains more than 70 % of throughput improvement and almost 100 × higher precision over the inverse square root Intellectual Property (IP) from Altera. In addition, Cholesky decomposition has been presented to validate the proposed architecture, which shows that 42 % of throughput improvement is achieved compared with the IP.DOI: http://dx.doi.org/10.5755/j01.eie.23.4.18717

The motivic class of the classifying stack of the special orthogonal group

We compute the class of the classifying stack of the special orthogonal group in the Grothendieck ring of stacks, and check that it is equal to the multiplicative inverse of the class of the group.

Carrier Dynamics in Graphene: Ultrafast Many‐Particle Phenomena

AbstractGraphene is an ideal material to study fundamental Coulomb‐ and phonon‐induced carrier scattering processes. Its remarkable gapless and linear band structure opens up new carrier relaxation channels. In particular, Auger scattering bridging the valence and the conduction band changes the number of charge carriers and gives rise to a significant carrier multiplication ‐ an ultrafast many‐particle phenomenon that is promising for the design of highly efficient photodetectors. Furthermore, the vanishing density of states at the Dirac point combined with ultrafast phonon‐induced intraband scattering results in an accumulation of carriers and a population inversion suggesting the design of graphene‐based terahertz lasers. Here, we review our work on the ultrafast carrier dynamics in graphene and Landau‐quantized graphene is presented providing a microscopic view on the appearance of carrier multiplication and population inversion.

APOE ε4 ALLELE EFFECT ON WHITE AND GRAY MATTER PERFUSION IN COGNITIVELY NORMAL AND MCI GROUPS

Cerebral perfusion in both white and gray matter may be an indicator of vascular dysfunction and cognition decline. In this study, simultaneous estimates of cerebral blood flow (CBF) and arterial transit time (ATT) using multiple inversion time arterial spin labeling (ASL) was analyzed in cognitively normal and mild cognitive impairment (MCI) groups. Lower CBF and shorter ATT in APOE ε4 carriers may indicate cerebrovascular functional disorder that impacts cognitive function. 87 subjects (62 cognitively normal (23% ε4+) and 25 MCI (48% ε4+); 23M/64F; age: 63.9±7.7) underwent baseline brain MRI exams as part of several on-going studies within the Wake Forest AD Center, including pseudo-continuous ASL to estimate voxel-wise whole brain CBF and ATT in white and gray matters using a partial volume correction. An example CBF and ATT maps are shown in Figure 1. All ASL images were co-registered to T1 weighted structural images and normalized into a study specific template. Age, Sex, BMI, and HbA1C were adjusted and 2-way ANOVA was performed for each voxel. A minimum cluster size was determined with p<0.05 and α=0.05. APOE ε4 carriers showed reduced CBF in a white matter cluster and four gray matter clusters as shown in Figure 2. The white matter hypo-perfusion cluster locates mainly in left sub-lobar region and extends over temporal and parietal lobes. Four small clusters in gray matter are in left hippocampus, thalamus, right lingual, and right hippocampus and amygdala (Table 1). Although were not statistically significant, ATT values measured in the clusters representing lower blood flow are also shorter in the ε4 carriers (Table 2). In addition, the group without ε4 Allele showed a trend of compensatory increased blood flow in MCI while that with ε4 Allele had impaired blood flow. In this small pilot study sample, lower CBF and shortened ATT were observed among APOE ε4 carriers in both white and gray matter and did not significantly differ by cognitive status. These data suggest evidence of that a perfusion abnormality indicative of flow dynamics of arterial stiffness / arteriolosclerosis are seen among ε4 carriers that may contribute to cerebrovascular disorders. CBF and ATT maps in GM and WM from a representative subject (82 yr. old, F). The partial volume fraction of 0.2 was applied to make the maps. Clusters in white and gray matters representing lower blood flow in the group with APOE ε4 Allele.

Tsunami inundation variability from stochastic rupture scenarios: Application to multiple inversions of the 2011 Tohoku, Japan earthquake

We develop a framework for assessing the sensitivity and variability of tsunami inundation characteristics for stochastic physics-based scenarios of mega-thrust subduction earthquakes. The method is applied to the 2011 Tohoku, Japan earthquake, and tested against observed inundation maps at several locations along the Tohoku coast, using 11 different, previously published, rupture models for this devastating tsunamgenic earthquake. The earthquake rupture models differ in fault dimension (length and width), geometry (dip, strike and top-edge depth), as well as asperity characteristics (slip heterogeneity on the fault plane). The resulting source variability allows exploring a wide range of tsunami scenarios for an Mw9 mega-thrust subduction earthquake in the Tohoku region to conduct thorough sensitivity analyses and to quantify the inundation variability. The numerical results indicate a strong influence of the reference source models on inundation variability, and demonstrate significant sensitivity of inundation to the details of the rupture realization. Therefore, relying on a single particular earthquake rupture model as a representative case when varying earthquake source characteristics may lead to under-representation of the variability of potential scenarios. Moreover, the proposed framework facilitates the rigorous development of critical scenarios for tsunami hazard and risk assessments, which are particularly useful for tsunami hazard mapping and disaster preparedness planning.

The Intrinsic Geometry on Bounded Pseudoconvex Domains

We study bounded pseudoconvex domains in 2-dimensional complex Euclidean spaces. We are interested in developing sufficient and necessary conditions for the Diederich–Fornaess index to be 1. It was known that an obstructive complex Hessian prevents the index from 1. We derive two estimates on this obstructive complex Hessian and its multiplicative inverse, respectively. A consequence of the first estimate gives almost an equivalent condition of the index to be 1. Our method is a new way to resolve problems with the Diederich–Fornaess index. This method contains a localization to the boundary and a geometric analysis on its Levi-flat sets.

A Programmable Galois Field Processor for the Internet of Things

This paper investigates the feasibility of a unified processor architecture to enable error coding flexibility and secure communication in low power Internet of Things (IoT) wireless networks. Error coding flexibility for wireless communication allows IoT applications to exploit the large tradeoff space in data rate, link distance and energy-efficiency. As a solution, we present a light-weight Galois Field (GF) processor to enable energy-efficient block coding and symmetric/asymmetric cryptography kernel processing for a wide range of GF sizes (2m, m = 2, 3, ..., 233) and arbitrary irreducible polynomials. Program directed connections among primitive GF arithmetic units enable dynamically configured parallelism to efficiently perform either four-way SIMD 5- to 8-bit GF operations, including multiplicative inverse, or a wide bit-width (e.g., 32-bit) GF product in a single cycle. To illustrate our ideas, we synthesized our GF processor in a 28nm technology. Compared to a baseline software implementation optimized for a general purpose ARM M0+ processor, our processor exhibits a 5-20 x speedup for a range of error correction codes and symmetric/asymmetric cryptography applications. Additionally, our proposed GF processor consumes 431μW at 0.9V and 100MHz, and achieves 35.5pJ/b energy efficiency while executing AES operations at 12.2Mbps. We achieve this within an area of 0.01mm2.

Deflection and Rotation of CMEs from Active Region 11158.

Between 13 and 16 February 2011, a series of coronal mass ejections (CMEs) erupted from multiple polarity inversion lines within active region 11158. For seven of these CMEs we employ the graduated cylindrical shell (GCS) flux rope model to determine the CME trajectory using both Solar Terrestrial Relations Observatory (STEREO) extreme ultraviolet (EUV) and coronagraph images. We then use the model called Forecasting a CME's Altered Trajectory (ForeCAT) for nonradial CME dynamics driven by magnetic forces to simulate the deflection and rotation of the seven CMEs. We find good agreement between ForeCAT results and reconstructed CME positions and orientations. The CME deflections range in magnitude between 10° and 30°. All CMEs are deflected to the north, but we find variations in the direction of the longitudinal deflection. The rotations range between 5° and 50° with both clockwise and counterclockwise rotations. Three of the CMEs begin with initial positions within 2° from one another. These three CMEs are all deflected primarily northward, with some minor eastward deflection, and rotate counterclockwise. Their final positions and orientations, however, differ by 20° and 30°, respectively. This variation in deflection and rotation results from differences in the CME expansion and radial propagation close to the Sun, as well as from the CME mass. Ultimately, only one of these seven CMEs yielded discernible in situ signatures near Earth, although the active region faced toward Earth throughout the eruptions. We suggest that the differences in the deflection and rotation of the CMEs can explain whether each CME impacted or missed Earth.

2D data-space cross-gradient joint inversion of MT, gravity and magnetic data

We have developed a data-space multiple cross-gradient joint inversion algorithm, and validated it through synthetic tests and applied it to magnetotelluric (MT), gravity and magnetic datasets acquired along a 95km profile in Benxi-Ji'an area of northeastern China. To begin, we discuss a generalized cross-gradient joint inversion for multiple datasets and model parameters sets, and formulate it in data space. The Lagrange multiplier required for the structural coupling in the data-space method is determined using an iterative solver to avoid calculation of the inverse matrix in solving the large system of equations. Next, using model-space and data-space methods, we inverted the synthetic data and field data. Based on our result, the joint inversion in data-space not only delineates geological bodies more clearly than the separate inversion, but also yields nearly equal results with the one in model-space while consuming much less memory.

The Cayley-Dickson Construction in ACL2

The Cayley-Dickson Construction is a generalization of the familiar construction of the complex numbers from pairs of real numbers. The complex numbers can be viewed as two-dimensional vectors equipped with a multiplication. The construction can be used to construct, not only the two-dimensional Complex Numbers, but also the four-dimensional Quaternions and the eight-dimensional Octonions. Each of these vector spaces has a vector multiplication, v_1*v_2, that satisfies: 1. Each nonzero vector has a multiplicative inverse. 2. For the Euclidean length of a vector |v|, |v_1 * v_2| = |v_1| |v2|. Real numbers can also be viewed as (one-dimensional) vectors with the above two properties. ACL2(r) is used to explore this question: Given a vector space, equipped with a multiplication, satisfying the Euclidean length condition 2, given above. Make pairs of vectors into "new" vectors with a multiplication. When do the newly constructed vectors also satisfy condition 2?