Multiplicative Inverse Research Articles

Rapid evolution of recombination landscapes during the divergence of cichlid ecotypes in Lake Masoko.

Variation of recombination rate along the genome is of crucial importance to rapid adaptation and organismal diversification. Many unknowns remain regarding how and why recombination landscapes evolve in nature. Here, we reconstruct recombination maps based on linkage disequilibrium and use subsampling and simulations to derive a new measure of recombination landscape evolution: the Population Recombination Divergence Index (PRDI). Using PRDI, we show that fine-scale recombination landscapes differ substantially between two cichlid fish ecotypes of Astatotilapia calliptera that diverged only ~2,500 generations ago. Perhaps surprisingly, recombination landscape differences are not driven by divergence in terms of allele frequency (FST) and nucleotide diversity (Δπ): although there is some association, we observe positive PRDI in regions where FST and Δπ are zero. We found a stronger association between evolution of recombination and 47 large haplotype blocks that are polymorphic in Lake Masoko, cover 21% of the genome, and appear to include multiple inversions. Among haplotype blocks, there is a strong and clear association between the degree of recombination divergence and differences between ecotypes in heterozygosity, consistent with recombination suppression in heterozygotes. Overall, our work provides a holistic view of changes in population recombination landscapes during early stages of speciation with gene flow.

Topological signatures of triply degenerate fermions in Heusler alloys: an ab initio study

Triply degenerate nodal point (TP) fermions, lacking elementary particle counterparts, have been theoretically anticipated as quasiparticle excitations near specific band crossing points constrained by distinct space-group symmetries instead of Lorentz invariance. Here, based onfirst-principlescalculations and symmetry analysis, we demonstrate the presence of TP fermions in Heusler alloys. Furthermore, we predict that these Heusler alloys are dynamically stable, exhibiting TP fermions along four distinctC3axes in the F-43m space group. We show thatα-LiCaPdSb harbours peculiar Fermi arcs and surface states on the (111) and (001) crystal facets, owing to the coexistence of threefold rotational and time reversal symmetry. More interestingly, a modest tensile strain can increase the distance of fermions along the Γ-Lhigh symmetric line by as much as 21.10%, which give rise to measurable Fermi arcs. Furthermore, we investigate non-trivial topological insulator phase inβ-LiCaPdSb, by changing the chemical environment through placing transition metal atoms at various Wyckoff positions. Theβ-LiCaPdSb harbour a semi-metallic nature, and by breaking cubic symmetry, it undergoes a transition from semi-metal to a non-trivial topological insulator. In addition, for the first time, rare-earth LaPtBi half-Heusler alloy is examined under strain to uncover multiple band inversions associated with the TP fermionic phase. The observed multiple band inversion is entirely unaffected by spin-orbit coupling. We show that the LaPtBi compound hosts TP fermions, which are linked to aZ2topological invariant. Remarkably, with clear band crossings and multiple band inversion, we point out the possibilities of the LaPtBi for displaying a rich topological phase diagram. Our work provides a prototype material platform for experimental detection through angle-resolved photoemission spectroscopy or scanning tunnelling spectroscopy and practical spintronic applications.

Quantitative myelin water assessment for multiple sclerosis using multi-inversion magnetic resonance fingerprinting.

Multiple sclerosis (MS) is a demyelination disease. Myelin water is a biomarker of myelin and thus myelin water imaging is a vital tool to provide insight into the demyelination process. This study aimed to characterize the multiple compartments including myelin water fraction (MWF), gray matter (GM) cellular water, white matter (WM) cellular water, and cerebrospinal fluid (CSF) using multiple inversion recovery (mIR) magnetic resonance fingerprinting (MRF) on a clinical MS cohort. The Phantom experiment was conducted with tubes containing different WM and GM concentrations extracted from pig brains. For the in-vivo experiment, 23 healthy control (HC) volunteers and 18 MS patients were recruited for this study. The experiments were performed using a clinical 3T MRI. A multi-slice, fast imaging with a steady-state precession (FISP) based mIR MRF protocol was used to obtain the MWF measurements, with 6min of scan time for each volunteer. The quantification was based on the iterative non-negative least squares (NNLS) with reweighting. The brain compartments quantified were myelin water, WM cellular water, GM cellular water, and CSF. A radiologist with 6 years of experience labeled the MS lesions on FLAIR, MPRAGE, and MWF. Statistical analysis was performed by applying unpaired and paired student's t-tests to compare the MWF results in different groups and in normal-appearing white matter (NAWM) and MS lesions. The phantom result demonstrated the ability to detect MWF with various myelin concentrations. The maps derived from mIR MRF, including MWF, WM cellular water, GM cellular water, and CSF were consistent with the anatomical structures observed in FLAIR and MPRAGE. The MWF values in the NAWM of MS patients were significantly different from those in HC, with values of 0.32±0.025 and 0.25±0.036, respectively. Additionally, the MWF values in WM lesions were significantly smaller than in NAWM at 0.034±0.036. The mIR-MRF technique, using multi-compartment analysis, can simultaneously generate maps of MWF, WM cellular water, GM cellular water, and CSF with sufficient brain coverage and in a reasonably short scan time. The MWF map might provide insights into the demyelination associated with MS.

A novel method for detecting tropopause structures based on the bi-Gaussian function

Abstract. The tropopause is an important transition layer and can be a diagnostic of upper-tropospheric and lower-stratospheric structures, exhibiting unique atmospheric thermal and dynamic characteristics. A comprehensive understanding of the evolution of fine tropopause structures is necessary and primary for the further study of complex multi-scale atmospheric physical–chemical coupling processes in the upper troposphere and lower stratosphere. A novel method utilizing the bi-Gaussian function is capable of identifying the characteristic parameters of vertical tropopause structures and providing information on double-tropopause (DT) structures. The new method improves the definition of the cold-point tropopause and detects one (or two) of the most significant local cold points by fitting the temperature profiles to the bi-Gaussian function, which defines the point(s) as the tropopause height(s). The bi-Gaussian function exhibits excellent potential for explicating the variation trends of temperature profiles. The results of the bi-Gaussian method and lapse rate tropopause, as defined by the World Meteorological Organization, are compared in detail for different cases. Results indicate that the bi-Gaussian method is able to more stably and obviously identify the spatial and temporal distribution characteristics of the thermal tropopauses, even in the presence of multiple temperature inversion layers at higher elevations. Moreover, 5 years of historical radiosonde data from China (from 2012 to 2016) revealed that the occurrence frequency and thickness of the DT, as well as the single-tropopause height and the first and second DT heights, displayed significant meridional monotonic variations. The occurrence frequency (thickness) of the DT increased from 1.07 % (1.96 km) to 47.19 % (5.42 km) in the latitude range of 16–50° N. The meridional gradients of tropopause height were relatively large in the latitude range of 30–40° N, essentially corresponding to the climatological locations of the subtropical jet and the Tibetan Plateau.

One-dimensional photonic crystal enhancing spin-to-orbital angular momentum conversion for single-particle tracking

Single-particle tracking (SPT) is an immensely valuable technique for studying a variety of processes in the life sciences and physics. It can help researchers better understand the positions, paths, and interactions of single objects in systems that are highly dynamic or require imaging over an extended time. Here, we propose an all-dielectric one-dimensional photonic crystal (1D PC) that enhances spin-to-orbital angular momentum conversion for three-dimensional (3D) SPTs. This well-designed 1D PC can work as a substrate for optical microscopy. We introduce this effect into the interferometric scattering (iSCAT) technique, resulting in a double-helix point spread function (DH-PSF). DH-PSF provides more uniform Fisher information for 3D position estimation than the PSFs of conventional microscopy, such as encoding the axial position of a single particle in the angular orientation of DH-PSF lobes, thus providing a means for 3D SPT. This approach can address the challenge of iSCAT in 3D SPT because DH-PSF iSCAT will not experience multiple contrast inversions when a single particle travels along the axial direction. DH-PSF iSCAT microscopy was used to record the 3D trajectory of a single microbead attached to the flagellum, facilitating precise analysis of fluctuations in motor dynamics. Its ability to track single nanoparticles, such as 3D diffusion trajectories of 20 nm gold nanoparticles in glycerol solution, was also demonstrated. The DH-PSF iSCAT technique enabled by a 1D PC holds potential promise for future applications in physical, biological, and chemical science.

Seismic shear wave noise suppression and application to well tie

Abstract Seismic shear waves have been used in oil and gas exploration for decades. A 2D seismic shear wave inline was acquired in the Sanhu area, located in the Qaidam Basin in western China. Although the acquired shear wave data showed high resolution and comparable bandwidth to the compressional wave, it was contaminated by various types of noise, including linear noise, single-frequency noise, and especially internal multiples. Internal multiples seriously compromise the primary reflections at both near offset and far offset and are difficult to suppress. This paper presents a case study of noise attenuation for the seismic shear wave. First, single-frequency noise and linear noise are attenuated through filtering methods. Then, two methods (the Radon transform and the frequency-wavenumber (F-K) filtering) are evaluated for their effectiveness in multiple suppression and amplitude preservation. The results indicate that both methods successfully reduce long-period multiples at the far offset, enhancing the signal-to-noise ratio. We show that F-K filtering retains the characteristic ‘strong–weak–strong’ amplitude variation in the SV-SV-wave data gather, making it preferable for subsequent amplitude variation with offset analysis and inversion. Finally, a wave equation-based multiple suppression inversion method is used to suppress near-offset internal multiples. This involves iteratively predicting internal multiples and adaptively subtracting them from the original data. Stacked sections of different offsets are compared to demonstrate the de-multiple result, and the result is also validated by the improvement of well calibration with the seismic shear wave data.

Respiratory motion-corrected T1 mapping of the abdomen.

The purpose of this study was to investigate an approach for motion-corrected T1 mapping of the abdomen that allows for free breathing data acquisition with 100% scan efficiency. Data were acquired using a continuous golden radial trajectory and multiple inversion pulses. For the correction of respiratory motion, motion estimation based on a surrogate was performed from the same data used for T1 mapping. Image-based self-navigation allowed for binning and reconstruction of respiratory-resolved images, which were used for the estimation of respiratory motion fields. Finally, motion-corrected T1 maps were calculated from the data applying the estimated motion fields. The method was evaluated in five healthy volunteers. For the assessment of the image-based navigator, we compared it to a simultaneously acquired ultrawide band radar signal. Motion-corrected T1 maps were evaluated qualitatively and quantitatively for different scan times. For all volunteers, the motion-corrected T1 maps showed fewer motion artifacts in the liver as well as sharper kidney structures and blood vessels compared to uncorrected T1 maps. Moreover, the relative error to the reference breathhold T1 maps could be reduced from up to 25% for the uncorrected T1 maps to below 10% for the motion-corrected maps for the average value of a region of interest, while the scan time could be reduced to 6-8s. The proposed approach allows for respiratory motion-corrected T1 mapping in the abdomen and ensures accurate T1 maps without the need for any breathholds.

Multiple Chirality Switching of a Dye‐Grafted Helical Polymer Film Driven by Acid & Base

AbstractA stimuli‐responsive multiple chirality switching material, which can regulate opposed chiral absorption characteristics, has great application value in the fields of optical modulation, information storage and encryption, etc. However, due to the rareness of effective functional systems and the complexity of material structures, developing this type of material remains an insurmountable challenge. Herein, a smart polymer film with multiple chirality inversion properties was fabricated efficiently based on a newly‐designed acid & base‐sensitive dye‐grafted helical polymer. Benefited from the cooperative effects of various weak interactions (hydrogen bonds, electrostatic interaction, etc.) under the aggregated state, this polymer film exhibited a promising acid & base‐driven multiple chirality inversion property containing record switchable chiral states (up to five while the solution showed three‐state switching) and good reversibility. The creative exploration of such a multiple chirality switching material can not only promote the application progress of current chiroptical regulation technology, but also provide a significant guidance for the design and synthesis of future smart chiroptical switching materials and devices.

Multiple Chirality Switching of a Dye-Grafted Helical Polymer Film Driven by Acid & Base.

A stimuli-responsive multiple chirality switching material, which can regulate opposed chiral absorption characteristics, has great application value in the fields of optical modulation, information storage and encryption, etc. However, due to the rareness of effective functional systems and the complexity of material structures, developing this type of material remains an insurmountable challenge. Herein, a smart polymer film with multiple chirality inversion properties was fabricated efficiently based on a newly-designed acid & base-sensitive dye-grafted helical polymer. Benefited from the cooperative effects of various weak interactions (hydrogen bonds, electrostatic interaction, etc.) under the aggregated state, this polymer film exhibited a promising acid & base-driven multiple chirality inversion property containing record switchable chiral states (up to five while the solution showed three-state switching) and good reversibility. The creative exploration of such a multiple chirality switching material can not only promote the application progress of current chiroptical regulation technology, but also provide a significant guidance for the design and synthesis of future smart chiroptical switching materials and devices.

Inversion of Gravity Data Constrained by a Magnetotelluric Resistivity Model: Application to the Asal Rift, Djibouti

AbstractBefore exploiting a geothermal resource in a volcanic setting such as the Asal rift, it is necessary to acquire a better knowledge of the subsoil, with the objective of locating the geothermal reservoir and evaluating the resource characteristic (permeability, temperature, etc.). For this type of resource, geophysical exploration methods are essential (such as gravimetry, magnetotellurics, etc.). However, a particular data type does not necessarily have the resolution and sensitivity. Furthermore, individual inversions of these geophysical data face the ambiguity of the non‐uniqueness of the inverse solution. In this paper, we present a new linear approach of gravity data using the constraint of a MT resistivity model. We coupled the resistivity and density using inversion cross‐gradients and the linear correlations. The approach was tested and validated on synthetic data and applied to gravity and MT data in the Asal Rift. Multiple inversions with different levels of coupling provided a series of density models. We applied the principal component analysis (PCA) technique to assess these models. We were able to define two dominant processes acting differently on the density and resistivity distribution at depth, namely the geothermal activity of the rift and the structural control of active tectonics.

Associativity and commutativity of partially ordered rings

Consider a commutative monoid (M,+,0) and a biadditive binary operation μ:M×M→M. We will show that under some additional general assumptions, the operation μ is automatically both associative and commutative. The main additional assumption is localizability of μ, which essentially means that a certain canonical order on M is compatible with adjoining some multiplicative inverses of elements of M. As an application we show that a division ring F is commutative provided that for all a∈F there exists a natural number k such that a−k is not a sum of products of squares. This generalizes the classical theorem that every archimedean ordered division ring is commutative to a more general class of formally real division rings that do not necessarily allow for an archimedean (total) order. Similar results about automatic associativity and commutativity are well-known for special types of partially ordered extended rings (“extended” in the sense that neither associativity nor commutativity of the multiplication is required by definition), namely in the uniformly bounded and the lattice-ordered cases, i.e. for (extended) f-rings. In these cases the commutative monoid in question is the positive cone of the partially ordered extended ring. We also discuss how these classical results can be obtained from our main theorem.

Long-read sequencing and optical genome mapping identify causative gene disruptions in noncoding sequence in two patients with neurologic disease and known chromosome abnormalities.

Despite advances in next generation sequencing (NGS), genetic diagnoses remain elusive for many patients with neurologic syndromes. Long-read sequencing (LRS) and optical genome mapping (OGM) technologies improve upon existing capabilities in the detection and interpretation of structural variation in repetitive DNA, on a single haplotype, while also providing enhanced breakpoint resolution. We performed LRS and OGM on two patients with known chromosomal rearrangements and inconclusive Sanger or NGS. The first patient, who had epilepsy and developmental delay, had a complex translocation between two chromosomes that included insertion and inversion events. The second patient, who had a movement disorder, had an inversion on a single chromosome disrupted by multiple smaller inversions and insertions. Sequence level resolution of the rearrangements identified pathogenic breaks in noncoding sequence in or near known disease-causing genes with relevant neurologic phenotypes (MBD5, NKX2-1). These specific variants have not been reported previously, but expected molecular consequences are consistent with previously reported cases. As the use of LRS and OGM technologies for clinical testing increases and data analyses become more standardized, these methods along with multiomic data to validate noncoding variation effects will improve diagnostic yield and increase the proportion of probands with detectable pathogenic variants for known genes implicated in neurogenetic disease.

Pulse-doubling perovskite nanowire lasers enabled by phonon-assisted multistep energy funneling

Laser pulse multiplication from an optical gain medium has shown great potential in miniaturizing integrated optoelectronic devices. Perovskite multiple quantum wells (MQWs) structures have recently been recognized as an effective gain media capable of doubling laser pulses that do not rely on external optical equipment. Although the light amplifications enabled with pulse doubling are reported based on the perovskite MQWs thin films, the micro-nanolasers possessed a specific cavity for laser pulse multiplication and their corresponding intrinsic laser dynamics are still inadequate. Herein, a single-mode double-pulsed nanolaser from self-assembled perovskite MQWs nanowires is realized, exhibiting a pulse duration of 28 ps and pulse interval of 22 ps based on single femtosecond laser pulse excitation. It is established that the continuous energy building up within a certain timescale is essential for the multiple population inversion in the gain medium, which arises from the slowing carrier localization process owning to the stronger exciton–phonon coupling in the smaller-n QWs. Therefore, the double-pulsed lasing is achieved from one fast energy funnel process from the adjacent small-n QWs to gain active region and another slow process from the spatially separated ones. This report may shed new light on the intrinsic energy relaxation mechanism and boost the further development of perovskite multiple-pulse lasers.

Assessment of Ecosystem Service Values of Urban Wetland: Taking East Lake Scenic Area in Wuhan as an Example

Urban wetlands represent a significant ecosystem type within urban landscapes. The quantitative assessment of their ecological service value holds great significance in guiding and improving the urban habitat. However, due to the insufficient spatial resolution of traditional low-to-medium resolution remote sensing imagery for surface monitoring, previous studies have conducted relatively limited research on the ecosystem services of urban wetlands. In this paper, based on multi-source data including multi-scale remote sensing data, a spatial-temporal fusion model and multiple ecological parameter inversion models were employed to invert three key ecological parameters at high spatial resolution, thereby assessing the ecosystem service values (ESVs) of urban wetlands. Taking the East Lake Scenic Area (ELSA) in Wuhan as an example, the dynamics of its ecosystem services’ value components were comparatively analyzed. The results indicate that, while the total value of ecosystem services declined slightly in 2015 compared to 2011, there was a notable increase in their value to CNY 3.219 billion by 2019, which represents a doubling of the total value relative to 2011. This trend could be primarily attributed to a significant rise in cultural services within the region. Specifically, the value of tourism services reached CNY 2.090 billion in 2019, representing a threefold increase compared to 2011. This demonstrates that ecosystem services in the ELSA have been significantly optimized and enhanced through associated ecological projects. Further research should investigate the mechanisms by which urbanization affects these crucial ecosystem services, particularly the characterization of cultural services in urban wetlands, and develop more effective strategies to enhance urban resilience and sustainable development.

Impact of Anthropogenic Activities on Sedimentary Records in the Lingdingyang Estuary of the Pearl River Delta, China

High-intensity anthropogenic activities have greatly altered the estuarine-shelf depositional processes of sediments, and the intensity and frequency of the impacts of human interventions have far exceeded the natural development of estuarine systems. Since the reform and opening up, human activities such as dams, sand mining, channel dredging, and reclamation have already caused anomalous changes in the dynamical–sedimentary–geomorphological processes of the Lingdingyang Estuary (LE). Analyzing the impact of high-intensity anthropogenic activities on sedimentary processes and the hydrodynamic environment through sedimentary records can provide a scientific basis for predicting the evolution of the estuary and the sustainable development of the Guangdong–Hongkong–Macao Greater Bay Area. The aims of this study are to reveal the impact of varying intensity human activities across different periods on depositional pattern and conduct a preliminary investigation into the spatial differences in sedimentary characteristic attributed to human activities. Two cores (LD11 and LD13) located in the LE were selected for continuous scanning of high-resolution XRF, grain size, and 210Pbex dating tests, and scrutinized with the previous studies of the historical process of human activities in the LE. The results show the following: (1) The abrupt alterations in 210Pbex, geochemical indices, and grain size in LD13 happened in close proximity to the 95 cm layer, suggesting a shift in the sedimentary environment during 1994. (2) In the context of the continuous reduction in water and sediment flux into the LE after 1994, the large-scale and high-intensity human activities like sand mining, channel dredging, and reclamation are responsible for the sedimentation rate increase rather than decrease, the coarsening of sediment fractions, the frequent fluctuations in Zr/Rb, Zr/Al, Sr/Fe, and Sr/Al ratios, and the increase in anomalous extremes. (3) Sedimentary records found in locations varying in anthropogenic intensities differ greatly. Compared with the nearshore siltation area, the grain size composition in the channel area is noticeably coarser and exhibits a wider range of grain size variations. The 210Pbex is strongly perturbed and the vertical distribution is disturbed; the phenomenon of multiple inversions from the surface downwards is shown, making it impossible to carry out sedimentation rate and dating analysis, and the geochemical indicators have changed drastically without any obvious pattern. The evidence of the human activities can be retrieved in the sedimentary record of the estuary and provide a different angle to examine the impacts of the human activities.

Some Involutory Pascal Matrices Can Make More Involutory Pascal Matrices

Summary There is an intuitive way to flip signs within a lower triangular matrix n × n matrix whose entries form the first n – 1 rows of Pascal’s triangle to cause the matrix to be its own multiplicative inverse. For any given positive integer n, we find how many unintuitive choices of flipped signs will also cause the n × n matrix to be its own multiplicative inverse by first seeing how such matrices may or may not fit into larger matrices from the same family.

New 3-D Fluorescence Spectral Indices for Multiple Pigment Inversions of Plant Leaves via 3-D Fluorescence Spectra

High-sensitivity fluorescence monitoring has been widely used in agriculture and environmental science. However, the active fluorescence detection information of leaf segments mainly focuses on total chlorophyll, and the fluorescence information of chlorophyll a, chlorophyll b, and some other pigments has not been explored. This only considers the fluorescence spectrum characteristics at a single wavelength or the fluorescence integral from a range of wavelength regions and does not completely consider the linkage relation between the excitation, emission, and interference information. In this paper, the three-dimensional fluorescence spectrum, containing the excitation and emission fluorescence spectra, and the corresponding multiple pigment characteristics from the upgraded LOPEX_ZJU database were collected. The linkages of excitation and emission of the three-dimensional fluorescence spectra of these pigments were analyzed for the newly built multiple pigment 3-D fluorescence spectral indices (3-D FSIs), including those of chlorophyll a, chlorophyll b, carotenoid, anthocyanin, and flavonoid 3-D FSIs. Then, these pigment inversion models were established and validated. The results show that the 3-D FSIs performances for the photosynthetic pigment content inversion (including chlorophyll a and b, and carotenoids) were much better than those for the photo-protective pigments (including anthocyanins and flavonoids) from the 3-D fluorescence spectra of these plant leaves. Here, the 3-D fluorescence normalization index (FNI ((F430,690-F430,763)/(F430,690+F430,763))) for the chlorophyll a inversion model has a high accuracy, the RMSE is 2.96 μg/cm2, and the 3-D fluorescence reciprocal difference index (FRI (F650,704/F650,668) for the chlorophyll b model has an encouraging RMSE (2.01 μg/cm2). The RMSE of the 3-D fluorescence ratio index (FRI (F500,748/F500,717)) for the carotenoid inversion is 3.77 μg/cm2 RMSE. Only FRI (F370,615/F370,438) was selected for the modeling and validating evaluation of the leaf Flas content inversion, but the evaluation metrics were not good, with an RMSE (151.13 μg/cm2). For Ants, although there was a 3-D FSI (FRDI (1/F540,679-1/F540,557)), and its evaluation metrics, with an RMSE (2.8 μg/cm2), were at or over 0.05 level, the validating evaluation metric VC (98.3577%) was not encouraging. These results showed that fluorescence, as a nondestructive and efficient detection method, could determine the contents of chlorophyll a, chlorophyll b, and carotenoid in plant leaves, providing a new method to detect plant information. It can also provide a potential chance for the fluorescence images of fine photo-protective pigments, especially chlorophyll a and b, using the special active fluorescence excitation light source and a few fluorescence imaging channels from the optimal FSIs.

Quantum ratchet with Lindblad rate equations.

A quantum random-walk model is established on a one-dimensional periodic lattice that fluctuates between two possible states. This model is defined by Lindblad rate equationsthat incorporate the transition rates between the two lattice states. Leveraging the system's symmetries, the particle velocity can be described using a finite set of equations, even though the state space is of infinite dimension. These equationsyield an analytical expression for the velocity in the long-time limit, which is employed to analyze the characteristics of directed motion. Notably, the velocity can exhibit multiple inversions, and to achieve directed motion, distinct, nonzero transition rates between lattice states are required.

Adder-Only Reverse Converters for 5-Moduli Set {2 q , 2 q − 1, 2 q+1 ± 1, 2 q+2 − 1}

We propose a balanced 5 -moduli set P = { 2 q , 2 q − 1 , 2 q + 1 − 1 , 2 q + 1 + 1 , 2 q + 2 − 1 } , for odd q ≥ 3 . Our reverse conversion scheme is based on a multi-stage new Chinese remainder theorem, where some of the difficult-to-derive multiplicative inverse coefficients are expressed as geometric series. Only carry-save and ripple-carry adders are used as components of the corresponding circuits. Analytical gate-level evaluations are performed on the proposed and reference converters, whose results are confirmed by the synthesis tool. A comparison of the converters for moduli sets with equal dynamic range shows that P is similar to previous 5-moduli set { 2 q , 2 q − 1 , 2 q + 1 , 2 q + 1 − 1 , 2 q − 1 − 1 } and shows slight advantage in delay and energy consumption.

Coupling of twelve putative chromosomal inversions maintains a strong barrier to gene flow between snail ecotypes.

Chromosomal rearrangements can lead to the coupling of reproductive barriers, but whether and how they contribute to the completion of speciation remains unclear. Marine snails of the genus Littorina repeatedly form hybrid zones between populations segregating for multiple inversion arrangements, providing opportunities to study their barrier effects. Here, we analyzed 2 adjacent transects across hybrid zones between 2 ecotypes of Littorina fabalis ("large" and "dwarf") adapted to different wave exposure conditions on a Swedish island. Applying whole-genome sequencing, we found 12 putative inversions on 9 of 17 chromosomes. Nine of the putative inversions reached near differential fixation between the 2 ecotypes, and all were in strong linkage disequilibrium. These inversions cover 20% of the genome and carry 93% of divergent single nucleotide polymorphisms (SNPs). Bimodal hybrid zones in both transects indicated that the 2 ecotypes of Littorina fabalis maintain their genetic and phenotypic integrity following contact. The bimodality reflects the strong coupling between inversion clines and the extension of the barrier effect across the whole genome. Demographic inference suggests that coupling arose during a period of allopatry and has been maintained for > 1,000 generations after secondary contact. Overall, this study shows that the coupling of multiple chromosomal inversions contributes to strong reproductive isolation. Notably, 2 of the putative inversions overlap with inverted genomic regions associated with ecotype differences in a closely related species (Littorina saxatilis), suggesting the same regions, with similar structural variants, repeatedly contribute to ecotype evolution in distinct species.