Angle Pairs Research Articles

Grover-QAOA for 3-SAT: quadratic speedup, fair-sampling, and parameter clustering

Abstract The SAT problem is a prototypical NP-complete problem of fundamental importance in computational complexity theory with many applications in science and engineering; as such, it has long served as an essential benchmark for classical and quantum algorithms. This study shows numerical evidence for a quadratic speedup of the Grover Quantum Approximate Optimization Algorithm (G-QAOA) over random sampling for finding all solutions to 3-SAT (All-SAT) and Max-SAT problems. G-QAOA is less resource-intensive and more adaptable for these problems than Grover’s algorithm, and it surpasses conventional QAOA in its ability to sample all solutions. We show these benefits by classical simulations of many-round G-QAOA on thousands of random 3-SAT instances. We also observe G-QAOA advantages on the IonQ Aria quantum computer for small instances, finding that current hardware suffices to determine and sample all solutions. Interestingly, a single-angle-pair constraint that uses the same pair of angles at each G-QAOA round greatly reduces the classical computational overhead of optimizing the G-QAOA angles while preserving its quadratic speedup. We also find parameter clustering of the angles. The single-angle-pair protocol and parameter clustering significantly reduce obstacles to classical optimization of the G-QAOA angles.

Robust flat bands in twisted trilayer graphene moiré quasicrystals

Moiré structures formed by twisting three layers of graphene with two independent twist angles present an ideal platform for studying correlated quantum phenomena, as an infinite set of angle pairs is predicted to exhibit flat bands. Moreover, the two mutually incommensurate moiré patterns among the twisted trilayer graphene (TTG) can form highly tunable moiré quasicrystals. This enables us to extend correlated physics in periodic moiré crystals to quasiperiodic systems. However, direct local characterization of the structure of the moiré quasicrystals and of the resulting flat bands are still lacking, which is crucial to fundamental understanding and control of the correlated moiré physics. Here, we demonstrate the existence of flat bands in a series of TTGs with various twist angle pairs and show that the TTGs with different magic angle pairs are strikingly dissimilar in their atomic and electronic structures. The lattice relaxation and the interference between moiré patterns are highly dependent on the twist angles. Our direct spatial mappings, supported by theoretical calculations, reveal that the localization of the flat bands exhibits distinct symmetries in different regions of the moiré quasicrystals.

Rapid repair of RC columns with post-tensioned external clamps

A recent technique for repair of damaged reinforced concrete (RC) columns is reviewed. The technique involves the application of external post-tensioned clamps. The clamps are composed of steel angles and high-strength steel rods. The pairs of angles are placed on the corners of the cross-section, and they are connected with steel rods to each other. To evaluate the effectiveness of the repair technique, four large-scale RC columns with insufficient transverse reinforcement were subjected to lateral displacement reversals and constant axial load. The tests were conducted in two phases: initial testing of columns with none to light transverse reinforcement, followed by the application of clamps on the damaged columns and further testing. The study focused on the efficacy of the clamps to a) restore the lateral-carrying capacity of damaged RC columns, and b) increase drift capacity. Variations in lateral expansion of the column core and their plausible correlations with damage and ‘repairability’ are examined. Within the conditions investigated, two key requirements are proposed for safe column repair: 1) the concrete in damaged columns with cross-sectional expansion exceeding 1% should be replaced or repaired before clamps are applied as a repair measure, and 2) clamps should be proportioned to resist 100% of the maximum plausible shear demand even though perceptible contributions to shear resistance attributable to the concrete were observed in columns repaired before excessive expansion occurred. In columns with crisscrossing inclined cracks leading to lateral cross-sectional expansion of up to 1%, clamps were observed to provide effective shear resistance comparable to what conventional transverse reinforcement can provide.

Activation of contraction twins during compression and related texture characteristics in α-titanium

This work demonstrates that axial compression along 0002and101¯0 in individual grains of α-Titanium can effectively activate up to six variants of 112¯2112¯3¯ contraction twins (CT). Compression parallel to 101¯0 primarily introduces 101¯2101¯1¯ type extension twins (ET), orienting the c-axis almost along the compression axis. Further compression activates up to six 112¯2112¯3¯ CT variants, each with a specific orientation having Euler angles of (0°−60°+n60°, 63.5°, 30°), where n is the sequence number of the CT variant. All six CT variants may not be activated during uniaxial compression due to the deviation of the parent grains' c-axis from the compression direction (CD) and deformation heterogeneities. The nucleation and interaction of CT variants lead to the formation of coincident site lattice boundaries with characteristics (θ−uvtw) angle axis pair of 63.5°101¯0−∑7b, 51.2°11¯00−∑23a, 60°112¯1−∑19b, and 77.3°18¯70−∑17b. The activation of multi CT variants and their interaction can contribute to grain fragmentation and texture weakening. From statistical analyses, the nucleation and growth of CT variants appeared to follow the Schmid law. However, deviations from the Schmid behavior occurred by the activation of low Schmid factor CT variants and could be attributed to slip and twin activities in neighbor grains.

Sectorial Equidistribution of the Roots of x2 + 1 Modulo Primes

Abstract The equation $x^2 + 1 = 0\mod p$ has solutions whenever p = 2 or $4n + 1$. A famous theorem of Fermat says that these primes are exactly the ones that can be described as a sum of two squares. The roots of the former equation are equidistributed is a beautiful theorem of Duke, Friedlander and Iwaniec. The angles associated to the representation of such prime as a sum of squares are equidistributed is a famous theorem of Hecke. We give a natural way to associate between roots and angles and prove that the joint equidistribution of the sequence of pairs of roots and angles is equidistributed as well. Our approach involves an automorphic interpretation, which reduces the problem to the study of certain Poincare series on an arithmetic quotient of $SL_2(\mathbb{R})$. Since our Poincare series have a nontrivial dependence on their Iwasawa θ-coordinate, they do not factor into functions on the upper half plane, as in the case studied by Duke et al. Spectral analysis on these higher dimensional varieties involves the nonspherical spectrum, making this paper the first complete study of a nonspherical equidistribution problem, with an arithmetic application. A couple of notable challenges we had to overcome were that of obtaining pointwise bounds for nonspherical Eisenstein series and utilizing a non-spherical analogue of the Selberg inversion formula, which we believe may have further implications beyond this work.

FINITE DIFFERENCE METHOD BASED-NUMERICAL SIMULATIONS AND CAVITY TILTING ANALYSIS ON MAGNETOCONVECTION IN AN INCLINED PARALLELOGRAMMIC POROUS ENCLOSURE

This article numerically investigates the buoyancy-assisted convective flow and associated thermal characteristics in an inclined parallelogram-shaped porous geometry containing heat source and sink of different lengths placed at various locations. The left tilted wall has a hot source, and right tilted wall contains a cold sink, while the remaining regions of the inclined sidewalls are thermally insulated. The geometry is filled with fluid-saturated porous material and, in addition, an externally applied magnetic field (MF) has been supplied in lateral direction. The model equations governing the physical processes involve Darcy's law for the momentum equations and energy equations to account thermal variations. Using a stable and implicit finite difference methodology, these set of coupled and nonlinear partial differential equations are solved by reducing them to a system of linear algebraic equations. A wide range of numerical experiments are performed to determine the influence of various physical and geometrical parameters on the flow and thermal structure as well as thermal dissipation rate inside the geometry. Further, a suitable pair of inclination angles is found, at which maximum heat transport could be produced as compared to other combination of angles. Furthermore, an optimum size and location for the source-sink combination has been predicted which induces higher heat transport rates.

Effect of initial twins on mechanical properties of additive manufacturing CoCrNi alloy and molecular dynamic simulation

The influence of twins on laser additive CoCrNi MEA was analyzed by experiments and molecular dynamic simulation. Results showed that the traditional laser additive CoCrNi MEA was prone to slip in the (111) direction. EBSD analysis showed an obvious 60°(111} axial angle pair relationship, which is related to the slower cooling rate. The results of molecular dynamic simulation showed that the yield strength of CoCrNi MEA increases first and then decreases, and the material has a critical twin density. When the twin density is less than the critical twin density, the strength of the material increases due to the thinning effect of the twin boundary on the grain. When the twin density is greater than the boundary twin density, the nucleation and proliferation of the twin boundary and the junction of the two become the dominant factors of the material deformation. When the twin density is far from the critical value, the twin spacing becomes smaller, the dislocation sources increase, the dislocation nucleation and proliferation increase, and the strength of the material decreases.

A GPU-Based, Real-Time Dealiasing Framework for High-Frame-Rate Vector Doppler Imaging.

Vector Doppler is well regarded as a potential way of deriving flow vectors to intuitively visualize complex flow profiles, especially when it is implemented at high frame rates. However, this technique's performance is known to suffer from aliasing artifacts. There is a dire need to devise real-time dealiasing solutions for vector Doppler. In this paper, we present a new methodological framework for achieving aliasing-resistant flow vector estimation at real-time throughput from precalculated Doppler frequencies. Our framework comprises a series of compute kernels that have synergized: 1) an extended least squares vector Doppler (ELS-VD) algorithm, 2) single-instruction, multiple-thread (SIMT) processing principles, and 3) implementation on a graphical processing unit (GPU). Results show that this new framework, when executed on an RTX-2080 GPU, can effectively generate aliasing-free flow vector maps using high-frame-rate imaging datasets acquired from multiple transmit-receive angle pairs in a carotid phantom imaging scenario. Over the entire cardiac cycle, the frame processing time for aliasing-resistant vector estimation was measured to be less than 16 ms, which corresponds to a minimum processing throughput of 62.5 fps. In a human femoral bifurcation imaging trial with fast flow (150 cm/s), our framework was found to be effective in resolving two-cycle aliasing artifacts at a minimum throughput of 53 fps. The framework's processing throughput was generally in the real-time range for practical combinations of ELS-VD algorithmic parameters. Overall, this work represents the first demonstration of real-time, GPU-based aliasing-resistant vector flow imaging using vector Doppler estimation principles.

Curved-creased origami mechanical metamaterials with programmable stabilities and stiffnesses

Curved Crease Origami (CCO) structures exhibit intrinsic elastic behavior, resulting from a combination of crease folding and facet bending. In this work, we introduce a generic theoretical framework for constructing and predicting the mechanical properties of OMMs composed of curved crease unit cells, and an inverse design method that could achieve programmable stiffness and stability of CCO metamaterials, the CCO stacked unit with 2n-stability is first designed. Theoretical models, which could predict the in- and out-of-plane Poisson's ratios, uniaxial forces and stiffnesses of a single CCO tessellation, are constructed and validated by comparing with the finite element numerical method and experiment. Based on the analytical framework, the mechanical properties of the proposed CCO metamaterial with different crucial parameters are investigated, the results show that the combination of the initial folding angle pair could prominently affects the presence of bistability of the CCO unit. Our framework reveals that stacking two distinct layers of CCO units enables unique properties, such as bistability and zero stiffness, expanding the design space for CCO metamaterials. To determine the most suitable parameters for the unit cell to achieve programmable stabilities and targeted stiffness, the genetic algorithm is employed to optimize the basic model parameters and to carry out the inverse design, several case studies are demonstrated to show that the bistability model with specific stiffness, assigned stable locations, zero-stiffness in stable states and multistability model could be achieved. In summary, this work presents a comprehensive framework for designing and analyzing the curved crease origami mechanical metamaterials and proposes the inverse design method that could pave the way for a range of novel applications.

Balanced of Countries Development Determinants: Barycentric Model

The authors investigate the issue of modelling the balance of countries development determinants based on determining the center of mass. They have identified the most relevant factors characterizing countries' social, economic, political spheres, digital capability and cybersecurity. The research has been carried based on empirical values of the selected 17 indicators for 127 world countries in 2018. As a result, the four-pole barycentric models were built as quadrangles, the vertices of which are composite targets formed by the determinants of the four spheres. The models' calculations were carried out taking into account three components: the values of the composite targets (as a geometric mean), the level of pairs balance (as the sum of opposite pairs of quadrilateral angles), and all four targets (as the distance between the actual and standard value of the center of mass). According to the analysis result of the first component, developed countries have the most effective targets (top five - Switzerland, Denmark, Norway, Finland, the Netherlands). Research of the results of the second component has revealed an imbalance in target pairs for most countries. Determinants of socio-political development are the most effective for developed countries. The economic sphere is most unbalanced for the least developed countries. Various determinants can cause an imbalance for developing and new industrial countries. The analysis of the center of mass distances revealed that not only developed countries could be balanced, but also developing, new industrial and the least developed, that indicates a balanced development of their determinants, which is pretty slow. New Zealand, Mauritius, South Africa and Mali were the most balanced in each group of countries economic growth.

Designing a Transition Photonic Band with a Moiré Synthetic Sphere

In recent years, twisted bilayer graphene has become a hot topic and inspired the upsurge of research on the photonic moir\'e lattice. Here, we design a photonic moir\'e superlattice with two synthetic twist angles and construct a synthetic moir\'e sphere based on these two angles. Thus, we have more degrees of freedom to design the band structure flexibly. A type of transition photonic band (TPB) is obtained in such a moir\'e superlattice. We investigate the influence of two twist angles on TPBs and find a series of magic angle pairs with optimal band compression of the TPB. Interesting optical properties of TPBs are experimentally demonstrated, including pulse delay, nonlinear optical enhancement, and pulse-width compression. Our work introduces an alternative path to explore multitwist-angle moir\'e superlattices and reveals that the designed photonic moir\'e superlattice based on moir\'e spheres has broad application prospects, including optical signal processing, nonlinear optic processes, and other light-matter interactions.

Influence of α+β solution treatments on Ti65 ultrathin sheets: Silicide precipitation, mechanical behaviour and novel [formula omitted] twinning system

To cope with the urgent demands of the aerospace industry for lightweight and excellent high-temperature performance titanium alloy components, the microstructure evolution, silicide precipitation and mechanical behaviour of a novel high-temperature Ti65 titanium alloy ultrathin sheet with different heat treatments were systematically investigated. Submicron (Ti,Zr)6Si3 silicides are observed after solution treatments followed by air cooling, leading to a decline and significant fluctuations in tensile properties. For furnace cooling samples, (Ti,Zr)5Si3 silicide crossing grain boundaries and (Ti,Zr)6Si3 silicide near grain boundaries are observed after solution treatment at 950 °C. When the solution temperature increases to 1010 °C, the third silicide (Ti,Zr)3Si appears near dislocations. The combined effect of the strong size effect of the alloy ultrathin sheet and silicide precipitation results in great performance fluctuation, sharp drop of ductility and even brittle fracture. In addition, silicide precipitation differs little with various holding time during low-temperature solution treatment. Moreover, novel {101¯1} twins appear after the rolling process at 990 °C and are only inside coarse basal texture α grains, with an axis—angle pair of 65° 〈844¯3〉.

Models and Algorithms for the Refinement of Therapeutic Approaches for Retinal Diseases.

We are developing a Virtual Eye for in silico therapies to accelerate research and drug development. In this paper, we present a model for drug distribution in the vitreous body that enables personalized therapy in ophthalmology. The standard treatment for age-related macular degeneration is anti-vascular endothelial growth factor (VEGF) drugs administered by repeated injections. The treatment is risky, unpopular with patients, and some of them are unresponsive with no alternative treatment. Much attention is paid to the efficacy of these drugs, and many efforts are being made to improve them. We are designing a mathematical model and performing long-term three-dimensional Finite Element simulations for drug distribution in the human eye to gain new insights in the underlying processes using computational experiments. The underlying model consists of a time-dependent convection-diffusion equation for the drug coupled with a steady-state Darcy equation describing the flow of aqueous humor through the vitreous medium. The influence of collagen fibers in the vitreous on drug distribution is included by anisotropic diffusion and the gravity via an additional transport term. The resulting coupled model was solved in a decoupled way: first the Darcy equation with mixed finite elements, then the convection-diffusion equation with trilinear Lagrange elements. Krylov subspace methods are used to solve the resulting algebraic system. To cope with the large time steps resulting from the simulations over 30 days (operation time of 1 anti-VEGF injection), we apply the strong A-stable fractional step theta scheme. Using this strategy, we compute a good approximation to the solution that converges quadratically in both time and space. The developed simulations were used for the therapy optimization, for which specific output functionals are evaluated. We show that the effect of gravity on drug distribution is negligible, that the optimal pair of injection angles is (50∘,50∘), that larger angles can result in 38% less drug at the macula, and that in the best case only 40% of the drug reaches the macula while the rest escapes, e.g., through the retina, that by using heavier drug molecules, more of the drug concentration reaches the macula in an average of 30 days. As a refined therapy, we have found that for longer-acting drugs, the injection should be made in the center of the vitreous, and for more intensive initial treatment, the drug should be injected even closer to the macula. In this way, we can perform accurate and efficient treatment testing, calculate the optimal injection position, perform drug comparison, and quantify the effectiveness of the therapy using the developed functionals. We describe the first steps towards virtual exploration and improvement of therapy for retinal diseases such as age-related macular degeneration.

Observation of Buried Magnetic Domains in Grain-Oriented Electrical Steel

Bulk-sensitive microscopic measurements of buried magnetic domains are reported. Utilizing a new magneto-optical effect in the hard X-ray regime, referred to as X-ray magnetic circularly polarized emission (XMCPE), the internal transverse domains in a grain-oriented (GO) electrical steel sheet are unambiguously observed. This allows the lateral shapes of the transverse domains to be successfully visualized. In addition, we discuss the magnetic domain structure of the supplementary domains below the surface from measurements performed at several pairs of incident and exit angles.

Dosimetric comparison of robust angles in carbon-ion radiation therapy for prostate cancer.

The objective of this study is to compare the plan robustness at various beam angles. Hence, the influence of the beam angles on robustness and linear energy transfer (LET) was evaluated in gantry-based carbon-ion radiation therapy (CIRT) for prostate cancer. 10 patients with prostate cancer were considered, and a total dose of 51.6 Gy (Relative biological effectiveness (RBE) was prescribed for the target volume in 12 fractions. Five beam field plans comprising two opposed fields with different angle pairs were characterized. Further, dose parameters were extracted, and the RBE-weighted dose and LET values for all angle pairs were compared. All plans considering the setup uncertainty satisfied the dose regimen. When a parallel beam pair was used for perturbed scenarios to take into account set-up uncertainty in the anterior direction, the LET clinical treatment volume (CTV) D 95% standard deviation was 1.5 times higher, and the standard deviation of RBE-weighted CTV D 95% was 7.9 times higher compared to an oblique pair. The oblique beam fields were superior in terms of dose sparing for the rectum compared to the dose distribution using two conventional lateral opposed fields for prostate cancer.

Revisiting the Ramachandran plot based on statistical analysis of static and dynamic characteristics of protein structures

Ramachandran plots, which describe protein structures by plotting the dihedral angle pairs of the backbone on a two-dimensional plane, have played an important role in structural biology over the past few decades. However, despite continued discovery of new protein structures to date, the Ramachandran plot is still constructed by only a small number of data points, and further it cannot reflect the steric information of proteins. Here, we investigated the secondary structure of proteins in terms of static and dynamic characteristics. As for static feature, the Ramachandran plot was revisited for the dataset consisting of 9,148 non-redundant high-resolution protein structures released in the protein data bank until April 1, 2022. By calculating amino acid propensities, it was found that the proportion of secondary structures with respect to residue depth is directly related to their hydrophobicity. As for dynamic feature, normal mode analysis (NMA) based on an elastic network model (ENM) was carried out for the dataset using our KOSMOS web server (http://bioengineering.skku.ac.kr/kosmos/). All ENM-based NMA results were stored in the KOSMOS database, allowing researchers to use them in various ways. In this process, it was commonly found that high B-factors appeared at the edge of the alpha helix region, which was elucidated by introducing residue depth. In addition, by investigating the change in dihedral angle, it was possible to quantitatively survey the contribution of structural change of protein on the Ramachandran plot. In conclusion, our statistical analysis of protein characteristics will provide insight into a range of protein structural studies.

Compressed Channel Estimation for Near-Field XL-MIMO Using Triple Parametric Decomposition

With the presence of the conventional angular-domain representation, the energy leakage effect is evident for the near-field extremely large-scale multiple-input-multiple-output (XL-MIMO) channel, which further leads to ambiguous channel power detection, significantly eroding channel estimation performance. To tackle this challenge, this paper proposes a novel Triple Parametric Decomposition (TPD) framework to facilitate compressed channel estimation in the XL-MIMO system. Specifically, we examine the case of a uniform planar array (UPA) with the geometry parameters involving a pair of azimuth-elevation angles and distances in an attempt to achieve independent decomposition by constructing their own covariance matrices. Then, by utilizing the on- and off-grid techniques, we obtain the sparse recovery of angles and distances information in the absence of energy leakage effect at reduced gridding complexity. Simulation results demonstrate that our proposed TPD achieves significant performance improvement over the state-of-the-art methods.

When Triangles Are Similar

Summary For any given triangle, we define its index of similarity. We then prove that two triangles are similar if and only if they share both an index of similarity and a pair of congruent angles.

Covert Communication Gains From Adversary’s Uncertainty of Phase Angles

This work investigates the phase gain of intelligent reflecting surface (IRS) covert communication over complex-valued additive white Gaussian noise (AWGN) channels. The transmitter Alice intends to transmit covert messages to the legitimate receiver Bob via reflecting the broadcast signals from a radio frequency (RF) source, while rendering the adversary Willie’s detector arbitrarily close to ineffective. Our analyses show that, compared to the covert capacity for classical AWGN channels, we can achieve a covertness gain of value 2 by leveraging Willie’s uncertainty of phase angles. This covertness gain is achieved when the number of possible phase angle pairs <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> = 2. More interestingly, our results show that the covertness gain will not further increase with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> as long as <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> ≥ 2, even if it approaches infinity.

The barycentric model of determining the sustainable growth determinants

The authors investigate the issue of modelling the balance of sustainable growth determinants based on determining the center of mass. They have identified the most relevant factors that characterize countries' social, economic, and political spheres, digital capability, and cybersecurity to determine sustainable development and growth. The research has been carried out based on empirical values of the selected 17 indicators for 127 world countries in 2018. As a result, the four–pole barycentric models were built as quadrangles, the vertices of which are composite targets formed by the determinants of the four spheres. The models' calculations were carried out taking into account three components: the values of the composite targets (as a geometric mean), the level of pairs balance (as the sum of opposite pairs of quadrilateral angles), and all four targets (as the distance between the actual and standard value of the center of mass). According to the analysis result of the first component, developed countries have the most effective targets (top five – Switzerland, Denmark, Norway, Finland, and the Netherlands). Research of the results of the second component has revealed an imbalance in target pairs for most countries. Determinants of socio–political development are the most effective for developed countries. The economic sphere is most unbalanced for the least developed countries. Various determinants can cause an imbalance for developing and new industrial countries. The analysis of the center of mass distances revealed that not only developed countries could be balanced, but also developing, new industrial and the least developed, which indicates a balanced development of their determinants, which is pretty slow. New Zealand, Mauritius, South Africa and Mali were the most balanced in each country's sustainable growth group.