Projection Scheme Research Articles

Kernels for noncommutative projective schemes

We give a noncommutative geometric description of the internal Hom dg-category in the homotopy category of dg-categories between two noncommutative projective schemes in the style of Artin–Zhang. As an immediate application, we give a noncommutative projective derived Morita statement along the lines of Rickard and Orlov.

Frobenius–Perron theory of representations of quivers

The Frobenius–Perron theory of an endofunctor of a category was introduced in recent years (Chen et al. in Algebra Number Theory 13(9):2005–2055, 2019; Chen et al. in Frobenius–Perron theory for projective schemes. Preprint. arXiv:1907.02221, 2019). We apply this theory to monoidal (or tensor) triangulated structures of quiver representations.

A new synchronisation method of fractional-order chaotic systems with distinct orders and dimensions and its application in secure communication

In this paper, an adaptive generalised function projective synchronisation scheme of fractional-order chaotic systems with different dimensions and orders and fully unknown parameters is presented. On the basis of the Lyapunov method of fractional-order systems, a stability theorem of the fractional-order system with non-identical orders is proven. Using the fractional-order controller and adaptive control theory, sufficient conditions for synchronisation and unknown parameters update rules are obtained. Theoretical analysis and numerical simulations are provided to verify the validity of the proposed scheme. Moreover, synchronisation results are applied to secure communication via modified chaotic masking (MCM) method. The unpredictability of the scaling function matrix and the use of fractional-order systems with different orders can increase the security of the cryptosystem. The security analysis shows that the introduced algorithm has large key space, high sensitivity to encryption keys, higher security and the acceptable encryption speed.

Analisis Dampak Penanaman Modal Asing Dan Tenaga Kerja Asing Tiongkok terhadap Perekonomian Indonesia

This study will discuss the influence of the influx of foreign investment and Chinese foreign workers on the Indonesian economy, where cooperation between the two countries uses a turnkey project scheme. This study uses secondary data with time-series data types and is sourced from the Central Statistics Agency, the Investment Coordinating Board, and the Ministry of Manpower for the 2010-2019 period. The method used in this research is quantitative and statistical descriptive using multiple linear regression or OLS (Ordinary Least Square). The study results show a positive influence of Chinese foreign investment on the Indonesian economy and Chinese foreign workers who positively impact the Indonesian economy. Although both are below 1 percent, the percentage of Chinese foreign workers' influence on the Indonesian economy is greater than that of Chinese foreign investment.

Analysis of one class of optimal control problems for distributed-parameter systems

In the paper, the method of straight lines approximately solves one class of optimal control problems for systems, the behavior of which is described by a nonlinear equation of parabolic type and a set of ordinary differential equations. Control is carried out using distributed and lumped parameters. Distributed control is included in the partial differential equation, and lumped controls are contained both in the boundary conditions and in the right-hand side of the ordinary differential equation. The convergence of the solutions of the approximating boundary value problem to the solution of the original one is proved when the step of the grid of straight lines tends to zero, and on the basis of this fact, the convergence of the approximate solution of the approximating optimal problem with respect to the functional is established. A constructive scheme for constructing an optimal control by a minimizing sequence of controls is proposed. The control of the process in the approximate solution of a class of optimization problems is carried out on the basis of the Pontryagin maximum principle using the method of straight lines. For the numerical solution of the problem, a gradient projection scheme with a special choice of step is used, this gives a converging sequence in the control space. The numerical solution of one variational problem of the mentioned type related to a one-dimensional heat conduction equation with boundary conditions of the second kind is presented. An inequality-type constraint is imposed on the control function entering the right-hand side of the ordinary differential equation. The numerical results obtained on the basis of the compiled computer program are presented in the form of tables and figures. The described numerical method gives a sufficiently accurate solution in a short time and does not show a tendency to «dispersion». With an increase in the number of iterations, the value of the functional monotonically tends to zero

Alternative constraints for improved multiplane hologram generation.

In this work, we introduce a modified hologram plane constraint to improve the accuracy of the global Gerchberg-Saxton (GGS) algorithm used for multiplane phase-only hologram generation. This constraint consists of a modified phase factor that depends on the amplitude of the field in the hologram plane. We demonstrate that this constraint produces an increase in the mean correlation coefficient between the reconstructed planes from a multiplane hologram and the corresponding amplitude targets for each plane. Furthermore, this constraint can be applied together with a mixed constraint in the reconstruction planes, leading to a more uniform and controllable reproduction of a target intensity distribution. To confirm the validity of our proposal, we show numerical and experimental results for multiplane holograms with six discrete planes, using both high and low contrast targets. For the experimental results, we implement a holographic projection scheme based on a phase-only spatial light modulator.

A counterexample to an optimistic guess about étale local systems

In p-adic Hodge theory, it is known that if a Galois representation is de Rham, then it becomes semistable after extension of the base field. Liu and Zhu asked whether a corresponding result holds in the relative setting: given an \'etale local system on a quasi-compact rigid analytic variety (for example, a projective scheme) over a p-adic field, does it become semistable after a finite extension of the base field? We give a counterexample.

Research on the implementation of West Africa-North Africa grid interconnection using new electricity-water composite transmission technology

Combining the characteristics of the reverse distribution of solar resources and water resources in North Africa, West Africa and the Sahara, this paper proposes the West Africa-North Africa grid interconnection project to realize the optimal configuration of desert solar resources and surrounding water resources, and introduce the water resources of West Africa's Niger River and North Africa's desalinated seawater to improve the living environment and development conditions in the hinterland of the Sahara Desert; build photovoltaic bases along the route to send clean electricity to North Africa and West Africa. This paper studies the transmission channel path, electricity-water composite transmission technology and project scheme, and analyzes the economics of the project and the water supply and demand conditions of the Niger River. The research results show that it is feasible in hydrological characteristics to lead the Niger River water along the power transmission channel that crosses the Sahara Desert, and the new electricity-water composite transmission technology has obvious economic advantages.

Combination of multi-focus Raman spectroscopy and compressive sensing for parallel monitoring of single-cell dynamics

To overcome the low efficiency of conventional confocal Raman spectroscopy, many efforts have been devoted to parallelizing the Raman excitation and acquisition, in which the scattering from multiple foci is projected onto different locations on a spectrometer’s CCD, along either its vertical, horizontal dimension, or even both. While the latter projection scheme relieves the limitation on the row numbers of the CCD, the spectra of multiple foci are recorded in one spectral channel, resulting in spectral overlapping. Here, we developed a method under a compressive sensing framework to demultiplex the superimposed spectra of multiple cells during their dynamic processes. Unlike the previous methods which ignore the information connection between the spectra of the cells recorded at different time, the proposed method utilizes a prior that a cell’s spectra acquired at different time have the same sparsity structure in their principal components. Rather than independently demultiplexing the mixed spectra at the individual time intervals, the method demultiplexes the whole spectral sequence acquired continuously during the dynamic process. By penalizing the sparsity combined from all time intervals, the collaborative optimization of the inversion problem gave more accurate recovery results. The performances of the method were substantiated by a 1D Raman tweezers array, which monitored the germination of multiple bacterial spores. The method can be extended to the monitoring of many living cells randomly scattering on a coverslip, and has a potential to improve the throughput by a few orders.

Scientific Technological Interventions on Rapeseed and Mustard: Recent Advances and Future Prospects

In order to increase production, popularization of improved technology as well as for uplifting the socio-economic conditions of the small and marginal farmers of Sonitpur district which typically lies in North Bank Plain Agro-climatic Zone of Assam, a Crop demonstration was conducted among 100 numbers of agricultural beneficiaries in 5 clusters namely Chaiduar, Bihaguri, Balipara, Dhekiajuli and Gabhoru in the year 2020-2021 for the popularization of technology as well as cultivars. Selection of the beneficiaries and Villages were done based on their cropping sequence by the resource person working under the project entitled "Augmenting Rapeseed-Mustard Production of Assam farmers for Sustainable Livelihood Security" linked with Assam Agribusiness and Rural Transformation Project (APART) scheme. During the period of the cropping season, the selected farmers for adoption had shown keen interest in attending farmer’s technical training programme conducted at the cluster level for adopting scientific production techniques and methods gradually, which was considered as a very important technique to be followed by the marginal farmers of Assam to obtain good crop population and ultimately higher yield. Adopting scientific agricultural techniques had helped farmers to reduce the labour cost thus benefitted the farmers by reducing the cost of cultivation. Due to its suitable soil and agro-climatic conditions as well as through their dedication and continuous efforts towards farming, they could be able to achieve higher yield and income within a short period of time as well as could motivate the other small and marginal farmers of nearby villages for further uplifting their economic status thereby preserving their ancestral occupation for future generations.

A Finite Element Penalized Direct Forcing Immersed Boundary Method for infinitely thin obstacles in a dilatable flow

In the framework of the development of new passive safety systems for the second and third generations of nuclear reactors, the numerical simulations, involving complex turbulent two-phase flows around thin or massive inflow obstacles, are privileged tools to model, optimize and assess new design shapes. In order to match industrial demands, computational fluid dynamics tools must be the fastest, most accurate and most robust possible. To face this issue, we have chosen to solve the Navier-Stokes equations using a projection scheme for a mixture fluid coupled with an Immersed Boundary (IB) approach: the penalized direct forcing method – a technique whose characteristics inherit from both penalty and immersed boundary methods – adapted to infinitely thin obstacles and to a Finite Element (FE) formulation. Various IB conditions (slip, no-slip or Neumann) for the velocity on the IB can be managed by imposing Dirichlet values in the vicinity of the thin obstacles. To deal with these imposed Dirichlet velocities, we investigated two variants: one in which we use the obstacle velocity and another one in which we use linear interpolations based on discrete geometrical properties of the IB (barycenters and normal vectors) and the FE basis functions. This last variant is motivated by an increase of the accuracy/computation time ratio for coarse meshes. As a first step, concerning academic test cases for one-phase dilatable-fluid laminar flows, the results obtained via those two variants are in good agreement with analytical and experimental data. Moreover, when compared to each other, the linear interpolation variant increases the spatial order of convergence as expected. An industrial test case illustrates the advantages and drawbacks of this approach. In a shortcoming second step, to face two-phase turbulent fluid simulations, some methodology modifications will be considered such as adapting the projection scheme to low-compressible fluid and immersed wall-law boundary conditions.

An isogeometric finite element-boundary element approach for the vibration analysis of submerged thin-walled structures

In this paper, the isogeometric formulations of the finite element and boundary element methods are applied to the dynamic analysis of thin-walled structures submerged in an infinite, inviscid, and incompressible fluid medium. This fluid–structure interaction problem is decoupled using the modal analysis technique, and the fluid effect on the structure is taken into account through the generalized added mass matrix. The structure is modeled with NURBS-based Kirchhoff–Love shell elements. The fluid response is computed using a regularized boundary integral equation. We take advantage of the geometry preserving property of the NURBS refinement techniques to reduce the computational cost without the need for a projection scheme. The implementation is benchmarked with three test cases, and good accuracy is obtained for a relatively low number of degrees of freedom.

Rank 3 quadratic generators of Veronese embeddings

Let $L$ be a very ample line bundle on a projective scheme $X$ defined over an algebraically closed field $\Bbbk$ with ${\rm char}\,\Bbbk \neq 2$. We say that $(X,L)$ satisfies property $\mathsf {QR}(k)$ if the homogeneous ideal of the linearly normal embedding $X \subset {\mathbb {P}} H^{0} (X,L)$ can be generated by quadrics of rank less than or equal to $k$. Many classical varieties, such as Segre–Veronese embeddings, rational normal scrolls and curves of high degree, satisfy property $\mathsf {QR}(4)$. In this paper, we first prove that if ${\rm char}\,\Bbbk \neq 3$ then $({\mathbb {P}}^{n} , \mathcal {O}_{{\mathbb {P}}^{n}} (d))$ satisfies property $\mathsf {QR}(3)$ for all $n \geqslant 1$ and $d \geqslant 2$. We also investigate the asymptotic behavior of property $\mathsf {QR}(3)$ for any projective scheme. Specifically, we prove that (i) if $X \subset {\mathbb {P}} H^{0} (X,L)$ is $m$-regular then $(X,L^{d} )$ satisfies property $\mathsf {QR}(3)$ for all $d \geqslant m$, and (ii) if $A$ is an ample line bundle on $X$ then $(X,A^{d} )$ satisfies property $\mathsf {QR}(3)$ for all sufficiently large even numbers $d$. These results provide affirmative evidence for the expectation that property $\mathsf {QR}(3)$ holds for all sufficiently ample line bundles on $X$, as in the cases of Green and Lazarsfeld's condition $\mathrm {N}_p$ and the Eisenbud–Koh–Stillman determininantal presentation in Eisenbud et al. [Determinantal equations for curves of high degree, Amer. J. Math. 110 (1988), 513–539]. Finally, when ${\rm char}\,\Bbbk = 3$ we prove that $({\mathbb {P}}^{n} , \mathcal {O}_{{\mathbb {P}}^{n}} (2))$ fails to satisfy property $\mathsf {QR}(3)$ for all $n \geqslant 3$.

An all-Mach, low-dissipation strategy for simulating multiphase flows

Liquid-gas flows that involve compressibility effects occur in many engineering contexts, and high-fidelity simulations can unlock further insights and developments. Introducing several numerical innovations, this work details a collocated, volume-of-fluid, finite volume flow solver that is robust, conservative, and capable of simulating flows with shocks, liquid-gas interfaces, and turbulence. A novel hybrid advection scheme provides stability while minimizing dissipation. An unsplit semi-Lagrangian method provides the robustness and precision to handle discontinuities in the flow, and a centered scheme eliminates numerical kinetic energy dissipation elsewhere, allowing accurate simulation of turbulence. A pressure projection scheme makes multiphase compressible simulations much less costly, and formulating this projection as incremental reduces numerical dissipation further. Local relaxation to mechanical equilibrium is used to properly solve for the pressure and energy fields in multiphase contexts. Within this framework, a consistent methodology for implementing multiphase pressure projection is derived, including surface tension. The complete algorithm is validated with benchmark tests in one, two, and three dimensions that evaluate the accuracy and stability of the approach in predicting compressible effects, turbulent dissipation, interface dynamics, and more through comparisons with theory, experiments, and reference simulations. Finally, the utility of the numerical approach is demonstrated by simulating an atomizing liquid jet in a Mach 2 crossflow.

Adiabatic Molecular Orbital Tracking in Ab Initio Molecular Dynamics.

The ab initio molecular dynamics (AIMD) method provides a computational route for the real-time simulation of reactive chemistry. An often-overlooked capability of this approach is the opportunity to examine the electronic evolution of a chemical system. For AIMD trajectories based on Hartree-Fock or density functional theory methods, the real-time evolution of single-particle molecular orbitals (MOs) can provide detailed insights into the time-dependent electronic structure of molecules. The evolving electronic Hamiltonians at each MD step pose problems for tracking and visualizing a given MO's character, ordering, and associated phase throughout an MD trajectory, however. This report presents and assesses a simple algorithm for correcting these deficiencies by exploiting similarity projections of the electronic structure between neighboring MD steps. Two aspects bring this analysis beyond a simple step-to-step projection scheme. First, the challenging case of coincidental orbital degeneracies is resolved via a quadrupole-field perturbation that nonetheless rigorously preserves energy conservation. Second, the resulting orbitals are shown to evolve adiabatically, in spite of the "preservation of character" concept that undergirds a projection of neighboring steps' MOs. The method is tested on water clusters, which exhibit considerable dynamic degeneracies, as well as a classic organic nucleophilic substitution reaction, in which the adiabatic evolution of the bonding orbitals clarifies textbook interpretations of the electronic structure during this reactive collision.

Experimental investigation and CALPHAD modeling of the Cu–Cr–Si ternary system

The phase equilibria of the Cu–Cr–Si ternary system were investigated via thermodynamic modeling coupled with key experiments. Seventeen ternary alloys were prepared to determine the isothermal sections of the Cu–Cr–Si system at 700 and 800 °C by combining X-ray diffraction (XRD) and scanning electron microscopy with energy dispersive X-ray spectroscopy (SEM/EDS). No ternary compound was found. The solubilities of the third element in binary compounds in the Cu–Si and Cr–Si systems were measured. Based on the thermodynamic descriptions of three constitutive binary systems available in the literature as well as the experimental phase equilibria data obtained from the present work and literature, thermodynamic re-assessment of the Cu–Cr–Si system was carried out by the CALPHAD (CALculation of PHAse Diagrams) approach. The substitutional model and sublattice model were used to describe the solution phases and intermediate phases, respectively. A set of thermodynamic parameters of the Cu–Cr–Si system was obtained. The calculated isothermal sections and vertical section are in good agreement with most of the reliable experimental data. The liquidus projection and reaction scheme of the Cu–Cr–Si system over the whole composition were also presented.

Volumes of line bundles on schemes

Volumes of line bundles are known to exist as limits on generically reduced projective schemes. However, it is not known if they always exist as limits on more general projective schemes. We show that they do always exist as a limit on a codimension one subscheme of a nonsingular projective variety.

Sensitive behavior and optical solitons of complex fractional Ginzburg–Landau equation: A comparative paradigm

This article obtains the optical solitons of the complex fractional Ginzburg–Landau equation by the hypothesis of traveling wave and generalized projective Riccati equation scheme. There are four conditions, Kerr law, parabolic law, power law and dual power law of nonlinearity associated with the model. The constraint conditions for the existence of these solutions have also been discussed. Moreover, the physical significance of the constructed solutions has been provided using graphical representation. A comparative study is made by using two distinct definitions of fractional derivatives namely as Beta and M-truncated. Furthermore, a quantitative overview is also included, which involves solutions to the model under discussion. The complex Ginzburg–Landau equation is subjected to a comprehensive sensitivity analysis. Finally, the modulation instability (MI) analysis of proposed model is also carried out on the basis of linear stability analysis. A dispersion relation is obtained between the wave number and frequency.

Investigation of REFINED CNN ensemble learning for anti-cancer drug sensitivity prediction.

MotivationAnti-cancer drug sensitivity prediction using deep learning models for individual cell line is a significant challenge in personalized medicine. Recently developed REFINED (REpresentation of Features as Images with NEighborhood Dependencies) CNN (Convolutional Neural Network)-based models have shown promising results in improving drug sensitivity prediction. The primary idea behind REFINED-CNN is representing high dimensional vectors as compact images with spatial correlations that can benefit from CNN architectures. However, the mapping from a high dimensional vector to a compact 2D image depends on the a priori choice of the distance metric and projection scheme with limited empirical procedures guiding these choices.ResultsIn this article, we consider an ensemble of REFINED-CNN built under different choices of distance metrics and/or projection schemes that can improve upon a single projection based REFINED-CNN model. Results, illustrated using NCI60 and NCI-ALMANAC databases, demonstrate that the ensemble approaches can provide significant improvement in prediction performance as compared to individual models. We also develop the theoretical framework for combining different distance metrics to arrive at a single 2D mapping. Results demonstrated that distance-averaged REFINED-CNN produced comparable performance as obtained from stacking REFINED-CNN ensemble but with significantly lower computational cost.Availability and implementationThe source code, scripts, and data used in the paper have been deposited in GitHub (https://github.com/omidbazgirTTU/IntegratedREFINED).Supplementary information Supplementary data are available at Bioinformatics online.

구속 포텐셜에서 반도체 물질(Ge)의 자기장 의존성

This paper proposes an application of artificial neural networks for analyzing electricity market that has insufficient information for calculating equilibrium. Neural networks are constructed and trained on two representative cases in the electricity market. One is for calculating equilibrium price in perfect competition market and the other is for determining whether the transmission congestion occurs. The neural network uses a multilayer structure and learns with backpropagation algorithms for training. The neural networks trained in the case studies calculate the market price with a high probability and also determines an occurrence of the transmission congestion accurately. We study optical quantum transition line shapes (QTLS) showing the absorption power and quantum transition line widths (QTLW) of an electron deformation potential phonon interaction system. In order to analyze quantum transfer, the QTLW and QTLS with the magnetic field dependence was compared in two transfer processes, I.e., intra-Land level transfer process. In order to apply quantum transport theory (QTR) to a system that confines electrons by a square well confining potential, the Liouville equation projected with the Equilibrium Average Projection Scheme (EAPS) was used.