Rule acquisition of three-way semi-concept lattices in formal decision context

Three-way concept analysis is an important tool for information processing,and rule acquisition is one of the research hotspots of three-way concept analysis.However,compared with three-way concept lattices,three-way semi-concept lattices have three-way operators with weaker constraints,which can generate more concepts.In this article,the problem of rule acquisition for three-way semi-concept lattices is discussed in general.The authors construct the finer relation of three-way semi-concept lattices,and propose a method of rule acquisition for three-way semi-concept lattices.The authors also discuss the set of decision rules and the relationships of decision rules among object-induced three-way semi-concept lattices,object-induced three-way concept lattices,classical concept lattices and semi-concept lattices.Finally,examples are provided to illustrate the validity of our conclusions.

Band structures of strained kagome lattices

Materials with kagome lattices have attracted significant research attention due to their nontrivial features in energy bands.We theoretically investigate the evolution of electronic band structures of kagome lattices in response to uniaxial strain using both a tight-binding model and an antidot model based on a periodic muffin-tin potential.It is found that the Dirac points move with applied strain.Furthermore,the flat band of unstrained kagome lattices is found to develop into a highly anisotropic shape under a stretching strain along y direction,forming a partially flat band with a region dispersionless along ky direction while dispersive along kx direction.Our results shed light on the possibility of engineering the electronic band structures of kagome materials by mechanical strain.

On Discrete Hopf Fibrations, Grand Unification Groups, the Barnes-Wall, Leech Lattices, and Quasicrystals

A discrete Hopf fibration of S15 over S8 with S7 (unit octonions) as fibers leads to a 16D Polytope P16 with 4320 vertices obtained from the convex hull of the 16D Barnes-Wall lattice Λ16. It is argued (conjectured) how a subsequent 2-1 mapping (projection) of P16 onto a 8D-hyperplane might furnish the 2160 vertices of the uniform 241 polytope in 8-dimensions, and such that one can capture the chain sequence of polytopes 241,231,221,211in D=8,7,6,5dimensions, leading, respectively, to the sequence of Coxeter groups E8,E7,E6,SO(10)which are putative GUT group candidates. An embedding of the E8⊕E8and E8⊕E8⊕E8lattice into the Barnes-Wall Λ16 and Leech Λ24 lattices, respectively, is explicitly shown. From the 16D lattice E8⊕E8one can generate two separate families of Elser-Sloane 4D quasicrystals (QC’s) with H4 (icosahedral) symmetry via the “cut-and-project” method from 8D to 4D in each separate E8 lattice. Therefore, one obtains in this fashion the Cartesian product of two Elser-Sloane QC’s Q×Qspanning an 8D space. Similarly, from the 24D lattice E8⊕E8⊕E8one can generate the Cartesian product of three Elser-Sloane 4D quasicrystals (QC’s) Q×Q×Qwith H4 symmetry and spanning a 12D space.

Design and optimization of diffraction-limited storage ring lattices based on many-objective evolutionary algorithms

Multi-objective evolutionary algorithms(MOEAs) are typically used to optimize two or three objectives in the accelerator field and perform well. However, the performance of these algorithms may severely deteriorate when the optimization objectives for an accelerator are equal to or greater than four. Recently, many-objective evolutionary algorithms(MaOEAs)that can solve problems with four or more optimization objectives have received extensive attention. In this study, two diffraction-limited storage ring(DLSR) lattices of the Extremely Brilliant Source(ESRF-EBS) type with different energies were designed and optimized using three MaOEAs and a widely used MOEA. The initial population was found to have a significant impact on the performance of the algorithms and was carefully studied. The performances of the four algorithms were compared, and the results demonstrated that the grid-based evolutionary algorithm(GrEA) had the best performance.Ma OEAs were applied in many-objective optimization of DLSR lattices for the first time, and lattices with natural emittances of 116 and 23 pm·rad were obtained at energies of 2 and 6 GeV, respectively, both with reasonable dynamic aperture and local momentum aperture(LMA). This work provides a valuable reference for future many-objective optimization of DLSRs.

Modulational instability of a resonantly polariton condensate in discrete lattices

We study modulational instability of a resonantly polariton condensate in a discrete lattice.Employing a discrete gain-saturation model,we derive the dispersion relation for the modulational instability by means of the linear-stability analysis.Effects of the pumping strength,the nonlinearity,the strength of the detuning,and the coupling strength on the modulation instability are investigated.It is found that the interplay between these parameters will dramatically change the modulational instability condition.We believe that the predicted results in this work can be useful for future possible experiment of exciton-polariton condensate in lattices.

An Unbounded Fully Homomorphic Encryption Scheme Based on Ideal Lattices and Chinese Remainder Theorem

We propose an unbounded fully homomorphic encryption scheme, i.e. a scheme that allows one to compute on encrypted data for any desired functions without needing to decrypt the data or knowing the decryption keys. This is a rational solution to an old problem proposed by Rivest, Adleman, and Dertouzos [1] in 1978, and to some new problems that appeared in Peikert [2] as open questions 10 and open questions 11 a few years ago. Our scheme is completely different from the breakthrough work [3] of Gentry in 2009. Gentry’s bootstrapping technique constructs a fully homomorphic encryption (FHE) scheme from a somewhat homomorphic one that is powerful enough to evaluate its own decryption function. To date, it remains the only known way of obtaining unbounded FHE. Our construction of an unbounded FHE scheme is straightforward and can handle unbounded homomorphic computation on any refreshed ciphertexts without bootstrapping transformation technique.

Design and comparison of hybrid multi-bend achromat lattices for HALF storage ring

The Hefei Advanced Light Facility(HALF)proposed by the National Synchrotron Radiation Laboratory is a green-field vacuum ultraviolet and soft X-ray diffraction-limited storage ring light source with a beam energy of 2.2 GeV and emittance goal of less than 100 pm rad.Inspired by the ESRF-EBS hybrid multi-bend achromat(HMBA),SLS-2,and Diamond-II lattices,we have proposed and designed a modified H6BA lattice as the baseline lattice of the HALF storage ring with 20 identical cells and a natural emittance of approximately 86 pm rad.In this paper,three other types of HMBA lattices including two H7BA lattices and a H6BA lattice are designed for HALF with the same number of cells.The main storage ring proper-ties of these four HMBA lattices are compared.Because the intra-beam scattering(IBS)effect is significant in the HALF storage ring,we calculate and compare the equilibrium emittances of the four lattices with IBS included.These comparisons show that the present modified H6BA lattice,which has a relatively low equilibrium emittance and more straight sections,is preferred for the HALF storage ring after a comprehensive consideration.

Evaluation of Codebook Design Using SCMA Scheme Based on A_(n) and D_(n) Lattices

The sparse code multiple access(SCMA)scheme is a Non-Orthogonal Multiple Access(NOMA)type of scheme that is used to handle the uplink com-ponent of mobile communication in the current generation.A need of the 5G mobile network is the ability to handle more users.To accommodate this,the SCMA allows each user to deploy a variety of sub-carrier broadcasts,and several consumers may contribute to the same frequency using superposition coding.The SCMA approach,together with codebook design for each user,is used to improve channel efficiency through better management of the available spectrum.How-ever,developing a codebook with a greater number of value sets is still another challenge.With enhanced techniques of encoding and decoding for 5G networks,mapping the multidimensional constellations in the SCMA system plays a signif-icant role in improving the system performance and enhancing the overall system performance.The creation of a codebook utilizing the SCMA approach in con-junction with the lattice theory is suggested in this study.The prototype is shaped using a popular lattice,such as A n and D n,as the basis.Afterward,from the primary lattice constellation,the multidimensional complex mother constellation with the most noticeable variance in power is discovered.The lattice-based cod-ing is generated by combining the codebooks with the mother constellation,and the codes in the matrices are mapped by rotating the constellations in this context.The suggested technique,in conjunction with the investigation of novel SCMA codebook sets,provides improved performance in terms of Bit Error Rate(BER)and complexity with regard to Signal to Noise Ratio(SNR).Finally,the bit error rate is reduced for various SNRs during transmission in the channel.

Rectangular Body-centered Cuboid Packing Lattices and Their Possible Applications

We first introduce several sphere packing ways such as simple cubic packing(SC),face-centered cubic packing(FCC),body-centered cubic packing(BCC),and rectangular body-centered cuboid packing(recBCC),where the rectangular body-centered cuboid packing means the packing method based on a rectangular cuboid whose base is square and whose height is times the length of one side of its square base such that the congruent spheres are centered at the 8 vertices and the centroid of the cuboid.The corresponding lattices are denoted as SCL,FCCL,BCCL,and recBCCL,respectively.Then we consider properties of those lattices,and show that FCCL and recBCCL are the same.Finally we point out some possible applications of the recBCC lattices.

GENERALIZATIONS AND CARTESIAN CLOSED SUBCATEGORIES OF SEMICONTINUOUS LATTICES

In this article, the authors mainly study how to obtain new semicontinuous lattices from the given semicontinuous lattices and discuss the conditions under which the image of a semicontinuous projection operator is also semicontinuous. Moreover, the authors investigate the relation between semicontinuous lattices and completely distributive lattices. Finally, it is proved that the strongly semicontinuous lattice category is a Cartesian closed category.

Stereolithographic 3D Printing-Based Hierarchically Cellular Lattices for High-Performance Quasi-Solid Supercapacitor

3D printing-based supercapacitors have been extensively explored,yet the rigid rheological requirement for corresponding ink preparation significantly limits the manufacturing of true 3D architecture in achieving superior energy storage.We proposed the stereolithographic technique to fabricate the metallic composite lattices with octet-truss arrangement by using electroless plating and engineering the 3D hierarchically porous graphene onto the scaffolds to build the hierarchically cellular lattices in quasi-solid supercapacitor application.The supercapacitor device that is composed of composite lattices span several pore size orders from nm to mm holds promising behavior on the areal capacitance(57.75 mF cm-2),rate capability(70% retention,2-40 mA cm-2),and long lifespan(96% after 5000 cycles),as well as superior energy density of 0.008 mWh cm-2,which are comparable to the state-of-the-art carbon-based supercapacitor.By synergistically combining this facile stereolithographic 3D printing technology with the hierarchically porous graphene architecture,we provide a novel route of manufacturing energy storage device as well as new insight into building other high-performance functional electronics.

Cascades with coupled map lattices in preferential attachment community networks

In this paper, cascading failure is studied by coupled map lattice （CML） methods in preferential attachment community networks. It is found that external perturbation R is increasing with modularity Q growing by simulation. In particular, the large modularity Q can hold off the cascading failure dynamic process in community networks. Furthermore, different attack strategies also greatly affect the cascading failure dynamic process. It is particularly significant to control cascading failure process in real community networks.

New Identity Based Proxy Re-Encryption Scheme from Lattices

Identity-Based Proxy Re-Encryption (IB-PRE) allows a semi-trusted proxy to convert the ciphertext encrypted under Alice’s identity into Bob’s ciphertext of the same message without leaking plaintext. Lattice-based cryptography enjoys potential resistance to quantum analysis and low computational complexity. A multi-hop and unidirectional IB-PRE from lattices is presented. We split the functions of decryption and ciphertext transformation separately, and design the double private keys mechanism, where two keys are generated for each user, one key is used to decrypt the ciphertext by Pre-Image Sampling technique, and the other is used to generate the re-encryption key by Bonsai Trees technique. The generation of the re-encryption key is non-interactive and collusion resistant. Moreover, its IND-sID-CPA security over the decisional Learning With Errors (LWE) assumption under the standard model is proved. Compared with some previous IBPRE schemes from Bilinear Pairings, the format of transformed ciphertext in our scheme remains unchanged, furthermore, it can also resist quantum analysis. Compared with some existing IB-PRE schemes from lattices with similar properties, the space of the message in our scheme is a vector of length l and the encryption process remains a lower encryption blowup factor. At last, a proof-of-concept implementation is provided.

Partial and complete periodic synchronization in coupled discontinuous map lattices

The partial and complete periodic synchronization in coupled discontinuous map lattices consisting of both discon- tinuous and non-invertible maps are discussed. We classify three typical types of periodic synchronization states, which give rise to different spatiotemporal patterns including static partial periodic synchronization, dynamically periodic syn- chronization, and complete periodic synchronization patterns. A special prelude dynamics of partial and complete periodic synchronization motion, which is shown by five separated concave curves in the time series plots of the order parameters, is observed. The detailed analysis shows that the special prelude dynamics is induced by the competition between two synchronized clusters, and the analytical expression for the corresponding order parameter is obtained.

Excitation of defect modes from the extended photonic band-gap structures of 1D photonic lattices

This paper stuides numerically the model equation in a one dimensional defective photonic lattice by modifying the potential function to a periodic function. It is found that defect modes （DMs） can be regarded as Bloch modes which are excited from the extended photonie band-gap structure at Bloch wave-numbers with kx = 0. The DMs for both positive and negative defects are considered in this method.

Chaotic Ratchet Effect for Bose-Einstein Condensed Atoms in 1D Optical Lattices

The chaotic ratchet effect for Bos-Einstein condensed atoms in an optical lattice is investigated. By using the direct perturbation method we obtain the chaotic solution of the condensed system. Theoretical analysis reveals that the transport of the condensed atoms in the ratchet potential is a chaotic one, and corresponding numerical results agree well with the theoretical results.

Ratchet transport of overdamped particles in superimposed driven lattices

Ratchet transport of overdamped particles is investigated in superimposed driven lattices using Langevin dynamics simulations. It is found that noise can strongly affect the transport of the particles. When lattices driving dominates the transport, the noise acts as a disturbance of the directed transport and slows down the average velocity of the particles.When the driving phase has less impact on particle transport, Gaussian white noise can play a positive role. By simply modulating these two parameters, we can control efficiency and the direction of the directed currents.

Impurity-induced localization of Bose-Einstein condensates in one-dimensional optical lattices

The impurity-induced localization of two-component Bose-Einstein condensates loaded into deep one-dimensional optical lattices is studied both analytically and numerically. It is shown that, the analytical criteria for self-trapping and moving soliton/breather of the primary-component condensate are modified significantly by an admixture of an impurity component （the second component）. The realization of the self-trapped state and the moving soliton/breather states of the primary-component becomes more easy with the minor admixture of the impurity-component, even if the two components are partly overlapped.

2D hierarchical lattices' imperfection sensitivity to missing bars defect

Commercially available lattices contain various kinds of morphological imperfections which result in great degradation in lattices＇ mechanical properties, therefore, to obtain imperfection insensitive lattice structure is obviously a practical research subject. Hierarchical structure materials were found to be a class of promising anti-defect materials, This paper builds hierarchical lattice by adding soft adhesion to lattice＇s cell edges and numerical results show that its imperfection sensitivity to missing bars is minor compared with the classic lattice. Soft adhesion with appropriate properties reinforce cell edge＇s bending stiffness and thus reduce the bending deformation in lattice caused by missing bars defect, which is confirmed by statistical analysis of normalized node displacements of imperfect lattices under hydrostatic compression and shear loads.

Controllable optical multi-well trap and its optical lattices using compounded cosine patterns

This paper proposes a flexible scheme to form various optical multi-well traps for cold atoms or molecules by using a simple optical system composed of an compounded amplitude cosine-only grating and a single lens illuminated by a plane light wave or a Gaussian beam. Dynamic manipulation and evolution of multi-well trap can be easily implemented by controlling the modulation frequency of the cosine patterns. It also discusses how to expand this multi-well trap to two-dimensional lattices with single- or multi-well trap by using an orthogonally or non-orthogonally modulated grating, as well as using incoherent multi-beam illumination, and these results show that all the symmetric structures of two-dimensional Bravais lattices can be obtained facilely by using proposed scheme.