Multiplicative Inverse Research Articles

Inland Reservoir Water Quality Inversion and Eutrophication Evaluation Using BP Neural Network and Remote Sensing Imagery: A Case Study of Dashahe Reservoir

In this study, an inland reservoir water quality parameters’ inversion model was developed using a back propagation (BP) neural network to conduct reservoir eutrophication evaluation, according to multi-temporal remote sensing images and field observations. The inversion model based on the BP neural network (the BP inversion model) was applied to a large inland reservoir in Jiangmen city, South China, according to the field observations of five water quality parameters, namely, Chlorophyl-a (Chl-a), Secchi Depth (SD), total phosphorus (TP), total nitrogen (TN), and Permanganate of Chemical Oxygen Demand (CODMn), and twelve periods of Landsat8 satellite remote sensing images. The reservoir eutrophication was evaluated. The accuracy of the BP inversion model for each water parameter was compared with that of the linear inversion model, and the BP inversion models of two parameters (i.e., Chl-a and CODMn) with larger fluctuation range were superior to the two multiple linear inversion models due to the ability of improving the generalization of the BP neural network. The Dashahe Reservoir was basically in the state of mesotrophication and light eutrophication. The area of light eutrophication accounted for larger proportions in spring and autumn, and the reservoir inflow was the main source of nutrient salts.

Controlling the Multiple Chiroptical Inversion in Biphasic Liquid‐Crystalline Polymers

AbstractWhile controlling the chirality and modulating the helicity is a challenging task, it attracts great research interest for gaining a better understanding of the origin of chirality in nature. Herein, structurally similar azobenzene (Azo) vinyl monomers were designed in which the alkyl chains comprised the chiral stereocenter with different achiral tail lengths. Combining the synchronous polymerization, supramolecular stacking and self‐assembly, the multiple chiroptical inversion of the Azo‐polymer supramolecular assemblies can be modulated by the tail length and DP of Azo blocks during in situ polymerization. The DP‐, UV light‐, temperature‐, aging time‐dependent chiroptical properties and liquid‐crystalline (LC) characterization indicated that the amorphous‐to‐LC phase transition and biphasic LC interconversion allow the transcription of intra‐chain π–π stacking, inter‐chain H‐ and J‐aggregation, thereby controlling the dynamic multiple reversal of supramolecular chirality.

Controlling the Multiple Chiroptical Inversion in Biphasic Liquid-Crystalline Polymers.

While controlling the chirality and modulating the helicity is a challenging task, it attracts great research interest for gaining a better understanding of the origin of chirality in nature. Herein, structurally similar azobenzene (Azo) vinyl monomers were designed in which the alkyl chains comprised the chiral stereocenter with different achiral tail lengths. Combining the synchronous polymerization, supramolecular stacking and self-assembly, the multiple chiroptical inversion of the Azo-polymer supramolecular assemblies can be modulated by the tail length and DP of Azo blocks during in situ polymerization. The DP-, UV light-, temperature-, aging time-dependent chiroptical properties and liquid-crystalline (LC) characterization indicated that the amorphous-to-LC phase transition and biphasic LC interconversion allow the transcription of intra-chain π-π stacking, inter-chain H- and J-aggregation, thereby controlling the dynamic multiple reversal of supramolecular chirality.

Sensitivity of Arterial Spin Labeling for Characterization of Longitudinal Perfusion Changes in Frontotemporal Dementia and Related Disorders

BackgroundAdvances in the understanding of the pathophysiology of frontotemporal dementia (FTD) and related disorders, along with the development of novel candidate disease modifying treatments, have stimulated the need for tools to assess the efficacy of new therapies. While perfusion imaging by arterial spin labeling (ASL) is an attractive approach for longitudinal imaging biomarkers of neurodegeneration, sources of variability between sessions including arterial transit times (ATT) and fluctuations in resting perfusion can reduce its sensitivity. Establishing the magnitude of perfusion changes that can be reliably detected is necessary to delineate longitudinal perfusion changes related to disease processes from the effects of these sources of error. PurposeTo assess the feasibility of ASL for longitudinal monitoring of patients with FTD by quantifying between-session variability of perfusion on a voxel-by-voxel basis. Methods and materialsASL data were collected in 13 healthy controls and 8 patients with FTD or progressive supra-nuclear palsy. Variability in cerebral blood flow (CBF) by single delay pseudo-continuous ASL (SD-pCASL) acquired one month apart were quantified by the coefficient of variation (CV) and intraclass correlation coefficient (ICC). Additionally, CBF by SD-pCASL and ATT by low-resolution multiple inversion time ASL (LowRes-pCASL) were compared to Hadamard encoded sequences which are able to simultaneously measure CBF and ATT with improved time-efficiency. ResultsAgreement of grey-matter perfusion between sessions was found for both patients and controls (CV = 10.8% and 8.3% respectively) with good reliability for both groups (ICC > 0.6). Intensity normalization to remove day-to-day fluctuations in resting perfusion reduced the CV by 28%. Less than 5% of voxels had ATTs above the chosen post labelling delay (2 s), indicating that the ATT was not a significant source of error. Hadamard-encoded perfusion imaging yielded systematically higher CBF compared to SD-pCASL, but produced similar transit-time measurements. Power analysis revealed that SD-pCASL has the sensitivity to detect longitudinal changes as low as 10% with as few as 10 patient participants. ConclusionWith the appropriate labeling parameters, SD-pCASL is a promising approach for assessing longitudinal changes in CBF associated with FTD.

Impact of Late Cretaceous inversion and Cenozoic extension on salt structure growth in the Baltic sector of the North German Basin

AbstractThe Late Cretaceous to Cenozoic is known for its multiple inversion events, which affected Central Europe's intracontinental sedimentary basins. Based on a 2D seismic profile network imaging the basin fill without gaps from the base Zechstein to the seafloor, we investigate the nature and impact of these inversion events on Zechstein salt structures in the Baltic sector of the North German Basin. These insights improve the understanding of salt structure evolution in the region and are of interest for any type of subsurface usage. We link stratigraphic interpretation to previous studies and nearby wells and present key seismic depth sections and thickness maps with a new stratigraphic subdivision for the Upper Cretaceous and Cenozoic covering the eastern Glückstadt Graben and the Bays of Kiel and Mecklenburg. Time‐depth conversion is based on velocity information derived from refraction travel‐time tomography. Our results show that minor salt movement in the eastern Glückstadt Graben and in the Bay of Mecklenburg started contemporaneous with Late Cretaceous inversion in the Coniacian‐Santonian. Minor salt movement continued until the end of the Late Cretaceous. Overlying upper Paleocene and lower Eocene deposits show constant thickness without indications for salt movement suggesting a phase of tectonic quiescence from the late Paleocene to middle Eocene. In the late Eocene to Oligocene, major salt movement recommenced in the eastern Glückstadt Graben. In the Bays of Kiel and Mecklenburg, late Neogene uplift removed much of the Eocene‐Miocene succession. Preserved deposits indicate major post‐middle Eocene salt movement, which likely occurred coeval with the revived activity in the Glückstadt Graben. Cenozoic salt structure growth critically exceeded salt flow during Late Cretaceous inversion. Cenozoic salt movement could have been triggered by Alpine/Pyrenean‐controlled thin‐skinned compression, but is more likely controlled by thin‐skinned extension, possibly related to the beginning development of the European Cenozoic Rift System.

Efficient hardware prototype of ECDSA modules for blockchain applications

This paper concentrates on the hardware implementation of efficient and re- configurable elliptic curve digital signature algorithm (ECDSA) that is suitable for verifying transactions in Blockchain related applications. Despite ECDSA architecture being computationally expensive, the usage of a dedicated stand-alone circuit enables speedy execution of arithmetic operations. The prototype put forth supports N-bit elliptic curve cryptography (ECC) group operations, signature generation and verification over a prime field for any elliptic curve. The research proposes new hardware framework for modular multiplication and modular multiplicative inverse which is adopted for group operations involved in ECDSA. Every hardware design offered are simulated using modelsim register transfer logic (RTL) simulator. Field programmable gate array (FPGA) implementation of var- ious modules within ECDSA circuit is compared with equivalent existing techniques that is both hardware and software based to highlight the superiority of the suggested work. The results showcased prove that the designs implemented are both area and speed efficient with faster execution and less resource utilization while maintaining the same level of security. The suggested ECDSA structure could replace the software equivalent of digital signatures in hardware blockchain to thwart software attacks and to provide better data protection.

Characterizing hydrogen bonds in intact RNA from MS2 bacteriophage using magic angle spinning NMR

RNA is a polymer with pivotal functions in many biological processes. RNA structure determination is thus a vital step toward understanding its function. The secondary structure of RNA is stabilized by hydrogen bonds formed between nucleotide basepairs, and it defines the positions and shapes of functional stem-loops, internal loops, bulges, and other functional and structural elements. In this work, we present a methodology for studying large intact RNA biomolecules using homonuclear 15N solid-state NMR spectroscopy. We show that proton-driven spin-diffusion experiments with long mixing times, up to 16 s, improved by the incorporation of multiple rotor-synchronous 1H inversion pulses (termed radio-frequency dipolar recoupling pulses), reveal key hydrogen-bond contacts. In the full-length RNA isolated from MS2 phage, we observed strong and dominant contributions of guanine-cytosine Watson-Crick basepairs, and beyond these common interactions, we observe a significant contribution of the guanine-uracil wobble basepairs. Moreover, we can differentiate basepaired and non-basepaired nitrogen atoms. Using the improved technique facilitates characterization of hydrogen-bond types in intact large-scale RNA using solid-state NMR. It can be highly useful to guide secondary structure prediction techniques and possibly structure determination methods.

Valid sequential inference on probability forecast performance

Summary Probability forecasts for binary events play a central role in many applications. Their quality is commonly assessed with proper scoring rules, which assign forecasts numerical scores such that a correct forecast achieves a minimal expected score. In this paper, we construct e-values for testing the statistical significance of score differences of competing forecasts in sequential settings. E-values have been proposed as an alternative to $p$-values for hypothesis testing, and they can easily be transformed into conservative $p$-values by taking the multiplicative inverse. The e-values proposed in this article are valid in finite samples without any assumptions on the data-generating processes. They also allow optional stopping, so a forecast user may decide to interrupt evaluation, taking into account the available data at any time, and still draw statistically valid inference, which is generally not true for classical $p$-value-based tests. In a case study on post-processing of precipitation forecasts, state-of-the-art forecast dominance tests and e-values lead to the same conclusions.

Numerical and experimental evidence of topological interface state in a periodic acoustic black hole

Although the topological interfaces in periodic acoustic black holes (ABHs) have been theoretically reported, there is no published experimental evidence to support this. In this paper, we present experimental evidence and the mechanism explanation of such phenomenon. Meanwhile, the topological protection features are confirmed by introducing defects and geometrical imperfections. The structure under consideration is composed of uniform parts and ABHs with symmetry, which is a necessary condition of Dirac cone. Different from previous works, we used a hybrid mechanism (local resonant and Bragg scattering effect) to generate the multiple topological interface states, resulting in multiple topological inversion points (TIPs). The experiment results are in good agreements with the numerical prediction. This work opens new possibility for manipulating the TIPs in a certain range, which was proved to achieve subwavelength wave control and flexible tunability.

Robust and reversible image watermarking in homomorphic encrypted domain

This paper proposes a robust and reversible watermarking scheme for the encrypted image by using Paillier cryptosystem. In the proposed method, the original image is divided into a number of non-overlapping blocks sized by 8 × 8 and Paillier cryptosystem is applied to encrypt the pixels in each block. Firstly, a data hider can calculate the statistical values of encrypted blocks by employing modular multiplicative inverse (MMI) method and looking for a mapping table. Then a watermark sequence can be embedded into the encrypted image by shifting the histogram of the statistical values. On the receiver side, the shifted histogram can be obtained from both the encrypted image and the decrypted image. Furthermore, the embedded watermark can be extracted from the shifted histogram. The encrypted original image can be restored by employing inverse operations of histogram shifting. This is followed by a decryption operation to restore the original image. In the proposed method, the hidden bits can still be extracted correctly under some typical content-preserving operations, such as JPEG/JPEG2000 compression and additive Gaussian noise. Compared with the previous reversible watermarking methods in plaintext domain, the proposed method has satisfactory performance in image quality and robustness. Experimental results have shown the validity of the proposed method.

Geology differentiation by applying unsupervised machine learning to multiple independent geophysical inversions

SUMMARY Effective quantitative methods for integrating multiple inverted physical property models are necessary to increase the value of information and advance interpretation further to produce interpretable geology models through geology differentiation. Geology differentiation is challenging in greenfield exploration areas where specific a priori geological information is scarce. The main problem is to identify geological units quantitatively with appropriate 3-D integration of these models. The integration of multiple sources of information has been conducted with different unsupervised machine learning methods (e.g. clustering), which can identify relationships in the data in the absence of training information. For this reason, we investigate the performance of five different clustering methods on the identification of the geological units using inverted susceptibility, density, and conductivity models that image a synthetic geological model. We show that the correlation-based clustering yields the best results for the geology differentiation among those investigated by identifying the correlation between physical properties diagnostic of each unit. The result of the differentiation is a quasi-geology model, which is a model that represents the geology with inferred geological units and their spatial distribution. The resulting integrated quasi-geology model demonstrates that individually inverted models with minimal constraints have sufficient information to jointly identify different geological units.

Palaeostress analysis based on multiple inversion in 9-dimensional space in relation to hydrothermal calcite veins in the SE margin of the Elbe Fault Zone (Bohemian Cretaceous Basin, the Czech Republic)

Palaeostress analysis based on multiple inversion in 9-dimensional space in relation to hydrothermal calcite veins in the SE margin of the Elbe Fault Zone (Bohemian Cretaceous Basin, the Czech Republic)

Direct depth-domain Bayesian amplitude-variation-with-offset inversion

We have developed a new approach to perform Bayesian linearized amplitude-variation-with-offset (AVO) inversion in the depth domain using nonstationary wavelets. Bayesian linearized AVO inversion, a hybrid approach combining physics-based models with statistical learning, has gained immense popularity because of its superior computational speed and ability to estimate uncertainties in inverted model parameters. Bayesian linearized AVO inversion is performed on time-domain seismic data; therefore, depth-imaged seismic cannot be inverted directly using this method and would require depth-to-time conversion before AVO inversion can be done. Subsequently, time-to-depth conversion of the inverted volumes would be required for reservoir modeling and well placement. Domain conversions introduce additional uncertainty in geophysical workflows. In conventional AVO inversion, the seismic wavelet is assumed to be stationary, and this assumption leads to a restriction in the length of the time window over which the inversion can be performed. Therefore, AVO inversion is usually restricted to a narrow time window around the target of interest, and if multiple targets are present at different depths, multiple inversions must be run on the same volume. Depth-domain amplitude inversion is a recent development and has been previously presented in an iterative formulation. Implementing linearized Bayesian inversion directly in the depth domain using nonstationary wavelets is a convenient new approach that takes advantage of superior computational speed and uncertainty quantification without compromising the accurate spatial location that depth imaging provides. Combining these two ideas creates a novel, unique, and powerful seismic inversion technique that can be useful for quantitative interpretation and reservoir characterization.

Secure Elliptic Curve Crypto-Processor for Real-Time IoT Applications

Cybersecurity is a critical issue for Real-Time IoT applications since high performance and low latencies are required, along with security requirements to protect the large number of attack surfaces to which IoT devices are exposed. Elliptic Curve Cryptography (ECC) is largely adopted in an IoT context to provide security services such as key-exchange and digital signature. For Real-Time IoT applications, hardware acceleration for ECC-based algorithms can be mandatory to meet low-latency and low-power/energy requirements. In this paper, we propose a fast and configurable hardware accelerator for NIST P-256/-521 elliptic curves, developed in the context of the European Processor Initiative. The proposed architecture supports the most used cryptography schemes based on ECC such as Elliptic Curve Digital Signature Algorithm (ECDSA), Elliptic Curve Integrated Encryption Scheme (ECIES), Elliptic Curve Diffie-Hellman (ECDH) and Elliptic Curve Menezes-Qu-Vanstone (ECMQV). A modified version of Double-And-Add-Always algorithm for Point Multiplication has been proposed, which allows the execution of Point Addition and Doubling operations concurrently and implements countermeasures against power and timing attacks. A simulated approach to extract power traces has been used to assess the effectiveness of the proposed algorithm compared to classical algorithms for Point Multiplication. A constant-time version of the Shamir’s Trick has been adopted to speed-up the Double-Point Multiplication and modular inversion is executed using Fermat’s Little Theorem, reusing the internal modular multipliers. The accelerator has been verified on a Xilinx ZCU106 development board and synthesized on both 45 nm and 7 nm Standard-Cell technologies.

Multistate Switching of Spin Selectivity in Electron Transport through Light-Driven Molecular Motors.

It is established that electron transmission through chiral molecules depends on the electron's spin. This phenomenon, termed the chiral‐induced spin selectivity (CISS), effect has been observed in chiral molecules, supramolecular structures, polymers, and metal‐organic films. Which spin is preferred in the transmission depends on the handedness of the system and the tunneling direction of the electrons. Molecular motors based on overcrowded alkenes show multiple inversions of helical chirality under light irradiation and thermal relaxation. The authors found here multistate switching of spin selectivity in electron transfer through first generation molecular motors based on the four accessible distinct helical configurations, measured by magnetic‐conductive atomic force microscopy. It is shown that the helical state dictates the molecular organization on the surface. The efficient spin polarization observed in the photostationary state of the right‐handed motor coupled with the modulation of spin selectivity through the controlled sequence of helical states, opens opportunities to tune spin selectivity on‐demand with high spatio‐temporal precision. An energetic analysis correlates the spin injection barrier with the extent of spin polarization.

Multiplicative inverse with quantum search algorithm under π/18 phase rotation

Multiplicative inverse with quantum search algorithm under π/18 phase rotation

The Ethnographer from Within: Wild Thought in Stefano D’Arrigo’s Horcynus Orca

Abstract The present article aims to demonstrate how ethnography is present, discussed, and criticized in Stefano D’Arrigo’s novel Horcynus Orca (1975). Through a comparison with a passage from Claude Lévi-Strauss’s Tristes Tropiques (1955), the novel is shown to adopt and challenge central tenets of ethnography. D’Arrigo imagines the possibility of an ‘ethnographer from within,’ a member of a Sicilian fishermen community who, by virtue of his personal experience, possesses the necessary distance to report about his community of origin, yet cannot help but impact it significantly as he in turn brings along and into the community a different system of thought. The article exposes the multiple inversions and subversions that the novel operates with respect to the dichotomic pairs nature/culture, civilized/primitive, indigenous/foreign, as well as to ethnography itself by focussing on the occurrence of ethnographic documents in key passages of the novel. Lévi-Strauss’s Tristes Tropiques and possibly to an even greater extent Horcynus Orca are concerned with the contradictions inherent in the study of humankind, its various manifestations, and its position in the world, without aspiring to resolve them in any univocal or definitive way.

A Note on the Computation of the Modular Inverse for Cryptography

In literature, there are a number of cryptographic algorithms (RSA, ElGamal, NTRU, etc.) that require multiple computations of modulo multiplicative inverses. In this paper, we describe the modulo operation and we recollect the main approaches to computing the modulus. Then, given a and n positive integers, we present the sequence (zj)j≥0, where zj=zj−1+aβj−n, a<n and GCD(a,n)=1. Regarding the above sequence, we show that it is bounded and admits a simple explicit, periodic solution. The main result is that the inverse of a modulo n is given by a−1=⌊im⌋+1 with m=n/a. The computational cost of such an index i is O(a), which is less than O(nlnn) of the Euler’s phi function. Furthermore, we suggest an algorithm for the computation of a−1 using plain multiplications instead of modular multiplications. The latter, still, has complexity O(a) versus complexity O(n) (naive algorithm) or complexity O(lnn) (extended Euclidean algorithm). Therefore, the above procedure is more convenient when a<<n (e.g., a<lnn).

Strain-tunable triple point Fermions in diamagnetic rare-earth half-Heusler alloys

Topologically non-trivial electronic structure is a feature of many rare-earth half-Heusler alloys, which host atoms with high spin-orbit coupling bringing in the non-triviality. In this article, using the first-principles simulations, rare-earth half-Heusler YPdBi, ScPdBi, LaPdBi, LuPdBi, YPtBi and LuPtBi alloys are studied under strain to reveal multiple band inversions associated with topological phase transitions. From our simulations we find that, as a result of first band-inversion, the Brillouin zone of the diamagnetic half-Heusler alloys hosts eight triple points whereas, the second band inversion causes the emergence of sixteen more triple points. These band-inversions are observed to be independent of the spin-orbit coupling and are the reason behind increasing occupation of bismuth 7s orbitals as volume of the unit cell increases. The surface electronic transport in different triple point semi-metallic phases is found to evolve under strain, as the number of Fermi arcs change due to multiple band inversions. Once the second band inversion occurs, further application of tensile strain does not increase the number of triple points and Fermi arcs. However, increasing tensile strain (or decreasing compressive strain) pushes the triple point crossing to higher momenta, making them more effective as source of highly mobile electrons. These observations make a pathway to tune the bulk as well as surface transport through these semi-metals by application of tensile or compressive strain depending on the unstrained relative band-inversion strength of the material.

Karyological Diversification in the Genus Lyciasalamandra (Urodela: Salamandridae).

Simple SummaryThe Lycian salamanders of the genus Lyciasalamandra are characterized by a debated taxonomy and phylogenetic relationships. They have been the subject of various molecular and phylogenetic analyses, but their chromosomal diversity is completely unknown. We here present a comparative cytogenetic analysis on five out of the seven described species and seven subspecies of Lyciasalamandra, providing the first karyological assessment on the genus and comparing them to closely related representatives of the genus Salamandra. We analyzed the occurrence and distribution of different conserved (chromosome number and morphology) and highly variable karyological features. We found an impressive diversity in the configuration of nucleolus organizing regions (NORs), which alternatively occur either as heteromorphic or homomorphic loci on distinct regions of different chromosome pairs. We highlight that the observed peculiar taxon-specific pattern of chromosome markers supports the taxonomic validity of the different studied evolutionary lineages and is consistent with a scenario of synchronous evolution in the Lycian salamanders.We performed the first cytogenetic analysis on five out of the seven species of the genus Lyciasalamandra, including seven subspecies, and representatives of its sister genus Salamandra. All the studied species have a similar karyotype of 2n = 24, mostly composed of biarmed elements. C-bands were observed on all chromosomes, at centromeric, telomeric and interstitial position. We found a peculiar taxon-specific NOR configuration, including either heteromorphic and homomorphic NORs on distinct regions of different chromosomes. Lyciasalamandra a. antalyana and L. helverseni showed two homomorphic NORs (pairs 8 and 2, respectively), while heteromorphic NORs were found in L. billae (pairs 6, 12), L. flavimembris (pairs 2, 12), L. l. luschani (pairs 2, 12), L. l. basoglui (pairs 6, 12), L. l. finikensis (pairs 2, 6) and S. lanzai (pairs 8, 10). Homomorphic NORs with an additional supernumerary site were shown by S. s. salamandra (pairs 2, 8) and S. s. gigliolii (pairs 2, 10). This unexpected highly variable NOR configuration is probably derived from multiple independent NOR translocations and paracentric inversions and correlated to lineage divergence in Lyciasalamandra. These results support the taxonomic validity of the studied taxa and are consistent with a hypothesized scenario of synchronous evolution in the genus.