On the NP-Hardness of Approximating Ordering Constraint Satisfaction Problems

We show improved NP-hardness of approximating Ordering Constraint Satisfaction Problems (OCSPs). For the two most well-studied OCSPs, Maximum Acyclic Subgraph and Maximum Betweenness, we prove inapproximability of $14/15+\epsilon$ and $1/2+\epsilon$. An OCSP is said to be approximation resistant if it is hard to approximate better than taking a uniformly random ordering. We prove that the Maximum Non-Betweenness Problem is approximation resistant and that there are width-$m$ approximation-resistant OCSPs accepting only a fraction $1 / (m/2)!$ of assignments. These results provide the first examples of approximation-resistant OCSPs subject only to P $\neq$ \NP

Fourier PCA and Robust Tensor Decomposition

Fourier PCA is Principal Component Analysis of a matrix obtained from higher order derivatives of the logarithm of the Fourier transform of a distribution.We make this method algorithmic by developing a tensor decomposition method for a pair of tensors sharing the same vectors in rank-$1$ decompositions. Our main application is the first provably polynomial-time algorithm for underdetermined ICA, i.e., learning an $n \times m$ matrix $A$ from observations $y=Ax$ where $x$ is drawn from an unknown product distribution with arbitrary non-Gaussian components. The number of component distributions $m$ can be arbitrarily higher than the dimension $n$ and the columns of $A$ only need to satisfy a natural and efficiently verifiable nondegeneracy condition. As a second application, we give an alternative algorithm for learning mixtures of spherical Gaussians with linearly independent means. These results also hold in the presence of Gaussian noise.Comment: Extensively revised; details added; minor errors corrected; exposition improve

Zero delay synchronization of chaos in coupled map lattices

We show that two coupled map lattices that are mutually coupled to one another with a delay can display zero delay synchronization if they are driven by a third coupled map lattice. We analytically estimate the parametric regimes that lead to synchronization and show that the presence of mutual delays enhances synchronization to some extent. The zero delay or isochronal synchronization is reasonably robust against mismatches in the internal parameters of the coupled map lattices and we analytically estimate the synchronization error bounds.Comment: 9 pages, 9 figures ; To appear in Phys. Rev.

Multiplier methods for engineering optimization

International audienceMultiplier methods used to solve the constrained engineering optimization problem are described. These methods solve the problem by minimizing a sequence of unconstrained problems defined using the cost and constraint functions. The methods, proposed in 1969, have been determined to be quite robust, although not as efficient as other algorithms. They can be more effective for some engineering applications, such as optimum design and control oflarge scale dynamic systems. Since 1969 several modifications and extensions of the methods have been developed. Therefore, it is important to review the theory and computational procedures of these methods so that more efficient and effective ones can be developed for engineering applications. Recent methods that are similar to the multiplier methods are also discussed. These are continuous multiplier update, exact penalty and exponential penalty methods

Parallelizing Deadlock Resolution in Symbolic Synthesis of Distributed Programs

Previous work has shown that there are two major complexity barriers in the synthesis of fault-tolerant distributed programs: (1) generation of fault-span, the set of states reachable in the presence of faults, and (2) resolving deadlock states, from where the program has no outgoing transitions. Of these, the former closely resembles with model checking and, hence, techniques for efficient verification are directly applicable to it. Hence, we focus on expediting the latter with the use of multi-core technology. We present two approaches for parallelization by considering different design choices. The first approach is based on the computation of equivalence classes of program transitions (called group computation) that are needed due to the issue of distribution (i.e., inability of processes to atomically read and write all program variables). We show that in most cases the speedup of this approach is close to the ideal speedup and in some cases it is superlinear. The second approach uses traditional technique of partitioning deadlock states among multiple threads. However, our experiments show that the speedup for this approach is small. Consequently, our analysis demonstrates that a simple approach of parallelizing the group computation is likely to be the effective method for using multi-core computing in the context of deadlock resolution

A Hypergraph Dictatorship Test with Perfect Completeness

A hypergraph dictatorship test is first introduced by Samorodnitsky and Trevisan and serves as a key component in their unique games based \PCP construction. Such a test has oracle access to a collection of functions and determines whether all the functions are the same dictatorship, or all their low degree influences are $o(1).$ Their test makes $q\geq3$ queries and has amortized query complexity $1+O(\frac{\log q}{q})$ but has an inherent loss of perfect completeness. In this paper we give an adaptive hypergraph dictatorship test that achieves both perfect completeness and amortized query complexity $1+O(\frac{\log q}{q})$.Comment: Some minor correction

The Effects of Air and Underwater Blast on Composite Sandwich Panels and Tubular Laminate Structures

The resistance of glass-fibre reinforced polymer (GFRP) sandwich panels and laminate tubes to blast in air and underwater environments has been studied. Procedures for monitoring the structural response of such materials during blast events have been devised. High-speed photography was employed during the air-blast loading of GFRP sandwich panels, in conjunction with digital image correlation (DIC), to monitor the deformation of these structures under shock loading. Failure mechanisms have been revealed by using DIC and confirmed in post-test sectioning. Strain gauges were used to monitor the structural response of similar sandwich materials and GFRP tubular laminates during underwater shocks. The effect of the backing medium (air or water) of the target facing the shock has been identified during these studies. Mechanisms of failure have been established such as core crushing, skin/core cracking, delamination and fibre breakage. Strain gauge data supported the mechanisms for such damage. These studies were part of a research programme sponsored by the Office of Naval Research (ONR) investigating blast loading of composite naval structures. The full-scale experimental results presented here will aid and assist in the development of analytical and computational models. Furthermore, it highlights the importance of support and boundary conditions with regards to blast resistant design

On Generalizations of Network Design Problems with Degree Bounds

Iterative rounding and relaxation have arguably become the method of choice in dealing with unconstrained and constrained network design problems. In this paper we extend the scope of the iterative relaxation method in two directions: (1) by handling more complex degree constraints in the minimum spanning tree problem (namely, laminar crossing spanning tree), and (2) by incorporating `degree bounds' in other combinatorial optimization problems such as matroid intersection and lattice polyhedra. We give new or improved approximation algorithms, hardness results, and integrality gaps for these problems.Comment: v2, 24 pages, 4 figure

Molecular composition of particulate matter emissions from dung and brushwood burning household cookstoves in Haryana, India

Emissions of airborne particles from biomass burning are a significant source of black carbon (BC) and brown carbon (BrC) in rural areas of developing countries where biomass is the predominant energy source for cooking and heating. This study explores the molecular composition of organic aerosols from household cooking emissions with a focus on identifying fuel-specific compounds and BrC chromophores. Traditional meals were prepared by a local cook with dung and brushwood-fueled cookstoves in a village in Palwal district, Haryana, India. Cooking was done in a village kitchen while controlling for variables including stove type, fuel moisture, and meal. Fine particulate matter (PM2.5) emissions were collected on filters, and then analyzed via nanospray desorption electrospray ionization-high-resolution mass spectrometry (nano-DESI-HRMS) and high-performance liquid chromatography-photodiode array-high-resolution mass spectrometry (HPLC-PDA-HRMS) techniques. The nano-DESI-HRMS analysis provided an inventory of numerous compounds present in the particle phase. Although several compounds observed in this study have been previously characterized using gas chromatography methods a majority of the species in the nano-DESI spectra were newly observed biomass burning compounds. Both the stove (chulha or angithi) and the fuel (brushwood or dung) affected the composition of organic aerosols. The geometric mean of the PM2.5 emission factor and the observed molecular complexity increased in the following order: brushwood-chulha (7.3±1.8 g kg-1 dry fuel, 93 compounds), dung-chulha (21.1±4.2 g kg-1 dry fuel, 212 compounds), and dung-angithi (29.8±11.5 g kg-1 dry fuel, 262 compounds). The mass-normalized absorption coefficient (MACbulk) for the organic-solvent extractable material for brushwood PM2.5 was 3.7±1.5 and 1.9±0.8m2 g-1 at 360 and 405 nm, respectively, which was approximately a factor of two higher than that for dung PM2.5. The HPLC-PDA-HRMS analysis showed that, regardless of fuel type, the main chromophores were CxHyOz lignin fragments. The main chromophores accounting for the higher MACbulk values of brushwood PM2.5 were C8H10O3 (tentatively assigned to syringol), nitrophenols C8H9NO4, and C10H10O3 (tentatively assigned to methoxycinnamic acid)