Gaussian Elimination Meets Maximum Satisfiability

Given a set of constraints F and a weight function W over the assignments, the problem of MaxSAT is to compute a maximum weighted solution of F. MaxSAT is a fundamental problem with applications in numerous areas. The success of MaxSAT solvers has prompted researchers in AI and formal methods communities to develop algorithms that can use MaxSAT solver as oracle. One such problem that stands to benefit from advances in MaxSAT solving is discrete integration. Recently, Ermon et al. achieved a significant breakthrough by reducing the problem of integration to polynomially many queries to an optimization oracle where $F$ is conjuncted with randomly chosen XOR constraints. Unlike approximate model counting, where hashing-based approaches have been able to achieve scalability as well as rigorous formal guarantees, the practical evaluation of Ermon et al's approach, called WISH, often sacrifice theoretical guarantees, largely due to lack of existing MaxSAT solvers with native XOR support. The primary contribution of this paper is a new MaxSAT solver, GaussMaxHS, with built-in XOR support. The architecture of GaussMaxHS is inspired by CryptoMiniSAT, which has been the workhorse of hashing-based approximate model counting techniques. The resulting solver, GaussMaxHS, outperforms MaxHS over 9628 benchmarks arising from spin glass models and network reliability domains. In particular, with a timeout of 5000 seconds, MaxHS could solve only 5473 benchmarks while GaussMaxHS could solve 6120 benchmarks.

Accurate Open Channel Flowrate Estimation Using 2D RANS Modelization and ADCP Measurements

Boat-mounted Acoustic Doppler Current Profilers (ADCP) are commonly used to measure the streamwise velocity distribution and discharge in rivers and open channels. Generally, the method used to integrate the measurements is the velocity-area method, which consists of a discrete integration of flow velocity over the whole cross-section. The discrete integration is accomplished independently in the vertical and transversal direction without assessing the hydraulic coherence between both dimensions. To address these limitations, a new alternative method for estimating the discharge and its associated uncertainty is here proposed. The new approach uses a validated 2D RANS hydraulic model to numerically compute the streamwise velocity distribution. The hydraulic model is fitted using state estimation (SE) techniques to accurately reproduce the measurement field and hydraulic behaviour of the free-surface stream. The performance of the hydraulic model has been validated with measurements on two different trapezoidal cross-sections in a real channel, even with asymmetric velocity distribution. The proposed method allows extrapolation of measurement information to other points where there are no measurements with a solid and consistent hydraulic basis. The 2D-hydraulic velocity model (2D-HVM) approach discharge values have been proven more accurate than the ones obtained using velocity-area method, thank to the enhanced use of the measurements in addition to the hydraulic behaviour represented by the 2D RANS model.

AWR: Adaptive Weighting Regression for 3D Hand Pose Estimation

In this paper, we propose an adaptive weighting regression (AWR) method to leverage the advantages of both detection-based and regression-based method. Hand joint coordinates are estimated as discrete integration of all pixels in dense representation, guided by adaptive weight maps. This learnable aggregation process introduces both dense and joint supervision that allows end-to-end training and brings adaptability to weight maps, making network more accurate and robust. Comprehensive exploration experiments are conducted to validate the effectiveness and generality of AWR under various experimental settings, especially its usefulness for different types of dense representation and input modality. Our method outperforms other state-of-the-art methods on four publicly available datasets, including NYU, ICVL, MSRA and HANDS 2017 dataset.

Phase Transition Behavior of Cardinality and XOR Constraints

The runtime performance of modern SAT solvers is deeply connected to the phase transition behavior of CNF formulas. While CNF solving has witnessed significant runtime improvement over the past two decades, the same does not hold for several other classes such as the conjunction of cardinality and XOR constraints, denoted as CARD-XOR formulas. The problem of determining satisfiability of CARD-XOR formulas is a fundamental problem with wide variety of applications ranging from discrete integration in the field of artificial intelligence to maximum likelihood decoding in coding theory. The runtime behavior of random CARD-XOR formulas is unexplored in prior work. In this paper, we present the first rigorous empirical study to characterize the runtime behavior of 1-CARD-XOR formulas. We show empirical evidence of a surprising phase-transition that follows a non-linear tradeoff between CARD and XOR constraints.

SOWAT: High-resolution imaging with only partial AO correction

Observations of dense stellar systems such as globular clusters (GCs) are limited in resolution by the optical aberrations induced by atmospheric turbulence (atmospheric seeing). At the example of holographic speckle imaging, we now study, to which degree image reconstruction algorithms are able to remove residual aberrations from a partial adaptive optics (AO) correction, such as delivered from ground-layer AO (GLAO) systems. Simultaneously, we study, how such algorithms benefit from being applied to pre-corrected instead of natural point-spread functions (PSFs). We find that using partial AO corrections already lowers the demands on the holography reference star by ∼3 mag, what makes more fields accessible for this technique, and also that the discrete integration times may be chosen about 2–3× longer, since the effective wavefront evolution is slowed down by removing the perturbation power.

Fractional-order value identification of the discrete integrator from a noised signal. part I

In the paper we investigate the fractional-order evaluation of the fractional-order discrete integration element. We assume that the input and output signals are known. The main problem is to calculate fractional-order value. From a theoretical point of view there is no mathematical problem of the solution. One should solve linear algebraic equation or find roots of a polynomial in a variable ν. The problem arises when the measured output signal contains a noise. Then, the solution is unsettled because the polynomial roots are very sensitive to coefficients variability. In the paper we propose a method of evaluating of the discrete integrator fractional-order. The investigations are supported by numerical examples.

Mass, Momentum and Energy Flux in Nonlinear Water Wave Based on HAM Solution

In this paper, the Homotopy Analysis Method (HAM) is applied to solve the fully nonlinear partial differential equation for the steady propagating periodic gravity wave of finite water depth. The series solution of the wave elevation and the velocity potential function are obtained. And then the velocity and pressure fields are plotted and discussed carefully. In order to overcome the drawback of the integral calculations with complex free surface elevation, the discrete integration and fitting procedure based on high-order Fourier series is developed. Based on the accurate HAM solution and fitting technique, the mass, momentum and energy conservation equations are validated. At last, the corresponding mean fluxes are calculated and the velocities of the mass transport and energy transport are supplied accurately.