Zigzag Order Research Articles

The vicinity of hyper-honeycomb β-Li2IrO3 to a three-dimensional Kitaev spin liquid state.

Due to the combination of a substantial spin-orbit coupling and correlation effects, iridium oxides hold a prominent place in the search for novel quantum states of matter, including, e.g., Kitaev spin liquids and topological Weyl states. We establish the promise of the very recently synthesized hyper-honeycomb iridate β-Li2IrO3 in this regard. A detailed theoretical analysis reveals the presence of large ferromagnetic first-neighbor Kitaev interactions, while a second-neighbor antiferromagnetic Heisenberg exchange drives the ground state from ferro to zigzag order via a three-dimensional Kitaev spin liquid and an incommensurate phase. Experiment puts the system in the latter regime but the Kitaev spin liquid is very close and reachable by a slight modification of the ratio between the second- and first-neighbor couplings, for instance via strain.

Polymery and nectary chambers in Codon (Codonaceae): Flower and fruit development in a small, capsule-bearing family of Boraginales

Flower and fruit ontogeny in both species of Codon D. Royen (Codonaceae) has been investigated. Morphological differences and similarities between the Hydrophyllaceae I and II (Nameae) (Wigandia Kunth), as well as the Boraginaceae s.str. and Wellstediaceae are discussed. Flowers and fruits representing different ontogenetic stages were collected from culture and observed by scanning electron microscopy and light microscopy. The polymerous calyx, corolla and androecium develop acropetally. Sepals and stamens arise in two steps: after initiation of the first half in a 2/5-spiral, the second half arises subsimultaneously. Petals and stamens arrange later on in zigzag order to form two pseudowhorls and usually differ in size. In the mature stage, the gynoecium is nearly completely superior and symmetrical. Nectar compartments are formed by partitioning septa developing between filaments and corolla tube. They are covered by trichomes and laterally broadened filaments and present nectar from a nectary at the base of the gynoecium. This nectary formation leading to a revolver flower is unique in Boraginales. Our results indicate that Codonaceae share similarities with Wellstediaceae (Boraginales I) and Hydrophyllaceae I and II (Boraginales II). They are similar in gynoecium and fruit ontogeny and morphology, but differ dramatically in flower morphology. Especially polymery and the formation of nectary chambers are unique to these plants within the Boraginales and support their treatment as a separate family.

Watermarking technique based on three-coefficient comparison in DCT domain

In order to hide information, Yu et al. (Appl Res Comput 26(3):1082---1083, 1103, 2009) presented a method by using the numerical value relation of three pixel values in spatial domain. Their algorithm is very easy to realize and has a big hiding capacity. But its visual performance is not very good, because it is based on spatial domain and cannot control the modification value effectively in edge region or texture region of image. Our work embedded watermark by comparing the numerical value relation of three neighboring DCT coefficients with Zig-Zag order of block image to enhance the visual performance. First, each block of the host image was transformed by DCT. Then the DCT coefficient matrix was scanned by Zig-Zag scanning order to ensure the continuity of the neighboring coefficients. And then through modifying the numerical value relation of three Zig-Zag neighboring DCT coefficients, the three corresponding watermark bits were embedded in. To further improve its performance, the algorithm also employed redundant encoding, watermark scrambling encryption techniques, etc. The experiments show that the algorithm can guarantee a better quality of watermarked image, and has stronger robust to general image processing operations than the method proposed by Yu et al. (Appl Res Comput 26(3):1082---1083, 1103, 2009).

Modified Heisenberg model for the zig-zag structure in multiferroic RMn2O5

The class of RMn2O5 (R = Ho, Tb, Y, Eu) compounds offers multiferroic properties where the refined magnetic zig-zag order breaks the inversion symmetry. Varying the temperature, the system undergoes a magnetic and a subsequent ferroelectric phase transition where the ferroelectricity is magnetically induced. We propose a modified anisotropic Heisenberg model that can be used as a tractable analytical model studying the properties of those antiferromagnetic zig-zag spin chains. Based on a finite temperature Green's function method, it is shown that the polarization is induced solely by different exchange couplings of the two different Mn4+ and Mn3+ magnetic ions. We calculate the excitation energy of the spin system for finite temperatures, which for its part determines the temperature dependent magnetization and polarization. The ferroelectric phase transition is manifested as a kink in the excitation energy. The variation of the polarization by an external magnetic field depends strongly on the direction of that field. Whereas, the polarization in b-direction increases with an external magnetic field as well in b-direction it can be switched for strong fields in a-direction. The results based on that modified Heisenberg model are in qualitative agreement with experimental data.

Image Compression Based on Discrete Cosine Transform and Multistage Vector Quantization

In this paper, an image compression scheme is proposed, based on discrete cosine transform (DCT). This scheme is a hybrid method, which combines vector quantization (VQ) and differential pulse code modulation (DPCM). This scheme begins with transforming image from spatial domain to frequency domain using DCT. Then the block data is transformed into a vector according to zigzag order, and then truncated. After that, the vector is split into DC coefficient and AC coefficients. After scale quantization, DC coefficient is coded using DPCM. AC coefficients are coded using multistage vector quantization (MSVQ). Then, entropy encoding is performed on index-tables and DC part, separately. The experimental results show that, compared to conventional VQ and DCTVQ schemes, proposed scheme has a better performance.

Magnetic order inα−RuCl3: A honeycomb-lattice quantum magnet with strong spin-orbit coupling

We report magnetic and thermodynamic properties of single crystal $\alpha$-RuCl$_3$, in which the Ru$^{3+}$ ($4d^5$) ion is in its low spin state and forms a honeycomb lattice. Two features are observed in both magnetic susceptibility and specific heat data; a sharp peak at 7~K and a broad hump near 10-15K. In addition, we observe a metamagnetic transition between 5~T and 10~T. Our neutron diffraction study of single crystal samples confirms that the low temperature peak in the specific heat is associated with a magnetic order with unit cell doubling along the honeycomb (100) direction, which is consistent with zigzag order, one of the types of magnetic order predicted within the framework of the Kitaev-Heisenberg model.

Zigzag order and phase competition in expanded Kitaev–Heisenberg model on honeycomb lattice

The Kitaev–Heisenberg model on the honeycomb lattice is investigated in two cases: (I) with the Kitaev interaction between the nearest neighbors, and (II) with the Kitaev interaction between the next nearest neighbors. In the full parameter range, the ground states are searched by Monte Carlo simulation and identified by evaluating the correlation functions. The energies of different phases are calculated and compared with the simulated result to show the phase competition. It is observed from both energy calculation and the density of states that the zigzag order shows a symmetric behavior to the stripy phase in the pure Kitaev–Heisenberg model. By considering more interactions in both cases, the energy of zigzag order can be reduced lower than the energies of other states. Thus the zigzag phase may be stabilized in more parameter region and even extended to the whole parameter range.

Magnetism in spin models for depleted honeycomb-lattice iridates: Spin-glass order towards percolation

Iridates are characterized by a fascinating interplay of spin-orbit and electron-electron interactions. The honeycomb-lattice materials ${A}_{2}{\mathrm{IrO}}_{3}$ $(A=\text{Na},\text{Li})$ have been proposed to realize pseudospin-1/2 Mott insulating states with strongly anisotropic exchange interactions, described by the Heisenberg-Kitaev model, but other scenarios involving longer-range exchange interactions or more delocalized electrons have been put forward as well. Here we study the influence of nonmagnetic doping, i.e., depleted moments, on the magnetic properties of experimentally relevant variants of the Heisenberg-Kitaev and Heisenberg ${J}_{1}\text{\ensuremath{-}}{J}_{2}\text{\ensuremath{-}}{J}_{3}$ models. We generically find that the zigzag order of the clean system is replaced, upon doping, by a spin-glass state with short-ranged zigzag correlations. We determine the spin-glass temperature as a function of the doping level and show that this quantity allows one to assess the importance of longer-range exchange interactions when the doping is driven across the site-percolation threshold of the honeycomb lattice.

Generic Spin Model for the Honeycomb Iridates beyond the Kitaev Limit

Recently, realizations of Kitaev physics have been sought in the A2IrO3 family of honeycomb iridates, originating from oxygen-mediated exchange through edge-shared octahedra. However, for the jeff=1/2 Mott insulator in these materials, exchange from direct d-orbital overlap is relevant, and it was proposed that a Heisenberg term should be added to the Kitaev model. Here, we provide the generic nearest-neighbor spin Hamiltonian when both oxygen-mediated and direct overlap are present, containing a bond-dependent off-diagonal exchange in addition to Heisenberg and Kitaev terms. We analyze this complete model using a combination of classical techniques and exact diagonalization. Near the Kitaev limit, we find new magnetic phases, 120° and incommensurate spiral order, as well as extended regions of zigzag and stripy order. Possible applications to Na2IrO3 and Li2IrO3 are discussed.

Scalable Video Compression by Employing TEMPO-SPA Arrangement along with Combined ADCT, Retaining-RLE Method

Motion based prediction used for video coding is an efficient method in the field of video compression. But the complexity and computation time involved in this method is a burden to apply them in real time applications. In this paper, an arrangement of video frames in temporal-spatial (TEMPOSPA) domain, which is 3D to 2D mapping of video signals is proposed. As video signals are more redundant in temporal domain compared to spatial domain, the video frames are arranged in such a manner to exploit both temporal and spatial redundancies to achieve good compression ratio. In order to reduce the time and complexity of DCT computation, Approximated DCT (ADCT) is used along with combined Retaining-RLE method. ADCT is an approximation of DCT, whose transformation matrix contains most of them zeros which reduces the number of multiplications involved in the normal DCT computation. The quantized 8x8 blocks are then encoded by combination of Retaining and Run Length Encoding (RLE) methods. Out of 64 quantized coefficients in an 8x8 block, only certain number of coefficients is retained while zig-zag scanning order and RLE is applied to this retained sequence of coefficients to reduce the data in retained sequence. Thus providing high level of compression compared to previous compression standards. General Terms Scalable video coding, Video compression algorithms, Efficient video signal storage and transmission, Data compression, Digital Video processing.

An Efficient Hand-Based Biometric Recognition System Using Finger- Knuckle-Print Data

Automatic personal identification is playing an important role in secure and reliable applications, such as access control, surveillance systems, information systems, physical buildings and many more applications. In contrast with traditional approaches, based on what a person knows (password) or what a person has (tokens), biometric based identification is providing an improved security for their users. Biometrics is the measurement of physiological traits such as palmprints, fingerprints, iris etc., and/or behavioral traits such as gait, signature etc., of an individual person for personal recognition. Hand-based person identification provides a good user acceptance, distinctiveness, universality, relatively easy to capture and low-cost. However, Finger-Knuckle-Print (FKP), which provides different information from a variety of finger types, has been recently used to improve the performance of hand-based biometric identification because each finger has a specific feature, making it possible to collect more information to improve the accuracy of hand-based biometric systems. In this paper, we presented an efficient online personal identification based on FKP using the twodimensional Block based Discrete Cosine Transform (2D-BDCT) and MultiVariate Normal density function (MVN). In this study, a segmented FKP is firstly divided into non-overlapping and equal-sized blocks, and then, applies the 2DBDCT over each block. By using zig-zag scan order, each transform block is reordered to produce the feature vector. Subsequently, we use the MVN for modeling the feature vector of each FKP. Finally, Log-likelihood scores are used for FKP matching. Finally, performance of all finger types is determined individually and several fusion rules are applied to develop a multimodal system based on fusion at the matching score level. Experimental results show that FKPs modalities show best performance for identifying a person as they provide an excellent identification rate and with more security. Here we also discuss few patents that are relevant to the article.

Zigzag Magnetic Order in the Iridium OxideNa2IrO3

We explore the phase diagram of spin-orbit Mott insulators on a honeycomb lattice, within the Kitaev-Heisenberg model extended to its full parameter space. Zigzag-type magnetic order is found to occupy a large part of the phase diagram of the model, and its physical origin is explained as due to interorbital t(2g)-e(g) hopping. The magnetic susceptibility, spin wave spectra, and zigzag order parameter are calculated and compared to the experimental data, obtaining thereby the spin coupling constants in Na(2)IrO(3) and Li(2)IrO(3).

Semi-fragile watermarking based content image authentication scheme

This paper presents a block-wise semi-fragile watermarking scheme for image content authentication, with tamper area localization and recovery capability. Before the watermark sequence is generated, the original image is divided into two regions: The Region of Interest (ROI) and the Region of Embedding (ROE), where the ROI is selected manually by the owner of the image and the ROE is rest of the whole image after subtracting region belonging to the ROI. The binary watermark of each ROI block is generated by the DC and the 6 lowest AC components in the zig-zag order of the DCT coefficients of these blocks. These extracted bit sequence are embedded into the LSB of the DCT coefficients of the corresponding ROE blocks which are indicated by a mapping list previously generated using a secret key. In the authentication process, the watermark sequence is extracted from the ROI blocks. Then it is compared with the sequence extracted from the corresponding ROE blocksto determine if the ROI block has been altered; in this case the tampered ROI blocks are recovered replacing them by the extracted watermark sequence from ROE. Simulation results show that the reconstructed image quality and the watermark robustness to JPEG compression are better than the previously reported methods by other authors under the same conditions.

Design of welded double layer pipelines

The methods of producing two-layer pipelines of different design, including bimetallic pipes, consisting of carbon and high-alloyed stainless steels, are investigated. It is shown that at optimum design, the welded joints in the pipes should be distributed in a zigzag order so that the welded joints on the external and internal pipes are away from each other.

Iterative Sphere Detectors for Imperfect Channel State Information

This manuscript presents an iterative detector based on a generalized Schnorr-Euchner enumeration for the case of imperfect channel state information. The detector determines the most contributive N∈{1,2} terms in each of the two log-sum-exponents. The objective function of the tree search is modified to account for (a) the channel estimation error variance and (b) the input a priories. Due to (a), the decomposition of the objective into the form used in conventional tree search is not possible. Moreover, both (a) and (b) invalidate the use of the progressive zigzag order. Because of this, a generalized Schnorr-Euchner enumeration is proposed where explicit sorting is done. Unlike the conventional tree search, the node weights are not computed in an additive way where the weight of a child node is the sum of the weights of the parent and the branch connecting them. The advantage of the proposed detectors compared to iterative channel estimation and decoding is that the repetition of the channel estimation and the QR decomposition is not needed. Also since they are based on the Schnorr-Euchner enumeration, they do not require an initial radius estimation and if channel estimation errors are small enough to be ignored, the search step becomes division- and square-root-free.

Partially Zig-Zag Advanced Higher Order Shear Deformation Theories Based on the Generalized Unified Formulation

The Generalized Unified Formulation (GUF) is a multi-theory and a multi-fidelity architecture for the generation of a virtually infinite class of Advanced Higher Order Shear Deformation Theories (AHSDT) or Zig-Zag theories or Layer-Wise (LW) theories with any order of expansion for each of the primary variables. This work will present, for the first time in the literature, an extension of GUF to address problems in which every single variable can have either an Equivalent Single Layer (ESL) or a Zig-Zag-enhanced ESL description [Partially Zig-Zag Advanced Higher Order Shear Deformation Theories (PZZAHSDT)]. Applications to the case of thick sandwich structures are presented: starting from a baseline fourth-order AHSDT which also includes the transverse strain effects, all the possible types of PZZAHSDT are generated and compared with the baseline and with a fourth-order fully Zig-Zag theories.

Iterative Sphere Detectors Based on the Schnorr-Euchner Enumeration

Two kinds of iterative sphere detectors based on modifications of the Schnorr-Euchner enumeration are presented. The first is capable of finding good candidate lattice points relatively soon. Its complexity and performance are controlled by an adaptive radius backlash update strategy. The second systematically searches for the most contributive term in each of the two log-sum-exponents. Both kinds require modifications to the original Schnorr-Euchner enumeration. The objective function must account for the input a priories and explicit sorting of the branches stemming from the tree nodes must be done because the simple zigzag order in this case is not valid. The impact of the a priories on the log-likelihood ratio clipping is also addressed. The advantages of the new detectors compared to the Fincke-Pohst-based ones are: i) No initial radius is required, ii) the search step is division- and square-root-free and iii) the average computational complexity is lower.

A Self-Reconfigurable Platform for Scalable DCT Computation Using Compressed Partial Bitstreams and BlockRAM Prefetching

In this paper, we propose a self-reconfigurable platform which can reconfigure the architecture of discrete cosine transform (DCT) computations during run-time using dynamic partial reconfiguration. The scalable architecture of DCT computations can compute different numbers of DCT coefficients in a zig-zag scan order to adapt to different requirements, such as power consumption, hardware resources, and performance. We propose a configuration manager, which is implemented in the embedded processor in order to adaptively control the reconfiguration of scalable DCT architecture during run-time. In addition, we use the Lempel-Ziv-Storer-Szymanski algorithm for compression of the partial bitstreams and on-chip BlockRAM as a cache to reduce latency overhead for loading the partial bitstreams from the off-chip memory for run-time reconfiguration. A hardware module is designed for parallel reconfiguration of the partial bitstreams. The experimental results show that our approach can reduce the external memory accesses by 69% and can achieve a 400 MB/s reconfiguration rate. Detailed trade-offs of power, throughput, and quality are investigated, and used as a criterion for self-reconfiguration.

Improved Efficient Zigzag and Third Order Theories for Circular Cylindrical Shells Under Thermal Loading

An improved efficient zigzag theory (IZIGT) and an improved third order theory (ITOT) are presented for laminated circular cylindrical shells and shell panels under thermal loading. The transverse deflection is approximated nonuniformly to explicitly account for the transverse strain due to temperature. The inplane displacements are modelled in ITOT to have global cubic variation across the thickness and are modelled in IZIGT to have additional layerwise zigzag linear variation. The number of primary variables is reduced to 5 by imposing conditions on transverse shear at outer and inner surfaces for ITOT and also at layer interfaces for IZIGT. The governing equations and boundary conditions are derived using the principle of virtual work. The IZIGT, ZIGT, ITOT and TOT are assessed in comparison with exact 3D thermoelasticity solution for simply supported shells and shell panels of different lay-ups. The comparison reveals that IZIGT and ITOT are an improvement over ZIGT and TOT respectively, and in general, IZIGT is more accurate than ITOT for thermal loading.

Optimal Huffman Coding of DCT Blocks

It is a well-observed characteristic that, when a discrete cosine transform block is traversed in the zigzag order, ac coefficients generally decrease in size and the runs of zero coefficients increase in length. This paper presents a minor modification to the Huffman coding of the JPEG baseline compression algorithm to exploit this characteristic. During the run-length coding, instead of pairing a nonzero ac coefficient with the run-length of the preceding zero coefficients, our encoder pairs it with the run-length of subsequent zeros. This small change makes it possible for our codec to code a pair using a separate Huffman code table optimized for the position of the nonzero coefficient denoted by the pair. These position-dependent code tables can be encoded efficiently without incurring a sizable overhead. Experimental results show that our encoder produces a further reduction in the ac coefficient Huffman code size by about 10%-15%.