Set Of Functions Research Articles

Genome-wide identification of novel flagellar motility genes in Pseudomonas syringae pv. tomato DC3000

Pseudomonas syringae pv. tomato DC3000 (Pst DC3000) is a plant pathogenic bacterium that possesses complicated motility regulation pathways including a typical chemotaxis system. A significant portion of our understanding about the genes functioning in Pst DC3000 motility is based on comparison to other bacteria. This leaves uncertainty about whether gene functions are conserved, especially since specific regulatory modules can have opposite functions in sets of Pseudomonas. In this study, we used a competitive selection to enrich for mutants with altered swimming motility and used random barcode transposon-site sequencing (RB-TnSeq) to identify genes with significant roles in swimming motility. Besides many of the known or predicted chemotaxis and motility genes, our method identified PSPTO_0406 (dipA), PSPTO_1042 (chrR) and PSPTO_4229 (hypothetical protein) as novel motility regulators. PSPTO_0406 is a homolog of dipA, a known cyclic di-GMP degrading enzyme in P. aeruginosa. PSPTO_1042 is part of an extracytoplasmic sensing system that controls gene expression in response to reactive oxygen species, suggesting that PSPTO_1042 may function as part of a mechanism that enables Pst DC3000 to alter motility when encountering oxidative stressors. PSPTO_4229 encodes a protein containing an HD-related output domain (HDOD), but with no previously identified functions. We found that deletion and overexpression of PSPTO_4229 both reduce swimming motility, suggesting that its function is sensitive to expression level. We used the overexpression phenotype to screen for nonsense and missense mutants of PSPTO_4229 that no longer reduce swimming motility and found a pair of conserved arginine residues that are necessary for motility suppression. Together these results provide a global perspective on regulatory and structural genes controlling flagellar motility in Pst DC3000.

Optimal Strategies for Filament Orientation in Non-Planar 3D Printing

The structural integrity and surface quality of parts produced using traditional fused deposition modeling depend on factors such as layer height, filament and build orientation, print speed, nozzle temperature, and, crucially for this study, both planar and non-planar slicing. Recent research on non-planar slicing techniques has shown significant improvements in surface smoothness and mechanical properties. Key approaches include non-planar slicing for 3-axis printers, adaptive slicing to optimize material placement in critical areas, and post-processing. However, current studies lack a comprehensive method for parameterizing filament direction across both planar and non-planar layers. This work presents an approach to generate optimal trajectories for planar and non-planar layers using contours derived from level set functions. The methodology demonstrates the advantages of non-planar printing, particularly with a filament orientation of 30° for inclined surfaces, ensuring better surface quality, uniformity, and structural integrity. This emphasizes the importance of trajectory planning and filament orientation in achieving high-quality prints on inclined geometries. This research highlights the necessity of a methodology that tailors filament paths based on the load-bearing requirements of each part, demonstrating its potential to enhance surface quality and structural performance, and further the advancement of the 3D printing industry.

A novel SRAM with SET and RESET functions using a novel 5-input majority gate in quantum-dot cellular automata (QCA) technology

Abstract In the nanoscale VLSI industry, Quantum-dot Cellular Automata (QCA) presents a novel substitute for conventional Complementary Metal-Oxide-Semiconductor (CMOS) technology. This paper introduces a new design that uses QCA technology. The design includes a 5-input Majority Gate (5-MG), a fundamental component in QCA, and a Static Random Access Memory (SRAM) cell with set and reset features. The recommended design offers a minimum clock cycle, a small QCA layout area, less cost function, and a sustainable arrangement to get the ideal size and latency while consuming less power. The proposed 5-input majority gate (MG) has a total area of 0.009 μm2 and a QCA cell count of 14. Further, a novel SRAM cell is implemented using the 5-input MG logic. The SRAM cell designed using 44 QCA cells has a clock latency of 1 and a layout area of 0.03 μm2. Compared to the conventional 5-MG SRAM cell the proposed 5-MG SRAM cell shows a 50% reduction in cell counts and a 62.5% reduction in total layout area.

Condenser capacities and capacitary potentials for unbounded sets, and global p-harmonic Green functions on metric spaces

. We study the condenser capacity cap p ⁡(E, Ω) on unbounded open sets Ω in a proper connected metric space X equipped with a locally doubling measure supporting a local p-Poincaré inequality, where 1 < p < ∞ . Using a new definition of capacitary potentials, we show that cap p is countably subadditive and that it is a Choquet capacity. We next obtain formulas for the capacity of superlevel sets for the capacitary potential. These are then used to show that p-harmonic Green functions exist in an unbounded domain Ω if and only if either X is p-hyperbolic or the Sobolev capacity C p ( X ∖ Ω ) > 0 . As an application, we deduce new results for Perron solutions and boundary regularity for the Dirichlet boundary value problem for p-harmonic functions in unbounded open sets.

Computational modeling of the Nb -CO chemisorption process.

The transition metal niobium (Nb) has attracted considerable attention from the scientific community due to its intriguing electronic properties and applications in catalysts suitable for chemical reactions. Thus, this work investigates the adsorption of the atmospheric polluting gas carbon monoxide (CO) by the niobium cluster (Nb ), to describe the reactive nature of Nb . This entire study was carried out by applying the Coupled-Cluster method and Density Functional Theory (through the HSE06 functional) and the def2-QZVP plus Def2-TZVP/C auxiliary basis set functions. The results of electronic structure calculations and IR vibrational spectra suggest that both Nb and the Nb -CO clusters can be considered stable. Furthermore, the obtained results also indicate that there is a chemisorption of carbon monoxide by the Nb niobium cluster. This feature can serve as motivation for future theoretical-experimental studies, as it suggests that the Nb cluster may have possible technological applications in automotive catalytic processes. Initial three-dimensional structures were constructed. Complete optimization of the geometry was performed in coupled cluster and density functional theory methods. From the optimization configuration, it was possible to investigate the stability, chemisorption process, binding energies, charge analysis, molecular orbital energies, and IR vibrational spectra of the systems.

Combinatorial reduction of set functions and matroid permutations through minor invertible product assignment

We introduce an algebraic model, based on the determinantal expansion of the product of two matrices, to test combinatorial reductions of set functions. Each term of the determinantal expansion is deformed through a monomial factor in d indeterminates, whose exponents define a Zd-valued set function. By combining the Grassmann-Plücker relations for the two matrices, we derive a family of sparse polynomials, whose factorisation properties in a Laurent polynomial ring are studied and related to information-theoretic notions.Under a given genericity condition, we prove the equivalence between combinatorial reductions and determinantal expansions with invertible minor products; specifically, a deformation returns a determinantal expansion if and only if it is induced by a diagonal matrix of units in C(t) acting as a kernel in the original determinant expression. This characterisation supports the definition of a new method for checking and recovering combinatorial reductions for matroid permutations.

Plug-and-play segment anything model improves nnUNet performance.

The automatic segmentation of medical images has widespread applications in modern clinical workflows. The Segment Anything Model (SAM), a recent development of foundational models in computer vision, has become a universal tool for image segmentation without the need for specific domain training. However, SAM's reliance on prompts necessitates human-computer interaction during the inference process. Its performance on specific domains can also be limited without additional adaptation. In contrast, traditional models like nnUNet are designed to perform segmentation tasks automatically during inference and can work well for each specific domain, but they require extensive training on domain-specificdatasets. To leverage the advantages of both foundational and domain-specific models and achieve fully automated segmentation with limited training samples, we propose nnSAM, which combines the robust feature extraction capabilities of SAM with the automatic configuration abilities of nnUNet to enhance the accuracy and robustness of medical image segmentation on smalldatasets. We propose the nnSAM model for small sample medical image segmentation. We made optimizations for this goal via two main approaches: first, we integrated the feature extraction capabilities of SAM with the automatic configuration advantages of nnUNet, which enables robust feature extraction and domain-specific adaptation on small datasets. Second, during the training process, we designed a boundary shape supervision loss based on level set functions and curvature calculations, enabling the model to learn anatomical shape priors from limited annotationdata. We conducted quantitative and qualitative assessments on the performance of our proposed method on four segmentation tasks: brain white matter, liver, lung, and heart segmentation. Our method achieved the best performance across all tasks. Specifically, in brain white matter segmentation using 20 training samples, nnSAM achieved the highest DICE score of 82.77 ( 10.12) % and the lowest average surface distance (ASD) of 1.14 ( 1.03) mm, compared to nnUNet, which had a DICE score of 79.25 ( 17.24) % and an ASD of 1.36 ( 1.63) mm. A sample size study shows that the advantage of nnSAM becomes more prominent under fewer trainingsamples. A comprehensive evaluation of multiple small-sample segmentation tasks demonstrates significant improvements in segmentation performance by nnSAM, highlighting the vast potential of small-samplelearning.

Normal Approximation of Random Gaussian Neural Networks

In this paper, we provide explicit upper bounds on some distances between the (law of the) output of a random Gaussian neural network and (the law of) a random Gaussian vector. Our main results concern deep random Gaussian neural networks with a rather general activation function. The upper bounds show how the widths of the layers, the activation function, and other architecture parameters affect the Gaussian approximation of the output. Our techniques, relying on Stein’s method and integration by parts formulas for the Gaussian law, yield estimates on distances that are indeed integral probability metrics and include the convex distance. This latter metric is defined by testing against indicator functions of measurable convex sets and so allows for accurate estimates of the probability that the output is localized in some region of the space, which is an aspect of a significant interest both from a practitioner’s and a theorist’s perspective. We illustrated our results by some numerical examples. Funding: This research was supported by the European Union’s Horizon 2020 research project WARIFA under grant agreement no. 101017385, by the PRIN project 2022 “Variational Analysis of Complex Systems in Materials Science, Physics and Biology” (CUP B53D23009290006), and by the INdAM project “Modelli ed Algoritmi per dati ad elevata dimensionalità” (CUP E53C23001670001).

Three-dimensional buckling analysis of stiffened plates with complex geometries using energy element method

A novel numerical method, energy element method (EEM), is proposed for the three-dimensional (3D) buckling analysis of stiffened plates with complex geometries. The problem is formulated in a cuboidal domain, and any complex geometric stiffened plate is modeled by assigning cutouts within the cuboidal domain. The stiffened plate is considered as an energy body and is discretized using Gauss points with variable stiffness properties to simulate its energy distribution. Incorporating the extended interval integration, Gauss quadrature, variable stiffness properties, and Chebyshev polynomials, the strain energy of stiffened plates with complex geometries can be numerically simulated by putting the stiffness and thickness of Gauss points in the cutouts to zero in the cuboidal domain. Using the principle of minimum potential energy and Ritz solution procedure, the deformation and buckling behaviors of stiffened plates with complex geometries can be captured. As a result of the new formulations in EEM, new standard energy functionals and solving procedures have been developed. In addition, Gauss points are generated within the energy elements accounting for the geometric boundaries of the stiffened plate, which are characterized by level set functions. EEM is employed to investigate complex-shaped stiffened plates with straight or curvilinear stiffeners, and the results are compared to those obtained using FEM or mesh-free method. The precision, generalization, and stability of EEM are demonstrated.

Efficient random walks for generating random fuzzy measures in Möbius representation in large universe

Random generation of fuzzy measures plays a pivotal role in large-scale decision-making and optimization. Random walks ensure uniform generation and adequate coverage. The Möbius representation of set functions is a valuable tool for establishing the sparse structure of fuzzy measures, with its non-negativity closely linked to monotonicity and convexity/supermodularity checking. We propose three efficient methods for monotonicity verification and convexity/supermodularity verification applicable to random walks in Möbius representations, specifically tailored for universal sets larger than ten inputs and k-order fuzzy measures. We first present the baseline methods by directly inspecting monotonicity and convexity constraints. Building on the observation that the majority of initially generated values exhibit non-negativity, we intentionally track negative Möbius values to enhance the computational performance of these baseline approaches. Further, we introduce the more agile methods that employ insertion and merge sorting techniques for both monotonicity and convexity checks in random walks that involve small perturbations of fuzzy measures. To address sparsity in large-scale scenarios, we focus on two major types of measures: k-additive and k-interactive measures, demonstrating their effectiveness through theoretical analysis and experimental results.

Design of concatenative complete complementary codes for CCC-CDMA via specific sequences and extended Boolean functions

A complete complementary code (CCC) consists of M sequence sets with size M. The sum of the auto-correlation functions of each sequence set is an impulse function, and the sum of cross-correlation functions of the different sequence sets is equal to zero. Thanks to their excellent correlation, CCCs received extensive use in engineering. In addition, they are strongly connected to orthogonal matrices. In some application scenarios, additional requirements are made for CCCs, such as recently proposed for concatenative CCC (CCCC) division multiple access (CCC-CDMA) technologies. In fact, CCCCs are a special kind of CCCs which requires that each sequence set in CCC be concatenated to form a zero-correlation-zone (ZCZ) sequence set. However, this requirement is challenging, and the literature is thin since there is only one construction in this context. We propose to go beyond the literature through this contribution to reduce the gap between their interest and our limited knowledge of CCCCs. This paper will employ novel methods for designing CCCCs and precisely derive two constructions of these objects. The first is based on perfect cross Z-complementary pair and Hadamard matrices, and the second relies on extended Boolean functions. Specifically, we highlight that optimal and asymptotic optimal CCCCs could be obtained through the proposed constructions. Besides, we shall present a comparison analysis with former structures in the literature and examples to illustrate our main results.

Structural fatigue crack propagation simulation and life prediction based on improved XFEM-VCCT

To simulate structural crack propagation and predict fatigue life, the extended finite element method (XFEM) combined with the virtual crack closure technique (VCCT) is adopted in this paper. Firstly, the underlying principles of the XFEM-VCCT framework are elaborated comprehensively, mainly including the calculation of crack tip energy release rate based on VCCT, the simulation of element cracking utilizing the phantom nodes, and the computation of structural responses under cyclic loading through the direct cyclic analysis. In addition, to calculate the crack propagation length, an interpolation method to obtain the crack tip coordinates is developed based on tracking and locating the crack by the level set functions. Meanwhile, to compensate the defect that the fatigue life is often overestimated when dealing with the complex mode crack in complex structure through XFEM-VCCT, a simple improved algorithm based on the average rate concept is proposed without altering the XFEM-VCCT framework. Based on specific examples, the necessity and accuracy of the improved algorithm are fully verified by comparing with the original method, and the fatigue life predicted by the improved algorithm is more consistent with reality. Finally, this method is successfully applied to the simulation and analyses for a typical ship stiffened plate structure, demonstrating good engineering applicability.

A mini immersed finite element method for two-phase Stokes problems on Cartesian meshes

Abstract This paper presents a mini immersed finite element (IFE) method for solving two- and three-dimensional two-phase Stokes problems on Cartesian meshes. The IFE space is constructed from the conventional mini element, with shape functions modified on interface elements according to interface jump conditions while keeping the degrees of freedom unchanged. Both discontinuous viscosity coefficients and surface forces are taken into account in the construction. The interface is approximated using discrete level set functions, and explicit formulas for IFE basis functions and correction functions are derived, facilitating ease of implementation.The inf-sup stability and the optimal a priori error estimate of the IFE method, along with the optimal approximation capabilities of the IFE space, are derived rigorously, with constants that are independent of the mesh size and the manner in which the interface intersects the mesh, but may depend on the discontinuous viscosity coefficients. Additionally, it is proved that the condition number has the usual bound independent of the interface. Numerical experiments are provided to confirm the theoretical results.

Theoretical modeling of electronic absorption spectra of ionized species of β-diketones.

Direct DFT evaluation of negatively charged or highly π-delocalized systems is intrinsically problematic. Single ionized (anionic) forms of β-diketones combine both these issues. In this article, we have summarized and analyzed the experimental and theoretical spectral dataset for anionic forms of different substituted perfluorinated β-diketones that were obtained by our team during the past few years. Using previously collected experimental data, spectra of anion of diketones containing phenol, 2-furoyl, 2-thiophen, 2-selenophen, 2-tellorphe, 2-pyridin, 2-naphthyl, and N-methyl-pyrrole substituted rings were considered and chosen for the simulation. The X3LYP density functional demonstrates good results in both ultraviolet and visible parts of the diketones spectra. Minnesota family show predictable ability within the reasonable errors. The linear correlation between the Hartree-Fock exchange and the errors of estimation has been observed. Density functionals with a low contribution of HF weight (0-30%) provide better prediction accuracy. Quantum chemistry calculations were performed under eighteen density functionals (Slater, Becke, OPTX, LYP, PW91C, BPE0, B3LYP, CAM-B3LYP, X3LYP, TPSS, revTPSS, TPSSh, M06-L, M06, M06-2X, M06-HF, M11-L, MN15-L), paired with the SMD solvation model implemented in GAMESS US program package. Def2-SVP basis set functions were applied to light atoms, and CRENBL effective core potential was used to Tellurium.

Exploring the molecular solvatochromism, stability, reactivity, and non-linear optical response of resveratrol.

This work analyzes the isomerization effects and solvent contributions to the stability, electronic excitations, reactivity, and non-linear optical properties (NLO) of resveratrol molecules within the formalism of the Density Functional Theory. The findings suggest that resveratrol solvatochromism is significantly influenced by solvent polarization. The electronic and free energies (E and G) indicate that trans is the most stable conformer. The system is classified as a strong nucleophile. However, the analysis of the Fukui functions and the Mulliken charges indicate that cis-trans isomerization jointly affects the reactive indices of the carbon and hydrogen atoms. The results also suggest that solvent is relevant to solvatochromism and the NLO response. Both cis and trans conformers present strong excitations that undergo a visible hypsochromic change when the polarity of the solvent increases. Once the absorption spectra are connected to the first hyperpolarization ( ) by the Oudar and Chemla relation, the hypsochromism of resveratrol is the reason for the drop in the generation of the second harmonic when the ambient polarity decreases. The CAM-B3LYP DFT results suggest that resveratrol is interesting for NLO applications. Depending on the choice of solvent, values 50 times those observed for urea ( esu), which is a standard NLO material. The optimized geometries of cis and trans isomers of resveratrol in vacuum were obtained using Density Functional Theory (DFT) with the hybrid exchange-correlation function (CAM-B3LYP) and Pople basis set functions, specifically 6-311++G(d,p). The solvent effect on the geometries of both isomers was included using the polarizable continuum model (PCM) with the same level of QM calculation. Vibrational analysis was conducted to confirm that all optimized geometries correspond to the minimum energy. Various electronic properties, including dipole moments, molecular orbitals, transition energy, dipole polarizabilities, and global reactivity parameters, were calculated using both continuum and discrete solvation models based on the sequential QM/MM methodology. All QM calculations were performed with the Gaussian 09 program and the MC simulations with the DICE program. All NLO analysis was carried out using the Multiwfn code.

Data-Driven Control-Oriented Modeling for Response of Fluidic Thrust Vectoring

Response to control input is of significance to the application of real-time active flow control (AFC). In this paper, a novel data-driven framework is used to discover the underlying physics of the dynamic response process of fluidic thrust vectoring (FTV), a typical application of AFC. In the proposed framework, sparse identification of a nonlinear dynamics (SINDy) algorithm is used to identify the governing equations of the flow control responses of sets of noisy measurement data. The clustering algorithm is then used to seek the generalized coefficients of basis functions for different sets of data, which improve the robustness of the model to noisy measurement data. First, a simulated mechanical system is used to validate the effect of the framework. To simplify the modeling, control performance and characteristics are investigated in a detailed manner. Then a dimensionless parameter ΔCp based on the pressure coefficient is found to exhibit a linear relationship with the vector angle under different working conditions. This parameter is introduced in the proposed framework to model the dynamic process of response to control input. The obtained governing equations can describe the dynamic process accurately based on the validation of testing data. The form of the governing equation is rewritten and analyzed based on the control theory, revealing the physics of this process, which is significant to practical AFC implementation.

A new computational framework for spinor-based relativistic exact two-component calculations using contracted basis functions.

A new computational framework for spinor-based relativistic exact two-component (X2C) calculations is developed using contracted basis sets with a spin-orbit contraction scheme. Generally contracted, j-adapted basis sets of p-block elements using primitive functions in the correlation-consistent basis sets are constructed for the X2C Hamiltonian with atomic mean-field spin-orbit integrals (the X2CAMF scheme). The contraction coefficients are taken from atomic X2CAMF Hartree-Fock spinors, thereby following the simple concept of a linear combination of atomic orbitals. Benchmark calculations of spin-orbit splittings, equilibrium bond lengths, and harmonic vibrational frequencies demonstrate the accuracy and efficacy of the j-adapted spin-orbit contraction scheme.

USING THE GEOSPATIAL MULTI-CRITERIA DECISION ANALYSIS MODEL AND METHODS FOR SOIL DEGRADATION RISK MAPPING

Modern methods of spatial analysis and modeling are increasingly being combined with decision-making methods and fuzzy set theory. The latter are actively integrated into the environment of Geographic Information Systems (GIS), such as well-known ones like ArcGIS or QGIS, in the form of separate tools, plugins, or Python scripts. Decision-making methods allow structuring the problem in geographical space, as well as taking into account the knowledge and judgments of experts and the preferences of the decision-maker in determining the priorities of alternative solutions. This paper provides a description of a geospatial multi-criteria decision analysis model, which allows addressing a wide range of ecological and socio-economic issues. An example of applying this model to map soil degradation risk in Ukraine is presented in the paper. According to the object-spatial approach, the properties of a territory are determined as the result of the action (impact) of a set of objects (processes) belonging to this territory. The territory is represented as a two-dimensional discrete grid, each point of which (local area) is an alternative. The set of local areas of the territory constitutes the set of alternatives. The representation of the territory model as a system of objects and relationships between them allows justifying the choice of a set of criteria (factors) for assessing soil degradation risk. Each criterion is a separate raster layer of the map. To build a hierarchical decision-making structure and calculate the importance coefficients of the criteria, the Analytic Hierarchy Process (AHP) method is used. To account for uncertainty in assessments and judgments of experts at the stages of standardization of alternative attributes by different criteria and aggregation of their assessments, expert membership functions for fuzzy sets and fuzzy quantifiers are applied. The particular feature of the proposed multi-criteria decision analysis model is its low computational complexity and ease of integration into the GIS environment.

Greedy algorithm for maximization of semi-monotone non-submodular functions with applications

The problem of maximizing submodular set functions has received increasing attention in recent years, and significant improvements have been made, particularly in relation to objective functions that satisfy monotonic submodularity. However, in practice, the objective function may not be monotonically submodular. While greedy algorithms have strong theoretical guarantees for maximizing submodular functions, their performance is barely guaranteed for non-submodular functions. Therefore, in this paper, we investigate the problem of maximizing non-monotone non-submodular functions under knapsack constraints based on the problem of infectious diseases and provides a more sophisticated analysis through the idea of segmentation. Since our definition characterizes the function more elaborately, a better bound, i.e., a tighter approximation guarantee, is achieved. Finally, we generalize the relevant results for the more general problems.

Level set methods for gradient-free optimization of metasurface arrays

Global optimization techniques are increasingly preferred over human-driven methods in the design of electromagnetic structures such as metasurfaces, and careful construction and parameterization of the physical structure is critical in ensuring computational efficiency and convergence of the optimization algorithm to a globally optimal solution. While many design variables in physical systems take discrete values, optimization algorithms often benefit from a continuous design space. This work demonstrates the use of level set functions as a continuous basis for designing material distributions for metasurface arrays and introduces an improved parameterization which is termed the periodic level set function. We explore the use of alternate norms in the definition of the level set function and define a new pseudo-inverse technique for upsampling basis coefficients with these norms. The level set method is compared to the fragmented parameterization and shows improved electromagnetic responses for two dissimilar cost functions: a narrowband objective and a broadband objective. Finally, we manufacture an optimized level set metasurface and measure its scattering parameters to demonstrate real-world performance.