Multiplicative Inverse Research Articles

Mapping of Adaptive Traits Enabled by a High-Density Linkage Map for Lake Trout.

Understanding the genomic basis of adaptative intraspecific phenotypic variation is a central goal in conservation genetics and evolutionary biology. Lake trout (Salvelinus namaycush) are an excellent species for addressing the genetic basis for adaptive variation because they express a striking degree of ecophenotypic variation across their range; however, necessary genomic resources are lacking. Here we utilize recently-developed analytical methods and sequencing technologies to (1) construct a high-density linkage and centromere map for lake trout, (2) identify loci underlying variation in traits that differentiate lake trout ecophenotypes and populations, (3) determine the location of the lake trout sex determination locus, and (4) identify chromosomal homologies between lake trout and other salmonids of varying divergence. The resulting linkage map contains 15,740 single nucleotide polymorphisms (SNPs) mapped to 42 linkage groups, likely representing the 42 lake trout chromosomes. Female and male linkage group lengths ranged from 43.07 to 134.64 centimorgans, and 1.97 to 92.87 centimorgans, respectively. We improved the map by determining coordinates for 41 of 42 centromeres, resulting in a map with 8 metacentric chromosomes and 34 acrocentric or telocentric chromosomes. We use the map to localize the sex determination locus and multiple quantitative trait loci (QTL) associated with intraspecific phenotypic divergence including traits related to growth and body condition, patterns of skin pigmentation, and two composite geomorphometric variables quantifying body shape. Two QTL for the presence of vermiculations and spots mapped with high certainty to an arm of linkage group Sna3, growth related traits mapped to two QTL on linkage groups Sna1 and Sna12, and putative body shape QTL were detected on six separate linkage groups. The sex determination locus was mapped to Sna4 with high confidence. Synteny analysis revealed that lake trout and congener Arctic char (Salvelinus alpinus) are likely differentiated by three or four chromosomal fissions, possibly one chromosomal fusion, and 6 or more large inversions. Combining centromere mapping information with putative inversion coordinates revealed that the majority of detected inversions differentiating lake trout from other salmonids are pericentric and located on acrocentric and telocentric linkage groups. Our results suggest that speciation and adaptive divergence within the genus Salvelinus may have been associated with multiple pericentric inversions occurring primarily on acrocentric and telocentric chromosomes. The linkage map presented here will be a critical resource for advancing conservation oriented genomic research on lake trout and exploring chromosomal evolution within and between salmonid species.

Transdimensional and Hamiltonian Monte Carlo inversions of Rayleigh‐wave dispersion curves: a comparison on synthetic datasets

ABSTRACTWe compare two Monte Carlo inversions that aim to solve some of the main problems of dispersion curve inversion: deriving reliable uncertainty appraisals, determining the optimal model parameterization and avoiding entrapment in local minima of the misfit function. The first method is a transdimensional Markov chain Monte Carlo that considers as unknowns the number of model parameters, that is the locations of layer boundaries together with the Vs and the Vp/Vs ratio of each layer. A reversible‐jump Markov chain Monte Carlo algorithm is used to sample the variable‐dimension model space, while the adoption of a parallel tempering strategy and of a delayed rejection updating scheme improves the efficiency of the probabilistic sampling. The second approach is a Hamiltonian Monte Carlo inversion that considers the Vs, the Vp/Vs ratio and the thickness of each layer as unknowns, whereas the best model parameterization (number of layer) is determined by applying standard statistical tools to the outcomes of different inversions running with different model dimensionalities. This work has a mainly didactic perspective and, for this reason, we focus on synthetic examples in which only the fundamental mode is inverted. We perform what we call semi‐analytical and seismic inversion tests on 1D subsurface models. In the first case, the dispersion curves are directly computed from the considered model making use of the Haskell–Thomson method, while in the second case they are extracted from synthetic shot gathers. To validate the inversion outcomes, we analyse the estimated posterior models and we also perform a sensitivity analysis in which we compute the model resolution matrices, posterior covariance matrices and correlation matrices from the ensembles of sampled models. Our tests demonstrate that major benefit of the transdimensional inversion is its capability of providing a parsimonious solution that automatically adjusts the model dimensionality. The downside of this approach is that many models must be sampled to guarantee accurate posterior uncertainty. Differently, less sampled models are required by the Hamiltonian Monte Carlo algorithm, but its limits are the computational effort related to the Jacobian computation, and the multiple inversion runs needed to determine the optimal model parameterization.

Controlled-order multiple waveform inversion

Traditional full-waveform inversion (FWI) seeks to find the best model by minimizing an objective function defined as the difference between the model-predicted and observed data in amplitude and phase. In principle, FWI should fit all wave types including direct waves, diving waves, primaries, and multiples. However, when an initial model is far from the true model, FWI will encounter difficulties in matching multiples. Physically, multiples may contain more subsurface information compared to primary and diving waves. Multiples cover a wide range of reflection angles during wave propagation and offer the advantage of imaging the shadow zones that cannot be reached or are poorly illuminated by primary reflections. We have developed a new method of waveform inversion using multiples. We first separate the multiples into different orders. The objective function we seek to minimize consists of the data difference between the modeled data using a lower order multiple as the source and the higher order multiple as data. This method is called controlled-order multiple waveform inversion (CMWI). Our numerical examples determined that the CMWI is a promising method to improve velocity updates.

Free-running cardiac magnetic resonance fingerprinting: Joint T1/T2 map and Cine imaging

PurposeTo develop and evaluate a novel non-ECG triggered 2D magnetic resonance fingerprinting (MRF) sequence allowing for simultaneous myocardial T1 and T2 mapping and cardiac Cine imaging. MethodsCardiac MRF (cMRF) has been recently proposed to provide joint T1/T2 myocardial mapping by triggering the acquisition to mid-diastole and relying on a subject-dependent dictionary of MR signal evolutions to generate the maps. In this work, we propose a novel “free-running” (non-ECG triggered) cMRF framework for simultaneous myocardial T1 and T2 mapping and cardiac Cine imaging in a single scan. Free-running cMRF is based on a transient state bSSFP acquisition with tiny golden angle radial readouts, varying flip angle and multiple adiabatic inversion pulses. The acquired data is retrospectively gated into several cardiac phases, which are reconstructed with an approach that combines parallel imaging, low rank modelling and patch-based high-order tensor regularization. Free-running cMRF was evaluated in a standardized phantom and ten healthy subjects. Comparison with reference spin-echo, MOLLI, SASHA, T2-GRASE and Cine was performed. ResultsT1 and T2 values obtained with the proposed approach were in good agreement with reference phantom values (ICC(A,1) > 0.99). Reported values for myocardium septum T1 were 1043 ± 48 ms, 1150 ± 100 ms and 1160 ± 79 ms for MOLLI, SASHA and free-running cMRF respectively and for T2 of 51.7 ± 4.1 ms and 44.6 ± 4.1 ms for T2-GRASE and free-running cMRF respectively. Good agreement was observed between free-running cMRF and conventional Cine 2D ejection fraction (bias = −0.83%). ConclusionThe proposed free-running cardiac MRF approach allows for simultaneous assessment of myocardial T1 and T2 and Cine imaging in a single scan.

Probabilistic inversion for submerged source depth and strength from infrasound observations.

In seismology, the depth of a near-surface source is hard to estimate in the absence of local stations. The depth-yield trade-off leads to significant uncertainties in the source's depth and strength estimations. Long-range infrasound propagation from an underwater or underground source is very sensitive to variations in the source's depth and strength. This characteristic is employed in an infrasound based inversion for the submerged source parameters. First, a Bayesian inversion scheme is tested under the variations of the number of stations, the signal's frequency band, and the signal-to-noise ratio (SNR). Second, an ensemble of realistic perturbed atmospheric profiles is used to investigate the effect of atmospheric uncertainties on the inversion results. Results show that long-range infrasound signals can be used to estimate the depth and strength of an underwater source. Using a broadband signal proved to be a fundamental element to obtain the real source parameters, whereas the SNR was secondary. Multiple station inversions perform better than one-station inversions; however, variations in their position can lead to source strength estimations with uncertainties up to 50%. Regardless of the number of stations, their positions, and SNRs, all of the estimated depths were within 10% from the real source depth.

Seismic trace interpolation for irregularly spatial sampled data using convolutional autoencoder

Seismic trace interpolation is an important technique because irregular or insufficient sampling data along the spatial direction may lead to inevitable errors in multiple suppression, imaging, and inversion. Many interpolation methods have been studied for irregularly sampled data. Inspired by the working idea of the autoencoder and convolutional neural network, we have performed seismic trace interpolation by using the convolutional autoencoder (CAE). The irregularly sampled data are taken as corrupted data. By using a training data set including pairs of the corrupted and complete data, CAE can automatically learn to extract features from the corrupted data and reconstruct the complete data from the extracted features. It can avoid some assumptions in the traditional trace interpolation method such as the linearity of events, low-rankness, or sparsity. In addition, once the CAE network training is completed, the corrupted seismic data can be interpolated immediately with very low computational cost. A CAE network composed of three convolutional layers and three deconvolutional layers is designed to explore the capabilities of CAE-based seismic trace interpolation for an irregularly sampled data set. To solve the problem of rare complete shot gathers in field data applications, the trained network on synthetic data is used as an initialization of the network training on field data, called the transfer learning strategy. Experiments on synthetic and field data sets indicate the validity and flexibility of the trained CAE. Compared with the curvelet-transform-based method, CAE can lead to comparable or better interpolation performances efficiently. The transfer learning strategy enhances the training efficiency on field data and improves the interpolation performance of CAE with limited training data.

Certain sequence of arithmetic progressions and a new key sharing method

We consider a special type of sequence of arithmetic progressions, in which consecutive progressions are related by the property: ithterms ofjth, (j + 1)thprogressions of the sequence are multiplicative inverses of each other modulo(i + 1)thterm ofjthprogression. Such a sequence is uniquely defined for any pair of co-prime numbers. A computational problem, defined in the context of such a sequence and its generalization, is shown to be equivalent to the integer factoring problem. The proof is probabilistic. As an application of the equivalence result, we propose a method for how users securely agree upon secret keys, which are ensured to be random. We compare our method with factoring based public key cryptographic systems: RSA (Rivest et al., ACM 21, 120–126, 1978) and Rabin systems (Rabin 1978). We discuss the advantages of the method, and its potential use-case in the post quantum scenario.

GPU-Based Soil Parameter Parallel Inversion for PolSAR Data

With the development of polarimetric synthetic aperture radar (PolSAR), quantitative parameter inversion has been seen great progress, especially in the field of soil parameter inversion, which has achieved good results for applications. However, PolSAR data is also often many terabytes large. This huge amount of data also directly affects the efficiency of the inversion. Therefore, the efficiency of soil moisture and roughness inversion has become a problem in the application of this PolSAR technique. A parallel realization based on a graphics processing unit (GPU) for multiple inversion models of PolSAR data is proposed in this paper. This method utilizes the high-performance parallel computing capability of a GPU to optimize the realization of the surface inversion models for polarimetric SAR data. Three classical forward scattering models and their corresponding inversion algorithms are analyzed. They are different in terms of polarimetric data requirements, application situation, as well as inversion performance. Specifically, the inversion process of PolSAR data is mainly improved by the use of the high concurrent threads of GPU. According to the inversion process, various optimization strategies are applied, such as the parallel task allocation, and optimizations of instruction level, data storage, data transmission between CPU and GPU. The advantages of a GPU in processing computationally-intensive data are shown in the data experiments, where the efficiency of soil roughness and moisture inversion is increased by one or two orders of magnitude.

Generalizing pairs of complementary sequences and a construction of combinatorial structures

Pairs of complementary sequences such as Golay pairs have zero sum autocorrelation at all non-trivial phases. Several generalizations are known where conditions on either the autocorrelation function, or the entries of the sequences are altered. We aim to unify most of these ideas by introducing autocorrelation functions that apply to any sequences with entries in a set equipped with a ring-like structure which is closed under multiplication and contains multiplicative inverses. Depending on the elements of the chosen set, the resulting complementary pairs may be used to construct a variety of combinatorial structures such as Hadamard matrices, complex generalized weighing matrices, and signed group weighing matrices. We may also construct quasi-cyclic and quasi-constacyclic linear codes which over finite fields of order less than 5 are also Hermitian self-orthogonal. As the literature on binary and ternary Golay sequences is already quite deep, one intention of this paper is to survey and assimilate work on more general pairs of complementary sequences and related constructions of combinatorial objects, and to combine the ideas into a single theoretical framework.

Low‐power and area‐efficient design of AES S‐Box using enhanced transformation method for security application

SummaryIn implementing well‐known advanced encryption standard (AES) algorithm, the main part for constructing the hardware is S‐Box, which is abbreviated from substitution box. This is the basic component of symmetric key cryptographic algorithm, and it requires in AES because of its nonlinear organization with multiplicative inversion. This S‐Box is designed by two transformations, ie, inversing the multiplication part in Galois field directed with modified affine transformation. The limitation of S‐Box is more time and power consumption. This limitation has to be overcome by doing slight modification in affine and inverse affine transform. The time consumption for AES S‐Box is decreased by the proposed transformation method. The proposed system achieved 39% power when compared with the existing system; the proposed system is efficient.

Algebraic Properties of Bihyperbolic Numbers

In this paper, we study the four-dimensional real algebra of bihyperbolic numbers. Under consideration of the spectral representation of the bihyperbolic numbers, we give a partial order of bihyperbolic numbers which allows us to obtain some relations in the ordered vector space of bihyperbolic numbers. Moreover, we state that the set of bihyperbolic numbers form a real Banach algebra with a new defined norm. We introduce conjugates, three hyperbolic valued moduli, real moduli, and multiplicative inverse of the bihyperbolic numbers. We give the concept of the absolute value of a bihyperbolic number which generalizes that of real numbers. Also, we represent the polar form of invertible bihyperbolic numbers.

Session layer security enhancement with md5 and multiplicative inverse cryptographic mechanism

This paper proposes MD5 and Multiplicative Inverse based Data Encryption Model for security of data during data transmission. It discusses about Cloud computing mechanism which is used to deliver information technology services. In cloud computing, Data security is biggest issue and significant aspect of Internet for enterprises of each size and type. However there are several existing researches that proposed different security mechanisms but they have certain limitations. Therefore this proposed model is developed to enhance the security of data at multiple layers. User defined port and IP address is used to make this proposed model more secure data transmission model. Moreover, the early session timeout is also controlled by reducing packet size. Proposed work would be capable to increase the efficiency of data communication along with security. In addition, unauthentic access of data is restricted using IP validation process.

COMPUTING ev-DEGREE AND MULTIPLICATIVE ev-DEGREE INDICES OF CERTAIN CHEMICAL STRUCTURES.

Recently, the ev-degree concept is defined in Graph Theory. In this study, we introduce the modified ev-degree Zagreb index, ev-degree inverse index, F-ev-degree index, reciprocal ev-degree product index, general ev-degree index of a graph. Also we propose some multiplicative ev-degree indices such as multiplicative ev-degree index, multiplicative modified ev-degree index, multiplicative F-ev-degree index, multiplicative ev-degree inverse index, multiplicative ev-degree product index, multiplicative reciprocal ev-degree product index, general multiplicative ev-degree index of a graph. We compute these ev-degree and multiplicative ev-degree indices for certain chemical structures.

Online Spectrogram Inversion for Low-Latency Audio Source Separation

Audio source separation is usually achieved by estimating the short-time Fourier transform (STFT) magnitude of each source, and then applying a spectrogram inversion algorithm to retrieve time-domain signals. In particular, the multiple input spectrogram inversion (MISI) algorithm has been exploited successfully in several recent works. However, this algorithm suffers from two drawbacks, which we address in this paper. First, it has originally been introduced in a heuristic fashion: we propose here a rigorous optimization framework in which MISI is derived, thus proving the convergence of this algorithm. Besides, while MISI operates offline, we propose here an online version of MISI called oMISI, which is suitable for low-latency source separation, an important requirement for e.g., hearing aids applications. oMISI also allows one to use alternative phase initialization schemes exploiting the temporal structure of audio signals. Experiments conducted on a speech separation task show that oMISI performs as well as its offline counterpart, thus demonstrating its potential for real-time source separation.

Topological Insulator-to-Weyl Semimetal Transition in Strongly Correlated Actinide System UNiSn

Although strong electronic correlations are known to be responsible for some highly unusual behaviors of solids such as, metal--insulator transitions, magnetism and even high--temperature superconductivity, their interplay with recently discovered topological states of matter awaits full exploration. Here we use a modern electronic structure method combining density functional theory of band electrons with dynamical self-energies of strongly correlated states to predict that two well-known phases of actinide compound UNiSn, a paramagnetic semiconducting and antiferromagnetic metallic, correspond to Topological Insulator (TI) and Weyl semimetal (WSM) phases of topological quantum matter. Thus, the famous unconventional insulator-metal transition observed in UNiSn is also a TI-to-WSM transition. Driven by a strong hybridization between U f-electron multiplet transitions and band electrons, multiple energy gaps open up in the single-particle spectrum whose topological physics is revealed using the calculation of Z2 invariants in the strongly correlated regime. A simplified physical picture of these phenomena is provided based on a periodic Anderson model of strong correlations and multiple band inversions that occur in this fascinating compound. Studying the topology of interacting electrons reveals interesting opportunities for finding new exotic phase transitions in strongly correlated systems.

Tetrasomy 21 pter→q21.3 due to an extra +dic(21;21)mat in a severely psychomotor-retarded female patient without Down syndrome phenotype.

Complete or partial tetrasomy 21 has been reported only in rare cases. We report a Japanese female patient with tetrasomy 21 due to an extra chromosome derived from chromosome 21 (Chr21). The patient had severe psychomotor retardation without Down syndrome (DS) phenotype; she showed short stature, microcephaly, round face, cleft lip and palate, and other dysmorphic features. The chromosome analyses for the patient detected an extra dicentric Chr21 consisting of two partial Chr21 copies fused together within their long arms. Her karyotype was revealed to be 47,XX,+dic(21;21). Allelic ratios of heterozygous SNPs observed in the patient indicated the maternal origin of the extra Chr21. Copy number and structural variant analyses using whole genome sequencing data indicated that the distal breakpoint of the dicentric Chr21 was located within 21q21.3 and that the extra Chr21 did not simply consist of inverted duplications of the pter→q21.3 region, but likely contained multiple partial deletions, duplications, and inversions within it. Fluorescence in situ hybridization results were consistent with the karyotype and genomic analyses. The patient's lack of DS phenotype turned out to be due to the normal copy number of the DS critical region (21q22.13-22.3). A possible molecular mechanism leading to the complex genomic rearrangements in the tetrasomic region consists mainly of breakage-fusion-bridge cycles with an unequal crossing-over event.

The congruence equation a¯ + b¯ ≡c¯(modp)

In this paper, we consider the congruence equation [Formula: see text] with [Formula: see text] where [Formula: see text] denotes the multiplicative inverse of [Formula: see text]. We prove that its number of solutions is asymptotic to [Formula: see text] when [Formula: see text] by estimating a certain average of Kloosterman sums via Gauss sums. On the other hand, when [Formula: see text], the number of solutions has order of magnitude at least [Formula: see text]. It would be interesting to better understand its transition of behavior. By transforming the question slightly, one can relate the problem to a certain first moment of Dirichlet [Formula: see text]-functions at [Formula: see text].

Fast inversion of array laterolog measurements in an axisymmetric medium

The array laterolog is an important tool for complex formation logging evaluation due to its high resolution and large detection depth. However, its logging responses are seriously affected by leakage events due to the surrounding rock and by mud invasion. These factors must be considered when inverting array lateral logging data, so that the inversion results reflect the true formation conditions as much as possible. The difficulties encountered in the inversion of array lateral logging data are: too many inversion parameters cause the calculation of the Jacobian matrix to be difficult and the time required to select the initial inversion values due to the slow forward-modeling speed. In this paper, we develop a fast processing method for array laterolog data. First, it is important to clearly define the main controlling factors for the array laterolog response, such as thickness, the surrounding rock, and invasion. Second, based on a depth-window technique, processing the array laterolog data for the entire well is transformed into multiple 2D inversions of the layers using a series of continuous depth windows. For each formation in a depth window, combined with the 1D equivalent fast-forward algorithm, rapid extraction of the radial resistivity profile of the formation is achieved. Finally, the 1D inversion result is used as the initial state to further eliminate the influence of surrounding rocks and layer thicknesses on the apparent resistivity response. Numerical simulation results show that the factors affecting the response of the array laterolog are the invasion properties, the layer thicknesses, and the surrounding rocks; the windowing technique greatly reduces the number of inversion parameters needed and improves the inversion speed. A real application of the method shows that 2D inversion can rapidly reconstruct the actual resistivity distribution and improve the accuracy of reservoir saturation calculations.

Substitution Box Optimization

The basic principle of encryption is to transform plain data into unintelligible data via a series of steps referred to as an encryption algorithm. The input to this algorithm is called plaintext, and its output encoded version is called as cipher text. Even though there are various algorithms, Advanced Encryption Standard (AES) is adopted due to the availability of optimized hardware components for efficient implementation. The S-Box is one of the critical operations in AES algorithm and it consists of two sub-modules, namely the multiplicative inversion sub-module in GF(2^8) and the Affine transformation sub-module Each input to the S-Box is a 1-byte of intermediate data, x, and the S-Box will generate 1-byte of output S(x). There are variety of methods can used to implement AES S box. Through this project our aim is to optimize the S box for minimal access time. We are planning to implement an optimized implementation of the S-box in the Verilog HDL. By developing the Verilog code for substitution box by using different methods, compare them and implement the same in hardware using FPGA.

A fusion of decision-making method and neutrosophic linguistic considering multiplicative inverse matrix for coastal erosion problem

The recent boom of decision-making under uncertain information has attracted many researchers to the field of integrating various types of sets with decision-making methods. In this paper, a combined decision-making trial and evaluation laboratory (DEMATEL) with single-valued neutrosophic sets is proposed to solve the decision problem. This new model combines the advantages of multiplicative inverse of decision matrix in DEMATEL and neutrosophic numbers in linguistic variables, which can find the interrelationship among factors of decision problem. Differently from the typical multiplicative inverse of DEMATEL, which directly used inverse of matrix using real numbers, this method introduces the concept of inverse of matrix using the proposed left–right neutrosophic numbers. This step will enhance the validity of multiplicative inverse of decision matrix in the DEMATEL with neutrosophic numbers. The proposed neutrosophic DEMATEL is also be compared with the DEMATEL and fuzzy DEMATEL. This paper includes a case study that demonstrates the applicability of the neutrosophic DEMATEL in establishing the relationship among influential factors of coastal erosion. Extensive empirical studies using 12 factors of coastal erosion were presented to study the benefits of the proposed method. The result unveils the cause-and-effect relationships among the factors, where seven factors are identified as cause factors and five factors are grouped as effect factors. It is discovered that the factor ‘imbalance sediment supply’ gives a significant influence to coastal erosion. It is also shown that the degree of importance of the factors is almost consistent with the other two methods despite differences in type of numbers used in defining linguistic variables.