scholarly journals Decomposition Strategies to Count Integer Solutions over Linear Constraints

2021 ◽  
Author(s):  
Cunjing Ge ◽  
Armin Biere
Keyword(s):  
Structural Properties ◽  
State Of The Art ◽  
Linear Constraints ◽  
Decomposition Techniques ◽  
Counting Problems ◽  
Integer Points ◽  
Decomposition Strategies ◽  
Counting Algorithms ◽  
Integer Solutions ◽  
Elimination Of Variables

Counting integer solutions of linear constraints has found interesting applications in various fields. It is equivalent to the problem of counting integer points inside a polytope. However, state-of-the-art algorithms for this problem become too slow for even a modest number of variables. In this paper, we propose new decomposition techniques which target both the elimination of variables as well as inequalities using structural properties of counting problems. Experiments on extensive benchmarks show that our algorithm improves the performance of state-of-the-art counting algorithms, while the overhead is usually negligible compared to the running time of integer counting.

scholarly journals Approximating Integer Solution Counting via Space Quantification for Linear Constraints

2019 ◽  
Author(s):  
Cunjing Ge ◽  
Feifei Ma ◽  
Xutong Ma ◽  
Fan Zhang ◽  
Pei Huang ◽  
...  
Keyword(s):  
Experimental Data ◽  
State Of The Art ◽  
Solution Space ◽  
Linear Constraints ◽  
The State ◽  
Volume Estimation ◽  
Integer Solution ◽  
Counting Method ◽  
Volume Computation ◽  
Integer Solutions

Solution counting or solution space quantification (means volume computation and volume estimation) for linear constraints (LCs) has found interesting applications in various fields. Experimental data shows that integer solution counting is usually more expensive than quantifying volume of solution space while their output values are close. So it is helpful to approximate the number of integer solutions by the volume if the error is acceptable. In this paper, we present and prove a bound of such error for LCs. It is the first bound that can be used to approximate the integer solution counts. Based on this result, an approximate integer solution counting method for LCs is proposed. Experiments show that our approach is over 20x faster than the state-of-the-art integer solution counters. Moreover, such advantage increases with the problem scale.

scholarly journals The Multivariate Theory of Functional Connections: Theory, Proofs, and Application in Partial Differential Equations

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1303 ◽  
Author(s):  
Carl Leake ◽  
Hunter Johnston ◽  
Daniele Mortari
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
State Of The Art ◽  
Linear Constraints ◽  
Prior Work ◽  
Partial Differential ◽  
Seminal Paper ◽  
Functional Connections ◽  
Mathematical Proofs ◽  
Multivariate Theory

This article presents a reformulation of the Theory of Functional Connections: a general methodology for functional interpolation that can embed a set of user-specified linear constraints. The reformulation presented in this paper exploits the underlying functional structure presented in the seminal paper on the Theory of Functional Connections to ease the derivation of these interpolating functionals—called constrained expressions—and provides rigorous terminology that lends itself to straightforward derivations of mathematical proofs regarding the properties of these constrained expressions. Furthermore, the extension of the technique to and proofs in n-dimensions is immediate through a recursive application of the univariate formulation. In all, the results of this reformulation are compared to prior work to highlight the novelty and mathematical convenience of using this approach. Finally, the methodology presented in this paper is applied to two partial differential equations with different boundary conditions, and, when data is available, the results are compared to state-of-the-art methods.

scholarly journals A Review of PZT Patches Applications in Submerged Systems

Sensors ◽  
2018 ◽  
Vol 18 (7) ◽  
pp. 2251 ◽  
Author(s):  
Alexandre Presas ◽  
Yongyao Luo ◽  
Zhengwei Wang ◽  
David Valentin ◽  
Mònica Egusquiza
Keyword(s):  
Energy Harvesting ◽  
System Dynamics ◽  
Vibration Control ◽  
Structural Properties ◽  
Environmental Conditions ◽  
Review Paper ◽  
State Of The Art ◽  
Atomic Force ◽  
Working Medium ◽  
Mechanical And Structural Properties

Submerged systems are found in many engineering, biological, and medicinal applications. For such systems, due to the particular environmental conditions and working medium, the research on the mechanical and structural properties at every scale (from macroscopic to nanoscopic), and the control of the system dynamics and induced effects become very difficult tasks. For such purposes in submerged systems, piezoelectric patches (PZTp), which are light, small and economic, have been proved to be a very good solution. PZTp have been recently used as sensors/actuators for applications such as modal analysis, active sound and vibration control, energy harvesting and atomic force microscopes in submerged systems. As a consequence, in these applications, newly developed transducers based on PZTp have become the most used ones, which has improved the state of the art and methods used in these fields. This review paper carefully analyzes and summarizes these applications particularized to submerged structures and shows the most relevant results and findings, which have been obtained thanks to the use of PZTp.

scholarly journals Non-translational Alignment for Multi-relational Networks

2018 ◽  
Author(s):  
Shengnan Li ◽  
Xin Li ◽  
Rui Ye ◽  
Mingzhong Wang ◽  
Haiping Su ◽  
...  
Keyword(s):  
Structural Properties ◽  
Probabilistic Model ◽  
State Of The Art ◽  
Knowledge Bases ◽  
Network Embedding ◽  
Robust Solutions ◽  
Relational Networks ◽  
Alignment Task ◽  
Translational Approach ◽  
Knowledge Graphs

Most existing solutions for the alignment of multi-relational networks, such as multi-lingual knowledge bases, are ``translation''-based which facilitate the network embedding via the trans-family, such as TransE. However, they cannot address triangular or other structural properties effectively. Thus, we propose a non-translational approach, which aims to utilize a probabilistic model to offer more robust solutions to the alignment task, by exploring the structural properties as well as leveraging on anchors to project each network onto the same vector space during the process of learning the representation of individual networks. The extensive experiments on four multi-lingual knowledge graphs demonstrate the effectiveness and robustness of the proposed method over a set of state-of-the-art alignment methods.

MPCC-Based Set Point Optimisation for Machine Tools

2019 ◽  
Vol 13 (3) ◽  
pp. 407-418
Author(s):  
Titus Haas ◽  
Sascha Weikert ◽  
Konrad Wegener ◽  
◽  
Keyword(s):  
Machine Tools ◽  
State Of The Art ◽  
Linear Constraints ◽  
Numerical Control ◽  
Contour Error ◽  
Set Point ◽  
Dynamic Constraints ◽  
Control Code ◽  
Time Optimal ◽  
Optimal Set

Numerical control code is typically used for manufacturing a workpiece using machine tools. Most state-of-the-art approaches decouple the set point optimisation into two steps: the geometry and the feed rate optimisation that does not necessarily result in time-optimal set points for the desired geometry. Given the originally programmed geometry through the numerical control code, dynamic constraints of the machine tool, and maximum permissible contour error for the optimisation, a model predictive contouring control based set point optimisation approach is developed to generate time-optimal set points for machine tools globally. A suitable error definition and its linearisation are used whereby the optimisation problem can be represented by a quadratic programming problem with linear constraints. Compared to most state-of-the-art methods, a direct approach is presented and no previous geometry optimisation step is required. Depending on the demands of accuracy, different maximum contour error constraints and penalisation as well as various maximum permissible axis velocities and accelerations are presented and tested on a test bench. The method is shown to be adaptable to different demands on the set points, and the contour errors can be affected by either the constraints or penalising factors.

Enhanced Technology Mapping for FPGAs with Exploration of Cell Configurations

2015 ◽  
Vol 24 (03) ◽  
pp. 1550039 ◽  
Author(s):  
Grace Zgheib ◽  
Iyad Ouaiss
Keyword(s):  
State Of The Art ◽  
Variable Structure ◽  
Logic Circuits ◽  
Technology Mapping ◽  
Decomposition Techniques ◽  
Gate Arrays ◽  
Field Programmable ◽  
Boolean Matching ◽  
Programmable Gate Arrays ◽  
Logic Functions

In the state-of-the-art field-programmable gate arrays (FPGAs), logic circuits are synthesized and mapped on clusters of look-up tables. However, arithmetic operations benefit from an existing dedicated adder along with a carry chain used to ensure a fast carry propagation. This carry chain is a dedicated wire available in the architecture of the FPGA and is as such independent of the external programmable routing resources. In this paper, we propose a variable-structure Boolean matching technology mapper with embedded decomposition techniques to map nonarithmetic logic functions on carry chains. Previously synthesized and mapped logic functions are adapted so that their outputs are routed using the dedicated carry chains instead of the external programmable interconnects. The experimental results show a reduction in the used routing resources as well as the circuit area when using this Boolean matching-based mapper on the Altera Stratix-III FPGA.

scholarly journals A General Self-Adaptive Relaxed-PPA Method for Convex Programming with Linear Constraints

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Xiaoling Fu
Keyword(s):  
Convex Programming ◽  
State Of The Art ◽  
Adaptive Strategies ◽  
Linear Constraints ◽  
Proximal Point ◽  
Mild Conditions ◽  
Linearly Constrained Convex Programming ◽  
Linearly Constrained ◽  
Algorithmic Framework ◽  
Self Adaptive

We present an efficient method for solving linearly constrained convex programming. Our algorithmic framework employs an implementable proximal step by a slight relaxation to the subproblem of proximal point algorithm (PPA). In particular, the stepsize choice condition of our algorithm is weaker than some elegant PPA-type methods. This condition is flexible and effective. Self-adaptive strategies are proposed to improve the convergence in practice. We theoretically show under mild conditions that our method converges in a global sense. Finally, we discuss applications and perform numerical experiments which confirm the efficiency of the proposed method. Comparisons of our method with some state-of-the-art algorithms are also provided.

scholarly journals The Status of Technologies to Measure Forest Biomass and Structural Properties: State of the Art in SAR Tomography of Tropical Forests

2019 ◽  
Vol 40 (4) ◽  
pp. 779-801 ◽  
Author(s):  
Stefano Tebaldini ◽  
Dinh Ho Tong Minh ◽  
Mauro Mariotti d’Alessandro ◽  
Ludovic Villard ◽  
Thuy Le Toan ◽  
...  
Keyword(s):  
Structural Properties ◽  
Tropical Forests ◽  
State Of The Art ◽  
Forest Biomass ◽  
The Status

scholarly journals Melt Electrospinning Designs for Nanofiber Fabrication for Different Applications

2019 ◽  
Vol 20 (10) ◽  
pp. 2455 ◽  
Author(s):  
Yasseen Ibrahim ◽  
Essraa Hussein ◽  
Moustafa Zagho ◽  
Ghada Abdo ◽  
Ahmed Elzatahry
Keyword(s):  
Structural Properties ◽  
Process Parameters ◽  
State Of The Art ◽  
Electrospinning Process ◽  
The State ◽  
Electrospinning Technique ◽  
Melt Electrospinning ◽  
Physicochemical And Structural Properties

Nanofibers have been attracting growing attention owing to their outstanding physicochemical and structural properties as well as diverse and intriguing applications. Electrospinning has been known as a simple, flexible, and multipurpose technique for the fabrication of submicro scale fibers. Throughout the last two decades, numerous investigations have focused on the employment of electrospinning techniques to improve the characteristics of fabricated fibers. This review highlights the state of the art of melt electrospinning and clarifies the major categories based on multitemperature control, gas assist, laser melt, coaxial, and needleless designs. In addition, we represent the effect of melt electrospinning process parameters on the properties of produced fibers. Finally, this review summarizes the challenges and obstacles connected to the melt electrospinning technique.

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