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

Growth kinetics effects on self-assembled InAs/InP quantum dots

A systematic manipulation of the morphology and the optical emission properties of MOVPE grown ensembles of InAs/InP quantum dots is demonstrated by changing the growth kinetics parameters. Under non-equilibrium conditions of a comparatively higher growth rate and low growth temperature, the quantum dot density, their average size and hence the peak emission wavelength can be tuned by changing efficiency of the surface diffusion (determined by the growth temperature) relative to the growth flux. We further observe that the distribution of quantum dot heights, for samples grown under varying conditions, if normalized to the mean height, can be nearly collapsed onto a single Gaussian curve.Comment: 2 figure

State-insensitive trapping of Rb atoms: linearly versus circularly polarized lights

We study the cancellation of differential ac Stark shifts in the 5s and 5p states of rubidium atom using the linearly and circularly polarized lights by calculating their dynamic polarizabilities. Matrix elements were calculated using a relativistic coupled-cluster method at the single, double and important valence triple excitations approximation including all possible non-linear correlation terms. Some of the important matrix elements were further optimized using the experimental results available for the lifetimes and static polarizabilities of atomic states. "Magic wavelengths" are determined from the differential Stark shifts and results for the linearly polarized light are compared with the previously available results. Possible scope of facilitating state-insensitive optical trapping schemes using the magic wavelengths for circularly polarized light are discussed. Using the optimized matrix elements, the lifetimes of the 4d and 6s states of this atom are ameliorated.Comment: 13 pages, 13 tables and 4 figure

Smoothed Analysis of Tensor Decompositions

Low rank tensor decompositions are a powerful tool for learning generative models, and uniqueness results give them a significant advantage over matrix decomposition methods. However, tensors pose significant algorithmic challenges and tensors analogs of much of the matrix algebra toolkit are unlikely to exist because of hardness results. Efficient decomposition in the overcomplete case (where rank exceeds dimension) is particularly challenging. We introduce a smoothed analysis model for studying these questions and develop an efficient algorithm for tensor decomposition in the highly overcomplete case (rank polynomial in the dimension). In this setting, we show that our algorithm is robust to inverse polynomial error -- a crucial property for applications in learning since we are only allowed a polynomial number of samples. While algorithms are known for exact tensor decomposition in some overcomplete settings, our main contribution is in analyzing their stability in the framework of smoothed analysis. Our main technical contribution is to show that tensor products of perturbed vectors are linearly independent in a robust sense (i.e. the associated matrix has singular values that are at least an inverse polynomial). This key result paves the way for applying tensor methods to learning problems in the smoothed setting. In particular, we use it to obtain results for learning multi-view models and mixtures of axis-aligned Gaussians where there are many more "components" than dimensions. The assumption here is that the model is not adversarially chosen, formalized by a perturbation of model parameters. We believe this an appealing way to analyze realistic instances of learning problems, since this framework allows us to overcome many of the usual limitations of using tensor methods.Comment: 32 pages (including appendix

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

The role of hydrostatic stress in determining the bandgap of InN epilayers

We establish a correlation between the internal stress in InN epilayers and their optical properties such as the measured absorption band edge and photoluminescence emission wavelength. By a careful evaluation of the lattice constants of InN epilayers grown on c-plane sapphire substrates under various conditions by metalorganic vapor phase epitaxy we find that the films are under primarily hydrostatic stress. This results in a shift in the band edge to higher energy. The effect is significant, and may be responsible for some of the variations in InN bandgap reported in the literature.Comment: Submitted to Appl. Phys. Let

In pursuit of the dynamic optimality conjecture

In 1985, Sleator and Tarjan introduced the splay tree, a self-adjusting binary search tree algorithm. Splay trees were conjectured to perform within a constant factor as any offline rotation-based search tree algorithm on every sufficiently long sequence---any binary search tree algorithm that has this property is said to be dynamically optimal. However, currently neither splay trees nor any other tree algorithm is known to be dynamically optimal. Here we survey the progress that has been made in the almost thirty years since the conjecture was first formulated, and present a binary search tree algorithm that is dynamically optimal if any binary search tree algorithm is dynamically optimal.Comment: Preliminary version of paper to appear in the Conference on Space Efficient Data Structures, Streams and Algorithms to be held in August 2013 in honor of Ian Munro's 66th birthda

The parameterized complexity of some geometric problems in unbounded dimension

We study the parameterized complexity of the following fundamental geometric problems with respect to the dimension $d$: i) Given $n$ points in \Rd, compute their minimum enclosing cylinder. ii) Given two $n$-point sets in \Rd, decide whether they can be separated by two hyperplanes. iii) Given a system of $n$ linear inequalities with $d$ variables, find a maximum-size feasible subsystem. We show that (the decision versions of) all these problems are W[1]-hard when parameterized by the dimension $d$. %and hence not solvable in ${O}(f(d)n^c)$ time, for any computable function $f$ and constant $c$ %(unless FPT=W[1]). Our reductions also give a $n^{\Omega(d)}$-time lower bound (under the Exponential Time Hypothesis)

Conscious monitoring and control (reinvestment) in surgical performance under pressure.

Research on intraoperative stressors has focused on external factors without considering individual differences in the ability to cope with stress. One individual difference that is implicated in adverse effects of stress on performance is "reinvestment," the propensity for conscious monitoring and control of movements. The aim of this study was to examine the impact of reinvestment on laparoscopic performance under time pressure