Inseparability inequalities for higher-order moments for bipartite systems

There are several examples of bipartite entangled states of continuous variables for which the existing criteria for entanglement using the inequalities involving the second order moments are insufficient. We derive new inequalities involving higher order correlation, for testing entanglement in non-Gaussian states. In this context we study an example of a non-Gaussian state, which is a bipartite entangled state of the form $\psi(x_{\rm a},x_{\rm b})\propto (\alpha x_{\rm a}+\beta x_{\rm b})e^{-(x_{\rm a}^2+x_{\rm b}^2)/2}$. Our results open up an avenue to search for new inequalities to test entanglement in non-Gaussian states.Comment: 7 pages, Submitte

Aspects of Integrability in N =4 SYM

Various recently developed connections between supersymmetric Yang-Mills theories in four dimensions and two dimensional integrable systems serve as crucial ingredients in improving our understanding of the AdS/CFT correspondence. In this review, we highlight some connections between superconformal four dimensional Yang-Mills theory and various integrable systems. In particular, we focus on the role of Yangian symmetries in studying the gauge theory dual of closed string excitations. We also briefly review how the gauge theory connects to Calogero models and open quantum spin chains through the study of the gauge theory duals of D3 branes and open strings ending on them. This invited review, written for Modern Physics Letters-A, is based on a seminar given at the Institute of Advanced Study, Princeton.Comment: Invited brief review for Mod. Phys. Lett. A based on a talk at I.A.S, Princeto

Automated flight test management system

The Phase 1 development of an automated flight test management system (ATMS) as a component of a rapid prototyping flight research facility for artificial intelligence (AI) based flight concepts is discussed. The ATMS provides a flight engineer with a set of tools that assist in flight test planning, monitoring, and simulation. The system is also capable of controlling an aircraft during flight test by performing closed loop guidance functions, range management, and maneuver-quality monitoring. The ATMS is being used as a prototypical system to develop a flight research facility for AI based flight systems concepts at NASA Ames Dryden

The Computational Power of Optimization in Online Learning

We consider the fundamental problem of prediction with expert advice where the experts are "optimizable": there is a black-box optimization oracle that can be used to compute, in constant time, the leading expert in retrospect at any point in time. In this setting, we give a novel online algorithm that attains vanishing regret with respect to $N$ experts in total $\widetilde{O}(\sqrt{N})$ computation time. We also give a lower bound showing that this running time cannot be improved (up to log factors) in the oracle model, thereby exhibiting a quadratic speedup as compared to the standard, oracle-free setting where the required time for vanishing regret is $\widetilde{\Theta}(N)$. These results demonstrate an exponential gap between the power of optimization in online learning and its power in statistical learning: in the latter, an optimization oracle---i.e., an efficient empirical risk minimizer---allows to learn a finite hypothesis class of size $N$ in time $O(\log{N})$. We also study the implications of our results to learning in repeated zero-sum games, in a setting where the players have access to oracles that compute, in constant time, their best-response to any mixed strategy of their opponent. We show that the runtime required for approximating the minimax value of the game in this setting is $\widetilde{\Theta}(\sqrt{N})$, yielding again a quadratic improvement upon the oracle-free setting, where $\widetilde{\Theta}(N)$ is known to be tight

Off Resonant Pumping for Transition from Continuous to Discrete Spectrum and Quantum Revivals in Systems in Coherent States

We show that in parametrically driven systems and, more generally, in systems in coherent states, off-resonant pumping can cause a transition from a continuum energy spectrum of the system to a discrete one, and result in quantum revivals of the initial state. The mechanism responsible for quantum revivals in the present case is different from that in the non-linear wavepacket dynamics of systems such as Rydberg atoms. We interpret the reported phenomena as an optical analog of Bloch oscillations realized in Fock space and propose a feasible scheme for inducing Bloch oscillations in trapped ions.Comment: 5 pages, 4 figures, submitted to Jnl. of Optics

On the expected diameter, width, and complexity of a stochastic convex-hull

We investigate several computational problems related to the stochastic convex hull (SCH). Given a stochastic dataset consisting of $n$ points in $\mathbb{R}^d$ each of which has an existence probability, a SCH refers to the convex hull of a realization of the dataset, i.e., a random sample including each point with its existence probability. We are interested in computing certain expected statistics of a SCH, including diameter, width, and combinatorial complexity. For diameter, we establish the first deterministic 1.633-approximation algorithm with a time complexity polynomial in both $n$ and $d$. For width, two approximation algorithms are provided: a deterministic $O(1)$-approximation running in $O(n^{d+1} \log n)$ time, and a fully polynomial-time randomized approximation scheme (FPRAS). For combinatorial complexity, we propose an exact $O(n^d)$-time algorithm. Our solutions exploit many geometric insights in Euclidean space, some of which might be of independent interest

Mass-Gaps and Spin Chains for (Super) Membranes

We present a method for computing the non-perturbative mass-gap in the theory of Bosonic membranes in flat background spacetimes with or without background fluxes. The computation of mass-gaps is carried out using a matrix regularization of the membrane Hamiltonians. The mass gap is shown to be naturally organized as an expansion in a 'hidden' parameter, which turns out to be $\frac{1}{d}$: d being the related to the dimensionality of the background space. We then proceed to develop a large $N$ perturbation theory for the membrane/matrix-model Hamiltonians around the quantum/mass corrected effective potential. The same parameter that controls the perturbation theory for the mass gap is also shown to control the Hamiltonian perturbation theory around the effective potential. The large $N$ perturbation theory is then translated into the language of quantum spin chains and the one loop spectra of various Bosonic matrix models are computed by applying the Bethe ansatz to the one-loop effective Hamiltonians for membranes in flat space times. Apart from membranes in flat spacetimes, the recently proposed matrix models (hep-th/0607005) for non-critical membranes in plane wave type spacetimes are also analyzed within the paradigm of quantum spin chains and the Bosonic sectors of all the models proposed in (hep-th/0607005) are diagonalized at the one-loop level.Comment: 36 Page

Conditional Lower Bounds for Space/Time Tradeoffs

In recent years much effort has been concentrated towards achieving polynomial time lower bounds on algorithms for solving various well-known problems. A useful technique for showing such lower bounds is to prove them conditionally based on well-studied hardness assumptions such as 3SUM, APSP, SETH, etc. This line of research helps to obtain a better understanding of the complexity inside P. A related question asks to prove conditional space lower bounds on data structures that are constructed to solve certain algorithmic tasks after an initial preprocessing stage. This question received little attention in previous research even though it has potential strong impact. In this paper we address this question and show that surprisingly many of the well-studied hard problems that are known to have conditional polynomial time lower bounds are also hard when concerning space. This hardness is shown as a tradeoff between the space consumed by the data structure and the time needed to answer queries. The tradeoff may be either smooth or admit one or more singularity points. We reveal interesting connections between different space hardness conjectures and present matching upper bounds. We also apply these hardness conjectures to both static and dynamic problems and prove their conditional space hardness. We believe that this novel framework of polynomial space conjectures can play an important role in expressing polynomial space lower bounds of many important algorithmic problems. Moreover, it seems that it can also help in achieving a better understanding of the hardness of their corresponding problems in terms of time

Renormalization Group theory outperforms other approaches in statistical comparison between upscaling techniques for porous media

Determining the pressure differential required to achieve a desired flow rate in a porous medium requires solving Darcy's law, a Laplace-like equation, with a spatially varying tensor permeability. In various scenarios, the permeability coefficient is sampled at high spatial resolution, which makes solving Darcy's equation numerically prohibitively expensive. As a consequence, much effort has gone into creating upscaled or low-resolution effective models of the coefficient while ensuring that the estimated flow rate is well reproduced, bringing to fore the classic tradeoff between computational cost and numerical accuracy. Here we perform a statistical study to characterize the relative success of upscaling methods on a large sample of permeability coefficients that are above the percolation threshold. We introduce a new technique based on Mode-Elimination Renormalization-Group theory (MG) to build coarse-scale permeability coefficients. Comparing the results with coefficients upscaled using other methods, we find that MG is consistently more accurate, particularly so due to its ability to address the tensorial nature of the coefficients. MG places a low computational demand, in the manner that we have implemented it, and accurate flow-rate estimates are obtained when using MG-upscaled permeabilities that approach or are beyond the percolation threshold.Comment: 15 pages, 7 figures, Physical Review